## 3 Simulation Results and Analyses
### Simulation of a Four-Channel TIADC  
A 14-bit four-channel TIADC behavioral model is introduced in this subsection to evaluate the efficiency of the proposed calibration method. The time-skew errors were set as [0.0013, \(-\)0.0008, \(-\)0.0007, 0.0001]-Ts. The tap of the derivative FIR filter is 33 and N = 1024.  
Figure 8 illustrates the output spectra of a four-channel TIADC prior to and subsequent to calibration using a single-tone signal input at 0.432 \(\cdot f_{s}\). Notably, the spurs caused by timing mismatch are all suppressed effectively, and the SNDR and SFDR improved from 52.82 dB and 56.54 dB to 79.92 dB and 105.98 dB, respectively. The estimated timing mismatch convergence curve corresponding to Figure 6 is shown in Figure 9. Our proposed estimation method needs about 6000 samples to converge at the expected time-skew values.  
Figure 10a,b displays the SNDR and SFDR performances with different input sinusoidal frequencies, utilizing the proposed calibration technique. As can be seen, the proposed calibration technique can improve the SNDR and SFDR of TIADC remarkably at almost the entire Nyquist domain and such improvements reach a magnitude of 27 dB for SNDR and 49 dB for SFDR.  
The proposed calibration technique performance under different time-skew errors is shown in Figure 11. This demonstrates that our proposed calibration method possesses a stable calibration effect within a range of serious timing mismatches.  
Figure 12 illustrates the output spectra of the TIADC with and without calibration when the input signal is a multitone signal. The proposed calibration technique effectively suppresses all spurs caused by timing mismatches and reduces them to the noise floor.  
In the above discussion, we assume that both offset and gain mismatches were calibrated before timing mismatch calibration by our proposed technique. However, offset and gain mismatches cannot be completely eliminated in practice [11; 28]. To view the effectiveness of our calibration algorithm even in the presence of the three mismatches (i.e., offset, gain and timing mismatches), we set the offset mismatch = [0, 0.0001, \(-\)0.0002, 0.0002] and gain mismatch = [1, 1.0001, 1.0001, 0.9998]. The output frequency spectra before and after calibration are presented in Figure 13. It can be seen that our proposed calibration algorithm is able to eliminate the effect of timing-skew errors despite the interference of offset and gain mismatches.  
Nevertheless, limited by the bandwidth of the derivative FIR filter, the performance of the proposed calibration algorithm will decline when the input signal is near \(\frac{1}{2}f_{s}\). The dis  
Figure 7: The structure of CCM.  
advantage of the feedforward structure is that it has a limited margin-of-error estimate. Figure 11 shows that the performance of the calibration algorithm decreases as the standard deviation of the time-skew error increases. The main reason for this is the reduced precision of the estimation module.  
Figure 8: Spectra of a four-channel TIADC output for a single tone input at 0.432 \(\cdot\)\(f_{s}\). (**a**) Prior to and (**b**) subsequent to the proposed digital timing mismatch calibration.  
Figure 9: Convergences of the estimated timing mismatches.  
Figure 11: (**a**) SNDR and (**b**) SFDR versus different timing-skew mismatches for a four-channel TIADC by utilizing the proposed calibration technique.  
Figure 10: (**a**) SNDR and (**b**) SFDR versus different input frequencies with the adoption of the proposed calibration technique for a four-channel TIADC.  
Figure 12: Spectra of a four-channel TIADC output (**a**) without and (**b**) with calibration under a multitone input.  
Figure 13: The frequency spectra of the TIADC output with offset and gain mismatches: (**a**) before calibration (SFDR = 62.83 dB); (**b**) after calibration (SFDR = 72.09 dB).