Design Method of Non-Autonomous Constant Voltage Coreless Isolation Converter Based on PT Theory

Abstract

This invention discloses a design method for a non-autonomous constant-voltage coreless isolation converter based on PT theory. The non-autonomous constant-voltage coreless isolation converter includes a constant-frequency AC voltage source, a coreless transformer, an uncontrolled rectifier module, an output filter capacitor, and a load. The design method ensures that the input-output voltage ratio remains constant at 1 across the entire load range; and that at the rated output power point, it satisfies PT symmetry and the constant-frequency AC voltage source output power factor is 1. This invention, through a design method based on PT theory, achieves high efficiency and constant-voltage ratio output in the isolation converter using a coreless transformer, realizing coreless transformer operation.

Description

Technical Field

[0001] This invention relates to the field of power electronics, and in particular to a design method for a non-autonomous constant-voltage coreless isolation converter based on PT theory. Background Technology

[0002] Ferrite-core transformers exhibit magnetic saturation in high-frequency, high-power-density power conversion applications, and the temperature rise caused by hysteresis and eddy current losses reduces their reliability. Coreless transformers, using air as the magnetic medium, represent a highly attractive alternative to cored transformers.

[0003] In the design of coreless transformers, once the frame type, window utilization rate, and wire diameter are determined, the maximum self-inductance is limited to a small value. Traditional coreless converters require a large magnetizing inductance, and the transformer's coupling coefficient must be greater than 0.75. The design utilizes the transformer's leakage inductance and series (or parallel) compensation capacitors for resonance. However, the low leakage inductance increases the resonant current, leading to higher conduction losses and semiconductor device stress, and poor suppression of high-frequency harmonics. Therefore, traditional coreless converters are often designed for low-power, high-voltage, low-current input applications.

[0004] When analyzing the energy conversion cycle of a coreless transformer using the parity-time (PT) symmetry principle, if the Hamiltonian H of the system satisfies parity-time (PT) symmetry, the system's input and output voltages equal the turns ratio, consistent with the characteristics of a cored transformer. Coreless transformers based on PT symmetry have lower requirements for the coupling coefficient, thus allowing for a larger leakage inductance. This avoids the shortcomings of traditional coreless converters and further expands their application range.

[0005] To achieve stable operation of the coreless transformer in PT symmetry mode, the inverter output must satisfy a power factor of 1. Existing technologies all rely on the inverter output voltage frequency to self-track the output current, making the system autonomous. However, these solutions require high-cost, high-precision current sampling circuits. In conclusion, designing a non-autonomous, constant-voltage-ratio coreless transformer based on the PT symmetry principle is a highly efficient and low-cost solution for converter applications. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings and deficiencies of existing technologies and propose a design method for a non-autonomous constant-voltage coreless isolation converter based on PT theory. This method enables the coreless isolation converter to satisfy PT symmetry at the rated output power point, and the output power factor of the constant-frequency AC voltage source is 1. The converter maintains an approximately constant input-output voltage ratio of 1 across the entire load range. This invention, through a design method based on PT theory, achieves high efficiency and constant voltage ratio output of the coreless transformer in the isolation converter, realizing coreless transformer operation and improving the working efficiency of the coreless transformer.

[0007] To achieve the above objectives, the technical solution provided by this invention is as follows: a design method for a non-autonomous constant-voltage coreless isolation converter based on PT theory. The non-autonomous constant-voltage coreless isolation converter includes a constant-frequency AC voltage source, a coreless transformer, a primary-side series compensation capacitor, a secondary-side series compensation capacitor, an uncontrolled rectifier module, an output filter capacitor, and a load. The coreless transformer includes a primary winding, a primary leakage inductance, a primary magnetizing inductance, a primary stray resistance, a secondary winding, a secondary leakage inductance, and a secondary stray resistance. One end of the primary winding is connected to one end of the primary magnetizing inductance and one end of the primary-side series compensation capacitor, respectively. The other end of the primary-side series compensation capacitor is connected to the constant-frequency AC voltage source. The positive output of the voltage source is connected to the circuit, and the negative output of the constant frequency AC voltage source is connected to one end of the primary-side stray resistor. The other end of the primary-side stray resistor is connected to the other end of the primary-side winding and the other end of the primary-side magnetizing inductor. One end of the secondary-side winding is connected to one end of the secondary-side series compensation capacitor. The other end of the secondary-side series compensation capacitor is connected to one end of the uncontrolled rectifier module. The other end of the uncontrolled rectifier module is connected to one end of the secondary-side stray resistor, and the other end of the secondary-side stray resistor is connected to the other end of the secondary-side winding. The output of the uncontrolled rectifier module is connected to the output filter capacitor and the load. The design method includes the following steps:

[0008] Step 1: Input the parameters of the converter to be designed. The parameters include: U i 、U o 、P o f s f r Δ ref Among them, U i The input voltage of the constant frequency AC voltage source, U o For the output capacitor voltage, P o For the rated power of the converter, f s For switching frequency, f r For the resonant frequency, Δ ref To set the voltage regulation rate;

[0009] Step 2: Calculate the following parameters: Turns ratio n = U i / U oRated load Inductance ratio L p / L s =n 2 Primary winding current I p =P o / U i Secondary winding current I s =P o / U o In a coreless transformer, the resonant angular frequencies of the primary and secondary circuits are equal, denoted as ω. o =2πf r ; among which, L s The self-inductance of the secondary winding is denoted as L. s =(L m +L kp ) / n 2 L m L is the inductance value of the primary magnetizing inductance. kp L is the inductance value of the primary leakage inductance. ks L is the inductance value of the secondary leakage inductance. p The self-inductance of the primary winding is denoted as L. p =L m +L kp ;

[0010] Step 3: Select the initial quality factor Q o , To satisfy PT symmetry, Q o The value must satisfy And Q o >>0;R o This represents the resistance value of the load.

[0011] Step 4: From Step 3, we can obtain the self-inductance of the secondary winding. The secondary-side compensation capacitor is The self-inductance of the primary winding is The primary-side compensation capacitor is

[0012] Step 5: To achieve a constant input / output voltage ratio characteristic across the entire load range, the following must be satisfied:

[0013]

[0014] In the above equation, the left side represents the characteristic roots of the circuit equation satisfying the PT symmetry state; the right side represents the resonant frequency of the primary leakage inductance and the compensation capacitor; solving the above equation yields the coupling coefficient k.

[0015] Step 6: Calculate the inductance value of the primary leakage inductance based on the coupling coefficient k. The inductance value of the secondary leakage inductance

[0016] Step 7: Under full load conditions, the PT symmetry state is satisfied, and the voltage gain is G. full 10% P o Output voltage gain G under light load 10％ The calculation is as follows:

[0017]

[0018] In the formula, X p The primary reactance is represented as ω s The switching angular frequency is denoted as ω. s =2πf s ;X s The secondary reactance is represented as 10% P o Light load equivalent AC load resistance

[0019] Step 8: Calculate the voltage regulation rate based on Step 7. Determine if the voltage regulation rate is less than Δ ref If Q is less than 1, the design is complete; if Q is not less than 1, return to step 3 and increase Q. o The value is calculated and the operation continues until the voltage regulation rate is less than Δ. ref .

[0020] Furthermore, under full load conditions, the circuit satisfies PT symmetry, and the circuit parameters under full load conditions satisfy:

[0021]

[0022] In the formula, R′ is the negative resistance, expressed as: u p The output voltage of the constant frequency AC voltage source, i p For the output current of a constant frequency AC voltage source, u p and i p In phase, meaning the power factor of the constant frequency voltage source is 1.

[0023] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0024] 1. The application of coreless transformers in converters has been realized. Compared with traditional core transformers, the non-autonomous constant voltage coreless isolation converter designed in this invention does not require a magnetic core, resulting in lower device cost and lower loss.

[0025] 2. It achieves constant voltage ratio characteristics for input and output across the entire load range. Compared with traditional coreless transformers, the non-autonomous constant voltage coreless isolation converter designed in this invention has lower requirements for excitation inductance and lower device stress.

[0026] 3. It achieves open-loop, non-autonomous operation of the coreless transformer. Compared with the autonomous coreless transformer based on PT symmetry, the non-autonomous constant voltage coreless isolation converter designed in this invention satisfies PT symmetry at the rated operating point, operates in open-loop mode, is simple to implement, and is suitable for applications with stable output power, such as isolation power supplies and laser power supplies. Attached Figure Description

[0027] Figure 1 This is a block diagram of a non-autonomous constant-voltage coreless isolation converter.

[0028] Figure 2 This is a circuit diagram for a constant frequency AC voltage source.

[0029] Figure 3 This is a flowchart of the design method described in this invention.

[0030] Figure 4 This invention is fully loaded with (100% P) o The voltage u of the primary-side series compensation capacitor under operating conditions Cp Primary current i p The constant frequency AC voltage source output voltage u p Output voltage u o The simulation waveform diagram.

[0031] Figure 5 This invention is extremely lightweight (10% P) o The voltage u of the primary-side series compensation capacitor under operating conditions Cp Primary current i p The constant frequency AC voltage source output voltage u p Output voltage u o The simulation waveform diagram. Detailed Implementation

[0032] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0033] This embodiment discloses a design method for a non-autonomous constant-voltage coreless isolation converter based on PT theory, such as... Figure 1 As shown, the non-autonomous constant-voltage coreless isolation converter includes a constant-frequency AC voltage source (see...). Figure 2The system comprises a coreless transformer, a primary-side series compensation capacitor, a secondary-side series compensation capacitor, an uncontrolled rectifier module, an output filter capacitor, and a load. The coreless transformer includes a primary winding, a primary leakage inductance, a primary magnetizing inductance, a primary stray resistance, a secondary winding, a secondary leakage inductance, and a secondary stray resistance. One end of the primary winding is connected to one end of the primary magnetizing inductance and one end of the primary-side series compensation capacitor. The other end of the primary-side series compensation capacitor is connected to the positive output of a constant-frequency AC voltage source. The negative output of the constant-frequency AC voltage source is connected to the primary winding... One end of the stray resistor is connected to the primary side, and the other end of the primary side stray resistor is connected to the other end of the primary side winding and the other end of the primary side magnetizing inductor. One end of the secondary side winding is connected to one end of the secondary side series compensation capacitor. The other end of the secondary side series compensation capacitor is connected to one end of the uncontrolled rectifier module. The other end of the uncontrolled rectifier module is connected to one end of the secondary side stray resistor. The other end of the secondary side stray resistor is connected to the other end of the secondary side winding. The output of the uncontrolled rectifier module is connected to the output filter capacitor and the load.

[0034] like Figure 3 As shown, the design method includes the following steps:

[0035] Step 1: Input the parameters of the converter to be designed. The parameters include: U i 、U o 、P o f s f r Δ ref Among them, U i The input voltage of the constant frequency AC voltage source, U o For the output capacitor voltage, P o For the rated power of the converter, f s For switching frequency, f r For the resonant frequency, Δ ref To set the voltage regulation rate;

[0036] Step 2: Calculate the following parameters: Turns ratio n = U i / U o Rated load Inductance ratio L p / L s =n 2 Primary winding current I p =P o / U i Secondary winding current I s =P o / U o The resonant angular frequencies of the primary and secondary circuits are equal, which can be expressed as ω. o =2πf r ; among which, L sThe self-inductance of the secondary winding can be represented as L. s =(L m +L kp ) / n 2 L m L is the inductance value of the primary magnetizing inductance. kp L is the inductance value of the primary leakage inductance. ks L is the inductance value of the secondary leakage inductance. p The self-inductance of the primary winding can be represented as L. p =L m +L kp ;

[0037] Step 3: Select the initial quality factor Q o , To satisfy PT symmetry, Q o The value must satisfy And Q o >>0;R o This represents the resistance value of the load.

[0038] Step 4: From Step 3, we can obtain the self-inductance of the secondary winding. The secondary-side compensation capacitor is The self-inductance of the primary winding is The primary-side compensation capacitor is

[0039] Step 5: To achieve a constant input / output voltage ratio characteristic across the entire load range, the following must be satisfied:

[0040]

[0041] In the above equation, the left side represents the characteristic roots of the circuit equation satisfying the PT symmetry state; the right side represents the resonant frequency of the primary leakage inductance and the compensation capacitor; solving the above equation yields the coupling coefficient k.

[0042] Step 6: The inductance value of the primary leakage inductance can be calculated based on the coupling coefficient k. The inductance value of the secondary leakage inductance

[0043] Step 7: Under full load conditions, the PT symmetry state is satisfied, and the voltage gain is G. full Light load (10% P) o Output voltage gain G 10％ It can be calculated as:

[0044]

[0045] In the formula, X p The primary reactance can be expressed as: ω s The switching angular frequency can be expressed as ω. s =2πfs ;X s The secondary reactance can be expressed as Light load (10% P) o Corresponding equivalent AC load resistance

[0046] Step 8: From this, the voltage regulation rate can be calculated. Determine if the voltage regulation rate is less than Δ ref If Q is less than 1, the design is complete; if Q is not less than 1, return to step 3 and increase Q. o The value is calculated and the operation continues until the voltage regulation rate is less than Δ. ref .

[0047] The full-load operating condition satisfies PT symmetry, and the circuit parameters under full-load conditions satisfy:

[0048]

[0049] In the formula, R′ is the negative resistance, which can be expressed as: u p The output voltage of the constant frequency AC voltage source, i p For the output current of a constant frequency AC voltage source, u i and i p In phase, meaning the power factor of the constant frequency voltage source is 1.

[0050] To further illustrate the benefits and feasibility of the present invention, an embodiment is designed for illustration, wherein the input parameter is: input voltage U i =48V, output voltage U o =48V, rated power P o =300W, switching frequency f s =150kHz, resonant frequency f r =100kHz, voltage regulation Δ ref =5%.

[0051] Following the above design method, the design parameters are: n = 1, R o =7.68, L kp =43.6uH, L ks =43.6uH, L m =55.4uH, C p =25.6uF, C s =25.6uF, Q o =10.

[0052] Considering the device voltage drop and calculation offset, the turns ratio can be appropriately increased based on measured data to meet the rated voltage output. The turns ratio n is adjusted to 0.98, and the parameters are as follows: L kp =42.5uH, Lks =46.5uH, L m =56.5uH, C p =25.6uF, C s =24.6uF.

[0053] Figure 4 This invention is fully loaded with (100% P) o The primary-side series resonant capacitor voltage u under operating conditions Cp Primary current i p The constant frequency AC voltage source output voltage u p Output voltage u o The simulation waveform diagram shows that the output voltage is stable at 48V. The output voltage of the constant frequency AC voltage source is in phase with the resonant current, satisfying the PT symmetry state. There is no reactive power circulating current in the system, and the current capacity utilization rate of the switching devices is high.

[0054] Figure 5 This invention is extremely lightweight (10% P) o The primary-side series resonant capacitor voltage u under operating conditions Cp Primary current i p The constant frequency AC voltage source output voltage u p Converter output voltage u o The simulation waveform diagram shows that the stable output voltage is 49V, and the voltage regulation rate Δ = 2% < Δ ref =5%, which meets the design requirements.

[0055] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A design method for a non-autonomous constant-voltage coreless isolation converter based on PT theory. The non-autonomous constant-voltage coreless isolation converter includes a constant-frequency AC voltage source, a coreless transformer, a primary-side series compensation capacitor, a secondary-side series compensation capacitor, an uncontrolled rectifier module, an output filter capacitor, and a load. The coreless transformer includes a primary winding, a primary leakage inductance, a primary magnetizing inductance, a primary stray resistance, a secondary winding, a secondary leakage inductance, and a secondary stray resistance. One end of the primary winding is connected to one end of the primary magnetizing inductance and one end of the primary-side series compensation capacitor, respectively. The other end of the primary-side series compensation capacitor is connected to the positive output of the constant-frequency AC voltage source. The output phase is connected as follows: the negative output of the constant frequency AC voltage source is connected to one end of the primary-side stray resistor; the other end of the primary-side stray resistor is connected to the other end of the primary-side winding and the other end of the primary-side magnetizing inductor; one end of the secondary-side winding is connected to one end of the secondary-side series compensation capacitor; the other end of the secondary-side series compensation capacitor is connected to one end of the uncontrolled rectifier module; the other end of the uncontrolled rectifier module is connected to one end of the secondary-side stray resistor; and the other end of the secondary-side stray resistor is connected to the other end of the secondary-side winding. The output of the uncontrolled rectifier module is connected to the output filter capacitor and the load. Its characteristic is that... The design method includes the following steps: Step 1: Input the parameters of the converter to be designed. The parameters include: U i U o P o f s f r Δ ref Among them, U i The input voltage of the constant frequency AC voltage source, U o For the output capacitor voltage, P o For the rated power of the converter, f s For switching frequency, f r For the resonant frequency, Δ ref To set the voltage regulation rate; Step 2: Calculate the following parameters: Turns ratio n = U i / U o Rated load Inductance ratio L p / L s =n 2 Primary winding current I p =P o / U i Secondary winding current I s =P o / U o In a coreless transformer, the resonant angular frequencies of the primary and secondary circuits are equal, denoted as ω. o =2πf r ; among which, L s The self-inductance of the secondary winding is denoted as L. s =(L m +L kp ) / n 2 L m L is the inductance value of the primary magnetizing inductance. kp L is the inductance value of the primary leakage inductance. ks L is the inductance value of the secondary leakage inductance. p The self-inductance of the primary winding is denoted as L. p =L m +L kp ; Step 3: Select the initial quality factor Q o , To satisfy PT symmetry, Q o The value must satisfy And Q o >>0; Step 4: From Step 3, we can obtain the self-inductance of the secondary winding. The secondary-side compensation capacitor is The self-inductance of the primary winding is The primary-side compensation capacitor is Step 5: To achieve a constant input / output voltage ratio characteristic across the entire load range, the following must be satisfied: In the above equation, the left side represents the characteristic roots of the circuit equation satisfying the PT symmetry state; the right side represents the resonant frequency of the primary leakage inductance and the compensation capacitor; solving the above equation yields the coupling coefficient k. Step 6: Calculate the inductance value of the primary leakage inductance based on the coupling coefficient k. Inductance value of secondary leakage inductance Step 7: Under full load conditions, the PT symmetry state is satisfied, and the voltage gain is G. full 10% P o Output voltage gain G under light load 10％ The calculation is as follows: In the formula, X p The primary reactance is represented as ω s The switching angular frequency is denoted as ω. s =2πf s ;X s The secondary reactance is represented as 10% P o Light load equivalent AC load resistance Step 8: Calculate the voltage regulation rate based on Step 7. Determine if the voltage regulation rate is less than Δ ref If Q is less than 1, the design is complete; if Q is not less than 1, return to step 3 and increase Q. o The value is calculated and the operation continues until the voltage regulation rate is less than Δ. ref .

2. The design method for a non-autonomous constant-voltage coreless isolation converter based on PT theory according to claim 1, characterized in that, Under full load conditions, the circuit satisfies PT symmetry, and the circuit parameters satisfy the following: In the formula, R′ is the negative resistance, expressed as: u p The output voltage of the constant frequency AC voltage source, i p For the output current of a constant frequency AC voltage source, u p and i p In phase, meaning the power factor of the constant frequency voltage source is 1.

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