Method for performing ADC phase-frequency response test

Abstract

The present disclosure discloses a method for performing an ADC phase-frequency response test including: measuring a time delay of an analog mixer and low-pass filter (MLPF) in down-converting a specific carrier frequency narrowband frequency modulation (FM) signal; determining an effective sampling frequency required by an ADC for acquiring FM signals; acquiring a high carrier frequency FM signal and a low carrier frequency FM signal before and after down-conversion is performed by the analog MLPF; and demodulating the FM signals that are acquired, correcting an initial phase of a modulation signal of the high carrier frequency FM signal and an initial phase of a modulation signal of the low carrier frequency FM signal, and calculating a phase-frequency response of the ADC at a high carrier frequency. The present disclosure has advantages of a simple test process, a wide frequency range with frequencies and a test simultaneously performed on multiple channels.

Claims

1. A method for performing an analog-to-digital converter (ADC) phase-frequency response test, wherein the method comprises the following steps: demodulating, based on a phase unwrapping sine approximation method (PUSAM), a high carrier frequency narrowband FM signal and a low carrier frequency narrowband FM signal acquired by an HDO before and after down-conversion is performed by an analog MLPF, and calculating a down-conversion time delay of the analog MLPF by initial phases of modulation signals of the two FM signals obtained through demodulation; determining an effective sampling frequency required by an ADC for acquiring the high carrier frequency narrowband FM signal and the low carrier frequency narrowband FM signal to ensure an effective spectrum arrangement of the FM signals; simultaneously acquiring, by the ADC with the effective sampling frequency the high carrier frequency narrowband FM signal and the low carrier frequency narrowband FM signal before and after down-conversion is performed by the analog MLPF; and demodulating, based on the PUSAM, the high carrier frequency FM signal and the low carrier frequency FM signal that are acquired by the ADC, correcting an initial phase of a modulation signal of the high carrier frequency FM signal and an initial phase of a modulation signal of the low carrier frequency FM signal by the measured down-conversion time delay of the analog MLPF, and calculating a phase-frequency response of the ADC at a high carrier frequency by corrected initial phases of the modulation signals of the two FM signals.

2. The method for performing an ADC phase-frequency response test according to claim 1, wherein the step of demodulating, based on a PUSAM, a high carrier frequency narrowband FM signal and a low carrier frequency narrowband FM signal acquired by an HDO before and after down-conversion performed by an analog MLPF specifically comprises: (1) the FM signal down-conversion by the analog MLPF; a function signal generator (FSG) is configured to output a specific carrier frequency narrowband FM signal as follows:
u.sub.H(t)=u.sub.H cos [.sub.0+2f.sub.ct+2u.sub.m sin(2f.sub.mt+.sub.r)], wherein u.sub.H, .sub.0, and f.sub.c are respectively a peak voltage, an initial phase, and a carrier frequency of u.sub.H(t); u.sub.m, f.sub.m, and .sub.c are respectively a peak value, a frequency, and an initial phase of a modulation signal of the FM signal u.sub.H(t); and u.sub.H(t) is down-converted by the analog MLPF into a low carrier frequency FM signal:
u.sub.L(t)=u.sub.L cos [.sub.0+2(f.sub.cf.sub.LO)t+2u.sub.m sin(2f.sub.mt+.sub.d)], wherein u.sub.L and .sub.0 are respectively a peak voltage and an initial phase of u.sub.L(t), .sub.d is an initial phase of a modulation signal of u.sub.L(t), and f.sub.LO is a sine signal frequency at a local-frequency signal input end of a mixer (M); (2) the FM signal demodulation based on the PUSAM the HDO acquires u.sub.H(t) and u.sub.L(t) by using a sampling frequency satisfying a Nyquist sampling theorem, orthogonalizes the acquired u.sub.H(t) and u.sub.L(t) by using an orthogonal basis of a digital sine and cosine and a low-pass filter, and obtains phases .sub.H(t) and .sub.L(t) of the orthogonalized u.sub.H(t) and u.sub.L(t) after phase unwrapping: $\{\begin{array}{c}{}_H\left(t\right)={}_0+2\left(f_c-f_H\right)t+2u_m\sin \left(2f_{m}t+{}_r\right)+k\\ {}_L\left(t\right)=\stackrel{.}{{}_0}+2\left(f_c-f_{\mathrm{LO}}-f_L\right)t+2u_m\sin \left(2f_{m}t+{}_d\right)+k\end{array},$ wherein f.sub.H and f.sub.L are respectively orthogonal base frequencies for orthogonalizing u.sub.H(t) and u.sub.L(t), k is a compensating phase, and an integer k is equal to 0, 1, 2, ; and a sine approximation method is used to fit .sub.H(t) and .sub.L(t) to obtain the modulation signals of u.sub.H(t) and u.sub.L(t), wherein a fitting form of the sine approximation method is: $\{\begin{array}{c}{}_H\left(t\right)=A_H\cos \left(2f_{m}t\right)-B_H\sin \left(2f_{m}t\right)+C_{H}t+D_H\\ {}_L\left(t\right)=A_L\cos \left(2f_{m}t\right)-B_L\sin \left(2f_{m}t\right)+C_{L}t+D_L\end{array},$ wherein parameters A.sub.H and B.sub.H determine the peak value and the initial phase of the modulation signal of u.sub.H(t), and C.sub.H and D.sub.H are respectively a carrier frequency and a DC offset coefficient of .sub.H(t); parameters A.sub.L and B.sub.L determine a peak value and the initial phase of the modulation signal of u.sub.L(t), and C.sub.L and D.sub.L are respectively a carrier frequency and a DC offset coefficient of .sub.L(t); and the fitted parameters are used to calculate the initial phases .sub.r and .sub.d of the modulation signals of u.sub.H(t) and u.sub.L(t) as follows: $\{\begin{array}{c}{}_r=\arctan \left(B_H/A_H\right)\\ {}_d=\arctan \left(B_L/A_L\right)\end{array}.$

3. The method for performing an ADC phase-frequency response test according to claim 2, wherein the down-conversion time delay t.sub.d of the analog MLPF is calculated by using the initial phases .sub.r and .sub.d of the modulation signals of the two FM signals as follows:
t.sub.d=(.sub.d.sub.r)/(2f.sub.m).

4. The method for performing an ADC phase-frequency response test according to claim 1, wherein the step of determining the effective sampling frequency required by the ADC for acquiring the high carrier frequency narrowband FM signal and the low carrier frequency narrowband FM signal specifically comprises: when a maximum sampling frequency of the ADC is higher than twice of a carrier frequency u.sub.H(t), determining that the effective sampling frequency is the maximum sampling frequency of the ADC; or when a maximum sampling frequency of the ADC is lower than twice of a carrier frequency u.sub.H(t), determining, based on a band-pass sampling theorem, that a sampling frequency range for acquiring u.sub.H(t) without spectrum aliasing is: $\frac{2f_c+B}{n+1}{F}_s\frac{2f_c-B}{n},$ wherein a bandwidth B of u.sub.H(t) is:
B=4f.sub.mu.sub.m, wherein n is a non-negative integer that does not exceed int[(f.sub.cB/2)/B1]; because f.sub.c is far higher than B, u.sub.H(t) may be approximated to a cosine signal with frequency of f.sub.c; as n increases, the sampling frequency range becomes narrower, and the sampling frequency becomes lower; and a sampling frequency range in which a highest sampling frequency is close to but lower than the maximum sampling frequency of the ADC is selected, and guard bands B.sub.GL and B.sub.GU are introduced to calculate an effective sampling frequency of u.sub.N(t) as follows: $\{\begin{array}{cc}{F}_{s,c}=\frac{2f_c+B}{n+1}+F_s\frac{B_{\mathrm{GU}}}{B_{\mathrm{GU},\max }},& \mathrm{wherein}n\mathrm{is}\mathrm{an}\mathrm{odd}\mathrm{number}\\ F_{x,c}=\frac{2f_c-B}{n}-F_s\frac{B_{\mathrm{GL}}}{B_{\mathrm{GL},\max }},& \mathrm{wherein}n\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{number}\end{array},$ wherein F.sub.s is a maximum frequency variation in a sampling frequency range when the integer n is a determined value, and B.sub.GU,max and B.sub.GL,max are respectively a maximum upper-limit guard band and a maximum lower-limit guard band in a spectrum for u.sub.H(t) in the sampling frequency range.

5. The method for performing an ADC phase-frequency response test according to claim 1, wherein the ADC collects u.sub.H(t) and u.sub.L(t) before and after down-conversion is performed by the analog MLPF, demodulates by using an effective sampling frequency F.sub.s,e, u.sub.L(t) and u.sub.H(t) acquired by the ADC based on the PUSAM, and obtains initial phases of modulation signals of u.sub.L(t) and u.sub.H(t) respectively as follows: $\{\begin{array}{c}{}_1=\arctan \left(B_1/A_1\right)\\ {}_2=\arctan \left(B_2/A_2\right)\end{array},$ wherein A.sub.1, B.sub.1, and .sub.1 are respectively parameters and an initial phase of a modulation signal of u.sub.L(t), and A.sub.2, B.sub.2, and .sub.2 are respectively parameters and an initial phase of a modulation signal of u.sub.H(t); and the initial phase .sub.t of the modulation signal of u.sub.L(t) is corrected by using the measured down-conversion time delay of the analog MLPF, wherein a corrected initial phase .sub.1r is:
.sub.1r=.sub.12f.sub.mt.sub.d.

6. The method for performing an ADC phase-frequency response test according to claim 5, wherein the phase-frequency response of the ADC at the frequency f.sub.c is calculated by using the corrected initial phase .sub.1r of the modulation signal of u.sub.L(t) and the initial phase .sub.2 of the modulation signal of u.sub.H(t) as follows:
.sub.ADC=(.sub.2.sub.1r)f.sub.c/f.sub.m, wherein .sub.ADC is the phase-frequency response of the ADC at the frequency f.sub.c, and f.sub.c is higher than the maximum sampling frequency of the ADC.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic block diagram of a method for performing an ADC phase-frequency response test; and

(2) FIG. 2 is an experiment result diagram of an ADC phase-frequency response test in a specific embodiment of a method of the present disclosure.

DETAILED DESCRIPTION OF THE DISCLOSURE

(3) The present disclosure provides a method for performing an ADC phase-frequency response test. The following describes the present disclosure in detail with reference to accompanying drawings and specific embodiments, so that a person skilled in the art can better understand the test method of the present disclosure.

(4) Referring to FIG. 1, FIG. 1 is a schematic block diagram of a method for performing an ADC phase-frequency response test. The method mainly includes the following steps:

(5) demodulating, based on a PUSAM, a high carrier frequency narrowband FM signal and a low carrier frequency narrowband FM signal acquired by an HDO before and after down-conversion is performed by an analog MLPF, and calculating a down-conversion time delay of the analog MLPF by using initial phases of modulation signals of the two FM signals obtained through demodulation;

(6) determining an effective sampling frequency required by an ADC for acquiring the high carrier frequency narrowband FM signal and the low carrier frequency narrowband FM signal to ensure an effective spectrum arrangement of the FM signals;

(7) acquiring, by the ADC by using the effective sampling frequency, the high carrier frequency narrowband FM signal and the low carrier frequency narrowband FM signal before and after down-conversion is performed by the analog MLPF; and

(8) demodulating, based on the PUSAM, the high carrier frequency FM signal and the low carrier frequency FM signal acquired by the ADC, correcting an initial phase of a modulation signal of the high carrier frequency FM signal and an initial phase of a modulation signal of the low carrier frequency FM signal by using the measured down-conversion time delay of the analog MLPF, and calculating a phase-frequency response of the ADC at a high carrier frequency by using corrected initial phases of the modulation signals of the two FM signals.

(9) The step of demodulating, based on a PUSAM, a high carrier frequency narrowband FM signal and a low carrier frequency narrowband FM signal acquired by an HDO before and after down-conversion is performed by an analog MLPF specifically includes:

(10) (1) FM signal down-conversion by the analog MLPF: a FSG outputs a narrowband FM signal u.sub.H(t) with carrier frequency of f.sub.c. The analog MLPF converts the signal into a low carrier frequency FM signal u.sub.L(t). u.sub.H(t) and u.sub.L(t) acquired by the HDO by using a sampling frequency satisfying the Nyquist sampling theorem are as follows:

(11) $\begin{array}{cc}\{\begin{array}{c}{u}_H\left(t\right)=u_H\cos \left[{}_0+2f_{c}t+2u_m\sin \left(2f_{m}t+{}_r\right)\right]\\ u_L\left(t\right)=u_L\cos \left[\stackrel{.}{{}_0}+2\left(f_c-f_{\mathrm{LO}}\right)t+2u_m\sin \left(2f_{m}t+{}_d\right)\right]\end{array}& \left(1\right)\end{array}$

(12) where u.sub.H, .sub.0, and f.sub.c are respectively a peak voltage, an initial phase, and the carrier frequency of the high carrier frequency FM signal u.sub.H(t); u.sub.m, f.sub.m, and .sub.p are respectively a peak value, a frequency, and an initial phase of a modulation signal of u.sub.H(t); u.sub.L and .sub.0 are respectively a peak voltage and an initial phase of the low carrier frequency FM signal u.sub.L(t), .sub.d is an initial phase of a modulation signal of u.sub.L(t), and f.sub.LO is a sine signal frequency at a local-frequency signal input end of a mixer (M).

(13) (2) FM signal demodulation based on the PUSAM: The HDO acquires u.sub.H(t) and u.sub.L(t) by using the sampling frequency satisfying the Nyquist sampling theorem, uses an orthogonal basis of a digital sine and cosine and a low-pass filter to orthogonalize the u.sub.H(t) and u.sub.L(t) acquired by the HDO, and obtains phases .sub.H(t) and .sub.L(t) of the orthogonalized u.sub.H(t) and u.sub.L(t) after phase unwrapping:

(14) $\begin{array}{cc}\{\begin{array}{c}{}_H\left(t\right)={}_0+2\left(f_c-f_H\right)t+2u_m\sin \left(2f_{m}t+{}_r\right)+k\\ {}_L\left(t\right)=\stackrel{.}{{}_0}+2\left(f_c-f_{\mathrm{LO}}-f_L\right)t+2u_m\sin \left(2f_{m}t+{}_d\right)+k\end{array}& \left(2\right)\end{array}$

(15) where f.sub.H and f.sub.L are respectively orthogonal base frequencies for quadrature u.sub.H(t) and u.sub.L(t), k is a compensating phase, and an integer k is equal to 0, 1, 2, . . . ; and the sine approximation method is used to fit .sub.H(t) and .sub.L(t) to obtain the modulation signals of u.sub.H(t) and u.sub.L(t), where .sub.H(t) and .sub.L(t) are fitted by using the sine approximation method:

(16) $\begin{array}{cc}\{\begin{array}{c}{}_H\left(t\right)=A_H\cos \left(2f_{m}t\right)-B_H\sin \left(2f_{m}t\right)+C_{H}t+D_H\\ {}_L\left(t\right)=A_L\cos \left(2f_{m}t\right)-B_L\sin \left(2f_{m}t\right)+C_{L}t+D_L\end{array}& \left(3\right)\end{array}$

(17) where parameters A.sub.H and B.sub.H determine the peak value and the initial phase of the modulation signal of u.sub.H(t), and C.sub.H and D.sub.H are respectively a carrier frequency and a DC offset coefficient of .sub.H(t); parameters A.sub.L and B.sub.L determine a peak value and the initial phase of the modulation signal of u.sub.L(t), and C.sub.L and D.sub.L are respectively a carrier frequency and a DC offset coefficient of .sub.L(t); and the fitted parameters are used to calculate the initial phases .sub.r and .sub.d of the modulation signals of u.sub.H(t) and u.sub.L(t) as follows:

(18) $\begin{array}{cc}\{\begin{array}{c}{}_r=\arctan \left(B_H/A_H\right)\\ {}_d=\arctan \left(B_L/A_L\right)\end{array}& \left(4\right)\end{array}$

(19) (3) Calculating the down-conversion time delay t.sub.d of the analog MLPF by using the initial phases .sub.r and .sub.d of the modulation signals of the two FM signals u.sub.H(t) and u.sub.L(t) as follows:
t.sub.d=(.sub.d.sub.r)/(2f.sub.m)(5)

(20) The step of determining an effective sampling frequency required by an ADC for acquiring the high carrier frequency narrowband FM signal and the low carrier frequency narrowband FM signal specifically includes:

(21) (4) When a maximum sampling frequency of the ADC is higher than twice the carrier frequency of u.sub.H(t), determining that the effective sampling frequency is the maximum sampling frequency of the ADC; or when a maximum sampling frequency of the ADC is lower than twice the carrier frequency of u.sub.H(t), determining, based on a band-pass sampling theorem, that a sampling frequency range for acquiring u.sub.H(t) without spectrum aliasing is:

(22) $\begin{array}{cc}\frac{2f_c+B}{n+1}{F}_s\frac{2f_c-B}{n}& \left(6\right)\end{array}$

(23) where a bandwidth B of u.sub.H(t) is:
B=4f.sub.mu.sub.m(7)

(24) wherein a value of n is a non-negative integer that does not exceed int[(f.sub.cB/2)/B1]; because f.sub.c is far higher than B, u.sub.H(t) may be approximated to a cosine signal with frequency of f.sub.c; as n increases, the sampling frequency range becomes narrower, and the sampling frequency becomes lower; and a sampling frequency range in which a highest sampling frequency is close to but lower than the maximum sampling frequency of the ADC is selected, and guard bands B.sub.GL and B.sub.GU are introduced to calculate an effective sampling frequency of u.sub.H(t) as follows:

(25) $\begin{array}{cc}\{\begin{array}{cc}{F}_{s,c}=\frac{2f_c+B}{n+1}+F_s\frac{B_{\mathrm{GU}}}{B_{\mathrm{GU},\max }},& \mathrm{where}n\mathrm{is}\mathrm{an}\mathrm{odd}\mathrm{number}\\ F_{s,x}=\frac{2f_c-B}{n}-F_x\frac{B_{\mathrm{GL}}}{B_{\mathrm{GL},\max }},& \mathrm{where}n\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{number}\end{array}& \left(8\right)\end{array}$

(26) where F.sub.s is a maximum frequency variation in a sampling frequency range when the integer n is a determined value, and B.sub.GU,max and B.sub.GL,max are respectively a maximum upper-limit guard band and a maximum lower-limit guard band in a spectrum for u.sub.H(t) in the sampling frequency range.

(27) The step of testing a phase-frequency response of the ADC at the frequency specifically includes:

(28) (5) acquiring, by the ADC by using the effective sampling frequency F.sub.s,e, u.sub.H(t) and u.sub.L(t) before and after down-conversion is performed by the analog MLPF, demodulating, f.sub.c based on the PUSAM, u.sub.L (t) and u.sub.H(t) acquired by the ADC, and obtaining the initial phases of the modulation signals of u.sub.L(t) and u.sub.H(t) respectively as follows:

(29) $\begin{array}{cc}\{\begin{array}{c}{}_1=\arctan \left(B_1/A_1\right)\\ {}_2=\arctan \left(B_2/A_2\right)\end{array}& \left(9\right)\end{array}$

(30) where A.sub.1, B.sub.1, and .sub.1 are respectively parameters and the initial phase of the modulation signal of u.sub.L(t), and A.sub.2, B.sub.2, and .sub.2 are respectively parameters and the initial phase of the modulation signal of u.sub.H(t).

(31) (6) Correcting the initial phase .sub.1 of the modulation signal of u.sub.L(t) by using the down-conversion time delay of the analog MLPF measured in step (3), wherein a corrected initial phase .sub.1r is:
.sub.1r=.sub.12f.sub.mt.sub.d(10)

(32) (7) Calculating the phase-frequency response of the ADC at the frequency f.sub.c by using the initial phase .sub.2 of the modulation signal of u.sub.H(t) and the corrected initial phase .sub.1r of the modulation signal of u.sub.L(t) as follows:
.sub.ADC=(.sub.2.sub.1r)f.sub.c/f.sub.m(11)

(33) wherein .sub.ADC is the phase-frequency response of the ADC at the frequency f.sub.c, and f.sub.c may be higher than the maximum sampling frequency of the ADC.

(34) Referring to FIG. 2, FIG. 2 is an experiment result diagram of an ADC phase-frequency response test in a specific embodiment of a method of the present disclosure. Specific apparatus parameters in this embodiment are: a RIGOL function signal generator (FSG) DG4202 with maximum output frequency of 200 MHz, a mini-circuit mixer (M) with input frequency range from 0.5 MHz to 500 MHz, a mini-circuit low-pass filter (LPF) with cutoff frequency of 2.5 MHz, a TELEDYNE high definition oscilloscope (HDO) 6104 with maximum sampling frequency and bandwidth of both I GHz, and an ADLINK ADC 9816 with maximum sampling frequency of 10 MHz. In this test, a carrier frequency range of FM signals output by the FSG is 2 MHz to 99 MHz, a bandwidth thereof is approximately 5 kHz constantly, and the carrier frequencies are far higher than the bandwidth thereof. A carrier frequency of an FM signal down-converted by the analog MLPF is constantly 0.2 MHz. An effective sampling frequency selected for acquiring FM signals of different carrier frequencies is 10 MHz. According to a test result, it can be known that the test method of the present disclosure implements an ADC phase-frequency response test in a range of 2 MHz to 99 MHz, and that a maximum test frequency thereof is far higher than a maximum sampling frequency of the ADC. In addition, for testing phase-frequency responses of ADCs of different types and models, a down-conversion time delay of the analog MLPF needs to be measured only at the first time.

(35) A specific embodiment of the method of the present disclosure is described in detail above, so that a person skilled in the art can understand the method. The method is not intended to limit the application scope of the present disclosure. A person skilled in the art can make a series of optimizations, improvements, equivalent modifications, and the like on a basis of the present disclosure. Therefore, the protection scope of the present disclosure shall be defined by the appended claims.