TIME-INTERLEAVED ADC ERROR PARAMETER EXTRACTION AND CORRECTION METHOD

Abstract

A time-interleaved ADC error parameter extraction and correction method relates to an error correction technique for an analog-to-digital converter (ADC). This application discloses a method for extracting and correcting error parameters in a time-interleaved ADC, which takes the time-interleaved ADC channel n as the basis or reference channel, and corrects other channels to match the channel n. The steps include: a. Converting a time domain signal output of each ADC channel into a frequency domain signal; b. Calculating one or more error parameters according to the frequency domain signal; c. Correcting the frequency domain signal in one or more different channels according to the error parameter(s); and d. Converting the corrected frequency domain signal into a (corresponding) corrected time domain signal.

Claims

1. A method of extracting and correcting one or more error parameters in a time-interleaved ADC, wherein the time-interleaved ADC has an n-th channel and other channels to be calibrated and/or corrected to more closely match the n-th channel, comprising: a. converting a time domain signal output from each channel into a frequency domain signal; b. calculating one or more error parameters according to the frequency domain signal; c. correcting the frequency domain signal in one or more different channels according to the one or more error parameters; and d. converting the corrected frequency domain signal into one or more corrected time domain signals.

2. The method in claim 1, wherein n=1.

3. The method in claim 1, wherein calculating the one or more error parameters according to the frequency domain signal also includes correcting the one or more error parameters according to a change in a process-voltage-temperature (PVT) parameter.

4. The method in claim 3, wherein the one or more error parameters are corrected by a least mean square (LMS) method or algorithm.

5. The method in claim 1, wherein the one or more error parameters include a DC offset error parameter, an amplitude error parameter, and a phase error parameter.

6. The method in claim 5, wherein the DC offset error parameter, the amplitude error parameter, and the phase error parameter satisfy the following equations or formulas: $o_m\left(0\right)=Y_m\left(0\right);$ $A_m\left(f\right)=\mathrm{abs}\left(Y_m\left(f\right)\right)/\mathrm{abs}\left(Y_n\left(f\right)\right);$ $P_m\left(f\right)=\mathrm{phase}\left(Y_m\left(f\right)\right)+\mathrm{phase}\left(e^{-j2f\left(\frac{T_{CK}}{M}\right)}\right)-\mathrm{phase}\left(Y_n\left(f\right)\right);$ wherein m is the channel number, m=1, . . . M, and Mn; M is the number of channels; abs represents a modulus (or modulo) of a complex number; phase indicates an angle of the complex number; Y.sub.m(f) represents the frequency domain signal of an m-th channel; Y.sub.n(f) represents the frequency domain signal of the n-th channel; and Y.sub.m(0) represents a value of the frequency domain signal of the m-th channel when f=0.

7. The method in claim 6, wherein an input signal to the time-interleaved ADC or the channels thereof is a sinusoidal signal satisfying an equation or formula: $x\left(t\right)=A\sin \left(t+\right)$ wherein A is an amplitude of the sinusoidal signal; is a frequency of the sinusoidal signal; and is an initial phase of the sinusoidal signal.

8. The method in claim 6, wherein correcting the frequency domain signal in one or more different channels comprises: correcting the DC bias error by subtracting the offset error parameter in the frequency domain, correcting the amplitude error by multiplying or dividing by a correction coefficient at each frequency point in the frequency domain, and correcting the phase error by multiplying by a phase shift coefficient at each frequency point in the frequency domain.

9. The method in claim 8, wherein correcting the DC bias error, the amplitude error and the phase error satisfies the equation or formula: $Y_m^{}\left(f\right)=\left(Y_m\left(f\right)-o_m\left(0\right)\right)*e^{j{P}_m\left(f\right)}/A_m\left(f\right);$ wherein o.sub.m(0) is the offset error parameter, A.sub.m(f) is the correction coefficient, e.sup.jP.sup.M.sup.(f) is the phase shift coefficient, and Y.sub.m(f) is the corrected frequency domain signal of the m-th channel.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The drawings that form part of this application are used to provide further understanding of this application, and the specific embodiments, schematic embodiments and descriptions of this application are used to interpret this application and do not constitute limitations of this application. In the drawings:

[0035] FIG. 1 shows a flow chart of an exemplary time-interleaved ADC error parameter extraction and correction method of one or more embodiments of the present application; and

[0036] FIG. 2 shows a block diagram and signal flow diagram of an exemplary time-interleaved ADC error parameter extraction and correction circuit and method of one or more embodiments of the present application.

EMBODIMENTS

[0037] It should be noted that specific embodiments, exemplary embodiments, and features therein in this application may be combined without conflict. This application is described in detail with reference to the attached drawings and in conjunction with the following.

[0038] In order to enable those skilled in the art to better understand the application scheme, the following will be combined with specific embodiments of the application and the attached drawings, to give a clear and complete description of specific embodiments of the application and the technical scheme(s) in the exemplary embodiments. It is readily apparent that the application is not limited to the exemplary embodiments described herein, but extends beyond the described embodiments. Based on the specific embodiments and exemplary embodiments in this application, all other embodiments and embodiments obtained by ordinary skilled personnel in the field without making creative labor shall fall within the scope of protection in this application.

Embodiment

[0039] Referring to FIGS. 1 and 2, the process(es) of the time-interleaved (or time-multiplexed) ADC error parameter extraction and correction for specific embodiments of this application are described in detail as follows.

[0040] Step S101: Converting a time domain signal from each channel of the ADC into a frequency domain signal

[0041] For a multi-channel time-interleaved ADC (e.g., as shown in FIG. 2), the input signal is x(t). If there is no inter-channel error, the output of each ADC channel is x.sub.m(t), where m is the channel number, m=1, 2. . . . M, and M is the number of channels.

[0042] Let (t) be the unit impulse function. The output sequence or number of the k-th sampling period of the ADC channel can be expressed as x(t)(tkT.sub.C), where T.sub.C is the sampling period of the ADC channel of the time-interleaved ADC. x(t).sub.k(tkT.sub.C) is the output of the ADC channel for a total of k sampling periods:

[00004]$\begin{array}{c}{x}_1\left(t\right)=x\left(t\right)\underset{k}{.Math.}\left(t-k{T}_C\right)\\ x_2\left(t\right)=x\left(t\right)\underset{k}{.Math.}\left(t-k{T}_C-\frac{T_C}{M}\right)\\ .Math.\\ x_M\left(t\right)=x\left(t\right)\underset{k}{.Math.}\left(t-k{T}_C-\frac{\left(M-1\right)T_C}{M}\right)\end{array}$

[0043] Convert the M-channel ADC output to the frequency domain (e.g., using the time-to-frequency [T2F] converter in FIG. 2) for each channel in the TI-ADC (e.g., Channel 1 through Channel M in FIG. 2), for example according to the following equations or formulas:

[00005]$\begin{array}{c}{Y}_1\left(f\right)=\frac{1}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-{\mathrm{kf}}_C\right)\\ Y_2\left(f\right)=\frac{1}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-{\mathrm{kf}}_C\right)e^{-j2{\mathrm{fT}}_C/M}\\ .Math.\\ Y_M\left(f\right)=\frac{1}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-{\mathrm{kf}}_C\right)e^{-j2{\mathrm{fT}}_C*\left(M-1\right)/M}\end{array}$

where X(f) is the frequency domain conversion for x(t), Y.sub.M(f) is the frequency domain conversion for x.sub.M(t), (fkf.sub.C) is the frequency domain conversion for (tkT.sub.C), e.sup.j2fT.sup.C.sup.*(M1)/M is the phase shift, fc is the sampling frequency of the time-interleaved ADC, and T.sub.C is the sampling period of the time-interleaved ADC.

[0044] Step S102: Calculating one or more error parameters according to the frequency domain signal(s)

[0045] When there is a DC offset error, a gain error, a deviation in the sampling time and/or a bandwidth error, the frequency domain signal of each ADC channel can be expressed as:

[00006]$Y_1\left(f\right)=\frac{1}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-{\mathrm{kf}}_C\right)$$Y_2\left(f\right)=\frac{\left(g_2+G_2\left(f\right)\right)}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-{\mathrm{kf}}_C\right)e^{-j2f\left(T_C/M+t_2+T_2\left(f\right)\right)}+o_2\left(0\right)$$.Math.$$Y_M\left(f\right)=\frac{\left(g_M+G_M\left(f\right)\right)}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-{\mathrm{kf}}_C\right)e^{-j2f\left(T_C*\left(M-1\right)/M+t_M+T_M\left(f\right)\right)}+o_M\left(0\right)$

where g.sub.2 . . . g.sub.M is the gain error of other channels with respect to Channel 1 (e.g., the deviation in gain between the other channels and Channel 1), o.sub.2(0) . . . . o.sub.M(0) is the DC offset error of other channels with respect to Channel 1 (e.g., the deviation in DC offset between the other channels and Channel 1), t.sub.2 . . . . t.sub.M is the deviation in sampling time between the other channels and Channel 1, G.sub.2(f) . . . G.sub.M(f) is the amplitude error component of the bandwidth error in the other channels relative to the bandwidth error of Channel 1, and T.sub.2(f) . . . T.sub.M(f) is the phase error component of the bandwidth error in the other channels relative to the bandwidth error of Channel 1.

[0046] If the amplitude error component of the bandwidth error and the gain error are combined into the amplitude error A(f), and the phase error component of the bandwidth error and the sampling time deviation are combined into the phase error P(f), then the frequency domain signal of each of the other ADC channels (e.g., Channels 2 through M) become:

[00007]$Y_2\left(f\right)=\frac{A_2\left(f\right)}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-k{f}_C\right)e^{-j2f\left(\frac{T_C}{M}\right)}*e^{-j{P}_2\left(f\right)}+o_2\left(0\right)$$.Math.$$Y_m\left(f\right)=\frac{A_m\left(f\right)}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-k{f}_C\right)e^{-j2f\left(\frac{T_C}{m}\right)}*e^{-j{P}_m\left(f\right)}+o_m\left(0\right)$$.Math.$$Y_M\left(f\right)=\frac{A_M\left(f\right)}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-k{f}_C\right)e^{-j2f\left(\frac{T_C}{M}\right)}*e^{-j{P}_M\left(f\right)}+o_M\left(0\right)$$\mathrm{Where}:$$A_m\left(f\right)=g_m+G_m\left(f\right)$$P_m\left(f\right)=e^{-j2f\left(t_m+T_m\left(f\right)\right)}$$m=2,.Math.,M$

[0047] The above description uses the first channel (Channel 1) as the baseline or a reference channel for error detection and correction, but in the same way, it is also possible to select an n-th channel at random as the baseline or reference channel, and adjust the other channels to match the n-th channel. For example:

[00008]$Y_n\left(f\right)=\frac{1}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-k{f}_C\right)$$Y_m\left(f\right)=\frac{\left(g_m+G_m\left(f\right)\right)}{T_C}X\left(f\right)*\underset{k}{.Math.}\left(f-k{f}_C\right)e^{-j2f\left(T_C*\frac{m-1}{M}+t_m+T_m\left(f\right)\right)}+o_m\left(0\right)$$m=1,.Math.,M,mn.$

[0048] The DC offset error, amplitude error and phase error can be obtained by a fast Fourier transform (FFT) as follows: [0049] DC offset error: om(0)

[00009]$o_m\left(0\right)=Y_m\left(0\right)$ [0050] Amplitude error: A.sub.m(f)

[00010]$A_m\left(f\right)=\mathrm{abs}\left(Y_m\left(f\right)\right)/\mathrm{abs}\left(Y_1\left(f\right)\right)$ [0051] Phase error: P.sub.m(f)

[00011]$P_m\left(f\right)=\mathrm{phase}\left(Y_m\left(f\right)\right)+\mathrm{phase}\left(e^{-j2f\left(\frac{T_C}{M}\right)}\right)-\mathrm{phase}\left(Y_1\left(f\right)\right)$

where abs(Y.sub.m(0)) is the modulus (or modulo) of the complex number Y.sub.m(0), and phase (Y.sub.m(f)) is the angle of the complex number Y.sub.m(f).

[0052] The extraction and correction of the above error parameters are corrected by first sending known signals, such as sinusoidal signals, to calibrate the channels of the TI-ADC. This process can be termed initialization correction. The mathematical expression of a sinusoidal signal is:

[00012]$x\left(t\right)=A\sin \left(t+\right)$

where A is the amplitude of the sinusoidal signal, w is the frequency of the sinusoidal signal, and is the initial phase of the sinusoidal signal.

[0053] In initialization correction, the ADC data or signal in each channel is converted from the time domain to the frequency domain, and error information such as DC offset error, amplitude error and phase error is extracted from the signal in the frequency domain, and then the frequency domain signal is converted back to the time domain after correction in the frequency domain.

[0054] Because the errors (e.g., DC offset, amplitude and phase errors) change slowly with changes or variations in process, voltage and/or temperature (PVT) parameters, a least mean square (LMS) approach (e.g., method or algorithm) may be used to track the errors after initialization.

[0055] At time t=0, first perform a fast Fourier transform on time domain data (e.g., in a predetermined period of time, or a segment of predetermined length), and obtain the errors according to the formulas:

[00013]$o_m\left(0,t\right)=Y_m\left(0\right)$$A_m\left(f,t\right)=\mathrm{abs}\left(Y_m\left(f\right)\right)/\mathrm{abs}\left(Y_1\left(f\right)\right)$$P_m\left(f,t\right)=\mathrm{phase}\left(Y_m\left(f\right)\right)+\mathrm{phase}\left(e^{-j2f\left(\frac{T_C}{M}\right)}\right)-\mathrm{phase}\left(Y_1\left(f\right)\right)$

[0056] At time t+1 (e.g., at the end of the first predetermined period of time), the corresponding time domain data is obtained by the fast Fourier transform, and according to the above three formulas, the following is obtained:

[00014]$o_m\left(0,t+1\right)=o_m\left(0,t\right)+*\left(Y_m\left(0,t+1\right)--o_m\left(0,t\right)\right)$$A_m\left(f,t+1\right)=A_m\left(f,t\right)+*\left(\mathrm{abs}\left(Y_m\left(f,t+1\right)\right)/\mathrm{abs}\left(Y_1\left(f,t+1\right)\right)-A_m\left(f,t\right)\right)$$P_m\left(f,t+1\right)=P_m\left(f,t\right)+*\left(\mathrm{phase}\left(Y_m\left(f,t+1\right)\right)+\mathrm{phase}\left(e^{-j2f\left(\frac{T_C}{M}\right)}\right)-\mathrm{phase}\left(Y_1\left(f,t+1\right)\right)-P_m\left(f,t\right)\right)$

where is a tracking step size parameter (which may be predetermined, or set in advance, and is generally less than 1); o.sub.m(0, t) represents the DC offset error o.sub.m(0) at time (or moment) t; om(0, t+1) represents the DC offset error o.sub.m(0) at time (or moment) t+1; A.sub.m(f, t+1) represents the amplitude error A.sub.m(f) at time (or moment) t+1; and P.sub.m(f, t+1) represents the phase error P.sub.m(f) at time (or moment) t+1.

[0057] Step S103: Correcting the frequency domain signal(s) in different channels according to the error parameter(s)

[0058] After the above errors are obtained, the errors in the TI-ADC channel output signals are corrected in the frequency domain. The correction process may be expressed in the following formula or equation (1):

[00015]$\begin{array}{cc}{Y}_m^{}\left(f\right)=\left(Y_m\left(f\right)-o_m\left(0\right)\right)*e^{j{P}_m\left(f\right)}/A_m\left(f\right)& \left(1\right)\end{array}$

where Y.sub.m(f) is the frequency domain expression of the output signal of the m-th channel after correction; Y.sub.m(f) represents the frequency domain expression of the output signal of the m-th channel (e.g., before correction, for the input signal x(t)); o.sub.m(0) is the DC offset error parameter; A.sub.m(f) is the amplitude error parameter; and P.sub.m(f) is the phase error parameter.

[0059] The present correction method may be based on formula (1), where the DC offset error parameter or correction (a DC offset error o.sub.m(0) is directly subtracted from the channel output signal in the frequency domain, the amplitude error parameter or correction is represented by a coefficient 1/A.sub.m(f) by which the channel output signal is multiplied (or, equivalently, a coefficient A.sub.m(f) by which the channel output signal is divided) at each frequency point in the frequency domain, and the phase error parameter or correction is represented by a phase shift coefficient e.sup.jP.sup.m.sup.(f) by which the channel output signal is multiplied at each frequency point in the frequency domain.

[0060] Step S104: Converting the corrected frequency domain signal(s) into one or more corrected time domain signals

[0061] After correction by formula (1), the output signal Y.sub.m(f) in the frequency domain is converted from the frequency domain to the time domain as a corrected time domain signal x.sub.m(t).

[0062] For example, for a 4-channel time-interleaved or time-multiplexed ADC, a sinusoidal signal x(t)=Asine(wt+) is input to or received in each channel, and the corrected signal Y.sub.m(f) for each channel of the TI-ADC may be converted back to the time domain to provide corresponding corrected time domain signals as follows:

[00016]$x_i\left[n\right]=\underset{k=-N}{\overset{N}{.Math.}}x\left[n-k\right]*w_{i,N+1-k}+w_{i,0}$$x_1^{}\left(k\right)=A\sin \left(*k/T_C+\right);$$x_2^{}\left(k\right)=A\sin \left(*k/T_C+1/T_C+\right);$$x_3^{}\left(k\right)=A\sin \left(*k/T_C+2/T_C+\right);$$x_4^{}\left(k\right)=A\sin \left(*k/T_C+3/T_C+\right).$

[0063] Finally, the time domain expression of the corrected signal for the 4-channel time-interleaved ADC is:

[00017]$x\left(k\right)=A\sin \left(*k/\left(4*T_C\right)+\right)$

[0064] The invention is not limited to a 4-channel time-interleaved ADC, and can be applied to or incorporated into TI-ADCs having a different number of channels (an integer number3, such as 4, 5, 6, 8 or more, and more specifically, 2.sup.x channels, where x is an integer of 2 or more, such as 2-7).