TI ADC time skew background calibration using complex derivative signals

Abstract

A circuit is disclosed that includes timer interleaved (TI) analog-to-digital converter (ADC) circuitry that generates a digital output signal. Correction circuitry receives the digital output signal from the TI ADC circuitry and uses weight values to generate a corrected output signal to correct for time skew. The correction circuitry includes a derivative filter that removes a frequency dependency between the weight value and an input signal to the TI ADC circuitry. Weight update circuitry receives the correction output signal and generates an updated weight value for the correction circuitry. The weight update circuitry includes a notch filter that suppresses spectral content in the corrected output signal to eliminate spurious dependencies during a weight update process.

Description

Technical Field

[0001] This involves a time-interleaved (TI) analog-to-digital converter. Background Technology

[0002] Time-interleaved (TI) analog-to-digital converters (ADCs) use multiple ADC channels operating in parallel to sample the input signal at different times. Non-uniformly spaced sampling moments can lead to errors. Summary of the Invention

[0003] A circuit characterized by comprising: a time-interleaved (TI) analog-to-digital converter (ADC) circuit system configured to receive an input signal and responsively generate a digital output signal; a correction circuit system configured to receive the digital output signal from the TI ADC circuit system and responsively generate a corrected output signal using weight values, the correction circuit system including a first-order derivative filter; and a weight update circuit system configured to receive the corrected output signal and responsively generate updated weight values, the weight update circuit system including a notch filter configured to filter the corrected output signal to generate a filtered corrected output signal, the weight update circuit system further configured to use the filtered corrected output signal to generate the updated weight values.

[0004] In one or more embodiments, the first-order derivative filter is a finite impulse response (FIR) derivative filter, which is configured to remove the frequency dependence between the input signal and the calibration coefficients used in the correction circuit system.

[0005] In one or more embodiments, the weight update circuitry is configured to provide the updated weight values ​​to the correction circuitry in place of the weight values, and wherein the correction circuitry is configured to use the updated weight values ​​to generate the correction output signal.

[0006] In one or more embodiments, the TI ADC circuitry provides the digital output signal as the output of 'M' sequentially generated ADC channels.

[0007] In one or more embodiments, the correction circuit system further includes: a first Hilbert filter configured to receive the derivative of the digital output signal and responsively generate a Hilbert transform of the derivative of the digital output signal; a first delay circuit configured to receive the derivative of the digital output signal and provide a delayed derivative of the digital output signal; and a first mixer circuit coupled to the first Hilbert filter and the first delay circuit, the first mixer circuit being configured to generate a first complex signal by mixing the Hilbert transform of the derivative of the digital output signal and the delayed derivative of the digital output signal with a sine wave.

[0008] In one or more embodiments, the first mixer circuit is configured to combine the Hilbert transform of the derivative of the digital output signal and the delay derivative of the digital output signal with f. s The first complex signal is generated by mixing sinusoidal waves that are integer multiples of / M, where f s M is the sampling frequency, and M is the time interleaving factor.

[0009] In one or more embodiments, the first mixer circuit is configured to generate the first complex signal such that the input tone of the first complex signal is mixed to the frequency of the time-skewed spurious position.

[0010] In one or more embodiments, the first mixer circuit includes M-1 parallel first mixer circuits, each of which is configured to apply M-1 mixing functions to mix the Hilbert transform of the derivative of the digital output signal with the delayed derivative of the digital output signal.

[0011] In one or more embodiments, the weight value is a complex weight value, and the correction circuit system further includes: a first product circuit configured to multiply the first complex signal by the complex weight value to generate a first weighted complex signal; and a subtraction circuit configured to subtract the first weighted complex signal from the digital output signal to generate the corrected output signal.

[0012] In one or more embodiments, the notch filter of the weight update circuit system is configured to suppress approximately f from the corrected output signal in the filtered corrected output signal. s Any input tone that is an integer multiple of / M.

[0013] In one or more embodiments, the weight update circuit system further includes: a second-order derivative filter configured to generate the derivative of the filtered corrected output signal; a second Hilbert filter configured to receive the derivative of the filtered corrected output signal and responsively generate a Hilbert transform of the derivative of the filtered corrected output signal; a second delay circuit configured to receive the derivative of the filtered corrected output signal and provide a delayed derivative of the filtered corrected output signal; and a second mixer circuit coupled to the second Hilbert filter and the second delay circuit, the second mixer circuit being configured to combine the Hilbert transform of the derivative of the filtered corrected output signal and the delayed derivative of the filtered corrected output signal into f. s The second complex signal is generated by mixing sine waves that are integer multiples of / M.

[0014] In one or more embodiments, the weight update circuitry further includes: a third delay circuit configured to receive the filtered corrected output signal and provide a delayed filtered corrected output signal; and a second product circuit configured to generate a cross-correlation between the second complex signal and the delayed filtered corrected output signal, wherein the weight update circuitry is further configured to generate the updated weight values ​​as a function of the cross-correlation.

[0015] In one or more embodiments, the weight update circuitry further includes: a third product circuit configured to scale the cross-correlation using a learning rate factor to produce a scaled cross-correlation; and an adder circuit configured to add the scaled cross-correlation to the weight value to produce the updated weight value.

[0016] In one or more embodiments, a circuit is provided, characterized by comprising: a time-interleaved (TI) analog-to-digital converter (ADC) circuit system configured to receive an input signal and responsively generate a digital output signal, the TIADC circuit system providing sequentially generated outputs of 'M' ADC channels, wherein f s The sampling frequency; a correction circuit system configured to receive the digital output signal from the TI ADC circuit system and responsively generate a corrected output signal using complex weight values, the correction circuit system including a first-order derivative filter configured to generate a derivative of the digital output signal, wherein the corrected output signal is generated based on the derivative of the digital output signal; and a weight update circuit system configured to receive the corrected output signal and responsively generate updated complex weight values ​​to replace the complex weight values ​​for use by the correction circuit system.

[0017] In one or more embodiments, the weight update circuitry includes a notch filter configured to filter the corrected output signal to suppress spectral content in the corrected output signal at frequencies where time-interleaving spurious signals occur, thereby generating a filtered corrected output signal. The weight update circuitry is further configured to use the filtered corrected output signal to generate the updated complex weight values.

[0018] In one or more embodiments, the correction circuit system further includes: a first Hilbert filter configured to receive the derivative of the digital output signal and responsively generate a Hilbert transform of the derivative of the digital output signal, wherein the first Hilbert filter has unity gain and a constant phase shift of +90 or -90 degrees; a first delay circuit configured to receive the derivative of the digital output signal and provide a delayed derivative of the digital output signal; and a first mixer circuit coupled to the first Hilbert filter and the first delay circuit, the first mixer circuit being configured to combine the Hilbert transform of the derivative of the digital output signal and the delayed derivative of the digital output signal into f. s The first complex signal is generated by mixing sine waves that are integer multiples of / M.

[0019] In one or more embodiments, the first mixer circuit is configured to generate the first complex signal such that the input tone of the first complex signal is mixed to a frequency at which time-interleaved spurious signals occur.

[0020] In one or more embodiments, the correction circuit system further includes: a first product circuit configured to multiply the first complex signal by the complex weight value to generate a first weighted complex signal; and a subtraction circuit configured to subtract the first weighted complex signal from the digital output signal to generate the corrected output signal.

[0021] In one or more embodiments, the notch filter of the weight update circuit system is configured to suppress approximately f from the corrected output signal. s Any input tone that is an integer multiple of / M.

[0022] In one or more embodiments, the weight update circuit system further includes: a second-order derivative filter configured to generate the derivative of the filtered corrected output signal; a second Hilbert filter configured to receive the derivative of the filtered corrected output signal and responsively generate a Hilbert transform of the derivative of the filtered corrected output signal; a second delay circuit configured to receive the derivative of the filtered corrected output signal and provide a delayed derivative of the filtered corrected output signal; and a second mixer circuit coupled to the second Hilbert filter and the second delay circuit, the second mixer circuit being configured to combine the Hilbert transform of the derivative of the filtered corrected output signal and the delayed derivative of the filtered corrected output signal into f. s The second complex signal is generated by mixing a sine wave that is an integer multiple of / M; a third delay circuit is configured to receive the filtered corrected output signal and provide a delayed filtered corrected output signal; a second product circuit is configured to generate a cross-correlation between the second complex signal and the delayed filtered corrected output signal; a third product circuit is configured to scale the cross-correlation by a learning rate factor to generate a scaled cross-correlation; and an adder circuit is configured to add the scaled cross-correlation to the weight value to generate the updated weight value. Attached Figure Description

[0023] The invention will be better understood by referring to the accompanying drawings, which will make its many objectives, features and advantages clear to those skilled in the art.

[0024] Figure 1 It is a spectrogram of a single-tone signal with time-interleaved spurious signals used in a time-interleaved (TI) analog-to-digital (ADC) converter.

[0025] Figure 2 This is a circuit diagram of an ADC calibration circuit, which includes a calibration circuit system configured to correct the ADC output under the influence of timing skew and a weight update circuit system configured to calculate an update of the weights used by the calibration circuit system.

[0026] Figure 3 The spectrum of the analyzed signal and its modulation version is shown.

[0027] Figure 4 Shown by Figure 2 The weight update circuit system shown generates updated weight values ​​over time.

[0028] Figure 5 The signal-to-noise ratio (SNDR) within the frequency range of the first exemplary scenario is shown, demonstrating the use of Figure 2The calibration and weight update circuit shown improves SNDR within the frequency range.

[0029] Figure 6 Shown by Figure 2 The power spectrum of the multi-tone input in the second exemplary scenario generated by the weight update circuit system shown.

[0030] Figure 7 In the second exemplary scenario, it is shown that by Figure 2 The weight update circuit system shown represents the updated weight values ​​of the multi-tone input generated over time.

[0031] Figure 8 The power spectrum of the multi-tone input is shown in the second exemplary scenario.

[0032] Figure 9 Shown in by Figure 2 The weight update circuit system shown generates the SNDR of the ADC within the frequency range in the third exemplary scenario.

[0033] Figure 10 It can be shown that Figure 2 The transfer function of the linear phase notch filter used in the ADC calibration circuit shown.

[0034] Figure 11 The difference in time skew and bandwidth mismatch error of the bidirectional interleaved ADC system is shown. Detailed Implementation

[0035] The concepts disclosed in this discussion are described and illustrated with reference to illustrative embodiments. However, the application of these concepts is not limited to the details of the construction and arrangement of components in the illustrative embodiments and can be practiced or implemented in a variety of other ways. The terminology used herein is for describing illustrative embodiments and should not be considered limiting. Words such as “including / comprising” and “having” and variations thereof, as used herein, are intended to cover the items listed thereafter, their equivalents, and additional items.

[0036] The disclosed embodiments include circuitry and methods for mitigating the effects of non-uniformly spaced sampling moments when using time-interleaved (TI) analog-to-digital converters (ADCs). At least some of the disclosed embodiments and solutions can be tailored to reduce hardware costs or improve performance. At least some of the disclosed embodiments are independent of the frequency of tones appearing in the (distorted) output signal of the ADC, and the applicability of at least some of the disclosed embodiments is not limited to a specific number of TI slices. Using the disclosed methods, timing spurs of a TI ADC can be calibrated by using background calibration. For at least some embodiments, the calibration algorithm does not require a ground-based signal to identify the correct compensation and can therefore run in the background, i.e., during normal operation of the ADC.

[0037] In an exemplary embodiment, the output signal of the ADC is mixed to a frequency that exhibits time-interleaved spurious signals due to skew. In some embodiments, no prior knowledge of the ADC's output signal is required, nor is it necessary for the signal to have a specific spectral content.

[0038] It is known that the timing skew frequency occurs at f s / M±f in At integer multiples of f, where f s M is the sampling frequency of the entire system, and M is the time interleaving factor. Figure 1 The example spectrum with timing spurious signals is shown, where θ represents the normalized frequency: θ = 2πf / f s This exemplary spectrum is a single-tone signal with time-interleaved spurious signals (TI = 4 in this example). Pole 102 represents the signal component (which is ideally the only component), while poles 104 and 106 are artifacts added to the spectrum due to the non-uniform sampling moments of the TI slice. Figure 1 The amplitude of the signal shown is not proportional. The real signal is symmetrical about π radians (=fs / 2).

[0039] In an exemplary embodiment, the magnitude of the timing skew correction is approximately proportional to the input frequency. This dependency is eliminated from the calibration logic using a derivative finite impulse response (FIR) filter, thereby simplifying the required circuitry. The calibration algorithm learns complex weights with correct magnitude and phase using the cross-correlation between the input signal and the mixed and frequency-scaled input signal.

[0040] exist Figure 2The diagram illustrates a calibration circuit 150 configured to implement a calibration algorithm or correction scheme. Circuit 150 includes a correction circuit system 200 and a weight update circuit system 250. The correction circuit system 200 is configured to correct the ADC output under the influence of timing skew, while the weight update circuit system 250 is configured to calculate updates to the weights used by the correction circuit system 200. Both the correction circuit system 200 and the weight update circuit system 250 include the circuit components and their configured functionality described below.

[0041] Referring now more specifically to the correction circuit system 200, in response to the input signal 202, the ADC 204 generates the ADC digital output 206 (y dig ADC 204 provides a time-multiplexed output consisting of M ADC channels. While in some embodiments ADC 204 is considered part of the correction circuitry system 200, in other embodiments the ADC provides digital output 206 to the correction circuitry system, but the ADC itself is not considered part of the correction circuitry system 200. The ADC digital output 206 is provided to the derivative filter 208 (H... D The digital output 206 is scaled by the derivative filter 208 to represent the input tone in the ADC digital output. Given a certain time skew, the skew of higher frequency inputs results in a larger tone amplitude, and this filter 208 removes this dependency. dig The derivative of ).

[0042] The y provided at the output 210 of the derivative filter 208 dig The derivative is split and passed through a Hilbert filter (H HIL )212 to produce y' h (n), and y'(n) is generated by delay block (ΔT) 214. Delay block 214 has the same delay as filter 212. In an exemplary embodiment, Hilbert filter 212 ideally has unity gain across the full bandwidth and a constant phase shift of +90 degrees or -90 degrees (depending on whether the frequency is positive or negative). Since the skew error introduced in the TI system is a phase error, the correction mechanism needs to use a complex signal to compensate for this error. To create a complex signal, a Hilbert transform can be applied. Any phase shift can be achieved by adding the Hilbert transform to the original signal. Further discussion of exemplary embodiments of Hilbert filter 212 is provided below.

[0043] The Hilbert transform y' provided at the output of filter 212 h (n) and y provided at the output of delay block 214 digThe delayed derivative y'(n) is provided as input to mixer circuit 216. Mixer circuit 216 shows one of M-1 mixing functions or mixing circuits implemented in parallel. For illustrative purposes, the M-1 mixer circuits 216 are represented by a single mixer circuit. M-1 instances of the M-1 mixer circuits, as well as other components within the correction circuit system 200 and weight update circuit system 250, are specified within dashed line 217. Each of the M-1 instances of the mixing circuit system has a different mixing frequency. For example, if M = 4, then in each of the three (M-1) instances in 217, from top to bottom, the signals y'(n) and y'... are applied to the inputs of multiplier 215 of mixer circuit 216 (and multiplier 263 of mixer circuit 264). h The four sine waves of (n) are: cos(2πni / 4), sin(2πni / 4), -sin(2πni / 4), and cos(2πni / 4), where 'i' represents one of the instances of the parallel mixer circuit, and 'n' represents a point in discrete time (at the system sampling rate f). s (Sampling). Therefore, for the first instance (i=1), the modulation signal is given from top to bottom as follows: cos(2πn / 4), sin(2πn / 4), -sin(2πn / 4), cos(2πn / 4). For the second instance (i=2), the modulation signal is given from top to bottom as follows: cos(2πn / 2), sin(2πn / 2), -sin(2πn / 2), cos(2πn / 2). For the third instance (i=3), the modulation signal is given from top to bottom as follows: cos(3·2πn / 4), sin(3·2πn / 4), -sin(3·2πn / 4), cos(3·2πn / 4).

[0044] By using the M-1 mixer circuit to y dig The derivative y'(n) and its Hilbert transform y' h (n) and f s The input tone is mixed with a sine wave M-1 times, which is an integer multiple of M, thus mixing the input tone to one of the skew spurious positions to create a complex signal y. i B,I 218, y i B,R 220. Equation 1, discussed further below, shows the method for creating the complex signal y. i B,I 218, y i B, The function of 220. Then, the complex signals 218 and 220 are multiplied by the learned complex weights (w) shown at 228 and 226 using the product or multiplier circuit system 222 and 224. i B,R and wi B,I This generates weighted complex signals 230 and 232. Figure 2 The complex weights (w) shown i B,R and w i B,I In the diagram, the superscript 'i' indicates the range {1,2,…,M-1}, signifying that there is a pair of weights for each mixer. Since the correction circuit system 200 includes circuitry for implementing M-1 mixing functions 216 and M-1 corresponding weight multiplier functions 222, 224, these components are represented as being implemented M-1 times within the dashed line 217 for illustrative purposes. Dashed line 217 also shows other components implemented M-1 times within the correction circuit system 200 and the weight update circuit system 250, such as the weight update circuitry, which are discussed below.

[0045] The learned complex weights 229 can be obtained from the complex weight repository 229. The complex weights are provided by the weight update circuitry 250 described below. In some exemplary embodiments, the weight update circuitry initially sets the complex weights to zero, and the circuitry quickly adjusts the weights to the desired values. However, in other embodiments, the initial complex weight values ​​can be set to values ​​other than zero. The subtraction circuitry 234 then uses the uncorrected ADC output signal y... dig In step 206, weighted complex signals 230 and 232 are subtracted to create a corrected output signal 'z' at output 236. The corrected signal z at output 236 is the corrected ADC output signal. In circuit 234, the contributions of each of the (M-1) outputs of the mixer circuit are combined into a single signal, which is possible because different weights w are used. i Scaling is applied to all (M-1) parallel instances, allowing for individual scaling of these contributions mixed to different frequencies before being added to the final compensation signal.

[0046] Now, referring to the weight update circuit system 250 of the calibration circuit 150, the correction signal z is provided to the notch filter (H). N )252, the notch filter (H N )252 is configured to suppress approximately f s Any input tone that is an integer multiple of / M interferes with the filtering signal z provided at filter output 254. n The weight update process in the filter. The filtered signal z at position 254 of the filter output. n Through derivative filter 256(H) D The derivative filter 256(H) DThe input tone is configured to scale. Similar to the function of derivative filter 208, given a certain time skew, the skew of the higher frequency input causes the tone to have a larger amplitude, and filter 256 removes this dependency.

[0047] The filtered signal z provided at the output 258 of derivative filter 256 n The derivative is split and passed through a Hilbert filter (H HIL Hilbert filter 260 and delay block (ΔT) 262. Delay block 262 has the same delay as filter 260. In an exemplary embodiment, Hilbert filter 260 ideally has unity gain across the full bandwidth and a constant phase shift of +90 degrees or -90 degrees (depending on whether the frequency is positive or negative). Further discussion of exemplary embodiments of Hilbert filter 260 is provided below.

[0048] The Hilbert transform provided at the output of filter 260 and the filtered signal z provided at the output of delay block 262 n The delayed derivative is provided as input to mixer circuit 264. Similar to mixer circuit 216, mixer circuit 264 shows one of M-1 mixing functions implemented in parallel. z is then processed using multiplier 263 as discussed above. n The derivative and its Hilbert transform are related to the mixer frequency and f. s The relationship between them can be simply represented by f. s Sine wave mixing at integer multiples of / M, thus mixing the input tone to one of the skewed spurious positions to create M-1 complex signal pairs z. i B,I 266, z i B,R 268. Filtered signal z n (z i B,R and z i B,I The mixing derivatives of 266 and 268 are provided to the product or multiplier circuit systems 270 and 272 to generate the filtered signal z. n (z i B,R and z i B,I The mixing derivative and the delayed filtered signal z) n Cross-correlation 274, 276 between 281, the delayed filtered signal 281 is provided to the product or multiplier circuit system 270, 272 via serial delay blocks (ΔT) 278, 280. Filtered signal z n (z i B,R and z i B,IThe mixing derivative and the delayed filtered signal z) n The cross-correlation values ​​274 and 276 are used to update the weights. A larger cross-correlation means that spurious signals still exist in the corrected output signal, so the weights need to be increased. Conversely, a smaller correlation means that the basis function has been sufficiently scaled to remove spurious signals, so the weights need little or no update. As mentioned above, the weights can initially be set to zero and increased to reduce the cross-correlation. Notch filter (H N )252 when the frequency of the input signal is close to f s Training is "blocked" at / M because modulation of this input signal will incorrectly label the input itself as spurious content. Multiplier circuitry 282, 284 scales the cross-correlation 274, 276 with a factor "μ", which is the learning rate and is configurable to produce scaled cross-correlation 286, 288. The learning rate factor μ is selected by the designer of a specific implementation of the weight update circuitry based on testing. A learning rate factor that is too large will result in an unstable system, while a learning rate factor that is too small will result in an excessively long time required to achieve sufficient performance correction. Adder circuitry 290, 292 adds the scaled cross-correlation 286, 288 to the weight values ​​226, 228 to produce newly updated weight values ​​294, 296. The newly updated weight values ​​294, 296 can be stored in a weight repository 229 and used by the correction circuitry 200 in the next cycle as weight values ​​226, 228 to scale the basis functions.

[0049] refer to Figure 3 As an example, the spectrum of the analyzed signal and its modulated version (for TI=4) is shown. It should be noted that the signal amplitude is not proportional, and for the modulated signal, only the shifted signal component is shown. Figure 1 The spectral content of the TI ADC with single-tone input is depicted in the diagram. Figure 3 In the diagram, the second curve depicts the analytical signal (i.e., y′(n) + jy′) created using the Hilbert transform. h (n)). Note that the analyzed signal contains only spectral components within the interval 0 ≤ θ < π. Then, for example, [the signal can be analyzed using...] Figure 2 The mixer described herein mixes this analysis signal, which produces a modulated analysis signal. Figure 3 (The third curve). The real and imaginary parts of the complex spectrum show the same magnitude response but with different phases. Figure 3 The concept of mixing a signal to different frequencies is illustrated (i.e., the behavior of a mixer), but it is provided as an example and does not directly correspond to the above. Figure 2 The output of a specific node in the dataset.

[0050] Mixing a complex signal to time-interleaved spurious frequencies can be mathematically described as follows:

[0051] Equation 1

[0052]

[0053] Where i = {1, 2, ..., M-1}, and 'n' represents a point in discrete time (with the system sampling rate f). s (sampling), and y' h (n) is the Hilbert transform of y'(n). These are the basis functions of the correction algorithm.

[0054] By multiplying the basis functions by a certain weight, the modulated signal components can be altered in a way that eliminates time-interleaved spurious signals. The correction algorithm can be applied to a TIADC with any number of channels. For each added TI channel, two basis functions are created (one real and one imaginary).

[0055] The algorithm was tested using MATLAB models with various TI configurations, each with different amounts of skew added to each channel. Additionally, different frequencies and multi-tone inputs were tested. The ADC sampling frequency was 1.0 GHz. Figure 4 The diagram shows the updated weight values ​​over time, with dashed lines indicating switching to different input frequency tones, where the numbers indicate the input frequency in MHz.

[0056] Scenario 1

[0057] Number of TI channels: 4

[0058] Skewness for each channel: [0.45% - 0.9% - 0.75% - 1.0% of Ts]

[0059] Input frequency: 16.5MHz to 496.5MHz (single tone).

[0060] After obtaining the correct weight values, all input frequencies are tested to measure the signal-to-noise ratio (SNDR) improvement using the learned weights. Figure 5 The diagram illustrates an improvement in SNDR across the entire frequency range. This improvement is due to the use of the Hilbert filter H... HIL and derivative filter H D Given a finite number of coefficients for both, the algorithm's correction capability is within f. s The frequency drops abruptly around 2 (496.5 MHz in this example). To illustrate this degradation, we can recall the change in the transfer function of the filter described above due to a finite number of coefficients. Figure 6 The power spectrum of a single-tone input is shown.

[0061] Scenario 2

[0062] Number of TI channels: 4

[0063] Skewness for each channel: [1% - 1.5% 0.8% - 1%] * Ts

[0064] Input frequencies: Multi-tone frequencies at 166.5, 186.5, 206.5, 226.5MHz and 86.5, 186.5, 286.5, 386.5MHz

[0065] One improvement provided by the disclosed embodiments is that the learned weights are frequency-independent (because frequency dependence is removed by the derivative filter). Therefore, the weights do not need to be updated by changes in the frequency of the input signal. Furthermore, when multi-tone signals are used as input to the ADC, the correction algorithm works correctly even when the frequencies of the tones are further apart. For scenario 2, Figure 7 The updated weight values ​​of multi-tone inputs with input frequencies of 86.5MHz, 186.5MHz, 286.5MHz, and 386.5MHz are shown over time. Figure 8 The power spectra of multi-tone inputs with input frequencies of 86.5MHz, 186.5MHz, 286.5MHz, and 386.5MHz are shown. It can be seen that, compared to existing systems and methods, the disclosed method and algorithm do not experience interruptions when the frequencies of the ADC's input tones are spaced further apart.

[0066] Scenario 3

[0067] Number of TI channels: 6

[0068] Skewness for each channel: [-1.0% 0.9% 0.45% 0.75% -0.9% 0.45%] * Ts

[0069] Input frequency: 16.5MHz to 496.5MHz (single tone)

[0070] Figure 9 The SNDR of the ADC across the full frequency range for scenario 3 is shown.

[0071] Return to reference Figure 2 Hilbert filters 212 and 260 ideally have a phase shift of +90 degrees for negative frequencies and a phase shift of -90 degrees for positive frequencies. The frequency response of the Hilbert transform is:

[0072] Equation 2

[0073]

[0074] Therefore, the magnitude of the response should be consistent across the bandwidth. The effect of filter truncation can be mitigated by multiplying the filter coefficients by a window such as a Hanning window.

[0075] In an exemplary embodiment, the following FIR filter weights are used for implementation. Figure 2 The derivative filters 208 and 256 are shown below:

[0076] Equation 3

[0077]

[0078] A derivative filter ideally has the following frequency response:

[0079] Equation 4

[0080] H D (jω)=jω

[0081] This frequency response implies a 20 dB / decimal increase and a constant phase shift of +90 degrees for positive frequencies and -90 degrees for negative frequencies. As the frequency approaches the Nyquist frequency, the derivative filter can become inaccurate, making it difficult for calibration algorithms to correct frequencies very close to the Nyquist. The Hanning window can be used to reduce the non-ideal characteristics caused by the finite number of coefficients in the FIR filter.

[0082] In an exemplary embodiment, when the input signal contains spectral content very close to the frequency at which time-interleaving spurious signals occur, a notch filter 252 is used to avoid distortion in the learning process. For example, in a TI system with an interleaving factor of 4, [the following will be observed]. θ = π and Time interleaving spurious signals appear at this location. Now, if the input signal has a location at... The spectral content at the input signal, as determined by the weight update portion of the method or algorithm implemented by circuit system 250, will find a high correlation between the modulated signal (modulated with θ = π) and the input signal, leading to an erroneous increase in weights (i.e., the algorithm attempts to remove the input signal itself). Clearly, spectral content in the input signal close to the mixer frequency should not be used to update the weights. To avoid this problem, circuit system 250 applies a notch filter in the "weight update portion" of the algorithm. By applying notch filter 252, spectral content closely spaced from the mixing frequency is suppressed, thus the cross-correlation (which determines the weight update step) becomes very small for input frequencies closely spaced from the mixing frequency. Figure 10 The example linear-phase notch filter for TI=4 is shown. These filters can be easily constructed, for example, by using a comb filter.

[0083] ADC slice bandwidth mismatch

[0084] Compared to errors caused by time skew, bandwidth mismatch between different ADC slices leads to similar spectral distortion. While both time skew and bandwidth mismatch exhibit spurious content at the same frequency, the key difference lies in how each individual channel is affected. For time skew, the magnitude of the error spurious is a function of the time skew and the input frequency of the signal across all ADC slices. Each channel has a different phase shift, but the frequency dependence of the error is the same for all errors, i.e., a single zero at DC (derivative filter). For each spurious, only the phase and magnitude need to be learned, not the frequency response. On the other hand, for the bandwidth mismatch problem, spuriouss will be formed by the bandwidth mismatch in each channel. As a simple approximation of the mismatch effect, the bandwidth of each channel can be modeled as a single-pole network. Therefore, this first-order approximation is done using a single pole at a certain cutoff frequency; the location of the pole is different for each channel. This means that, in this case, the frequency dependence is not equal for all ADC slices.

[0085] Time skew correction relies on the relationship between the linearized input frequency and the magnitude of the error caused by the time skew (i.e., using a first-order Taylor approximation of e^(j*phi)). The same operation can be performed for bandwidth mismatch, but only after assuming the pole cutoff frequencies are spaced sufficiently higher than fs, because such a possibility exists. For clarity, Figure 11 The difference between the two errors in the bidirectional interleaving system is shown. For example... Figure 11 As can be seen, if the assumption of an effective Taylor expansion is satisfied, the bandwidth mismatch error can be linearized, and therefore the disclosed calibration system should be used for correction.

[0086] The features described herein with respect to one embodiment may be implemented in other embodiments herein.

[0087] In one embodiment, circuit 150 includes a TIADC circuit system 204 configured to receive an input signal 202 and responsively generate a digital output signal 206. The circuit includes a correction circuit system 200 configured to receive the digital output signal from the ADC circuit system and responsively generate a corrected output signal 236 using complex weight values ​​226, 228. The correction circuit system includes a first-order derivative filter 208 configured to generate a derivative 210 of the digital output signal to remove frequency dependence between the weight values ​​and the input signal. In an exemplary embodiment, the first-order derivative filter is a finite impulse response (FIR) filter. The circuit also includes a weight update circuit system 250 configured to receive the corrected output signal 236 and responsively generate updated weight values ​​294, 296. The weight update circuitry includes a notch filter 252 configured to filter the corrected output signal 236 to generate a filtered corrected output signal 254. The notch filter suppresses approximately f% of the corrected output signal in the filtered corrected output signal. s Any input tone that is an integer multiple of / M, where f s Where is the sampling frequency, and M is the time interleaving factor. The weight update circuit system uses the filtered, corrected output signal to generate updated weight values.

[0088] In an exemplary embodiment, the correction circuit system 200 includes a first Hilbert filter 212 configured to receive the derivative 210 of the digital output signal and responsively generate a Hilbert transform of the derivative of the digital output signal. The correction circuit system 200 also includes a first delay circuit 214 configured to receive the derivative of the digital output signal and provide a delayed derivative of the digital output signal. A mixer circuit 216 is also included in the correction circuit. A first mixer is coupled to the first Hilbert filter and the first delay circuit, and the first mixer converts the derivative of the digital output signal into a Hilbert transform and the delayed derivative of the digital output signal by combining f. s The first complex signal 218, 220 is generated by mixing a sine wave that is an integer multiple of / M. The first mixer generates the first complex signal such that the input tone of the first complex signal is mixed to the frequency of the time-skewed spurious position.

[0089] The correction circuit also includes first product circuits 222 and 224, which are configured to multiply the first complex signals 218 and 220 by complex weight values ​​294 and 296 to generate first weighted complex signals 230 and 232. A subtraction circuit 234 of the correction circuit is configured to subtract the first weighted complex signals 230 and 232 from the digital output signal 206 to generate a corrected output signal 236.

[0090] The weight update circuit system 250 includes a second-order derivative filter 256 configured to generate the derivative 258 of the filtered corrected output signal 254. A second Hilbert filter 260 of circuit 150 is included in the weight update circuit system 250. The Hilbert filter 260 receives the derivative 258 of the filtered corrected output signal 254 and responsively generates a Hilbert transform of the derivative of the filtered corrected output signal. A second delay circuit 262 provides a delayed derivative of the filtered corrected output signal. A second mixer circuit 264 of circuit 150 is also included in the weight update circuit system. The mixer circuit 264 is configured to combine the Hilbert transform of the derivative of the filtered corrected output signal and the delayed derivative of the filtered corrected output signal with f... s The second complex signals 266 and 268 are generated by mixing sinusoidal waves that are integer multiples of / M. The third delay circuits 278 and 280 are configured to receive the filtered corrected output signal (254) and provide a delayed filtered corrected output signal (281). The product circuits 270 and 272 of the weight update circuit system generate cross-correlations 274 and 276 between the second complex signals 266 and 268 and the delayed filtered corrected output signal 281, and the weight update circuit system generates updated weight values ​​294 and 296 as a function of the cross-correlation. The product circuits 282 and 284 of the weight update circuit system scale the cross-correlations using a learning rate factor to generate scaled cross-correlations 286 and 288, and the adder circuits 290 and 292 add the scaled cross-correlations to the weight values ​​to generate updated weight values.

[0091] In another embodiment, circuit 150 includes a TIADC circuit system 204 configured to receive an input signal 202 and responsively generate a digital output signal 206. The TIADC circuit system 204 outputs a time-multiplexed output of M ADC channels, where f sThe sampling frequency is specified. The circuit includes a correction circuit system 200 configured to receive a digital output signal from an ADC circuit system and responsively generate a corrected output signal 236 using complex weight values ​​226 and 228. The correction circuit system includes a first-order derivative filter 208 configured to generate a derivative 210 of the digital output signal 206. The corrected output signal is generated based on the derivative of the digital output signal. The circuit 150 also includes a weight update circuit system 250 configured to receive the corrected output signal 236 and responsively generate updated complex weight values ​​294 and 296 to replace the complex weight values ​​226 and 228 for use by the correction circuit system. The weight update circuit system includes a notch filter 252 configured to filter the corrected output signal 236 to suppress spectral content at frequencies where time-interleaved spurious signals occur in the corrected output signal, thereby generating a filtered corrected output signal 254. The notch filter suppresses approximately f from the corrected output signal. s Any input tone that is an integer multiple of / M. The filtered, corrected output signal is used to generate updated complex weight values ​​294 and 296.

[0092] The correction circuit system 200 includes a first Hilbert filter 212 configured to receive the derivative 210 of the digital output signal 206 and responsively generate a Hilbert transform of the derivative of the digital output signal. The first Hilbert filter has unity gain and a constant phase shift of +90 degrees or -90 degrees (depending on whether the frequency is positive or negative). The correction circuit also includes a first delay circuit 214 configured to receive the derivative of the digital output signal and provide a delayed derivative of the digital output signal. A first mixer circuit 216 is coupled to the first Hilbert filter and the first delay circuit. The first mixer circuit converts the Hilbert transform of the derivative of the digital output signal and the delayed derivative of the digital output signal into a Hilbert transform of approximately f. s The first complex signals 218 and 220 are generated by mixing sinusoidal waves that are integer multiples of / M. The first mixer circuit generates the first complex signals 218 and 220 such that the input tone of the first complex signals is mixed to a frequency at which time-interleaving spurious signals occur. The first product circuits 222 and 224 of the correction circuit system are configured to multiply the first complex signals by complex weight values ​​to generate first weighted complex signals 230 and 232. The subtraction circuit 234 of the correction circuit system is configured to subtract the first weighted complex signals 230 and 232 from the digital output signal 206 to generate a corrected output signal 236.

[0093] Circuit 150 also includes a second-order derivative filter 256 in the weight update circuit system 250, the second-order derivative filter 256 being configured to generate the derivative 258 of the filtered corrected output signal 254. A second Hilbert filter 260 included in the weight update circuit system is configured to receive the derivative of the filtered corrected output signal and responsively generate a Hilbert transform of the derivative of the filtered corrected output signal. A delay circuit 262 of the weight update circuit system is configured to receive the derivative of the filtered corrected output signal and provide a delayed derivative of the filtered corrected output signal. Circuit 150 also includes a second mixer circuit 264 in the weight update circuit system, the second mixer circuit 264 being coupled to the second Hilbert filter and the second delay circuit. The second mixer circuit is configured to combine the Hilbert transform of the derivative 258 of the filtered corrected output signal and the delayed derivative of the filtered corrected output signal with f... s The second complex signals 266 and 268 are generated by mixing sinusoidal waves that are integer multiples of / M.

[0094] The weight update circuit system 250 also includes third delay circuits 278 and 280 configured to receive the filtered corrected output signal (254) and provide a delayed filtered corrected output signal (281), and product circuits 270 and 272 configured to generate cross-correlations 274 and 276 between the second complex signals 266 and 268 and the delayed filtered corrected output signal 281. Another product circuit 282 and 284 are configured to scale the cross-correlations 274 and 276 using a learning rate factor to generate scaled cross-correlations 286 and 288. Adder circuits 290 and 292 are configured to add the scaled cross-correlations to the weight values ​​226 and 228 to generate updated weight values ​​294 and 296.

[0095] Although the invention has been described with reference to preferred embodiments, those skilled in the art will recognize that changes in form and detail may be made without departing from the scope of the discussion.

Claims

1. A circuit, characterized in that, include: A time-interleaved (TI) analog-to-digital converter (ADC) circuit system configured to receive an input signal and responsively generate a digital output signal; A correction circuit system configured to receive the digital output signal from the TI ADC circuit system and responsively generate a correction output signal using weight values, the correction circuit system including a first-order derivative filter; as well as A weight update circuit system configured to receive the correction output signal and responsively generate updated weight values, the weight update circuit system including a notch filter configured to filter the correction output signal to generate a filtered correction output signal, the weight update circuit system being further configured to use the filtered correction output signal to generate the updated weight values.

2. The circuit according to claim 1, characterized in that, The first-order derivative filter is a finite impulse response (FIR) derivative filter, which is configured to remove the frequency dependence between the input signal and the calibration coefficients used in the correction circuit system.

3. The circuit according to claim 1, characterized in that, The weight update circuit system is configured to provide the updated weight values ​​to the correction circuit system in place of the weight values, and wherein the correction circuit system is configured to use the updated weight values ​​to generate the correction output signal.

4. The circuit according to claim 1, characterized in that, The TIADC circuit system provides the digital output signal as the output of the sequentially generated 'M' ADC channels.

5. The circuit according to claim 1, characterized in that, The correction circuit system further includes: A first Hilbert filter is configured to receive the derivative of the digital output signal and responsively generate a Hilbert transform of the derivative of the digital output signal; A first delay circuit is configured to receive the derivative of the digital output signal and provide a delayed derivative of the digital output signal; and A first mixer circuit, coupled to a first Hilbert filter and a first delay circuit, is configured to generate a first complex signal by mixing the Hilbert transform of the derivative of the digital output signal and the delayed derivative of the digital output signal with a sine wave.

6. The circuit according to claim 5, characterized in that, The first mixer circuit is configured to combine the Hilbert transform of the derivative of the digital output signal and the delay derivative of the digital output signal with f. s The first complex signal is generated by mixing sinusoidal waves that are integer multiples of / M, where f s M is the sampling frequency, and M is the time interleaving factor.

7. The circuit according to claim 5, characterized in that, The first mixer circuit is configured to generate the first complex signal such that the input tone of the first complex signal is mixed to the frequency of the time-skewed spurious position.

8. The circuit according to claim 7, characterized in that, The first mixer circuit includes M-1 parallel first mixer circuits, each of which is configured to apply M-1 mixing functions to mix the Hilbert transform of the derivative of the digital output signal with the delayed derivative of the digital output signal.

9. The circuit according to claim 5, characterized in that, The weight value is a complex weight value, and the correction circuit system further includes: A first product circuit is configured to multiply the first complex signal by the complex weight value to generate a first weighted complex signal. A subtraction circuit is configured to subtract the first weighted complex signal from the digital output signal to generate the corrected output signal.

10. A circuit, characterized in that, include: A time-interleaved (TI) analog-to-digital converter (ADC) circuit system is configured to receive an input signal and responsively generate a digital output signal. The TI ADC circuit system provides sequentially generated outputs from 'M' ADC channels, where f s It is the sampling frequency; A correction circuit system configured to receive the digital output signal from the TI ADC circuit system and responsively generate a correction output signal using complex weight values, the correction circuit system including a first-order derivative filter configured to generate a derivative of the digital output signal, wherein the correction output signal is generated based on the derivative of the digital output signal; as well as A weight update circuit system is configured to receive the correction output signal and responsively generate updated complex weight values ​​to replace the complex weight values ​​for use by the correction circuit system.

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