Extremum-seeking controller and method with online parameter tuning

Abstract

The power supply system includes an RF power source configured to generate an output signal at an output frequency, a signal source configured to generate a perturbation signal, an extremum-seeking frequency controller configured to generate a frequency control signal based on the perturbation signal, and a frequency selector configured to select a perturbation frequency of the perturbation signal that is separated from at least one frequency tone associated with the power supply system. The frequency control signal varies the output frequency of the RF power source. Other exemplary power supply systems, methods for controlling an RF generator, and control systems for controlling an RF generator are also disclosed.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Application No. 17 / 940,047, filed September 8, 2022. The disclosures of the above applications are incorporated herein by reference in their entireties.

[0002] The present disclosure relates to RF generator systems and the control of RF generators. [Background technology]

[0003] Plasma processing is frequently used in semiconductor fabrication. In plasma processing, ions are accelerated by an electric field to etch material from or deposit material onto the surface of a substrate. In one basic implementation, the electric field is generated based on a radio frequency (RF) or direct current (DC) power signal generated by a respective RF or DC generator in a power supply system. The power signal generated by the generator must be precisely controlled to effectively perform plasma etching.

[0004] The background art discussion provided herein is intended to generally present the context for the present disclosure. The work of the presently designated inventors, and aspects of the discussion that may not be considered prior art at the time of filing, to the extent described in this background art section, are not admitted expressly or impliedly as prior art to the present disclosure. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] U.S. Patent No. 7,602,127 [Patent Document 2] U.S. Patent No. 8,110,991 [Patent Document 3] U.S. Patent No. 8,395,322 [Patent Document 4] U.S. Patent No. 10,821,542 [Patent Document 5] U.S. Patent No. 10,546,724 [Patent Document 6] U.S. Patent No. 10,049,857 [Patent Document 7] U.S. Patent No. 10,741,363 Summary of the Invention [Means for solving the problem]

[0006] One or more computer systems may be configured to perform specific operations or actions by having installed thereon software, firmware, hardware, or a combination thereof that causes the system to perform the actions during operation. One or more computer programs may be configured to perform specific operations or actions by including instructions that, when executed by a data processing device, cause the device to perform the actions. According to one aspect of the present disclosure, a power supply system for powering a load is disclosed. The power supply system includes an RF power source configured to generate an output signal at an output frequency; a signal source configured to generate a perturbation signal; an extremum-seeking frequency controller configured to generate a frequency control signal based on the perturbation signal; and a frequency selector configured to select a perturbation frequency of the perturbation signal that is separated from at least one frequency tone associated with the power supply system. The frequency control signal varies the output frequency of the RF power source. Other embodiments of this aspect include corresponding computer systems, devices, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of a method.

[0007] Implementations may include one or more of the following features: a power supply system may include a power controller coupled to an RF power source, the power controller configured to generate pulses to modulate an output signal of the RF power source, the pulses including a first state and a second state; a frequency selector may be configured to select a first perturbation frequency for the first state of the pulses and a second perturbation frequency for the second state, the first perturbation frequency and the second perturbation frequency being different; a frequency selector may be configured to select the perturbation frequencies for the first state and the second state of the pulse; a power supply system may include a power controller coupled to an RF power source, the power controller configured to generate at least two pulses to modulate the output signal of the RF power source, each pulse including a first state and a second state, the frequency selector configured to select a first perturbation frequency for the first state of each of the at least two pulses and a second perturbation frequency for the second state of each of the at least two pulses, the first perturbation frequency and the second perturbation frequency being different. The power supply system may include a power controller coupled to an RF power source, the power controller configured to generate pulses to modulate an output signal of the RF power source, and a frequency selector configured to select a perturbation frequency based on a bandwidth of the power controller. The frequency selector may be configured to determine a first delta between a minimum value of the bandwidth and at least one frequency tone and a second delta between the at least one frequency tone and a maximum value of the bandwidth, and to select the perturbation frequency to be equal to a frequency value within the larger of the first delta and the second delta. The frequency value may be a midpoint of the larger of the first delta and the second delta. The frequency selector may be configured to analyze data indicative of an operating parameter of the power supply system according to the selected perturbation frequency, and to adjust the perturbation frequency within the larger of the first delta and the second delta if the operating parameter is below a defined threshold.The frequency selector may be configured to analyze data indicative of an operating parameter of the power supply system with the adjusted perturbation frequency, and, if the operating parameter falls below a defined threshold, adjust the perturbation frequency again within the larger of the first delta and the second delta. The frequency selector may be configured to determine at least one frequency tone, where the at least one frequency tone may include an apparent frequency associated with a state of the pulse. The apparent frequency may be determined based on a duty cycle of the state, a repetition rate of the pulse, and a hold-off time associated with the state. The at least one frequency tone may include a first apparent frequency associated with a first state of the pulse and a second apparent frequency associated with a second state of the pulse, and the frequency selector may be configured to select perturbation frequencies for the first state and the second state that are separate from the first apparent frequency and the second apparent frequency. The frequency selector may be configured to perform a transformation to analyze data of the one or more feedback signals and to determine at least one frequency tone based on the analyzed data. The frequency selector may be configured to select the perturbation frequency based on the analyzed data. A frequency selector may be configured to perform a transformation and analyze data of the one or more feedback signals based on the output response with the perturbation frequency. The frequency selector may be configured to adjust the perturbation frequency based on the analyzed data. The data may be indicative of an operating parameter of the power supply system, and the frequency selector may be configured to adjust the perturbation frequency if the operating parameter falls below a defined threshold. The frequency selector may be configured to analyze the data indicative of the operating parameter of the power supply system with the adjusted perturbation frequency, and to adjust the perturbation frequency again if the operating parameter falls below a defined threshold. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.

[0008] According to another aspect of the present disclosure, a method for controlling an RF generator of a power supply system includes selecting a perturbation frequency of a perturbation signal that is separated from at least one frequency tone associated with the power supply system, generating the perturbation signal having the selected perturbation frequency, and generating a frequency control signal based on the perturbation signal, the frequency control signal varying an output frequency of the RF power source. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the method.

[0009] Implementations may include one or more of the following features: A method may include generating pulses to modulate an output signal of an RF power source, the pulses including a first state and a second state, and selecting a perturbation frequency includes selecting perturbation frequencies for the first state and the second state of the pulse, or selecting a first perturbation frequency for the first state of the pulse and a second perturbation frequency for the second state that is different from the first perturbation frequency. A method may include generating at least two pulses to modulate an output signal of an RF power source, each of the pulses including a first state and a second state, and selecting a perturbation frequency includes selecting a first perturbation frequency for the first state of each of the at least two pulses and a second perturbation frequency for the second state of each of the at least two pulses that is different from the first perturbation frequency. A method may include generating pulses to modulate an output signal of an RF power source using a power controller, and selecting a perturbation frequency includes selecting the perturbation frequency based on a bandwidth of the power controller. The method may include determining a first delta between a minimum value of a bandwidth and at least one frequency tone and a second delta between the at least one frequency tone and a maximum value of the bandwidth, and selecting a perturbation frequency to be equal to a frequency value within the larger of the first delta and the second delta. The frequency value may be a midpoint of the larger of the first delta and the second delta. The method may include analyzing data indicative of an operating parameter of the power supply system with the selected perturbation frequency, and adjusting the perturbation frequency within the larger of the first delta and the second delta if the operating parameter falls below a defined threshold. The method may include analyzing data indicative of an operating parameter of the power supply system with the adjusted perturbation frequency, and again adjusting the perturbation frequency within the larger of the first delta and the second delta if the operating parameter falls below a defined threshold.The method may include determining at least one frequency tone, where the at least one frequency tone may include an apparent frequency associated with a state of the pulse, and determining the at least one frequency tone may include determining the apparent frequency associated with the state of the pulse based on a duty cycle of the state, a repetition rate of the pulse, and a hold-off time associated with the state. The method may include selecting perturbation frequencies for a first state and a second state of the pulse that are separate from a first apparent frequency associated with the first state of the pulse and a second apparent frequency associated with the second state of the pulse. The method may include performing a transformation to analyze data of one or more feedback signals and determining at least one frequency tone based on the analyzed data. The method may include selecting the perturbation frequency based on the analyzed data. The method may include performing a transformation to analyze data of the one or more feedback signals based on an output response due to the perturbation frequency. The method may include adjusting the perturbation frequency based on the analyzed data. The data may indicate an operating parameter of the power supply system, and the method may further include adjusting the perturbation frequency if the operating parameter is below a defined threshold. The method may include analyzing data indicative of an operating parameter of the power supply system with the adjusted perturbation frequency, and adjusting the perturbation frequency again if the operating parameter falls below a defined threshold. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.

[0010] According to another aspect of the present disclosure, a non-transitory computer-readable medium storing processor-executable instructions for controlling an RF generator of a power supply system is disclosed. The RF generator includes an RF power source. The instructions include selecting a perturbation frequency of a perturbation signal that is separated from at least one frequency tone associated with the power supply system, generating the perturbation signal having the selected perturbation frequency, and generating a frequency control signal based on the perturbation signal, the frequency control signal varying an output frequency of the RF power source. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the method.

[0011] Implementations may include one or more of the following features. The instructions may include generating pulses to modulate an output signal of the RF power source with a power controller, and selecting a perturbation frequency of the perturbation signal includes selecting the perturbation frequency based on a bandwidth of the power controller. The instructions may include determining a first delta between a minimum value of the bandwidth and at least one frequency tone and a second delta between the at least one frequency tone and a maximum value of the bandwidth, and selecting a perturbation frequency of the perturbation signal includes selecting the perturbation frequency to be equal to a frequency value within the larger of the first delta and the second delta. The frequency value may be a midpoint of the larger of the first delta and the second delta. The instructions may include analyzing data indicative of an operating parameter of the power system with the selected perturbation frequency, and adjusting the perturbation frequency within the larger of the first delta and the second delta if the operating parameter is below a defined threshold. The instructions may include analyzing data indicative of an operating parameter of the power system with the adjusted perturbation frequency, and adjusting the perturbation frequency again within the larger of the first delta and the second delta if the operating parameter falls below a defined threshold. The instructions may include determining at least one frequency tone, the at least one frequency tone including an apparent frequency associated with a state of the pulse, and determining the at least one frequency tone including determining the apparent frequency associated with a state of the pulse based on a duty cycle, a repetition rate of the pulse, and a hold-off time associated with the state. The instructions may include determining the at least one frequency tone, the at least one frequency tone including a first apparent frequency associated with a first state of the pulse and a second apparent frequency associated with a second state of the pulse, and selecting a perturbation frequency of the perturbation signal including selecting perturbation frequencies for the first state and the second state that are decoupled from the first apparent frequency and the second apparent frequency.The instructions may include performing a transformation based on the output response with the perturbation frequency and analyzing data of one or more feedback signals, the data indicative of an operating parameter of the power supply system. The instructions may include adjusting the perturbation frequency if the operating parameter falls below a defined threshold. The instructions may include analyzing data indicative of the operating parameter of the power supply system with the adjusted perturbation frequency and adjusting the perturbation frequency again if the operating parameter falls below a defined threshold. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.

[0012] According to another aspect of the present disclosure, a control system for controlling an RF generator of a power supply system includes a signal source configured to generate a perturbation signal, an extremum-seeking frequency controller configured to generate a frequency control signal based on the perturbation signal, and a frequency selector configured to select a perturbation frequency of the perturbation signal that is separated from at least one frequency tone associated with the power supply system. The frequency control signal varies the output frequency of the RF power source. Other embodiments of this aspect include corresponding computer systems, apparatuses, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the method.

[0013] Implementations may include one or more of the following features: The control system may include a power controller configured to generate pulses to modulate an output signal of the RF power source, the pulses including a first state and a second state, the perturbation frequency being a first perturbation frequency, and the frequency selector may be configured to select the first perturbation frequency for the first state and a second perturbation frequency for the second state of the pulses, the first perturbation frequency and the second perturbation frequency being different. The control system may include a power controller configured to generate pulses to modulate the output signal of the RF power source, the pulses including a first state and a second state, and the frequency selector may be configured to select the perturbation frequencies for the first state and the second state of the pulses. The control system may include a power controller configured to generate at least two pulses to modulate the output signal of the RF power source, each of the at least two pulses including a first state and a second state, the perturbation frequency being a first perturbation frequency, and a frequency selector configured to select the first perturbation frequency for the first state of each of the at least two pulses and a second perturbation frequency for the second state of each of the at least two pulses, the first perturbation frequency and the second perturbation frequency being different. The control system may include a power controller configured to generate pulses to modulate the output signal of the RF power source, and the frequency selector may be configured to select the perturbation frequency based on a bandwidth of the power controller. The frequency selector may be configured to determine a first delta between a minimum value of the bandwidth and at least one frequency tone and a second delta between the at least one frequency tone and a maximum value of the bandwidth, and to select the perturbation frequency to be equal to a frequency value within the larger of the first delta and the second delta. The frequency selector may be configured to determine the at least one frequency tone.The frequency selector may be configured to perform a transformation to analyze data of the one or more feedback signals, determine at least one frequency tone based on the analyzed data, and select a perturbation frequency based on the at least one frequency tone. The frequency selector may be configured to perform a transformation to analyze data of the one or more feedback signals based on an output response due to the perturbation frequency, and adjust the perturbation frequency based on the analyzed data. The data may indicate an operating parameter of the power supply system, and the frequency selector may be configured to adjust the perturbation frequency if the operating parameter is below a defined threshold. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.

[0014] Further areas of applicability of the present disclosure will become apparent from the detailed description, the claims, and the drawings. The detailed description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.

[0015] The present disclosure will become more fully understood from the detailed description and accompanying drawings. [Brief explanation of the drawings]

[0016] [Figure 1] FIG. 1 is a schematic block diagram of a power supply system having multiple power sources arranged in accordance with various configurations of the present disclosure. [Figure 2] FIG. 2 is a diagram illustrating the waveform of an RF signal and pulses modulating the RF signal to explain a pulse operation mode. [Figure 3A] FIG. 10 shows a plot of the cost function as a function of cost and actuator frequency. [Figure 3B] FIG. 10 shows a plot of the cost function as a function of cost and actuator frequency. [Figure 4]FIG. 1 is a block diagram of an RF power delivery system implementing an extremum-seeking control (ESC) based approach. [Figure 5A] FIG. 1 shows a plot of apparent pulse frequency as a function of pulse repetition rate and duty cycle. [Figure 5B] FIG. 1 shows a plot of apparent pulse frequency as a function of pulse repetition rate and duty cycle. [Figure 6] 1A-1C show plots of various waveforms associated with an implemented sinusoidal frequency modulated signal. [Figure 7] FIG. 1 is a block diagram of an RF power supply system arranged in accordance with the principles of the present disclosure. [Figure 8A] FIG. 10 illustrates an exemplary method for selecting a perturbation frequency based on the bandwidth of a power control loop, arranged in accordance with the principles of the present disclosure. [Figure 8B] FIG. 10 illustrates an exemplary method for selecting a perturbation frequency based on the bandwidth of a power control loop, arranged in accordance with the principles of the present disclosure. [Figure 9] FIG. 1 illustrates an exemplary method for selecting perturbation frequencies, arranged in accordance with the principles of the present disclosure. [Figure 10A] FIG. 1 illustrates an exemplary method for selecting perturbation frequencies, arranged in accordance with the principles of the present disclosure. [Figure 10B] FIG. 1 illustrates an exemplary method for selecting perturbation frequencies, arranged in accordance with the principles of the present disclosure. [Figure 10C] FIG. 1 illustrates an exemplary method for selecting perturbation frequencies, arranged in accordance with the principles of the present disclosure. [Figure 10D] FIG. 1 illustrates an exemplary method for selecting perturbation frequencies, arranged in accordance with the principles of the present disclosure. [Figure 11A] FIG. 10 illustrates an exemplary method for selecting perturbation frequencies based on analyzed feedback data, arranged in accordance with the principles of the present disclosure. [Figure 11B] FIG. 10 illustrates an exemplary method for selecting perturbation frequencies based on analyzed feedback data, arranged in accordance with the principles of the present disclosure. [Figure 12] 1A-1C are functional block diagrams of exemplary control modules arranged according to various configurations. [Figure 13] 1 is a flowchart of the operation of a control system for perturbation frequency selection arranged in accordance with the principles of the present disclosure. [Figure 14] 1 is a flowchart of the operation of a control system for perturbation frequency selection arranged in accordance with the principles of the present disclosure. [Figure 15] 1 is a flowchart of the operation of a control system for perturbation frequency selection arranged in accordance with the principles of the present disclosure. [Figure 16] 1 is a flowchart of the operation of a control system for perturbation frequency selection arranged in accordance with the principles of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0017] In the drawings, reference numbers may be reused to identify similar and / or identical elements.

[0018] A power system may include a DC or RF power generator or generator, a matching network, and a load (such as a process chamber, plasma chamber, or reactor with fixed or variable impedance). The power generator generates a DC or RF power signal, which is received by a matching network or an impedance optimization controller or circuit. The matching network or impedance optimization controller or circuit matches the input impedance of the matching network to the characteristic impedance of the transmission line between the power generator and the matching network. Impedance matching helps maximize the amount of power transferred to the matching network ("forward power") and minimize the amount of power reflected from the matching network back to the power generator ("reverse power" or "reflected power"). Power delivered to the load can be maximized by minimizing reflected power when the input impedance of the matching network matches the characteristic impedance of the transmission line and the generator.

[0019] In the field of power sources or power supplies, there are typically two approaches to applying a power signal to a load. The first, more traditional approach is to apply a continuous power signal to the load. In continuous mode or continuous wave mode, the continuous power signal is typically a constant DC or sinusoidal RF power signal that is continuously output by the power source to the load. In the continuous mode approach, the power signal assumes a constant DC or sinusoidal output, and the amplitude and / or frequency (of an RF power signal) of the power signal can be varied to vary the output power applied to the load.

[0020] A second approach to applying a power signal to a load involves pulsing the RF signal rather than applying a continuous RF signal to the load. In a pulsed or pulsed mode of operation, the RF signal is modulated by a modulation signal to define an envelope for the modulated power signal. The RF signal can be, for example, a sinusoidal RF signal or other time-varying signal. The power delivered to the load is typically varied by varying the modulation signal.

[0021] In a typical power supply configuration, the output power applied to a load is determined using sensors that measure the forward and reflected power, or the voltage and current, of an RF signal applied to the load. Any set of these signals is analyzed in a control loop. The analysis typically determines a power value that is used to adjust the output of the power supply to vary the power applied to the load. In a power supply system where the load is a process chamber or other nonlinear or time-varying load, varying impedance of the load causes a corresponding variation in the power applied to the load, since the power applied is in part a function of the impedance of the load.

[0022] In systems where the fabrication of various devices relies on the introduction of power to a load to control the fabrication process, power is typically supplied in one of two configurations. In the first configuration, power is capacitively coupled to the load. Such systems are called capacitively coupled plasma (CCP) systems. In the second configuration, power is inductively coupled to the load. Such systems are typically called inductively coupled plasma (ICP) systems. Power coupling to the plasma can also be achieved via wave coupling at microwave frequencies. Such approaches typically use electron cyclotron resonance (ECR) or microwave sources. Helicon sources are another form of wave-coupled source and typically operate at RF frequencies similar to those of conventional ICP and CCP systems. The power supply system can include at least one bias power and / or source power applied to one or more electrodes of the load. The source power typically generates the plasma and controls the plasma density, while the bias power modulates ions in the buildup of the sheath. The bias and source may share the same electrode or use separate electrodes, depending on various design considerations.

[0023] When a power supply system drives a time-varying or nonlinear load, such as a process chamber or plasma chamber, the power absorbed by the bulk plasma and plasma sheath produces a density of ions with various ion energies. One characteristic measure of ion energy is the ion energy distribution function (IEDF). The IEDF can be controlled using bias power. One method of controlling the IEDF for a system in which multiple RF power signals are applied to a load is by varying the multiple RF signals, which are related by amplitude, frequency, and phase. The relative amplitude, frequency, and phase of the multiple RF power signals can also be related by Fourier series and associated coefficients. The frequencies between the multiple RF power signals can be locked, and the relative phases between the multiple RF signals can also be locked. Examples of such systems can be found in U.S. Pat. Nos. 7,602,127, 8,110,991, and 8,395,322, all of which are assigned to the assignee of the present application and incorporated herein by reference.

[0024] Time-varying or nonlinear loads may exist in various applications. In one application, a plasma processing system may also include components for plasma generation and control. One such component is a nonlinear load implemented as a process chamber, such as a plasma chamber or reactor. As an example, a typical plasma chamber or reactor utilized in a plasma processing system for thin film manufacturing or the like may utilize a dual power system. One power generator (source) controls plasma generation, and another power generator (bias) controls ion energy. Examples of dual power systems include those described in the above-referenced U.S. Pat. Nos. 7,602,127, 8,110,991, and 8,395,322. The dual power systems described in the above-referenced patents employ a closed-loop control system to adapt power supply operation for the purpose of controlling ion density and its corresponding ion energy distribution function (IEDF).

[0025] There are several approaches to controlling a process chamber, such as that used to generate a plasma. For example, in an RF power supply system, the phase and frequency of multiple driving RF signals operating at the same or nearly the same frequency can be used to control plasma generation. In RF-driven plasma sources, periodic waveforms that affect plasma sheath dynamics and corresponding ion energy are generally known and controlled by the frequency and associated phase interactions of the periodic waveforms. Another approach in RF power supply systems involves dual-frequency control. That is, two RF frequency sources operating at different frequencies are used to power the plasma chamber to provide substantially independent control of ion and electron densities.

[0026] Another approach utilizes a broadband RF power source to drive the plasma chamber. This broadband approach presents several challenges. One challenge is coupling power to the electrodes. A second challenge is that the transfer function of the generated waveform to the actual sheath voltage for the desired IEDF must be formulated for a wide process space to support material-surface interactions. One approach that is sensitive to inductively coupled plasma systems involves controlling the plasma density by controlling the power applied to the source electrode and modulating the ions to control the IEDF by controlling the power applied to the bias electrode, providing etch rate control. Using source and bias electrode control, the etch rate is controlled via ion density and energy.

[0027] As integrated circuit and device fabrication continues to evolve, so do the power requirements for controlling the fabrication process. For example, in memory device fabrication, the requirement for bias power continues to increase. Increasing power generates more energetic ions due to faster surface interactions, thereby increasing the etch rate and ion directionality. In RF systems, increasing bias power can be accompanied by a lower bias frequency requirement, along with an increase in the number of bias power sources coupled to the plasma sheath created in the plasma chamber. Increasing power at lower bias frequencies and an increase in the number of bias power sources can result in intermodulation distortion (IMD) emissions from sheath modulation. IMD emissions can significantly reduce the power supplied by the source where plasma generation occurs. U.S. Patent No. 10,821,542, entitled "Pulse Synchronization by Monitoring Power in Another Frequency Band," issued November 3, 2020, and assigned to the assignee of the present application and incorporated herein by reference, describes a method for pulse synchronization by monitoring power in another frequency band. In the referenced US patent, the pulsing of the second RF generator is controlled in accordance with detecting the pulsing of the first RF generator at the second RF generator, thereby synchronizing the pulsing between the two RF generators.

[0028] FIG. 1 illustrates an RF generator or power supply system 10. The power supply system 10 includes a pair of radio frequency (RF) generators or power supplies 12a, 12b, matching networks 18a, 18b, and a load 32, such as a nonlinear load, which may be a plasma chamber, a plasma reactor, a process chamber, or the like. In various configurations, the RF generator 12a is referred to as a source RF generator or power supply, and the matching network 18a is referred to as a source matching network. Also, in various configurations, the RF generator 12b is referred to as a bias RF generator or power supply, and the matching network 18b is referred to as a bias matching network. It will be understood that components may be referred to individually or collectively using reference numbers with and without letters, subscripts, or primes.

[0029] In various configurations, the source RF generator 12a receives a control signal 30 from the matching network 18b and / or a control signal 30' from the bias RF generator 12b. The control signal 30 or 30' represents an input signal to the source RF generator 12a that indicates one or more operating characteristics or parameters of the bias RF generator 12b. In various configurations, a synchronization bias detector 34 detects the RF signal output from the matching network 18b to the load 32 and outputs a synchronization or trigger signal 30 to the source RF generator 12a. In various configurations, a synchronization or trigger signal 30', rather than the trigger signal 30, may be output from the bias RF generator 12b to the source RF generator 12a. One difference between the trigger or synchronization signals 30, 30' may result from the effect of the matching network 18b, which can vary the phase between the input signal to the matching network and the output signal from the matching network. Signals 30, 30' contain information about the operation of bias RF generator 12b that, in various configurations, enables predictable responsiveness to address periodic variations in the impedance of load 32 caused by bias RF generator 12b. In the absence of control signals 30 or 30', RF generators 12a, 12b operate autonomously.

[0030] The RF generators 12a, 12b include respective RF power sources or amplifiers 14a, 14b, sensors 16a, 16b, and processors, controllers, or control modules 20a, 20b. The RF power sources 14a, 14b generate respective RF power signals 22a, 22b, which are output to the respective sensors 16a, 16b. The RF power signals 22a, 22b pass through the sensors 16a, 16b and are provided to matching networks 18a, 18b as respective RF power signals f1 and f2. While the sensors 16a, 16b are shown within the respective RF generators 12a, 12b, the sensors 16a, 16b can be located external to the RF power generators 12a, 12b. Such external sensing can occur at the output of the RF generators, at the input of an impedance matching device located between the RF generators and the load, or between the output of the impedance matching device (including within the impedance matching device) and the load.

[0031] The sensors 16a, 16b detect various operating parameters and output signals X and Y. The sensors 16a, 16b may include voltage, current, and / or directional coupler sensors. The sensors 16a, 16b detect (i) the voltage V and current I, and / or (ii) the forward power P output from the respective power amplifiers 14a, 14b and / or RF generators 12a, 12b. FWD and the reverse or reflected power P received from the respective matching network 18a, 18b or load 32 connected to the respective sensor 16a, 16b. REV It can detect voltage V, current I, forward power P FWD , and reverse power P REVmay be scaled, filtered, or scaled and filtered versions of the actual voltage, current, forward power, and reverse power associated with each power source 14a, 14b. Sensors 16a, 16b may be analog or digital sensors, or a combination thereof. In a digital implementation, sensors 16a, 16b may include an analog-to-digital (A / D) converter and a signal sampling component with a corresponding sampling rate. Signals X and Y may represent the voltage V and current I, or the forward (or source) power P FWD , reverse (or reflected) power P REV It can represent any of the following:

[0032] The sensors 16a, 16b generate sensor signals X, Y, which are received by respective power controllers or control modules 20a, 20b. The control modules 20a, 20b process the respective X and Y signals 24a, 26a and 24b, 26b and generate one or more feedforward or feedback control signals 28a, 28b to the respective power sources 14a, 14b. The power sources 14a, 14b adjust the RF power signals 22a, 22b based on the received one or more feedback or feedforward control signals. In various configurations, the control modules 20a, 20b may control the matching networks 18a, 18b, respectively, via respective control signals 29a, 29b, for example, based on the X and Y signals 24a, 26a and 24b, 26b. In some configurations, the control signals 29a, 29b may be the same as, similar to, or different from the control signals 28a, 28b. The control modules 20a, 20b may include at least a proportional-integral (PI), proportional-integral-derivative (PID) controller, a linear quadratic regulator (LQR), or a subset thereof, and / or a direct digital synthesis (DDS) component, and / or any of the various components described below with respect to the modules.

[0033] In various configurations, the control modules 20a, 20b may include functions, processes, processors, or sub-modules. The control signals 28a, 28b may be control or drive signals and may communicate DC offset or rail voltage, voltage or current magnitude, frequency, and phase components, etc. In various configurations, the feedback control signals 28a, 28b may be used as inputs to one or more control loops. In various configurations, the multiple control loops may include a control loop for RF drive and a control loop for rail voltage. In various configurations, the control signals 28a, 28b may be used in a single-input, single-output (SISO) or multiple-input, multiple-output (MIMO) control scheme. An example of a MIMO control scheme may be found in U.S. Patent No. 10,546,724, entitled "Pulsed Bidirectional Radio Frequency Source / Load," issued January 28, 2020, which is assigned to the assignee of the present application and incorporated herein by reference. In other configurations, signals 28a, 28b may provide feedforward control as described in US Pat. No. 10,049,857, which is assigned to the assignee of the present application and is incorporated herein by reference.

[0034] In various configurations, the power supply system 10 may include a controller 20′. The controller 20′ may be disposed external to either or both of the RF generators 12a, 12b and may be referred to as an external or common controller 20′. In various configurations, the controller 20′ may implement one or more functions, processes, or algorithms described herein with respect to either or both of the controllers 20a, 20b. Accordingly, the controller 20′ communicates with each of the RF generators 12a, 12b via a pair of respective links 36, 38, which enable the exchange of data and control signals between the controller 20′ and the RF generators 12a, 12b, as appropriate. In various configurations, the controllers 20a, 20b, 20′ may provide analysis and control of the RF generators 12a, 12b in a distributed and collaborative manner. In various other configurations, the controller 20′ may provide control of the RF generators 12a, 12b, eliminating the need for respective local controllers 20a, 20b.

[0035] In various configurations, the RF power source 14a, the sensor 16a, the controller 20a, and the matching network 18a may be referred to as the source RF power source 14a, the source sensor 16a, the source controller 20a, and the source matching network 18a. Similarly, in various configurations, the RF power source 14b, the sensor 16b, the controller 20b, and the matching network 18b may be referred to as the bias RF power source 14b, the bias sensor 16b, the bias controller 20b, and the bias matching network 18b. In various configurations, as explained above, the term source refers to the RF generator that generates the plasma, and the term bias refers to the RF generator that adjusts the ion potential or IEDF of the plasma. In various configurations, the source and bias RF power sources operate at different frequencies. In various configurations, the source RF power source operates at a higher frequency than the bias RF power source. In various other configurations, the source and bias RF power sources operate at the same frequency or substantially the same frequency.

[0036] According to various configurations, the source RF generator 12a and the bias RF generator 12b include multiple ports for communicating with the outside world. The source RF generator 12a includes a pulse synchronization output port 40, a digital communication port 42, an RF output port 44, and a control signal port 60. The bias RF generator 12b includes an RF input port 48, a digital communication port 50, and a pulse synchronization input port 52. The pulse synchronization output port 40 outputs a pulse synchronization signal 56 to the pulse synchronization input port 52 of the bias RF generator 12b. The digital communication port 42 of the source RF generator 12a and the digital communication port 50 of the bias RF generator 12b communicate via a digital communication link 57. The control signal port 60 of the source RF generator 12a receives the control signals 30 and / or 30′. The RF output port 44 generates an RF control signal 58 that is input to the RF input port 48. In various configurations, the RF control signal 58 is substantially the same as the RF control signal that controls the source RF generator 12a. In various other configurations, RF control signal 58 is the same as the RF control signal controlling source RF generator 12a, but is phase shifted within source RF generator 12a according to the desired phase shift generated by bias RF generator 12b. Thus, in various configurations, source RF generator 12a and bias RF generator 12b are driven by substantially equal RF control signals or by substantially equal RF control signals that are phase shifted by a predetermined amount.

[0037] FIG. 2 shows a voltage versus time plot illustrating a pulsed or pulsed mode of operation for powering a load, such as load 32 of FIG. 1. More specifically, FIG. 2 shows two multi-state pulses P1, P2 of pulse signal 70, each having a plurality of states S1-S4 and S1-S3. In FIG. 2, an RF signal 80 is modulated by pulses P1 and P2. When the pulses are ON, as shown in state S1 of P1 and state S1 of P2, RF generator 12 outputs RF signal 80 with an amplitude defined by the magnitude of the pulse in each state. Conversely, during state S4 of P1 and state S3 of P2, the pulses are OFF, and RF generator 12 does not output RF signal 80. Pulses P1, P2 can repeat at a constant duty cycle or a variable duty cycle, and states S1-S4, S1-S3 of each pulse P1, P2 can have the same or varying amplitude and width. Furthermore, pulse signal 70 need not be a square wave as shown in FIG. 2. By way of non-limiting example, pulse signal 70 may be trapezoidal, triangular, Gaussian, or other shape. Furthermore, pulses P1, P2 may have multiple states S1, ..., Sn of varying amplitude, duration, and shape. States S1, ..., Sn may repeat within a fixed or variable period. Also, as shown in FIG. 2, RF signal 80 operates at a frequency that varies between or within states.

[0038] In a typical RF power delivery system, a matching network (e.g., matching network 18a in FIG. 1) is adjusted to achieve maximum power delivery to a load via tunable mechanical components. Maximum power delivery indicates minimum reflected power. Because the response time of the electromechanical tuning elements in the matching network is relatively slow, adjusting the matching network may require a relatively extended period to complete the power adjustment. To improve impedance matching, the RF frequency output by a power amplifier (e.g., power amplifier 14a in FIG. 1) may also be adjusted. Frequency-based tuning improves performance and provides orders of magnitude faster response than adjusting the electromechanical components of the matching network.

[0039] When employing frequency-based impedance matching, it is desirable to find the optimum frequency that provides the minimum reflected power. The minimum reflected power can be indicated through the minimum absolute value |Γ| of the measured complex reflection coefficient gamma. There are several existing methods for adjusting the RF frequency.

[0040] For example, automated frequency tuning is a standard technique for fast impedance matching. By adjusting the RF carrier frequency, the RF generator steers toward lower reflected power and compensates for transients in the load, even at pulse state change boundaries. Examples of automated frequency tuning methods include extremum-seeking control (ESC) techniques and closed-form model-based (e.g., transfer function) techniques. An example of an ECS-based technique for performing automatic or automated frequency tuning can be found in U.S. Pat. No. 10,741,363, which is assigned to the assignee of the present application and is incorporated herein by reference.

[0041] The ESC technique minimizes reflected power without requiring extensive knowledge of the process. The ESC technique implements a dynamic adjustment mechanism for automatically tuning the frequency along the direction of the gradient of a cost function without requiring an explicit model of the system or process. The cost function may generally be referred to as a functional equation that maps a set of points to a single scalar value. The scalar value resulting from the evaluation of the cost function may be referred to as the cost. In frequency tuning applications, this cost may be expressed as the magnitude of gamma squared or gamma mag squared (|Γ| 2 ), or output response values ​​such as delivered power. Generally, it is desirable to minimize or maximize cost.

[0042] For example, Figure 3A shows the cost function J (or gamma magnitude squared (|Γ| 23 shows a plot 300A of a quadratic cost function 302 as a function of the input voltage, J, and the actuator frequency, U. As shown, the plot 300A includes a maximum 304 and locations 306, 308 along the cost function 302, with each location 306, 308 on a different side of the maximum 304. Thus, all points to the left of the maximum 304 have a positive slope (or gradient), and all points to the right of the maximum 304 have a negative slope. If it is desired to maximize the cost, J, and the actuator frequency is at location 306, the actuator frequency may be increased, thereby causing an increase in the cost, J (or output response value). In other embodiments, if it is desired to maximize the cost, J, and the actuator frequency is at location 308, the actuator frequency may be decreased, thereby causing an increase in the cost, J.

[0043] A similar relationship exists for quadratic cost functions that have a minimum. For example, FIG. 3B shows that the cost function J (or gamma magnitude squared (|Γ| 2 3B shows a plot 300B of a quadratic cost function 310 as a function of J and actuator frequency U. As shown, plot 300B includes a minimum 312 and locations 314, 316 along the cost function 310, with each location 314, 316 on a different side of minimum 312. Thus, in this example, all points to the left of minimum 312 have a negative slope, and all points to the right of minimum 312 have a positive slope. If it is desired to minimize cost J and the actuator frequency is at location 314, the actuator frequency may be increased, thereby causing a decrease in cost J (or output response value). In other embodiments, if it is desired to minimize cost J and the actuator frequency is at location 316, the actuator frequency may be decreased, thereby causing a decrease in cost J.

[0044] To maximize or minimize cost J in FIGS. 3A-3B, it is desirable to understand the directionality of the actuator frequency U required to move the cost function toward a minimum or maximum. In some ESC techniques, this can be achieved by injecting a sinusoidal perturbation signal over multiple cycles on the actuator to probe the system's response to changing actuator frequency (e.g., a change in the cost function). For example, based on the sinusoidal perturbation signal, the output response value changes in magnitude and direction depending on where its current position is (e.g., positions 306, 308, 314, 316 in FIGS. 3A-3B) relative to the minimum or maximum point (e.g., maximum 304, minimum 312). The output response value can be processed to estimate the local slope (or gradient) of the cost function (e.g., cost functions 302, 310), which indicates the direction of the actuator frequency adjustment required to move toward the minimum or maximum point. An example of an ESC technique employing a sinusoidal perturbation signal can be found by reference to US Pat. No. 10,741,363.

[0045] 4 illustrates an example of a power supply system 400 including an RF generator 410 that implements an ESC-based approach. As shown, the power supply system 400 provides an output to a match network 412, which provides an output to a load 414, such as a nonlinear load or a plasma chamber. The RF generator 410 includes a power controller 416, a power amplifier 418, and a sensor 420. The sensor 420 may be implemented as one of a voltage / current sensor (VI sensor) or a directional coupler, as described above. The power controller 416 controls the power supply 400 to generate an actuation signal 416 that is input to the power amplifier 418.

[0046]

number

[0047] Output.

[0048]

number

[0049] The signal represents a power control signal responsive to the feedback signal.

[0050]

number

[0051] , generates an output RF signal to a sensor 420 as commanded by the match network 412. The sensor 420 outputs the RF signal to the match network 412 for application to the load 414. The sensor 420 outputs feedback signals X, Y to a block 422. In various embodiments, the block 422 may be a scaling or calibration module that scales X and Y to output predetermined electrical parameters. The block 422 may also include a forward power value

[0052]

number

[0053] to the adder 424. The adder 424 also receives a power set point input and outputs the power set point input and the forward power value

[0054]

number

[0055] The difference between fb ) is determined. fb is input to the power controller 416. The error signal e fb is provided to the power amplifier 418 by the power controller 416

[0056]

number

[0057] Determine the desired adjustment to.

[0058] Block 422 also outputs the absolute value of the reflection coefficient |Γ|. The absolute value of the reflection coefficient |Γ| is input to block 426, which calculates the transfer function D filt (z) implements a high-pass filter. The filtered absolute value of |Γ| is input to mixer 423. Mixer 423 also receives the perturbation signal generated by signal source 429.

[0059]

number

[0060] As shown, the perturbation signal

[0061]

number

[0062] is a sinusoidal signal sin(ω pert t) and sinusoidal or perturbation frequency ω pert The mixer 423 receives the perturbation signal

[0063]

number

[0064] and the measured absolute value of the complex coefficient |Γ|. The output of the mixer 423 is the perturbation signal

[0065]

number

[0066] The output from mixer 423 is fed to integrator D esc (z) is input to 425 and integrator D esc (z) 425 is a frequency control or frequency feedback signal input to a signal combiner or adder 427

[0067]

number

[0068] Therefore, the feedback signal

[0069]

number

[0070] is the perturbation signal

[0071]

number

[0072] and a feedback component or frequency control signal.

[0073]

number

[0074] is generated. A feedback component or frequency control signal

[0075]

number

[0076] can be written in equation (1) below:

[0077]

number

[0078] however,

[0079]

number

[0080] is a frequency tuning signal component for adjusting the frequency to achieve automatic frequency tuning of the power supply system;

[0081]

number

[0082] is the perturbation signal component, which is the perturbation signal.

[0083] u t esc The signal can be a complete frequency control signal (center frequency and AFT offset) or just an automatic frequency tuning (AFT) offset from the center frequency. In various non-limiting embodiments, if the system center frequency is 13.56 MHz, then u t esc The signal may represent an offset from 13.56 MHz to allow for automatic frequency tuning, or may be the desired output frequency, for example 13.58 MHz.

[0084] In various other embodiments, adder 427 receives a match control signal u generated similarly to equation (1) above to control the operation of match network 412. t' esc In various other embodiments, the signal u t' esc can control one of the impedance tuning actuators, such as a reactive component embodied as a capacitor or inductor, to vary the reactance of the match network 412.

[0085] In various embodiments, the signals generated in the system 400 may be corrupted by various signals or noise sources having the same or similar frequencies, such as frequency control or frequency feedback signals.

[0086]

number

[0087] The perturbation signal used to generate the cost function may be similar in frequency (and possibly the same) as various other signals or noise sources in the system. This, in turn, may impair the system's ability to measure or possibly use the output response (or output gamma magnitude squared) and / or other related signals. Therefore, it is desirable to select a frequency for the perturbation signal that is within a frequency spectrum that is free of other strong signal components (e.g., other frequency tones). This allows for separation of the resulting related signals so that the local gradient of the cost function can be reliably and accurately measured.

[0088] One source of interference can come from the pulse train itself. For example, frequency tuners are typically layered, in that each tuner is receiving data related to one state of the pulse (or pulses). This can produce an "apparent" pulse frequency that oscillates based on the pulsing setup. For example, the apparent pulse frequency associated with each state can be calculated based on the duty cycle of the state, the repetition rate of the pulses, and the hold-off time associated with the state, as shown below in equation (2).

[0089]

number

[0090] however, T Pulse is the pulse period and is equal to 1 over the pulse repetition rate, The duty cycle is the ratio of the width of the state across the pulse, Holdoff_Time is the time period that the tuner is held idle on a pulse state transition.

[0091] For example, at a 2 kHz pulse repetition rate, a 20% duty cycle for one of the pulse states, and a 50 microsecond hold-off time, the tuner will see a significant frequency component (apparent frequency) at 20 kHz from the pulse train itself. If the duty cycle is changed from 20% to 15%, the apparent pulse frequency will move to 40 kHz.

[0092] For example, Figures 5A-5B show plots 500A and 500B illustrating the calculated apparent pulse frequency (Y-axis) as a function of pulse repetition rate (X-axis), duty cycle, and hold-off time according to equation (2) above. In the example of Figures 5A-5B, the hold-off time is constant; the hold-off time in Figure 5A is shorter than the hold-off time in Figure 5B, and the pulse repetition rate ranges between values ​​X1 and X2. Additionally, the apparent pulse frequency in Figure 5A ranges between values ​​y1 (e.g., 0 Hz) and y2, while the apparent pulse frequency in Figure 5B ranges between values ​​y1 and y3. In this example, value y3 in Figure 5B is greater than value y2 in Figure 5A. Each of lines 502, 504, 506, 508, 510, 512, 514, and 516 in Figures 5A-5B represents the apparent pulse frequency varying with pulse repetition rate while implementing different duty cycles. For example, lines 502, 510 represent the apparent pulse frequency as a function of pulse repetition rate and a first duty cycle, lines 504, 512 represent the apparent pulse frequency as a function of pulse repetition rate and a second duty cycle, lines 506, 514 represent the apparent pulse frequency as a function of pulse repetition rate and a third duty cycle, and lines 508, 516 represent the apparent pulse frequency as a function of pulse repetition rate and a fourth duty cycle.

[0093] As seen in FIGS. 5A-5B, for a number of repetition rate and duty cycle combinations, the data suggests that a high perturbation frequency may be acceptable. However, if the repetition rate is moved to, for example, a higher rate, the perturbation frequency may become too close to the apparent pulse frequency, resulting in impaired desired gradient measurements. In fact, in various embodiments, the apparent pulse frequency may be exactly at the perturbation frequency. Thus, while the data in FIGS. 5A-5B may suggest that selecting a relatively higher perturbation frequency may provide some assurance of avoiding pulse repetition rate effects, small setup changes dramatically affect the resulting apparent pulse frequency. Thus, for example, only small changes to the hold-off time, duty cycle, and / or repetition rate may significantly affect the resulting apparent pulse frequency and cause interference with the perturbation frequency.

[0094] Additionally, in some embodiments, selecting a high perturbation frequency can cause other problems in the control system. For example, a frequency tuner is constantly modulating the load impedance with its sinusoidal perturbation signal, and a power controller, such as power controller 416 of FIG. 4, may rely on sensed parameters from the load to control the power amplifier. If the power controller (more specifically, the power control loop) does not have sufficient bandwidth, this disturbance will bleed through and affect the power delivered to the load. Thus, in many instances, a higher perturbation frequency for the frequency tuning loop can result in the power control loop being less able to reject this disturbance. This can be seen in FIG. 6.

[0095] For example, FIG. 6 shows various waveforms 602, 604, 606, 608, 610, and 612 representing forward power, measured delivered power, actual power setpoint, gamma magnitude squared, power drive signal, and sinusoidal frequency modulation signal. As seen in FIG. 6, the effect of 40 kHz sinusoidal frequency modulation (waveform 612) is clearly visible in the measured delivered power (waveform 604). For example, it is desirable to deliver constant power to a load. However, 40 kHz sinusoidal frequency modulation causes + / - 5% delivered power fluctuations (e.g., wiggle or ripple) to the delivered power. This is because the power control loop does not have sufficient bandwidth to handle 40 kHz sinusoidal frequency modulation. However, if the perturbation frequency is within the controller's bandwidth, the controller can compensate for the impedance variations caused by the frequency tuning loop and maintain constant delivered power.

[0096] In view of the above, as recognized by the inventors, it is desirable to select a perturbation frequency of the perturbation signal that satisfies various design constraints. For example, as described further herein, the perturbation frequency is within a window that avoids other signal components (frequencies) that would interfere with the gradient measurement. In other words, the selected perturbation frequency is isolated from other frequency tones in the system (e.g., frequency tones associated with the RF generator utilizing the perturbation signal, other RF generators in the system, load components such as plasma chamber components, controllers in the system, etc.). Furthermore, the perturbation frequency is small enough (e.g., below a bandwidth limit) to avoid disturbances to the power control loop and / or large enough to avoid low frequency components not associated with the perturbation signal.

[0097] The present disclosure provides various solutions for selecting and / or adjusting the perturbation frequency of a perturbation signal that meet one or more of these various design constraints. For example, the perturbation frequency may be dynamically selected, adjusted, etc., so that it is sufficiently isolated from other frequency tones, such as apparent pulse frequencies, harmonics, etc., in the system while remaining below the bandwidth limit of the power control loop. This may be done based on current operating conditions while the system is in use (e.g., online), rather than during the design phase. Doing so improves tuning performance for ESC-based automatic frequency tuning systems in that the signals involved may be reliable and usable (e.g., not corrupted).

[0098] Additionally, as described further herein, perturbation frequencies may be selected for various scenarios. For example, based on operating conditions, a single perturbation frequency may be selected for each state of a pulse, a single perturbation frequency may be selected for the entire pulse, a single perturbation frequency may be selected for each corresponding state of multiple pulses (e.g., one perturbation frequency for state S1 of each pulse, another perturbation frequency for state S2 of each pulse, etc.).

[0099] 7 illustrates an example of a power supply system 700 including an RF generator 710 that implements an ESC-based approach in which a perturbation frequency may be desirably selected in accordance with the teachings herein. As shown, the power supply system 700 includes the match network 412 and load 414 of FIG. 4 and an RF generator 710 for providing an output to the load 414. The RF generator 710 includes the power controller 416 of FIG. 4, the power amplifier 418, the sensor 420, the control block 422 (e.g., including a scaling or calibration module), the mixer 423, the summer 424, the control block 425 (e.g., including an integrator), the control block 426 (e.g., including a high-pass filter), the signal combiner or summer 427, and the perturbation signal source 429. These components function and interact in a manner similar to that described above. Additionally, the RF generator 710 generates a perturbation signal generated by the signal source 429.

[0100]

number

[0101] 7. The frequency selector control block (or module) 702 includes a frequency selector control block (or module) for selecting the desired perturbation frequency of the .

[0102] According to various embodiments, various portions of RF generator 710 may be considered to cooperate to define a frequency controller, such as an extremum-seeking frequency controller. For example, in various embodiments, the frequency controller may include all or portions of mixer 423, control block 425, summer 427, perturbation signal source 429, and / or frequency selector block 702. In other embodiments, the frequency controller may include, for example, control block 425 and receive a perturbation signal-based signal from signal source 429. Additionally, according to various embodiments, various or all of the control elements in FIG. 7 may be implemented using controllers such as controllers 20a, 20b, 20′ in FIG. 1. For example, in FIG. 7, some or all of power controller 416, control block 422, mixer 423, summer 424, control block 425, control block 426, summer 427, perturbation signal source 429, and / or frequency selector control block 702 may be implemented as controllers 20a, 20b, 20′ in FIG. 1.

[0103] In various embodiments, frequency selector block 702 may determine one or more frequency tones associated with RF generator 710 and / or other RF generators in system 700, and then select a perturbation frequency that is separated from the frequency tones. For example, frequency selector block 702 may incorporate, or possibly receive, various known operating parameters, and then select a desired perturbation frequency based on the operating parameters. For example, the operating parameters may include a pulse repetition rate, a state duty cycle, and / or a hold-off time associated with RF generator 710, operating frequencies associated with RF generator 710 and / or one or more other RF generators in system 700, harmonic aliases, etc. In various embodiments, the operating frequencies of the RF generators may generate beat frequency tones (e.g., the difference between the operating frequencies of the RF generators). Based on this data, or portions thereof, frequency selector block 702 may calculate an apparent frequency (e.g., a frequency tone) associated with a particular state of the pulse as described above, and then select an appropriate perturbation frequency to avoid that apparent frequency, any related frequencies (e.g., harmonics of the apparent frequency), and other frequency tones (e.g., beat frequency tones). In other words, the perturbation frequency may be selected to ensure robust separation from the apparent frequency, its related frequencies, and / or other known frequency tones.

[0104] The operating parameters may include information for a single state of a pulse, multiple states of a single pulse, multiple states of multiple pulses, etc. Thus, frequency selector block 702 may calculate or, in some cases, determine an apparent frequency associated with a single state in a pulse and / or apparent frequencies associated with multiple states in a pulse (or multiple pulses) depending on the provided operating parameters. In some examples, the apparent frequency for one state may be the same as or different from the apparent frequency for another state.

[0105] Once the apparent frequency for a single state or apparent frequencies for multiple states is determined, the frequency selector block 702 may select an appropriate perturbation frequency. For example, the frequency selector block 702 may select a single perturbation frequency for each different state in a pulse. This may be necessary, for example, if the determined apparent frequencies of multiple states are such that no suitable frequency is available to avoid each apparent frequency. In other examples, the same perturbation frequency may be selected and used in multiple states of a pulse (if possible), or multiple corresponding states of multiple pulses (if possible), based on operating parameters. For example, the frequency selector block 702 may determine that multiple states in one or more pulses have apparent frequencies that are sufficiently similar to allow selection of a single perturbation frequency that avoids each of the apparent frequencies.

[0106] In other embodiments, as described further below, frequency selector block 702 may determine one or more frequency tones associated with RF generator 710 based on measured feedback and analysis of that feedback. For example, frequency selector block 702 may perform a transform (e.g., a fast Fourier transform (FFT)) to analyze data of one or more feedback signals, such as gamma magnitude squared, reflected power, etc., and determine one or more frequency tones based on the analyzed data. Once the frequency tones are determined, frequency selector block 702 may select appropriate perturbation frequencies to avoid the frequency tones.

[0107] Additionally, in selecting the perturbation frequency, the frequency selector block 702 may consider the bandwidth limitations of the power controller 416. For example, the frequency selector block 702 may select a frequency that is below a known control bandwidth limit while also avoiding frequency tones (e.g., apparent pulse frequencies for each state).

[0108] 8A-8B illustrate an exemplary method of such selection. For example, as shown in FIG. 8A-8B, frequency selector block 702 may receive or, in some cases, determine a bandwidth limit 804 of a control loop, such as a power control loop associated with power controller 416. After determining a frequency tone, such as an apparent frequency, frequency selector block 702 may select an optimal perturbation frequency to avoid both the frequency tone and the bandwidth limit 804.

[0109] 8A , the apparent frequency 806 is determined to be closer to the bandwidth limit 804 than to the bandwidth's DC value (0 Hz) 802. In other words, Delta 1 between the DC value 802 and the apparent frequency 806 is greater than Delta 2 between the apparent frequency 806 and the bandwidth limit 804. In such an example, the frequency selector block 702 selects the perturbation frequency 808 to fall within Delta 1 (the larger of the two deltas in FIG. 8A ). In other words, the perturbation frequency 808 is set equal to a frequency value or point within Delta 1.

[0110] 8B, however, the apparent frequency 816 is determined to be closer to the DC value 802 than to the bandwidth limit 804. Therefore, delta 2 between the apparent frequency 816 and the bandwidth limit 804 is greater than delta 1 between the DC value 802 and the apparent frequency 816. Thus, in this example, the frequency selector block 702 selects the perturbation frequency 818 to fall within delta 2 (the larger of the two deltas in FIG. 8B). In other words, the perturbation frequency 818 is set equal to a frequency value or point within delta 2.

[0111] In various embodiments, frequency selector block 702 selects the perturbation frequency to be at the midpoint of a larger delta. For example, in FIG. 8A , perturbation frequency 808 is selected to be at the midpoint of delta 1, while in FIG. 8B , perturbation frequency 818 is selected to be at the midpoint of delta 2. This may ensure that the perturbation frequency is a sufficient distance away from bandwidth limit 804, DC value 802, and apparent frequency 816. This may therefore ensure that the perturbation frequency is small enough (e.g., below the bandwidth limit) to avoid disturbances to the power control loop, and large enough to avoid low frequency components not associated with the perturbation signal and separated from apparent frequency 816. Otherwise, if the perturbation frequency is too close to apparent frequency 816, the frequency controller may not be able to tune to the minimum or maximum of the cost function (or gamma magnitude squared) and may instead tune to another, less desirable value.

[0112] In other embodiments, frequency selector block 702 may select a different perturbation frequency that is not necessarily at the midpoint of the maximum delta, but that still maintains a sufficient distance away from bandwidth limit 804, DC value 802, and apparent frequency 816. For example, frequency selector block 702 may select the lowest possible perturbation frequency in either delta (greater or smaller delta) that is at least a minimum distance (e.g., + / - 2.5 kHz, + / - 5 kHz, etc.) from apparent pulse frequency 816, but also maintains a defined distance (e.g., 5 kHz, 10 kHz, etc., depending on other frequency tones in the system, the value of the bandwidth limit, etc.) from DC value 802 or bandwidth limit 804.

[0113] In various embodiments, frequency selector block 702 may select an initial perturbation frequency to be at a point or frequency value (e.g., midpoint, not at midpoint, etc.) within one of Delta 1, 2, and then adjust the perturbation frequency to another point or frequency value in Delta. For example, once the initial perturbation frequency is determined by frequency selector block 702, data from a feedback signal (e.g., gamma magnitude squared or another signal) may be observed and analyzed. If the feedback signal indicates that an operating parameter of system 700 and / or RF generator 710 meets a threshold (e.g., supplied power wiggles below a defined threshold), frequency selector block 702 may adjust the perturbation frequency, for example, to another point further away from apparent pulse frequency 816. Adjustments to the perturbation frequency may be repeated until the feedback signal indicates that the threshold is not met (e.g., supplied power wiggles are at the defined threshold). Thus, in such an example, the bandwidth limit 804 may be increased in distance from the apparent pulse frequency 816 while still maintaining a sufficient distance away from the DC value 802 .

[0114] In some embodiments, it may be desirable to use the same perturbation frequency for multiple pulse states. This may allow for the reuse of some common elements (e.g., a high-pass filter in a feedback loop) across multiple pulse states. As a result, improved efficiency of resource usage may be achieved in some implementations, such as FPGA implementations, that utilize at least some common elements. In these embodiments, a single perturbation frequency would then need to be selected.

[0115] For example, a known pulsing setup, along with the pulse state holdoff, can be analyzed to calculate the apparent pulse frequency that will be seen by the tuner for each state. Using this information, desired exclusion zones (e.g., bands of frequencies near each apparent pulse frequency) can be identified as regions of operation that should be avoided.

[0116] 9-10 illustrate an exemplary method of such selection. For example, in FIG. 9, a plot 900 is shown illustrating apparent pulse frequency curves for a pulsed configuration with a defined hold-off time and four different values ​​of pulse state duty cycle. As shown, exclusion zone 902 is centered on the apparent pulse frequency curve at a first duty cycle value, exclusion zone 904 is centered on the apparent pulse frequency curve at a second duty cycle value, exclusion zone 906 is centered on the apparent pulse frequency curve at a third duty cycle value, and exclusion zone 908 is centered on the apparent pulse frequency curve at a fourth duty cycle value. In this embodiment, each exclusion zone 902, 904, 906, 908 represents a 5 kHz region on either side of its corresponding apparent frequency curve.

[0117] Once the exclusion zones have been identified, the frequency selector block 702 may select a single perturbation frequency for multiple pulse states, for example, based on the pulse repetition rate. For example, the exclusion zones or regions of Figure 9 may be overlaid with a particular pulse repetition rate to identify possible perturbation frequencies to avoid each of the exclusion zones or regions.

[0118] For example, FIG. 10A shows a plot 1000A of the resulting overlay of the exclusion zones or regions of FIG. 9 for a first pulse repetition rate. As shown, line 1002 has a value of 0 from frequency value x0 (e.g., 0 Hz (DC)) to frequency value x1, indicating that the perturbation frequency is not suitable within this region. This represents exclusion zones 908, 906, and 904 of FIG. 9 at the first pulse repetition rate. Line 1002 then has a value of 1 from frequency value x1 to frequency value x2, indicating that the perturbation frequency is suitable within this second region. This represents exclusion zones 904 and 902 of FIG. 9. Line 1002 again has a value of 0 from frequency value x2 to frequency value x3, indicating that the perturbation frequency is not suitable within this region. This represents exclusion zone 902 of FIG. 9. Line 1002 then has a value of 1 from frequency value x3 to frequency value x4, indicating that the perturbation frequency may be suitable within this region. This represents the region between the exclusion zone 902 in Figure 9 and the bandwidth limit of the power control loop. In such an example, the frequency selector block 702 may identify a maximum suitable region (e.g., between frequency values ​​x1 and x2) and select a perturbation frequency within that region (e.g., at the midpoint between frequency values ​​x1 and x2) for a plurality of pulse states having a first pulse repetition rate.

[0119] 10B shows plot 1000B, similar to plot 1000A, but with the resulting overlay of the exclusion zones or regions of FIG. 9 for a second pulse repetition rate greater than the first pulse repetition rate. As shown, line 1004 has a value of 0 from frequency value x0 (e.g., 0 Hz (DC)) to frequency value x5 (representing exclusion zones 908, 906 of FIG. 9 at the second pulse repetition rate), a value of 1 from frequency value x5 to frequency value x6 (representing the region between exclusion zones 906 and 904), a value of 0 from frequency value x6 to frequency value x7 (representing exclusion zone 904), and a value of 1 from frequency value x7 to frequency value x8 (representing the region between exclusion zone 904 and the bandwidth limit of the power control loop). In such an example, the frequency selector block 702 may again identify the largest suitable region (between frequency values ​​x7 and x8) and select a perturbation frequency within that region (e.g., at the midpoint between frequency values ​​x7 and x8) for a plurality of pulse states having a second pulse repetition rate.

[0120] In various embodiments, the frequency selector block 702 may take into account the entire set of pulsing conditions to select the most appropriate single perturbation frequency for multiple pulses. For example, computing a logical AND of the two profiles shown in Figures 10A-10B would indicate a particular operating perturbation frequency as most appropriate.

[0121] In various embodiments, the acceptable operating region (or, conversely, the undesirable exclusion zone) may vary with pulse repetition rate and duty cycle. For example, FIG. 10C shows plot 1000C of the resulting overlay of the exclusion zones or regions of FIG. 9 for three different repetition rates (represented by lines 1006, 1008, 1010) and four different duty cycles for four pulse states. Using the data from plot 1000C, frequency selector block 702 may compute a logical AND of the three profiles shown in FIG. 10C to generate plot 1000D of FIG. 10D. As shown, plot 1000D includes line 1012 having a value of 0 from frequency value x0 (e.g., 0 Hz (DC)) to frequency value x9, indicating an unsuitable region for the perturbation frequency, and a value of 1 from frequency value x9 to frequency value x10, indicating a suitable region for the perturbation frequency. In such an example, the frequency selector block 702 may select a perturbation frequency within a suitable region (e.g., at the midpoint between frequency values ​​x9 and x10) for multiple pulses having any one of three different pulse repetition rates.

[0122] In some cases, overlapping constraints may not result in a single perturbation frequency across the entire set of pulses. Therefore, in such instances, frequency selector block 702 may iteratively identify a minimum set of suitable operating perturbation frequencies. In such a scenario, rather than calculating the logical AND of the three profiles shown in FIG. 10C , frequency selector block 702 may calculate the sum of the profiles. The frequency that produces the largest sum indicates the frequency that satisfies the most overlapping pulse constraints. By selecting the frequency with the largest sum, frequency selector block 702 may then exclude these pulsing conditions and recalculate the sum across the remaining (not included) pulsing conditions. Therefore, by selecting the frequency with the largest sum, frequency selector block 702 may iteratively identify a minimum set of perturbation frequencies required to satisfy all of the pulsing conditions in a given recipe.

[0123] In various embodiments, the frequency selector block 702 may also take into account other frequency tones (e.g., other than the apparent pulse frequency) that may be present in the system when selecting the perturbation frequency. In other words, the frequency selector block 702 may determine other frequency tones that should be avoided. For example, the frequency selector block 702 may take into account known harmonic aliases for one of the RF frequencies (e.g., harmonics of the apparent pulse frequency), beat frequencies that occur between two RF carrier frequencies, and / or perturbation frequencies associated with another RF generator, for example, when the RF generators are pulsing in unison. These additional frequency tones may be in the form of a single frequency or an exclusion zone (a set of frequencies to be avoided), as described above. For example, using the frequency selection methods described above, the frequency selector block 702 may select appropriate perturbation frequencies that are isolated from (e.g., avoid) such frequency tones or constraints by selecting the perturbation frequencies via overlapping constraints.

[0124] In some embodiments, potentially interfering signal components, including apparent pulse frequencies and other frequency tones, can be determined via online frequency analysis. This can identify potentially unexpected signal components (e.g., strong harmonics) that can corrupt gradient measurements. For example, the frequency selector block 702 can collect a set of feedback data (gamma magnitude squared, reflected power, etc.) over a given operating pulse, states in the pulse, etc., and perform a transform (e.g., a fast Fourier transform (FFT)) to analyze the data. Based on this transform analysis, the frequency selector block 702 can determine possible interfering signal components (e.g., interfering frequency tones).

[0125] For example, FIG. 11A shows plot 1100A illustrating the spectrum (amplitude and frequency) of data for an operating condition based on feedback data analyzed using an FFT. As shown, plot 1100A includes multiple potentially interfering frequency tones 1102, 1104, and 1106A-I. Specifically, in FIG. 11A, frequency tone 1102 represents an identified apparent pulse frequency, frequency tone 1104 represents an identified harmonic of apparent pulse frequency 1102, and frequency tones 1106A-I represent other potentially interfering signals (that are indistinguishable). Once the potentially interfering signal components have been determined, frequency selector block 702 may identify one or more suitable regions (e.g., maximum regions) between frequency tones 1102, 1104, and 1106A-I and then select perturbation frequencies for each state, multiple states in a pulse, or multiple corresponding states in multiple pulses in one of the regions. For example, based on the determined signal components, the frequency selector block 702 may select a perturbation frequency to fall within the region between frequency tones 1106C-D (e.g., at the midpoint between frequency tones 1106C-D) or within the region between frequency tones 1106E-F (e.g., at the midpoint between frequency tones 1106E-F).

[0126] Further, in some embodiments, a perturbation frequency may be first selected (e.g., by frequency selector block 702), which may collect and analyze (e.g., by performing an FFT) a set of feedback data based on the output response of the perturbation frequency over a given operating pulse, states in the pulse, etc. In doing so, frequency selector block 702 may determine potentially interfering signal components near the perturbation frequency.

[0127] For example, FIG. 11B shows plot 1100B, which is similar to plot 1100A of FIG. 11A, but which shows the spectrum (amplitude and frequency) of data based on the output response of selected perturbation frequencies. Specifically, plot 1100B includes frequency tones 1102, 1104, and 1106A-I of FIG. 11A and perturbation frequency 1108. Based on the data in plot 1100B, it can be seen that perturbation frequency 1108 is located near multiple frequency tones, such as tones 1104, 1106D, and 1106E. Thus, in this example, frequency selector block 702 may select another perturbation frequency or adjust perturbation frequency 1108 based on the output response. For example, similar to FIG. 11A, frequency selector block 702 may select another perturbation frequency or adjust perturbation frequency 1108 to fall within the region between frequency tones 1106C-D or within the region between frequency tones 1106E-F. In various embodiments, a spectrum (amplitude and frequency) of the data based on the output response of the newly selected perturbation frequency may be created, ensuring that the new frequency does not overlap strongly with another signal source.

[0128] In various embodiments, the desired perturbation frequencies may be determined during an online learning / training phase. For example, perturbation frequency values ​​may be determined, selected, etc. for different setups (e.g., different pulsing conditions, etc.) during the online learning / training phase. In some examples, the perturbation frequency values ​​may be selected based on data provided by a transformation, as described herein. In this manner, one or more particular perturbation frequency values ​​may be applied whenever a particular setup is implemented in the future. Furthermore, as new setups with different operating conditions are developed, one or more perturbation frequency values ​​may be selected for each new setup.

[0129] In various embodiments, the systems and methods herein may implement various control processes after selecting a perturbation frequency. For example, after a perturbation frequency is selected, the systems and methods herein may implement any one of the control processes / systems described with respect to Figures 17-22 in U.S. Patent No. 10,741,363.

[0130] FIG. 12 illustrates a control module 1200. The control module 1200 incorporates various components of FIGS. 1, 4, and 7. The control module 1200 may include an amplitude control module 1202, a frequency control module 1204, a match network control module 1206, a perturbation module 1208, a frequency tuning module 1210, and a cost determination module 1212. As shown, the perturbation module 1208 includes a frequency selector module 1214. In various embodiments, the control module 1200 includes one or more processors that execute code associated with modules 1202, 1204, 1206, 1208, 1210, 1212, and 1214. Operation with one or more of modules 1202, 1204, 1206, 1208, 1210, 1212, and 1214 is described below with respect to the methods of FIGS. 13-16. Additionally, in various embodiments, operation with one or more of modules 1202, 1204, 1206, 1208, 1210, and 1212 is described with respect to the methods of FIGS. 17-22 in US Pat. No. 10,741,363.

[0131] For a further defined structure of controllers 20a, 20b, and 20′ in FIG. 1 and / or the various control elements in FIGS. 4 and 7, see the flowcharts in FIGS. 13-16 provided below, the flowcharts in FIGS. 17-22 of U.S. Pat. No. 10,741,363, and the definition for the term “module” provided below. The systems disclosed herein can be operated using numerous methods, examples, and various control system methods, some of which are illustrated in FIGS. 13-16. The following operations are primarily described with respect to the implementations of FIGS. 1, 4, and 7, but the operations can be readily modified to apply to other implementations of the present disclosure. The operations can be performed iteratively. While the following operations are shown and primarily described as being performed sequentially, one or more of the following operations can be performed while one or more of the other operations are being performed.

[0132] 13 shows a flow chart of a control process 1300 for perturbation frequency selection in an RF generator, such as, for example, RF generator 710 of FIG. 7. Control begins at block 1302, where initialization occurs. Control proceeds to block 1304.

[0133] At block 1304, control receives operating parameters associated with the RF generator. In various embodiments, the operating parameters may include a duty cycle of a pulse state, a pulse repetition rate, and a hold-off time associated with the state. In other embodiments, the operating parameters may include, for example, a duty cycle of multiple states of a pulse, a pulse repetition rate, and a hold-off time associated with the pulse state, and / or a duty cycle of multiple states of multiple pulses, a pulse repetition rate, and a hold-off time associated with the multiple pulse states. Control then proceeds to block 1306.

[0134] In block 1306, control determines, or possibly identifies, one or more potentially interfering frequency tones. For example, the potentially interfering frequency tones may be determined according to any one of the methods described herein, such as by determining one or more apparent pulse frequencies, determining one or more exclusion zones associated with the apparent pulse frequencies, etc. Once the potentially interfering frequency tones are determined, control proceeds to block 1308.

[0135] In block 1308, control selects one or more suitable perturbation frequencies that are away from the determined frequency tone. In other words, control selects suitable perturbation frequencies that are sufficiently separated from the frequency tone. This selection of one or more perturbation frequencies may be performed according to any one of the methods described herein. For example, control may select perturbation frequencies that fall within a region (e.g., a midpoint of a region) between the frequency tones, between an exclusion zone, between a frequency tone and a bandwidth limit, between a DC value and a frequency tone, etc. Once control selects one or more perturbation frequencies in block 1308, control may proceed to block 1310, thereby ending process 1300 (as shown in FIG. 13 ), or may return to block 1304, if desired.

[0136] 14 shows a flowchart of another example control process 1400 for perturbation frequency selection in an RF generator, such as, for example, RF generator 710 of FIG. 7. Control begins at block 1402, where initialization occurs. Control proceeds to block 1404. In block 1404, control receives one or more feedback signals associated with the RF generator. For example, feedback data associated with gamma magnitude squared, reflected power, and / or other related data may be provided by or derived from the feedback signals. Control then proceeds to block 1406.

[0137] At block 1406, control performs a transform to analyze data in or derived from the feedback signal. For example, control may perform an FFT or another suitable transform to analyze such data. Control then proceeds to block 1408.

[0138] In block 1408, control determines, or possibly identifies, one or more potentially interfering frequency tones. For example, the potentially interfering frequency tones may be determined according to any one of the methods described herein, such as by determining frequency tones across a spectrum for the operating conditions based on the analyzed feedback data. Control then proceeds to block 1410.

[0139] In block 1410, control selects one or more suitable perturbation frequencies away from the determined frequency tone. This selection may be performed in a manner similar to block 1308 of Figure 13. Once control selects one or more perturbation frequencies in block 1410, control may proceed to block 1412, thereby ending process 1400 (as shown in Figure 14), or may return to block 1404, if desired.

[0140] 15 shows a flowchart of another exemplary control process 1500 for perturbation frequency selection in an RF generator, such as, for example, RF generator 710 of FIG. 7. Control begins at block 1502, where initialization occurs. Control proceeds to block 1504. In block 1504, control receives or, in some cases, determines the bandwidth of a power controller, such as power controller 416 of FIG. 7, associated with the RF generator. Control proceeds to block 1506.

[0141] Control determines, or possibly identifies, one or more potentially interfering frequency tones in block 1506. This determination of potentially interfering frequency tones may be performed in a manner similar to that of blocks 1306, 1408 of Figures 13-14. Control proceeds to block 1508.

[0142] In block 1508, control determines the delta between the bandwidth lower limit or minimum (e.g., DC or 0 Hz) and one of the frequency tones, and between the same or a different frequency tone and the bandwidth upper limit or maximum. This may be done, for example, by taking the difference between the bandwidth lower limit and the frequency tone, and the difference between the bandwidth upper limit and the frequency tone. Control then passes to block 1510, where the largest of the deltas is identified. Control then passes to block 1512.

[0143] In block 1512, control selects a perturbation frequency at the midpoint of maximum delta. For example, after determining maximum delta, control may divide the value of delta by two and then select a perturbation frequency to place at that divided value. Alternatively, control may select a perturbation frequency at another suitable point (e.g., frequency value) within maximum delta, as described herein. Control then proceeds to block 1514, where control generates a perturbation signal based on the selected perturbation frequency (e.g., at the midpoint of maximum delta or another frequency value). Control then proceeds to blocks 1516 and 1518.

[0144] At block 1516, control analyzes feedback response data associated with the selected perturbation frequency as described herein. At block 1518, control determines whether the data indicates that a defined threshold is met (e.g., the supplied power wiggle is below a defined threshold). If not, control proceeds to block 1520. If yes, control proceeds to block 1522, thereby ending process 1500 (as shown in FIG. 15), or may return to block 1504, if desired.

[0145] In block 1520, control adjusts the selected perturbation frequency at another point (e.g., frequency value) at the maximum delta or selects another perturbation frequency. Control then returns to block 1514.

[0146] FIG. 16 shows a flowchart of another example control process 1600 for perturbation frequency selection in an RF generator, such as, for example, RF generator 710 of FIG. 7 . Control begins at block 1602, where initialization occurs. Control proceeds to block 1604. In block 1604, control receives one or more feedback signals associated with the RF generator, from which feedback data associated with, for example, gamma magnitude squared, reflected power, and / or other related data may be provided or derived. Control then proceeds to blocks 1606, 1608, and 1610. In block 1606, control performs a transform to analyze data in or derived from the feedback signal, for example, in a manner similar to that described in block 1406 of FIG. 14 . In block 1608, control determines or possibly identifies one or more potentially interfering frequency tones, for example, in a manner similar to that described in block 1408 of FIG. 14 . In block 1610, control selects one or more suitable perturbation frequencies away from the determined frequency tone, e.g., in a manner similar to that described in block 1410 of Figure 14. Control then passes to blocks 1612, 1614, and 1616.

[0147] In block 1612, control generates a perturbation signal based on the selected perturbation frequency. For example, in a manner similar to that described in blocks 1516, 1518 of FIG. 15 , in block 1614, control analyzes feedback response data associated with the selected perturbation frequency, and in block 1616, control determines whether the data indicates that a defined threshold is met. If the threshold is not met in block 1616, control proceeds to block 1618. Otherwise, control may proceed to block 1620, thereby ending process 1600 (as shown in FIG. 16 ), or may return to block 1604, if desired.

[0148] In block 1618, control adjusts the selected perturbation frequency at another point (e.g., frequency value) away from the determined frequency tone or selects another perturbation frequency. Control then returns to block 1612.

[0149] The systems and methods described herein, in various configurations, may provide one or more of the following advantages. For example, the systems and methods described herein may enable dynamic optimization of perturbation frequencies for ESC-based frequency tuning control. As a result, the robustness of perturbation-based signal extraction (e.g., gradient measurements) may be improved, thereby improving ESC-based frequency tuning control with respect to known pulsing artifacts and other signal components occurring within the system. Additionally, the systems and methods described herein may enable optimization over a single pulsing condition or over a complete pulsing recipe. Thus, the number of perturbation frequency changes required within the system may be minimized. Furthermore, the systems and methods described herein may improve efficiency through online adjustment of perturbation frequencies based on current or previous operating conditions, setup, etc., as described herein.

[0150] The above description is merely exemplary in nature and is in no way intended to limit the disclosure, its application, or uses. The broad teachings of the present disclosure may be embodied in a variety of forms. Thus, while the present disclosure includes specific examples, the true scope of the present disclosure should not be so limited, as other variations will become apparent upon review of the drawings, the specification, and the following claims. In the specification and claims, one or more steps within a method may be executed in a different order (or in parallel) without altering the principles of the present disclosure. Similarly, one or more instructions stored on a non-transitory computer-readable medium may be executed in a different order (or in parallel) without altering the principles of the present disclosure. Unless otherwise specified, numbering or other labeling of instructions or method steps is done for convenient reference, and not to indicate a fixed order.

[0151] Furthermore, while each of the embodiments is described above as having certain features, any one or more of those features described with respect to any embodiment of the present disclosure may be implemented in and / or combined with any feature of any other embodiment, even if that combination is not explicitly described. In other words, the described embodiments are not mutually exclusive, and one or more of the embodiments permuted with one another remain within the scope of the present disclosure.

[0152] Spatial and functional relationships between elements (e.g., between modules, circuit elements, semiconductor layers, etc.) are described using a variety of terms, including "connected," "engaged," "coupled," "adjacent," "next to," "on top of," "above," "below," and "disposed." Unless expressly described as "direct," when a relationship between a first element and a second element is described in the above disclosure, the relationship may be a direct relationship where no other intervening elements exist between the first and second elements, but may also be an indirect relationship where one or more intervening elements (either spatially or functionally) exist between the first and second elements.

[0153] The phrase "at least one of A, B, and C" should be interpreted to mean a logical (A OR B OR C) using a non-exclusive logical OR, and not to mean "at least one of A, at least one of B, and at least one of C." The term "set" does not necessarily exclude empty sets—in other words, in some situations, a "set" may have zero elements. The term "non-empty set" may be used to indicate the exclusion of empty sets—in other words, a non-empty set will always have one or more elements. The term "subset" does not necessarily require a proper subset. In other words, a "subset" of a first set may be coextensive (equal) with the first set. Furthermore, the term "subset" does not necessarily exclude empty sets—in some situations, a "subset" may have zero elements.

[0154] In the diagrams, the direction of the arrow, indicated by the arrowhead, generally indicates the flow of information (such as data or instructions) relevant to the example. For example, element A and element B exchange various information, and when information sent from element A to element B is relevant to the example, the arrow may point from element A to element B. This unidirectional arrow does not imply that there is no other information sent from element B to element A. Furthermore, in response to information sent from element A to element B, element B may send a request for the information or an acknowledgment of receipt of the information to element A.

[0155] In this application, including the definitions below, the term "module" may be replaced with the term "controller" or the term "circuitry." In this application, the term "controller" may be replaced with the term "module." The term "module" may refer to, be a part of, or include an application specific integrated circuit (ASIC), digital, analog, or mixed analog / digital discrete circuitry, digital, analog, or mixed analog / digital integrated circuitry, combinational logic circuitry, field programmable gate array (FPGA), processor hardware (shared, dedicated, or group) that executes code, memory hardware (shared, dedicated, or group) that stores code to be executed by the processor hardware, other suitable hardware components that provide the described functionality, or a combination of some or all of the above, such as in a system-on-chip.

[0156] The module may include one or more interface circuits. In some examples, the interface circuit may implement a wired or wireless interface that connects to a local area network (LAN) or a wireless personal area network (WPAN). Examples of LANs are the Institute of Electrical and Electronics Engineers (IEEE) Standard 802.11-2020 (also known as the WIFI wireless networking standard) and IEEE Standard 802.3-2018 (also known as the ETHERNET wired networking standard). Examples of WPANs are IEEE Standard 802.15.4 (including the ZIGBEE standard from the ZigBee Alliance) and the BLUETOOTH wireless networking standard from the Bluetooth Special Interest Group (SIG) (including Core Specification Versions 3.0, 4.0, 4.1, 4.2, 5.0, and 5.1 from the Bluetooth SIG).

[0157] Modules may communicate with other modules using interface circuits. Although modules may be shown in this disclosure to logically communicate directly with other modules, in various implementations, modules may actually communicate via a communication system. A communication system includes physical and / or virtual networking equipment such as hubs, switches, routers, and gateways. In some implementations, a communication system connects to or traverses a wide area network (WAN) such as the Internet. For example, a communication system may include multiple LANs connected to each other over the Internet or over point-to-point dedicated lines using technologies including multiprotocol label switching (MPLS) and virtual private networks (VPNs).

[0158] In various implementations, the functionality of a module may be distributed among multiple modules connected via a communication system. For example, multiple modules may implement the same function distributed by a load balancing system. In a further example, the functionality of a module may be divided between a server (also known as remote or cloud) module and a client (or user) module. For example, a client module may include a native or web application that runs on a client device and in network communication with a server module.

[0159] Some or all of the hardware features of a module may be defined using a language for hardware description, such as IEEE Standard 1364-2005 (commonly referred to as "Verilog") and IEEE Standard 1076-2008 (commonly referred to as "VHDL"). The hardware description language may be used to fabricate and / or program the hardware circuit. In some implementations, some or all of the features of a module may be defined by a language such as IEEE 1666-2005 (commonly referred to as "SystemC"), which encompasses both code and hardware description, as described below.

[0160] The term code, as used above, may include software, firmware, and / or microcode and may refer to programs, routines, functions, classes, data structures, and / or objects. Shared processor hardware encompasses a single microprocessor that executes some or all code from multiple modules. Group processor hardware encompasses a microprocessor that executes some or all code from one or more modules in combination with additional microprocessors. References to multiple microprocessors encompass multiple microprocessors on discrete dies, multiple microprocessors on a single die, multiple cores of a single microprocessor, multiple threads of a single microprocessor, or combinations of the above.

[0161] Memory hardware may also store data, either along with the code or separately from the code. Shared memory hardware encompasses a single memory device that stores some or all code from multiple modules. An example of shared memory hardware may be a level 1 cache on or near a microprocessor die, which may store code from multiple modules. Another example of shared memory hardware may be persistent storage, such as a solid-state drive (SSD), which may store code from multiple modules. Group memory hardware encompasses a memory device that, in combination with other memory devices, stores some or all code from one or more modules. An example of group memory hardware is a storage area network (SAN), which may store code for a particular module across multiple physical devices. Another example of group memory hardware is the random access memory of each of a set of servers, which, in combination, store code for a particular module.

[0162] The term memory hardware is a subset of the term computer-readable medium. As used herein, the term computer-readable medium does not encompass transient electrical or electromagnetic signals propagating through a medium (such as on a carrier wave), and therefore the term computer-readable medium is considered tangible and non-transitory. Non-limiting examples of non-transitory computer-readable media are non-volatile memory devices (such as flash memory devices, erasable programmable read-only memory devices, or mask read-only memory devices), volatile memory devices (such as static random access memory devices or dynamic random access memory devices), magnetic storage media (such as analog or digital magnetic tape or hard disk drives), and optical storage media (such as CDs, DVDs, or Blu-ray discs).

[0163] The apparatus and methods described in this application may be implemented in part or in whole by a special-purpose computer created by configuring a general-purpose computer to perform one or more specific functions embodied in a computer program. Such apparatus and methods may be described as computerized apparatuses and computerized methods. The functional blocks and flowchart elements described above act as software specifications that can be converted into a computer program by the routine work of a skilled engineer or programmer.

[0164] A computer program includes processor-executable instructions stored on at least one non-transitory computer-readable medium. A computer program may also include or rely on stored data. A computer program may encompass a basic input / output system (BIOS) that interacts with the hardware of a special-purpose computer, device drivers that interact with specific devices of a special-purpose computer, one or more operating systems, user applications, background services, background applications, etc.

[0165] A computer program may include (i) a descriptive statement to be parsed, such as HTML (Hypertext Markup Language), XML (Extensible Markup Language), or JSON (JavaScript Object Notation), (ii) assembly code, (iii) object code generated from source code by a compiler, (iv) source code for execution by an interpreter, (v) source code for compilation and execution by a just-in-time compiler, etc. By way of example only, the source code may be written using syntax from languages ​​including C, C++, C#, Objective C, Swift, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Perl, Pascal, Curl, OCaml, JavaScript®, HTML5 (Hypertext Markup Language Fifth Revision), Ada, ASP (Active Server Pages), PHP (PHP: Hypertext Preprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, Visual Basic®, Lua, MATLAB®, SIMULINK®, and Python®. [Explanation of symbols]

[0166] 10 RF generator or power supply system, power supply system 12, 410, 710 RF Generator 12a Radio Frequency (RF) Generator or Power Supply, RF Generator, Source RF Generator, RF Power Generator 12b Radio Frequency (RF) Generators or Power Supplies, RF Generators, Bias RF Generators, RF Power Generators 14a RF power source or amplifier, RF power source, power amplifier, power source, source RF power source 14b RF power source or amplifier, RF power source, power amplifier, power source, bias RF power source 16a Sensor, Source Sensor 16b sensor, bias sensor 18a Matching network, source matching network 18b Matching network, bias matching network 20a Processor, controller, or control module, power controller or control module, control module, local controller, source controller 20b Processor, controller, or control module, power controller or control module, control module, local controller, bias controller 20' Controller, External or Common Controller 22a, 22b RF power signal 24a, 24b X signal 26a, 26b Y signal 28a, 28b Feedforward or feedback control signal, control signal, feedback control signal, signal 29a, 29b Control signal 30 Control signal, synchronization or trigger signal, trigger signal, trigger or synchronization signal, signal 30' control signal, synchronization or trigger signal, trigger or synchronization signal, signal 32,414 Load 34 Synchronous Bias Detector 36, 38 Links 40 Pulse synchronous output port 42, 50 digital communication ports 44 RF output ports 48 RF input ports 52 Pulse sync input port 56 Pulse Sync Signal 57 Digital Communication Link 58 RF Control Signals 60 control signal port 70 Pulse Signal 80 RF signals 300A, 300B, 500A, 500B, 900, 1000A, 1000B, 1000C, 1000D, 1100A, 1100B plot 302, 310 Quadratic cost function, cost function 304 maximum 306, 308, 314, 316 positions 312 min 400, 700 power supply system, system 412 Match Network 416 Power Controller 418 Power Amplifier 420 Sensor 422, 426 blocks, control blocks 423 Mixer 424 Adder 425 Integrator D esc (z), control block 427 Signal combiner or adder, adder 429 Signal Source, Perturbation Signal Source 502, 504, 506, 508, 510, 512, 514, 516, 1002, 1004, 1006, 1008, 1010, 1012 lines 602, 604, 606, 608, 610, 612 waveform 702 frequency selector control block (or module), frequency selector block, frequency selector control block 802 DC value (0Hz), DC value 804 Bandwidth Limit 806 apparent frequency 808, 818 perturbation frequency 816 Apparent frequency, apparent pulse frequency 902, 904, 906, 908 Exclusion Zones 1102 Potentially Interfering Frequency Tones, Frequency Tones, Apparent Pulse Frequencies 1104 Potentially Interfering Frequency Tone, Frequency Tone, Tone 1106A~I Potentially interfering frequency tones, frequency tones 1106D, E Tone 1108 Perturbation Frequency 1200 Control Module 1202 Amplitude control module, module 1204 Frequency Control Module, Module 1206 Match Network Control Module, Module 1208 Perturbation Module, Module 1210 Frequency Tuning Module, Module 1212 Cost Determination Module, Module 1214 Frequency Selector Module, Module

Claims

1. 1. A power supply system for powering a load, comprising: a radio frequency (RF) power source configured to generate an output signal at an output frequency; a signal source configured to generate a perturbation signal; an extremum-seeking frequency controller configured to generate a frequency control signal based on the perturbation signal, the frequency control signal varying the output frequency of the RF power source; and a frequency selector configured to select a perturbation frequency of the perturbation signal that is separated from at least one frequency tone associated with the power supply system; and A power supply system comprising:

2. 10. The power system of claim 1, further comprising a power controller coupled to the RF power source, the power controller configured to generate pulses to modulate the output signal of the RF power source, the pulses including a first state and a second state.

3. the perturbation frequency is a first perturbation frequency; the frequency selector is configured to select the first perturbation frequency for the first state and a second perturbation frequency for the second state of the pulse; 3. The power supply system of claim 2, wherein the first perturbation frequency and the second perturbation frequency are different.

4. 3. The power supply system of claim 2, wherein the frequency selector is configured to select the perturbation frequency for the first state and the second state of the pulse.

5. the power supply system further comprising a power controller coupled to the RF power source, the power controller configured to generate at least two pulses to modulate the output signal of the RF power source, each of the at least two pulses including a first state and a second state; the perturbation frequency is a first perturbation frequency; the frequency selector is configured to select the first perturbation frequency for the first state of each of the at least two pulses and a second perturbation frequency for the second state of each of the at least two pulses; 2. The power supply system of claim 1, wherein the first perturbation frequency and the second perturbation frequency are different.

6. 10. The power system of claim 1, further comprising a power controller coupled to the RF power source, the power controller configured to generate pulses to modulate the output signal of the RF power source, and the frequency selector configured to select the perturbation frequency based on a bandwidth of the power controller.

7. The frequency selector determining a first delta between the minimum value of the bandwidth and the at least one frequency tone and a second delta between the at least one frequency tone and the maximum value of the bandwidth; selecting the perturbation frequency to be equal to a frequency value of the greater of the first delta and the second delta; The power supply system of claim 6 configured to:

8. 8. The power system of claim 7, wherein the frequency value is a midpoint of the larger of the first delta and the second delta.

9. 8. The power system of claim 7, wherein the frequency selector is configured to analyze data indicative of an operating parameter of the power system with the selected perturbation frequency, and adjust the perturbation frequency within a larger one of the first delta and the second delta if the operating parameter is below a defined threshold.

10. 10. The power system of claim 9, wherein the frequency selector is configured to analyze data indicative of the operating parameter of the power system with the adjusted perturbation frequency, and if the operating parameter falls below the defined threshold, adjust the perturbation frequency again within a larger one of the first delta and the second delta.

11. The power supply system of claim 1 , wherein the frequency selector is configured to determine the at least one frequency tone.

12. 12. The power system of claim 11, further comprising a power controller coupled to the RF power source, the power controller configured to generate pulses to modulate the output signal of the RF power source, and the at least one frequency tone comprising a nominal frequency associated with a state of the pulse.

13. 13. The power system of claim 12, wherein the apparent frequency is determined based on a duty cycle of the state, a repetition rate of the pulses, and a hold-off time associated with the state.

14. the state of the pulse is a first state and the apparent frequency is a first apparent frequency associated with the first state; the at least one frequency tone includes a second apparent frequency associated with a second state of the pulse; 13. The power supply system of claim 12, wherein the frequency selector is configured to select the perturbation frequencies for the first state and the second state that are separate from the first apparent frequency and the second apparent frequency.

15. 10. The power supply system of claim 1, wherein the frequency selector is configured to perform a conversion to analyze data of one or more feedback signals and to determine the at least one frequency tone based on the analyzed data.

16. 16. The power system of claim 15, wherein the frequency selector is configured to select the perturbation frequency based on the analyzed data.

17. 10. The power supply system of claim 1, wherein the frequency selector is configured to perform a transformation to analyze data of one or more feedback signals based on an output response due to the perturbation frequency.

18. 18. The power system of claim 17, wherein the frequency selector is configured to adjust the perturbation frequency based on the analyzed data.

19. 20. The power system of claim 17, wherein the data indicates an operating parameter of the power system, and wherein the frequency selector is configured to adjust the perturbation frequency if the operating parameter is below a defined threshold.

20. 20. The power system of claim 19, wherein the frequency selector is configured to analyze data indicative of the operating parameter of the power system with the adjusted perturbation frequency, and to again adjust the perturbation frequency if the operating parameter falls below the defined threshold.

21. 1. A method for controlling a radio frequency (RF) generator of a power system, the RF generator including an RF power source, the method comprising: selecting a perturbation frequency of a perturbation signal that is separated from at least one frequency tone associated with the power supply system; generating the perturbation signal having the selected perturbation frequency; generating a frequency control signal based on the perturbation signal, the frequency control signal varying an output frequency of the RF power source; A method comprising:

22. 22. The method of claim 21, the method further comprising generating a pulse to modulate an output signal of the RF power source, the pulse including a first state and a second state, and selecting the perturbation frequency of the perturbation signal comprises selecting a first perturbation frequency for the first state of the pulse and a second perturbation frequency for the second state that is different from the first perturbation frequency.

23. 22. The method of claim 21, further comprising generating a pulse to modulate an output signal of the RF power source, the pulse including a first state and a second state, and selecting the perturbation frequency of the perturbation signal comprises selecting the perturbation frequency for the first state and the second state of the pulse.

24. 22. The method of claim 21, wherein the method further comprises generating at least two pulses to modulate an output signal of the RF power source, each of the at least two pulses including a first state and a second state, and wherein selecting the perturbation frequencies of the perturbation signal comprises selecting a first perturbation frequency for the first state of each of the at least two pulses and a second perturbation frequency for the second state of each of the at least two pulses that is different from the first perturbation frequency.

25. 22. The method of claim 21, further comprising generating pulses to modulate an output signal of the RF power source with a power controller, and wherein selecting the perturbation frequency of the perturbation signal comprises selecting the perturbation frequency based on a bandwidth of the power controller.

26. 26. The method of claim 25, further comprising determining a first delta between a minimum value of the bandwidth and the at least one frequency tone and a second delta between the at least one frequency tone and a maximum value of the bandwidth, and wherein selecting the perturbation frequency of the perturbation signal comprises selecting the perturbation frequency to be equal to a frequency value of a larger one of the first delta and the second delta.

27. 27. The method of claim 26, wherein the frequency value is the midpoint of the larger of the first delta and the second delta.

28. 27. The method of claim 26, further comprising: analyzing data indicative of an operating parameter of the power supply system with the selected perturbation frequency; and adjusting the perturbation frequency within a larger one of the first delta and the second delta if the operating parameter is below a defined threshold.

29. 29. The method of claim 28, further comprising: analyzing data indicative of the operating parameter of the power supply system with the adjusted perturbation frequency; and if the operating parameter falls below the defined threshold, again adjusting the perturbation frequency within a larger one of the first delta and the second delta.

30. 22. The method of claim 21, further comprising determining the at least one frequency tone.

31. 31. The method of claim 30, wherein the at least one frequency tone comprises an apparent frequency associated with a state of a pulse.

32. 32. The method of claim 31 , wherein determining the at least one frequency tone comprises determining the apparent frequency associated with the state of the pulse based on a duty cycle of the state, a repetition rate of the pulse, and a hold-off time associated with the state.

33. the state of the pulse is a first state and the apparent frequency is a first apparent frequency associated with the first state; the at least one frequency tone includes a second apparent frequency associated with a second state of the pulse; 32. The method of claim 31 , wherein selecting the perturbation frequencies of the perturbation signal comprises selecting the perturbation frequencies for the first state and the second state that are separate from the first apparent frequency and the second apparent frequency.

34. 22. The method of claim 21, further comprising: performing a transformation to analyze data of one or more feedback signals; and determining the at least one frequency tone based on the analyzed data.

35. 35. The method of claim 34, wherein selecting the perturbation frequency of the perturbation signal comprises selecting the perturbation frequency based on the analyzed data.

36. 22. The method of claim 21, further comprising performing a transformation to analyze data for one or more feedback signals based on the output response due to the perturbation frequencies.

37. 37. The method of claim 36, further comprising adjusting the perturbation frequency based on the analyzed data.

38. the data indicative of operating parameters of the power supply system; 37. The method of claim 36, wherein the method further comprises adjusting the perturbation frequency if the operating parameter falls below a defined threshold.

39. 39. The method of claim 38, further comprising analyzing data indicative of the operating parameter of the power supply system with the adjusted perturbation frequency, and adjusting the perturbation frequency again if the operating parameter falls below the defined threshold.

40. 1. A non-transitory computer-readable medium storing processor-executable instructions for controlling a radio frequency (RF) generator of a power supply system, the RF generator including an RF power source, the instructions comprising: selecting a perturbation frequency of a perturbation signal that is separated from at least one frequency tone associated with the power supply system; generating the perturbation signal having the selected perturbation frequency; generating a frequency control signal based on the perturbation signal, the frequency control signal varying an output frequency of the RF power source; 1. A non-transitory computer-readable medium storing processor-executable instructions, including:

41. 41. The non-transitory computer-readable medium storing processor-executable instructions of claim 40, wherein the instructions further include generating, with a power controller, pulses to modulate an output signal of the RF power source, and selecting the perturbation frequency of the perturbation signal includes selecting the perturbation frequency based on a bandwidth of the power controller.

42. 42. A non-transitory computer-readable medium storing processor-executable instructions of claim 41, wherein the instructions further comprise determining a first delta between a minimum value of the bandwidth and the at least one frequency tone and a second delta between the at least one frequency tone and a maximum value of the bandwidth, and wherein selecting the perturbation frequency of the perturbation signal comprises selecting the perturbation frequency to be equal to a frequency value within a larger one of the first delta and the second delta.

43. 43. The non-transitory computer-readable medium storing processor-executable instructions of claim 42, wherein the frequency value is the midpoint of the larger of the first delta and the second delta.

44. 43. The non-transitory computer-readable medium storing processor-executable instructions of claim 42, wherein the instructions further comprise: analyzing data indicative of an operating parameter of the power supply system with the selected perturbation frequency; and adjusting the perturbation frequency within a larger one of the first delta and the second delta if the operating parameter is below a defined threshold.

45. 45. A non-transitory computer-readable medium storing processor-executable instructions of claim 44, wherein the instructions further comprise: analyzing data indicative of the operating parameter of the power supply system with the adjusted perturbation frequency; and if the operating parameter falls below the defined threshold, adjusting the perturbation frequency again within a larger one of the first delta and the second delta.

46. 41. A non-transitory computer-readable medium storing processor-executable instructions as recited in claim 40, wherein the instructions further comprise determining the at least one frequency tone.

47. the at least one frequency tone comprises an apparent frequency associated with a pulse state; 47. A non-transitory computer-readable medium storing processor-executable instructions of claim 46, wherein determining the at least one frequency tone comprises determining the apparent frequency associated with the state of the pulse based on a duty cycle of the state, a repetition rate of the pulse, and a hold-off time associated with the state.

48. the at least one frequency tone includes a first apparent frequency associated with a first state of a pulse and a second apparent frequency associated with a second state of the pulse; 47. A non-transitory computer-readable medium storing processor-executable instructions of claim 46, wherein selecting the perturbation frequencies of the perturbation signal comprises selecting the perturbation frequencies for the first state and the second state that are decoupled from the first apparent frequency and the second apparent frequency.

49. 41. The non-transitory computer-readable medium storing processor-executable instructions of claim 40, wherein the instructions further comprise: performing a transformation to analyze data of one or more feedback signals based on an output response due to the perturbation frequency, the data indicative of an operating parameter of the power supply system; and adjusting the perturbation frequency if the operating parameter is below a defined threshold.

50. 50. The non-transitory computer-readable medium storing processor-executable instructions of claim 49, wherein the instructions further comprise analyzing data indicative of the operating parameter of the power supply system with the adjusted perturbation frequency, and adjusting the perturbation frequency again if the operating parameter falls below the defined threshold.

51. 1. A control system for controlling a radio frequency (RF) generator of a power supply system, the RF generator including an RF power source configured to generate an output signal at an output frequency, the control system comprising: a signal source configured to generate a perturbation signal; an extremum-seeking frequency controller configured to generate a frequency control signal based on the perturbation signal, the frequency control signal varying the output frequency of the RF power source; and a frequency selector configured to select a perturbation frequency of the perturbation signal that is separated from at least one frequency tone associated with the power supply system; and A control system comprising:

52. the control system further comprising a power controller configured to generate pulses to modulate the output signal of the RF power source, the pulses including a first state and a second state; the perturbation frequency is a first perturbation frequency; the frequency selector is configured to select the first perturbation frequency for the first state and a second perturbation frequency for the second state of the pulse; 52. The control system of claim 51, wherein the first perturbation frequency and the second perturbation frequency are different.

53. 52. The control system of claim 51, further comprising a power controller configured to generate pulses to modulate the output signal of the RF power source, the pulses including a first state and a second state, and the frequency selector configured to select the perturbation frequencies for the first state and the second state of the pulses.

54. the control system further comprises a power controller configured to generate at least two pulses to modulate the output signal of the RF power source, each of the at least two pulses including a first state and a second state; the perturbation frequency is a first perturbation frequency; the frequency selector is configured to select the first perturbation frequency for the first state of each of the at least two pulses and a second perturbation frequency for the second state of each of the at least two pulses; 52. The control system of claim 51, wherein the first perturbation frequency and the second perturbation frequency are different.

55. 52. The control system of claim 51, wherein the control system further comprises a power controller configured to generate pulses to modulate the output signal of the RF power source, and wherein the frequency selector is configured to select the perturbation frequency based on a bandwidth of the power controller.

56. The frequency selector determining a first delta between the minimum value of the bandwidth and the at least one frequency tone and a second delta between the at least one frequency tone and the maximum value of the bandwidth; selecting the perturbation frequency to be equal to a frequency value of the greater of the first delta and the second delta; 56. The control system of claim 55 configured to:

57. 52. The control system of claim 51, wherein the frequency selector is configured to determine the at least one frequency tone.

58. 58. The control system of claim 57, wherein the frequency selector is configured to perform a transformation to analyze data of one or more feedback signals, determine the at least one frequency tone based on the analyzed data, and select the perturbation frequency based on the at least one frequency tone.

59. 52. The control system of claim 51 , wherein the frequency selector is configured to perform a transformation based on an output response at the perturbation frequency to analyze data of one or more feedback signals, and adjust the perturbation frequency based on the analyzed data.

60. the data indicative of operating parameters of the power supply system; 60. The control system of claim 59, wherein the frequency selector is configured to adjust the perturbation frequency if the operating parameter falls below a defined threshold.

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