METHOD FOR CALIBRATING A PHASE MODULATOR

Abstract

A method for calibrating a phase modulator includes determining a set of phase measurements, calculating a value for each error parameter of a set of error parameters corresponding to an error model relating to the phase modulator, using the set of phase measurements and at least one analytical function derived from the error model, and storing the calculated value for each error parameter of the set of error parameters in a memory for setting a phase correction on the phase modulator.

Description

BACKGROUNDIn the automotive radar, mobile communication, and other wireless applications, a certain number of transmit (TX) channels and receive (RX) channels are typically used to establish a large number of virtual antenna nodes to enable digital and / or analog beamforming or MIMO operation. For this purpose, an accurate and reliable phase shift of the radio frequency TX signal is required to enable a stable phase relationship between the TX channels. Some applications require accurate phase steps to preserve code orthogonality within a channel or from TX to TX channel (e.g., 90° steps as in the sequence 0°, 90°, 180°, 270°). Thus, resolution and accuracy are key requirements, which, for example, when using a 77 GHz automotive radar, must be in the range of fractions from one degree to several degrees.The document KIM, J. [et al.] "A Low-Complexity I / Q Imbalance Calibration Method for Quadrature Modulator. In: IEEE Transactions on Very Large Scale Integration (VLSI) Systems", vol. 27, no. 4, April 2019, pp. 972-977 discloses a low complexity I / Q calibration method (in-phase and quadrature components) for transmitters using quadrature modulation. Based on the theoretical mismatch analysis of the quadrature modulator, a low complexity I / Q imbalance extraction algorithm is proposed. After parameter extraction, the transmitter is calibrated by forcing the transmitter's counter-matching over digital baseband.In view of the foregoing, there is a need for a concept to provide accurate phase shift.SUMMARYAccording to a first aspect, a method of calibrating a phase modulator comprises determining a set of phase measurement values, wherein determining the set of phase measurement values comprises the following steps:applying an RF signal to an input of the phase modulator,selecting a phase value from a predetermined set of phase values, setting the phase modulator to the selected phase value,determining a phase measurement of the set of phase measurements, the phase measurement indicating a phase value measured by an RF output signal of the phase modulator set to the selected phase value, and repeating the steps of applying an RF signal to an input of the phase modulator, selecting a phase value from a predetermined set of phase values, setting the phase modulator to the selected phase value, and determining a phase measurement of the set of phase measurements until each phase value of the set of phase values is selected.A value for each error parameter of a set of error parameters is calculated according to an error model relating to the phase modulator, using the set of phase measurement values and at least one analytic function derived from the error model. The calculated value is stored for each error parameter of the set of error parameters in a memory for adjusting a phase correction at the phase modulator.In another aspect, a method of operating a phase modulator includes accessing a memory to read a set of values, each of the set of values corresponding to one of a set of error parameters of an error model of the phase modulator,calculating a phase adjustment value by transforming a target phase value into the phase adjustment value, wherein transforming the target phase value comprises non-arithmetically calculating the phase adjustment value based on the target adjustment value and the set of values corresponding to a set of error parameters of an error model of the phase modulator.applying an RF signal to the phase modulator and applying the calculated phase adjustment value to the phase modulator.According to another aspect, a monolithic microwave integrated circuit includes: a transmit path, the transmit path including a phase modulator; and a phase adjustment circuit coupled to the phase modulator, the phase adjustment circuit including a memory and a computing element, the memory configured to store a set of values, each of the set of values corresponding to one of a set of error parameters of an error model of the phase modulator. The computing element is configured to compute a phase adjustment value by transforming a target phase value into the phase adjustment value, wherein transforming the target phase value comprises non-arithmetically computing the phase adjustment value based on the target adjustment value and the set of values corresponding to the set of error parameters of an error model of the phase modulator.Those skilled in the art will recognize additional features and advantages upon reading the following detailed description and upon viewing the accompanying drawings.BRIEF DESCRIPTION OF THE DRAWINGSThe present disclosure is illustrated by way of example and not limitation in the figures of the accompanying drawings, in which like reference numerals refer to similar or identical elements. The elements of the drawings are not necessarily to scale relative to each other. The features of the various illustrated examples may be combined unless they are mutually exclusive. FIG. 1A illustrates a circuit block diagram of a transmitter according to an example. FIG. 1B illustrates a circuit block diagram of a phase modulator according to an example. FIG. 1C illustrates a block diagram of an error model, according to an example. FIG. 2 illustrates a flow diagram of a method according to an example. FIGS. 3A, 3B, 3C, and 3D show examples of I-Q diagrams. FIG. 4 shows a comparison of ideal set values and measurement points in an I / Q diagram according to an example. FIG. 5 shows a block diagram of a transmitter and a compensation circuit according to an example. FIG. 6 shows measurement results according to an example.DETAILED DESCRIPTIONExamples disclosed herein provide a novel concept for calibrating a phase modulator, which may be, for example, an I-Q phase modulator. The new concept is based on an error model of the phase modulator and on the calculation of a value for each error parameter of a set of error parameters corresponding to the error model. The new concept determines the error parameters based on setting the phase modulator to a predetermined set of phase values and measuring phase values. The concept enables estimates of the error parameters to be calculated from the measured phase values by simple analytical functions in a direct manner. As such, the new concept differs from existing solutions based on approximation and feedback optimization. In addition to more accurate phase adjustment, the novel concept disclosed herein enables shorter calibration times and enables calibration of a greater number of phase adjustment values. Furthermore, the power consumption and thus the heating is reduced, since no long and complicated calculations are required. Further, a new concept for correcting the phase errors will be described. The concept uses the estimated values of the error parameters and calculates pre-distortion values input to the phase modulator using analytical functions. The memory for storage is reduced because only the values for the error parameters need to be stored.Referring to FIG. 1A, shown is a block diagram of a monolithic microwave integrated circuit (MMIC) 10 that includes a plurality of transmission channels 12- 1, 12- 2, 12- 3, 12- 4. The MMIC 10 may be implemented, for example, as a transceiver device having, in addition to the plurality of transmission channels, a plurality of reception channels, which are omitted for the sake of clarity. The MMIC 10 may be, for example, an FMCW radar device, a mobile communication device, or any other wireless device. The MMIC 10 further includes a local oscillator implemented in FIG. 1 as a phase locked loop 14 that generates an LO signal SLO(t) that is transmitted via a splitter 16 to each input of the plurality of transmission channels 12- 1, 12- 2, 12- 3, 12- 4. Each of the plurality of transmission channels 12- 1, 12- 2, 12- 3, 12- 4 includes a phase modulator 18 and a power amplifier 20 to process the received LO signal and provide an RF output signal SRF(t) at an output of the respective transmission channel, which is transmitted to an antenna associated with the transmission channel. The phase of the respective transmission channel can be controlled or digitally adjusted in order to apply a defined phase shift for the transmission channel. Note that the circuit shown in FIG. 1A may be implemented in one semiconductor chip or may use multiple semiconductor chips. For example, the phase locked loop 14 or the power amplifier 20 may be implemented on dedicated semiconductor chips.FIG. 1B is a circuit block diagram to show the phase modulator 18 in more detail. To enable high accuracy and stability to changing operating conditions (e.g., small phase variation over temperature and frequency range), the phase modulator 18 is implemented as an I-Q phase modulator having an I path 22 (in-phase path) and a Q path 24 (quadrature path). I-Q phase modulators are the most common phase modulators used in light of the above requirements. The signal from the phase locked loop 14 is split at a node 23 into an I-path signal and a Q-path signal. The I path 22 includes a first mixer 26 (e.g., a Gilbert cell mixer) that is used to modulate the amplitude of the I path signal. The Q-path signal 24 includes a quadrature element 28 (quadrature network) that provides a phase shift of the received signal by π / 2 (90 degrees) to produce a Q-path signal. The Q path includes a second mixer 30 (e.g., a Gilbert cell mixer) that is used to modulate the amplitude of the Q path signal. The amplitude modulated I-path signal and the amplitude modulated Q-path signal are combined (summed) at a combining node 32. By applying amplitude control values I and Q via circuit blocks 34 and 36 to the first mixer 26 and the second mixer 30, the phase of the input LO signal having a frequency ω c can be rotated by a target phase shift angle φ=φ soll. The control values may be determined to be I=cos(φ), Q=sin(φ).FIG. 3A shows the I-Q diagram for the ideal I-Q phase modulator in which the intended phase shift is obtained at the output of the phase modulator by adjusting I-Q values according to the target phase shift angle φ. Note that the I and Q values are on a circle having a unit radius. In reality, however, the circuit components of phase modulator 18 are not ideal and suffer from degradations. This results in errors in phase adjustment if the tradeoffs are not corrected or compensated.Examples proposed herein provide efficient and accurate compensation of such disturbances by using an error model of the phase modulator and reducing the functional complexity of the error model to a set of analytic functions. Based on a set of measurements, values for error parameters of the error model can be determined by the set of analytic functions in a rather simple manner and the compensation can be achieved by inverting the analytic functions, so that the determined values of the error parameters can be input to the inverted analytic functions as variables. The compensation proposed herein is fast on the one hand and uses only a limited amount of memory to store the compensation parameters.Referring to FIG. 1C, an example of an error model for the phase modulator 18 will be explained. The error model is based on the block diagram shown in FIG. 1C and uses a set of error parameters to describe potential errors or non-ideal behavior. A first error of the error model is the gain error 40-1 which introduces an error or imbalance between the I path and the Q path. The gain error may be described by a first error parameter α, which affects the setting for the I-path by a scaling factor 1+a / 2 and affects the setting for the Q-path by a scaling factor 1-a / 2. FIG. 3B shows the effect of the gain error in the I-Q diagram, which results in distortion of the unit circle into an ellipsoidal shape.A second error is the offset error 42- 1, 42- 2 that adds an offset to the set values of the I path and Q path. The offset value is described by an error parameter I 0 for the I path and an error parameter Q 0 for the Q path. The effect of the offset error in the I-Q diagram is a displacement of the unitary circle in the direction of the I axis and / or the Q axis as a function of the values for I 0 and Q 0, see FIG. 3C.A third error is the quadrature error 44-1, 44-2 occurring in the quadrature element 28 and addressing imperfections in the generation of the quadrature signal, i.e., non-orthogonal generation of the quadrature signal. The orthogonality error is represented by an error parameter β and modifies the ideal 90° phase of the Q path signal by 90°-β / 2 and the ideal 0° phase of the I path signal by +β / 2. The effect in the I-Q diagram is a modification of the unitary circle in the direction of an ellipse with the major axis and the minor axis along two diagonal directions, see FIG. 1D.A fourth systematic error 46 is a constant phase shift ψ introduced by the phase modulator 18.Other errors, such as radio frequency (RF) crosstalk from the first mixer 26 to the second mixer 30, may be attributed to one of the described error parameters. For example, radio frequency (RF) crosstalk from an input of the first mixer 26 to its output may be attributed to the offset error, although the physical mechanism is different.Using the above model, the signal output by the phase modulator 18 excluding the systematic phase shift error can be described byThe corresponding phase including the phase error may be obtained according to the above-described model byIn the above equations, atan2is the 2-argument arctangent, a is the gain error, β is the quadrature error, I 0 is the I path offset error, and Q 0 is the Q path offset error, as described above.To avoid an iterative solution that requires many iterations and is therefore time consuming and difficult to implement, the examples disclosed herein use a non-repetitive analytic approach. To this end, the above equation is expanded in a series. In one example, first and second order terms of a Taylor series of the above equation are used and combined in a unique manner to obtain a set of equations that enables the above error parameters to be determined. Assuming that each of the error parameters a, β, I 0, Q 0 is much smaller than 1, products of error parameters are very small and can be considered to be disappearing. Further, when expanding cos terms in a Taylor series and considering the first order term, cosine terms of an error parameter may be assumed to be 1, while sine terms of an error parameter may be assumed to be the parameter itself. In other words, cos(x)-1 and sin(x)-x, where x is one of the above error parameters.Accordingly, the phase in the first-order approximation is obtained asCalibration measurements using the above approximation for determining the values of the error parameters will be described below. A set of phase measurements is determined based on applying a set of target phase settings to the phase modulator 18 and measuring the respective phase output of the phase modulator. FIG. 4 shows an I-Q diagram 400 indicating the respective target phase settings as crosses along the unitary circle and the measured phases for the respective target phase settings as circles.In one example, the set of target phase settings includes values 0, π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2, and 7π / 4 (in radians) as shown in the I-Q diagram 400 of FIG. 4. In other words, φ s( i)=i·π / 4, i=0,1,..., 7, where φ s( i) is the target phase setting for each target phase index i. For each of the target phase settings φ s( i), an analytical expression of the resulting phase is derived from the row extension by using first or second order terms. Each analytical expression includes one or more of the error parameters as variables. By setting these analytic expressions equal to the actual measurement result, a set of equations is derived. By solving the set of equations, analytical expressions for the error parameters can be determined that include the measured phases for the set of target phase settings as variables.Using the above example of the set of target phase settings, the above will be explained in more detail.For phase adjustment, the resulting phase is obtained as. Expanding atan2and using the first order term results inSimilarly, the following expressions can be obtained for each of the target phase settings as shown in Table 1. Table 1: Output phase based on Error Model with 1st Order Approximation Table 1: Output phase based on Error Model with 1st Order Approximation0π / π4π / π23π / 3π4π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π5π / 5π43π / 3π27π / 7π4Similarly, analytical expressions can be derived using both the first and second order terms of the Taylor series extension.This results in the following expressions shown in Table 2: Table 2: Output phase based on error model with 1st and 2nd order approximation Table 2: Output phase based on error model with 1st and 2nd order approximation0π / π4π / π23π / 3π4π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π5π / 5π43π / 3π27π / 7π4Examples disclosed herein intelligently combine the analytic expressions of Tables 1 and 2 to obtain a set of equations that enables a linear equation system to be established that can be solved analytically to obtain the error parameters.From the first order approximation, the following equations can be derived:From the first and second order approximations, the following equations can be derived:The error parameters may be estimated from the above equations according to the following.The systematic phase offset is independent of the target phase setting φ(i) and can be estimated as where φ m,o( i) is the measured output phase for each set phase φ(i) with i=1 to 8. Note that this corresponds to the average of the measured output phases.Once the estimated systematic phase error ψ est is determined, each measured phase for the estimated systematic phase shift may be corrected by introducing, for each measured phase, the systematically error corrected measured phase φ m( i) according to φ m( i)=φ m,o( i)-ψ est.The other error parameters may be estimated according to the following:The baseband offset error I 0 may be estimated from equation (2). Similarly, the baseband offset error Q 0 from equation (1) may be estimated.The orthogonality error β can be obtained from equation (8) as. Note that Io est1 and Qo est1 have already been estimated and may be used to determine the orthogonality error β.Finally, the gain error a can be estimated from equation (9). Again, the already estimated Io est1 and Qo est1 are used to determine the gain error a.The above-described concept enables all error parameters of the error model to be estimated using simple equations that require only simple calculation steps. For example, each of the error parameters may be estimated using an analytic expression that requires only 5 summation or subtraction operations at maximum and 3 multiplication or division by 2 n- operations to calculate a respective error parameter value.In some examples, a refinement operation may be performed using already estimated error parameters. The refinement operation may increase the accuracy for some or all of the error parameters. In some examples, only a portion of the error parameters may be subjected to a refinement operation.Equations used for the refinement operation may be similarly obtained using equations (1) through (9), or combinations thereof.An example of a refinement operation for the error parameters I 0 and Q 0 will be described below. The refinement operation uses equation (7) to obtain a term for the refined I 0- error parameter and equation (6) to obtain a term for the refined Q 0- error parameter. Using the approximation valid for small x, the I 0- error parameter and the Q 0- error parameter can be estimated and estimated assuming small values for the error parameter a est. It should be noted that with the above approximation, a division calculation other than division by 2 n is avoided and the estimates of the error parameters can be calculated using only summing, subtracting, multiplying and division by 2 n- operations. It should be noted that divide-by-2 n- operations are much easier to implement than other real or integer division operations. With the above-described processing, the errors of the phase modulator are completely modeled, and the error parameter can be estimated (determined) with good accuracy from the output of the measurements.FIG. 2 shows a basic flow diagram 200 for the above-described concept for calibrating a phase modulator. The flow chart 200 begins with a step S 10 of determining a set of phase measurement values, wherein the determination of the set of phase measurement values comprises the substeps S 20- 1 to S 20- 5. In substep S 20-1, an RF signal is applied to an input of the phase modulator and in substep S 20-2, a phase value is selected from a predetermined set of (target) phase values. At S 20-3, the phase modulator is set to the selected phase value and at S 20-4, a phase measurement of the set of phase measurements is determined, the phase measurement indicating a phase value measured from an RF output of the phase modulator set to the selected phase value. At S 20-5, substeps S 20-1 through S 20-4 are repeated until each phase value of the set of phase values is selected. At S 30, a value for each error parameter of a set of error parameters corresponding to an error model related to the phase modulator is calculated using the set of phase measurement values and at least one analytic function derived from the error model. At S 40, each error parameter of the set of error parameters is stored in a memory for adjusting a phase correction at the phase modulator.To provide phase correction to the phase modulator 18, the error model is used to provide compensation for the errors of the phase modulator 18. The compensation concept used herein uses the estimated values for the above-described error parameters and provides a pre-distortion value for each of the target adjustment phases to compensate for the errors. To this end, the estimated values for each error parameter are stored and the inverse of the analytic functions is used to obtain a pre-distortion value for each of the target phase settings that can be applied in a digital pre-distortion to compensate for the errors.A bijective function between the input phase and the output phase is defined by the equationNote that this equation maps a set target phase J s to an output phase φ e in a non-linear manner. The calculation of the compensation value is based on the inverse of φ e( φ s). With φ s= φ e( φ t)-1 the phase shifter output signal phase is φ e( φ s) = φ e φ e( φ t)-1) = φ t, whereby the intended target phase setting φ t is obtained as the output phase at the output of the phase modulator.Transforming the above equation into the inverse function, i.e., solving φ e( φ s) = φ t for φ s as a function of φ t, results in an analytic function with the target phase value φ t and the error parameters of the error model as variablesThe upper term in the atan2function represents the Q setting Q s of the phase setting φ s and the lower term represents the I setting I s of the phase setting φ s. Using approximations for small values of the error parameters, the I setting and Q settings can be calculated asThe above is an analytical function that allows the pre-distortion values I s and Q s for each target phase setting φ t to be obtained as a function of the error parameters. The pre-distortion values I s and Q s correspond to the control values I and Q of the values of the circuit blocks 34 and 36 which must be input to the mixers 26 and 30 to obtain the desired target phase setting φ t at the output of the phase modulator 18. Estimates of the error parameters may be calculated as described above and now used to measure the pre-distortion values.The above calculation may be realized by a calculation element implemented as a processing unit capable of simple calculation operations. In one example, the above computations may also be realized by a computational element implemented in pure hardware without using a programmable processing unit.FIG. 5A shows a block diagram of a computing element 500 implemented as dedicated pre-distortion hardware circuitry to compute the pre-distortion values I s and Q s. An input 502 provides the input target phase setting φ t to a first input of the adder 504. A second input of the adder 504 is connected to an input 503 providing the negative estimated systematic phase offset ψ est to the adder 504 to calculate as an output the corrected target value φ t- ψ est corrected for the systematic phase offset ψ est. The resulting corrected target value φ t, - ψ est is provided to an I path branch 506, and the sine value of the corrected target value φ t- ψ est is calculated by a block 508. Further, the corrected target value φ t- ψ est is provided to a Q path branch 510, and the cosine value of the corrected target value φ t- ψ est is calculated by a block 512. Blocks 508 and 512 may include, for example, circuitry implementing a coordinate rotation digital computer (CORDIC) algorithm, which may use a look-up table or table and an interpolation algorithm to calculate the sine and cosine values.Block 508 is connected to a first multiplier 514 and block 512 is connected to a second multiplier 516. The first multiplier 514 and the second multiplier 516 are further connected to an input 518 to provide the value of -β / 2 as a second input to the multipliers 514 and 516, where β is the estimated orthogonality error parameter, as explained above. Accordingly, multiplier 514 provides as output the result of -β est / 2 · sin(φ t- ψ est) and multiplier 516 provides as output the result of -β est / 2 · cos(φ t- ψ est).The output of the first multiplier 514 is coupled to a first input of an adder 520. A second input of the adder 520 is coupled to an output of the block 512 and a third input of the adder 520 is coupled to an input 522 to provide the negative value of the error parameter Io est2. The adder 520 sums the input values to calculate the term -β / 2·sin(φ t- ψ) + cos(φ t- ψ) - Io. Similarly, the output of the second multiplier 516 is coupled to a first input of an adder 524. A second input of the adder 524 is coupled to an output of the block 508 and a third input of the adder 520 is coupled to an input 526 to provide the negative value of the error parameter Qo est2. The adder 524 sums the input values to calculate the term -β est / 2 · cos(φ t- ψ est) + sin(φ t- ψ est) - Qo est2.The output of the adder 520 is coupled to a first input of a third multiplier 528. A second input of the third multiplier 528 is coupled to an output of an adder 532.A first inverting input of the adder 532 is connected to an input 534 providing the value of the error parameter α est / 2 and a second input of the adder 532 is connected to an input 536 to provide the integer value 1. At an output of the adder 532, the result of term 1-α est / 2 is provided to the input of the third multiplier 528. The third multiplier 528 calculates the result of the term (1-α est / 2)(- β est / 2 · sin(φ t- ψ est) + cos(φ t- ψ est) - Io est2) and provides the calculated value to an I S- output 540 of the calculation element 500.The output of the adder 524 is coupled to a first input of a fourth multiplier 530. A second input of the fourth multiplier 530 is coupled to an output of an adder 538.A first input of the adder 538 is connected to the input 534 which provides the value of the error parameter α est / 2 and a second input of the adder 538 is connected to the input 536 to provide the integer value 1. At an output of the adder 538, the result of the term 1 + α est / 2 is provided to the input of the fourth multiplier 530. The fourth multiplier 530 calculates the result of the term (1 + α est / 2)(- β est / 2- cos(φ t- ψ est) + sin(φt - ψ est) - Qo est2) and provides the calculated value to a Q S- output 542 of the calculation element 500.It should be noted that the above implementation is a digital feed-forward hardware circuit that does not implement feedback loops and therefore allows the pre-distortion values for each of the target settings to be calculated at high speed. The dedicated hardware circuit requires only one CORDIC block in addition to basic addition and multiplication operations. Thus, the calculation element 500 is capable of calculating the pre-distortion values with low computational cost at high speed and low implementation cost. The target phase values φ t can be freely selected in the interval [0, 2π [. Unlike existing solutions that store corresponding phase correction information for each phase value of a dedicated set of phase values and optionally use interpolation, the above concept requires only storing the values of the estimates for the error parameters that are ψ est, α est, β est, Io est, Qo est in the above example. The memory can therefore be reduced while the accuracy is increased. No interpolation is required to obtain accurate phase values.FIG. 5B shows how the computing element 500 is coupled to the phase modulator 18 to provide pre-distortion to the phase modulator 18. The I S- output 540 is coupled to an input of a first digital-to-analog converter 550. The first digital-to-analog converter 550 converts the digital value received from the I S- output 540 to an analog signal that is provided to the first mixer 26 in the I path 22 to control the gain of the first mixer 26. The Q S- output 542 is coupled to an input of a second digital-to-analog converter 552. The second digital-to-analog converter 552 converts the digital value received from the Q S- output 540 to an analog signal that is provided to the second mixer 30 in the Q path 24 to control the gain of the second mixer 30.To verify the described concept, a series of measurements were made. FIG. 6 shows measurement results for a plurality of semiconductor chips of the same type, each having four transmission channels Tx 1, Tx 2, Tx 3, Tx 4. The phases were measured using a reception channel Rx 1 of each semiconductor chip. The results are shown in FIG. 6 for 15 phase settings, each phase setting having a respective index "constellation idx". The axis of ordinates shows the deviation of the measured phase from the target phase in angular degrees, while the axis of abscissas indicates the index of the respective phase setting. The upper four plots show the results for the uncalibrated phase modulator for each of the transmit channels Tx 1, Tx 2, Tx 3, Tx 4, while the lower four plots show the respective results using calibration and pre-distortion as described above. For reference, the target phasing is also shown with a deviation of 0.It can be observed that the phase deviations of the uncalibrated phase modulators are distributed in a range between 0 and 10 degrees, most of them being in the range between 2 and 8 degrees. In contrast, according to the described concept, the phase deviations are in a range between -2 and +2 degrees, most of them being in the range between -1 and +1.The result confirms that the above concept is able to address the need required to use phase modulators in future devices that require a high degree of phase accuracy.In addition to the examples described above, the following examples utilize the proposed concept and are hereby disclosed.Example 1 is a method for calibrating a phase modulator, comprising: determining a set of phase measurement values, wherein determining the set of phase measurement values comprises the following steps:applying an RF signal to an input of the phase modulator,selecting a phase value from a predetermined set of phase values, setting the phase modulator to the selected phase value,determining a phase measurement of the set of phase measurements, the phase measurement indicating a phase value measured by an RF output signal of the phase modulator set to the selected phase value, repeating the steps of applying an RF signal to an input of the phase modulator, selecting a phase value from a predetermined set of phase values, setting the phase modulator to the selected phase value, and determining a phase measurement of the set of phase measurements until each phase value of the set of phase values is selected,calculating a value for each error parameter of a set of error parameters corresponding to an error model relating to the phase modulator using the set of phase measurement values and at least one analytic function derived from the error model,storing the calculated value for each error parameter of the set of error parameters in a memory for adjusting a phase correction at the phase modulator.Example 2 is the method of example 1, wherein the predetermined set of phase values comprises radians values of 0, π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2, and 7π / 4.Example 3 is the method of example 1 or 2, wherein the set of error parameters comprises an average of the phase offsets, an in-phase baseband offset, a quadrature baseband offset, an orthogonality error, and a gain mismatch, and wherein calculating a value for each error parameter of the set of error parameters of the error model comprises:calculating an average of the phase offsets using the plurality of phase measurements;calculating a set of corrected phase measurement values using the average of the phase offsets and the set of phase measurement values,calculating an in-phase baseband offset value using a first corrected phase measurement of the set of corrected phase measurement values and a second corrected phase measurement of the set of corrected phase measurement values, calculating a quadrature baseband offset value using a third corrected phase measurement of the set of corrected phase measurement values and a fourth corrected phase measurement of the set of corrected phase measurement values, calculating an orthogonality error value using the first corrected phase measurement of the set of corrected phase measurement values, the second corrected phase measurement of the set of corrected phase measurement values, the third corrected phase measurement of the set of corrected phase measurement values and the fourth corrected phase measurement of the set of corrected phase measurement values,calculating a gain mismatch error value using a fifth corrected phase measurement of the set of corrected phase measurement values, a sixth corrected phase measurement of the set of corrected phase measurement values, a seventh corrected phase measurement of the set of corrected phase measurement values, and an eighth corrected phase measurement of the set of corrected phase measurement values.Example 4 is the method of example 3, wherein calculating an average of the phase offset corresponds to calculating an average of the difference between a sum of each phase value in the predetermined set of phase values and the sum of each phase measurement in the set of measured phase values, and wherein calculating the set of corrected phase measurement values comprises subtracting the average of the phase offset from each phase measurement of the set of phase measurement values.Example 5 is the method of example 3 or 4, wherein the first corrected phase measurement is a subtraction of the average value of the phase offset from a first phase measurement of the set of phase measurements and the second corrected phase measurement is a subtraction of the average value of the phase offset from a second phase measurement of the set of phase measurements, wherein the first phase measurement corresponds to a first phase value of the set of predetermined phase values and the second phase measurement corresponds to a second phase value of the set of predetermined phase values, wherein a difference between the first phase value and the second phase value is π, wherein the third corrected phase measurement is a subtraction of the mean value of the phase offset from a third phase measurement of the set of phase measurement values and the fourth corrected phase measurement is a subtraction of the mean value of the phase offset from a fourth phase measurement of the set of phase measurement values, wherein the third phase measurement corresponds to a third phase value of the set of predetermined phase values and the fourth phase measurement corresponds to a fourth phase value of the set of predetermined phase values, wherein a difference between the third phase value and the fourth phase value is π, wherein the fifth corrected phase measurement is a subtraction of the mean value of the phase offset from a fifth phase measurement of the set of phase measurement values and the sixth corrected phase measurement is a subtraction of the mean value of the phase offset from a sixth phase measurement of the set of phase measurement values, wherein the fifth phase measurement value corresponds to a fifth phase value of the set of predetermined phase values and the sixth phase measurement value corresponds to a sixth phase value of the set of predetermined phase values, wherein a difference between the fifth phase value and the sixth phase value is π, wherein the seventh corrected phase measurement value is a subtraction of the mean value of the phase offset from a seventh phase measurement value of the set of phase measurement values and the eighth corrected phase measurement value is a subtraction of the mean value of the phase offset from an eighth phase measurement value of the set of phase measurement values, wherein the seventh phase measurement value corresponds to a seventh phase value of the set of predetermined phase values and the eighth phase measurement value corresponds to an eighth phase value of the set of predetermined phase values, wherein a difference between the seventh phase value and the eighth phase value is π.Example 6 is the method of example 5, wherein the first phase value is π / 2, the second phase value is 3π / 2, the third phase value is 0, the fourth phase value is π, the fifth phase value is π / 4, the sixth phase value is 5π / 4, the seventh phase value is 3π / 4 and the eighth phase value is 7π / 4, and wherein the calculating the in-phase baseband offset value is based on the calculating, wherein φ m(2) corresponds to the first corrected phase measurement value and φ m(6) corresponds to the second corrected phase measurement value, and wherein the calculating the quadrature baseband offset value is based on the calculating, where φ m(4) corresponds to the third corrected phase measurement and φ m(0) corresponds to the fourth corrected phase measurement, and wherein the calculating the orthogonality error value is based on the calculating, where IO est is the calculated in-phase baseband offset value and QO est is the calculated quadrature baseband offset value, and wherein the calculating the gain mismatch error value is based on the calculating, where φ m(1) corresponds to the fifth corrected phase measurement and φ m(5) corresponds to the sixth corrected phase measurement, where φ m(3) corresponds to the seventh corrected phase measurement and φ m(7) corresponds to the eighth corrected phase measurement.Example 7 is the method of example 6, wherein the calculating the in-phase baseband offset value and the calculating the quadrature baseband offset value are based on refining a previously calculated in-phase baseband offset value and a previously calculated quadrature baseband offset value.Example 8 is the method of any one of Examples 1 to 7, wherein calculating a value for each error parameter of a set of error parameters comprises non-transitory calculation of a value for at least one of an orthogonality error and a gain mismatch error of the set of error parameters.Example 9 is the method of any of Examples 1 to 8, wherein the RF signal is generated by a local oscillator implemented in a monolithic microwave integrated circuit, wherein determining a phase measurement comprises comparing a phase of the RF signal with a phase of the RF output signal.Example 10 is the method of any one of Examples 1 to 9, wherein calculating a value for each of the error parameters does not include division calculations in which the divisor is different from 2 n where n is a natural number.Example 11 is a method of operating a phase modulator, the method comprising:accessing a memory to read a set of values, each of the set of values corresponding to one of a set of error parameters of an error model of the phase modulator,calculating a phase adjustment value by transforming a target phase value into the phase adjustment value, wherein transforming the target phase value comprises non-arithmetically calculating the phase adjustment value based on the target adjustment value and the set of values corresponding to a set of error parameters of an error model of the phase modulator,applying an RF signal to the phase modulator; andapplying the calculated phase adjustment value to the phase modulator.Example 12 is the method of example 11, wherein calculating the phase adjustment value comprises applying the target phase value and the plurality of values as variables to at least one analytic function, wherein the at least one analytic function is derived from an error model of the I-Q modulator.Example 13 is the method of example 11 or 12, wherein the set of error parameters comprises an average phase offset, an in-phase baseband offset, a quadrature baseband offset, an orthogonality error, and a gain mismatch.Example 14 is the method of claim 13, wherein the calculating the phase adjustment value is based on calculating an I signal value corresponding to (1 - α / 2)(-β / 2·sin(φ t- ψ) + cos(φ t- ψ) - Io), and calculating a Q signal value corresponding to (1 + α / 2)(-β / 2·cos(φ t- ψ) + sin(φ t- ψ) - Qo), where α corresponds to a stored value of the gain mismatch, β corresponds to a stored value of the orthogonality error, ψ corresponds to a stored value of the mean phase offset, Io corresponds to a stored value of the in-phase baseband offset, Qo corresponds to a stored value of the quadrature baseband offset, and φt corresponds to the target phase value, and wherein applying the phase adjustment value to the phase modulator comprises applying the I signal value to an in-phase path of the phase modulator and applying the Q signal value to a quadrature path of the phase modulator.Example 15 is a monolithic microwave integrated circuit, wherein the monolithic microwave integrated circuit comprises:a transmission path, the transmission path comprising a phase modulator,a phase adjustment circuit coupled to the phase modulator, the phase adjustment circuit comprising a memory and a computing element, the memory configured to store a set of values, each of the set of values corresponding to one of a set of error parameters of an error model of the phase modulator; andwherein the computing element is configured to compute a phase adjustment value by transforming a target phase value into the phase adjustment value, wherein transforming the target phase value comprises non-arithmetically computing the phase adjustment value based on the target adjustment value and the set of values corresponding to the set of error parameters of an error model of the phase modulator.Example 16 is the monolithic microwave integrated circuit of example 15, wherein the computing element is configured to compute the phase adjustment value based on computing the result of at least one analytic function, wherein the at least one analytic function comprises the target phase value and the plurality of values as variables.Example 17 is the monolithic microwave integrated circuit of example 15 or 16, wherein the set of error parameters comprises an average phase offset, an in-phase baseband offset, a quadrature baseband offset, an orthogonality error, and a gain mismatch.Example 18 is the monolithic microwave integrated circuit of any of Examples 15 to 17, wherein the computing element is configured to compute a phase adjustment value without using a division operation.Example 19 is the monolithic microwave integrated circuit of Example 18, wherein the computing element is configured to compute the phase adjustment value based on computing an I signal value corresponding to (1 - α / 2)(-β / 2·sin(φ t- ψ) + cos(φ t- ψ) - I) and computing a Q signal value corresponding to (1 + α / 2)(-β / 2·cos(φ t- ψ) + sin(φ t- ψ) - I), where α corresponds to a stored value of the gain mismatch, β corresponds to a stored value of the orthogonality error, ψ corresponds to a stored value of the mean phase offset, / corresponds to a stored value of the in-phase baseband offset, Q corresponds to a stored value of the quadrature baseband offset, and φt corresponds to the target phase value, and wherein the phase adjustment circuit is configured to apply the I signal value to an in-phase path of the phase modulator and apply the Q signal value to a quadrature path of the phase modulator.Example 20 is the monolithic microwave integrated circuit of any of claims 12 to 19, wherein the computing element is implemented as a digital feed-forward hardware circuit.It should be noted that the methods and apparatus, including preferred embodiments thereof, as set forth herein may be used alone or in combination with the other methods and apparatus disclosed herein. In addition, the features set forth in the context of a device are also applicable to a corresponding method and vice versa. Further, all aspects of the methods and apparatus set forth in the present document may be combined arbitrarily. In particular, the features of the claims can be combined with one another in any desired manner.It should be noted that the description and drawings merely illustrate the principles of the proposed methods and systems. Those skilled in the art will be able to practice various arrangements which, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples and embodiments set forth in the present document are, in principle, expressly intended for purposes of illustration only to aid the reader in understanding the principles of the proposed methods and systems. Furthermore, all statements herein providing principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass equivalents thereof.

Claims

A method of calibrating a phase modulator comprising: determining a set of phase measurements, wherein determining the set of phase measurements comprises the steps of: applying an RF signal to an input of the phase modulator; selecting a phase value from a predetermined set of phase values; setting the phase modulator to the selected phase value; determining a phase measurement of the set of phase measurements, wherein the phase measurement indicates a phase value measured from an RF output signal of the phase modulator set to the selected phase value; repeating the steps of applying an RF signal to an input of the phase modulator; selecting a phase value from a predetermined set of phase values, setting the phase modulator to the selected phase value and determining a phase measurement value of the set of phase measurement values until each phase value of the set of phase values is selected, calculating a value for each error parameter of a set of error parameters corresponding to an error model relating to the phase modulator using the set of phase measurement values and at least one analytic function derived from the error model, storing the calculated value for each error parameter of the set of error parameters in a memory for setting a phase correction at the phase modulator.The method of claim 1, wherein the predetermined set of phase values comprises Radians values of 0, π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2, and 7π / 4.The method of claim 1 or 2, wherein the set of error parameters comprises an average of the phase offsets, an in-phase baseband offset, a quadrature baseband offset, an orthogonality error, and a gain mismatch, and wherein calculating a value for each error parameter of the set of error parameters of the error model comprises: calculating an average of the phase offsets using the plurality of phase measurements; calculating a set of corrected phase measurement values using the average of the phase offsets and the set of phase measurement values, calculating an in-phase baseband offset value using a first corrected phase measurement value of the set of corrected phase measurement values and a second corrected phase measurement value of the set of corrected phase measurement values, calculating a quadrature baseband offset value using a third corrected phase measurement of the set of corrected phase measurement values and a fourth corrected phase measurement of the set of corrected phase measurement values; calculating an orthogonality error value using the first corrected phase measurement of the set of corrected phase measurement values, the second corrected phase measurement of the set of corrected phase measurement values, the third corrected phase measurement of the set of corrected phase measurement values and the fourth corrected phase measurement of the set of corrected phase measurement values; calculating a gain mismatch error value using a fifth corrected phase measurement of the set of corrected phase measurement values, a sixth corrected phase measurement of the set of corrected phase measurement values, a seventh corrected phase measurement of the set of corrected phase measurement values and an eighth corrected phase measurement of the set of corrected phase measurement values.The method of claim 3, wherein calculating an average of the phase offset corresponds to calculating an average of the difference between a sum of each phase value in the predetermined set of phase values and the sum of each phase measurement value in the set of measured phase values, and wherein calculating the set of corrected phase measurement values comprises subtracting the average of the phase offset from each phase measurement value of the set of phase measurement values.The method of claim 3 or 4, wherein the first corrected phase measurement is a subtraction of the average of the phase offset from a first phase measurement of the set of phase measurements and the second corrected phase measurement is a subtraction of the average of the phase offset from a second phase measurement of the set of phase measurements, wherein the first phase measurement corresponds to a first phase value of the set of predetermined phase values and the second phase measurement corresponds to a second phase value of the set of predetermined phase values, wherein a difference between the first phase value and the second phase value is π, wherein the third corrected phase measurement is a subtraction of the mean value of the phase offset from a third phase measurement of the set of phase measurement values and the fourth corrected phase measurement is a subtraction of the mean value of the phase offset from a fourth phase measurement of the set of phase measurement values, wherein the third phase measurement corresponds to a third phase value of the set of predetermined phase values and the fourth phase measurement corresponds to a fourth phase value of the set of predetermined phase values, wherein a difference between the third phase value and the fourth phase value is π, wherein the fifth corrected phase measurement is a subtraction of the mean value of the phase offset from a fifth phase measurement of the set of phase measurement values and the sixth corrected phase measurement is a subtraction of the mean value of the phase offset from a sixth phase measurement of the set of phase measurement values, wherein the fifth phase measurement value corresponds to a fifth phase value of the set of predetermined phase values and the sixth phase measurement value corresponds to a sixth phase value of the set of predetermined phase values, wherein a difference between the fifth phase value and the sixth phase value is π, wherein the seventh corrected phase measurement value is a subtraction of the mean value of the phase offset from a seventh phase measurement value of the set of phase measurement values and the eighth corrected phase measurement value is a subtraction of the mean value of the phase offset from an eighth phase measurement value of the set of phase measurement values, wherein the seventh phase measurement value corresponds to a seventh phase value of the set of predetermined phase values and the eighth phase measurement value corresponds to an eighth phase value of the set of predetermined phase values, wherein a difference between the seventh phase value and the eighth phase value is π.The method of claim 5, wherein the first phase value is π / 2, the second phase value is 3π / 2, the third phase value is 0, the fourth phase value is π, the fifth phase value is π / 4, the sixth phase value is 5π / 4, the seventh phase value is 3π / 4, and the eighth phase value is 7π / 4, and wherein the calculating the in-phase baseband offset value is based on the calculating φ m (6) - φ m (2) - π 2 where φ m(2) corresponds to the first corrected phase measurement value and φ m(6) corresponds to the second corrected phase measurement value, and wherein the calculating the quadrature baseband offset value is based on the calculating φ m (0) - φ m (4) + π 2 wherein φ m(4) corresponds to the third corrected phase measurement value and φ m(0) corresponds to the fourth corrected phase measurement value, and wherein the calculating the orthogonality error value is based on the calculating φ m (0) + φ m (4) - (φ m (2) + φ m (6)) + 4 I o e s t Q o e s t + π 2 wherein IO est is the calculated inphase baseband offset value and QO est is the calculated quadrature baseband offset value, and wherein the calculating the gain mismatch error value is based on calculating - φ m (1) + φ m (5) - (φ m (3) + φ m (7)) + 2 I o e s t 2 + Q o e s t 2 + π 2 φ m(1) corresponding to the fifth corrected phase measurement value and φ m(5) corresponding to the sixth corrected phase measurement value, where φ m(3) corresponds to the seventh corrected phase measurement value and φ m(7) corresponds to the eighth corrected phase measurement value.The method of claim 6, wherein the calculating the in-phase baseband offset value and the calculating the quadrature baseband offset value are based on refining a previously calculated in-phase baseband offset value and a previously calculated quadrature baseband offset value.The method of any of claims 1 to 7, wherein calculating a value for each error parameter of a set of error parameters comprises non-transitory calculation of a value for at least one of an orthogonality error and a gain mismatch error of the set of error parameters.The method of any of claims 1 to 8, wherein the RF signal is generated by a local oscillator implemented in a monolithic microwave integrated circuit, wherein determining a phase measurement comprises comparing a phase of the RF signal to a phase of the RF output signal.The method of any of claims 1 to 9, wherein calculating a value for each of the error parameters does not comprise division calculations where the divisor is different from 2 n where n is a natural number.A method of operating a phase modulator, the method comprising: accessing a memory to read a set of values, each of the set of values corresponding to one of a set of error parameters of an error model of the phase modulator; calculating a phase adjustment value by transforming a target phase value into the phase adjustment value, wherein transforming the target phase value comprises non-arithmetically calculating the phase adjustment value based on the target adjustment value and the set of values corresponding to a set of error parameters of an error model of the phase modulator; applying an RF signal to the phase modulator; and applying the calculated phase adjustment value to the phase modulator.The method of claim 11, wherein calculating the phase adjustment value comprises applying the target phase value and the plurality of values as variables to at least one analytic function, wherein the at least one analytic function is derived from an error model of the I-Q modulator.The method of claim 11 or 12, wherein the set of error parameters comprises an average phase offset, an in-phase baseband offset, a quadrature baseband offset, an orthogonality error, and a gain mismatch.The method of claim 13, wherein the calculating the phase adjustment value is based on calculating an I signal value corresponding to (1 - α / 2)(-β / 2·sin(φ t- ψ) + cos(φ t- ψ) - Io), and calculating a Q signal value corresponding to (1 + α / 2)(-β / 2·cos(φ t- ψ) + sin(φ t- ψ) - Qo), where α corresponds to a stored value of the gain mismatch, β corresponds to a stored value of the orthogonality error, ψ corresponds to a stored value of the mean phase offset, Io corresponds to a stored value of the in-phase baseband offset, Qo corresponds to a stored value of the quadrature baseband offset and φ t corresponds to the target phase value, and wherein applying the phase adjustment value to the phase modulator comprises applying the I signal value to an in-phase path of the phase modulator and applying the Q signal value to a quadrature path of the phase modulator.A monolithic microwave integrated circuit, the monolithic microwave integrated circuit comprising: a transmit path, the transmit path comprising a phase modulator; a phase adjustment circuit coupled to the phase modulator, the phase adjustment circuit comprising a memory and a computing element, wherein the memory is configured to store a set of values, each of the set of values corresponding to one of a set of error parameters of an error model of the phase modulator; and wherein the computing element is configured to compute a phase adjustment value by transforming a target phase value into the phase adjustment value, wherein transforming the target phase value comprises non-arithmetically computing the phase adjustment value based on the target adjustment value and the set of values corresponding to the set of error parameters of an error model of the phase modulator.The monolithic microwave integrated circuit according to claim 15, wherein the calculation element is configured to calculate the phase adjustment value based on calculating the result of at least one analytic function, the at least one analytic function comprising the target phase value and the plurality of values as variables.The monolithic microwave integrated circuit of claim 15 or 16, wherein the set of error parameters comprises an average phase offset, an in-phase baseband offset, a quadrature baseband offset, an orthogonality error, and a gain mismatch.The monolithic microwave integrated circuit according to any one of claims 15 to 17, wherein the calculation element is configured to calculate a phase adjustment value without using a division operation in which the divisor is different from 2 n where n is a natural number.The monolithic microwave integrated circuit of claim 15, wherein the computing element is configured to compute the phase adjustment value based on computing an I signal value corresponding to (1 - α / 2)(-β / 2·sin(φ t- ψ) + cos(φ t- ψ) - I) and computing a Q signal value corresponding to (1 + α / 2)(-β / 2·cos(φ t- ψ) + sin(φ t- ψ) - I), where α corresponds to a stored value of the gain mismatch, β corresponds to a stored value of the orthogonality error, ψ corresponds to a stored value of the mean phase offset, / corresponds to a stored value of the in-phase baseband offset, Q corresponds to a stored value of the quadrature baseband offset, and φ t corresponds to the target phase value, and wherein the phase adjustment circuit is configured to apply the I signal value to an in-phase path of the phase modulator and apply the Q signal value to a quadrature path of the phase modulator.The monolithic microwave integrated circuit according to any one of claims 15 to 19, wherein the computing element is implemented as a digital feedforward hardware circuit.

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