Frequency response mismatch calibration in 2-channel time-interleaved oscilloscopes

Abstract

The time-interleaved (TI) structure has been widely implemented in high speed, wideband data acquisition systems to increase the system sampling rate. However, the frequency responses of each sub-sampling path are not identical. This is named frequency response mismatches (FRMs). In TI-based printed circuit board level systems, due to the impact of the parasitic parameters, the FRMs are more complicated than the mismatches in TI analog-to-digital converters (TIADCs), which degrade the system performance severely. Therefore, the FRM calibration in 2-channel TI acquisition systems with two features is researched. The first one is that the TI system has a larger mismatch range than in most previous research. The second one is that the channel frequency response uses the general model. The calibration structure is established by the analysis of the digital TI model, which implements the TI operation in the digital domain to reconstruct the mismatches in the time domain. Furthermore, the problem of designing an arbitrary frequency response filter is transformed to the question of designing a three-stage cascaded filter group, which gives a method to realize the arbitrary frequency response in a real system. An oscilloscope prototype is proposed to verify the calibration performance. The simulation and experiment show the following: (i) Even though it uses the general frequency response and the FRMs are significant, the proposed method is still effective. (ii) The mismatch range of magnitude and phase responses is highly suppressed, and the spurious-free dynamic range is improved by 16.26 dB after calibration of the prototype.

Hadamard transformation based frequency response mismatch calibration for a 4-channel TIADC

“…However, a drawback is that it is usually only applicable to input signals within the first Nyquist bandwidth of the sub ADC. Furthermore, there are also some calibration strategies that do not calculate an expression for the frequency response but instead use the measured frequency response directly in the calibration [22][23][24][25][26][27][28][29]. Singh et al [22,23] introduced a method that uses adaptive I/Q signal processing to calibrate frequency response mismatches.…”

“…This scheme necessitates the use of interpolation techniques and includes sophisticated matrix operations that are less suitable for practical applications. Another design option is to apply the time-varying filter [26][27][28][29]. Time-varying filters can be implemented in several ways, most typically using a bank of time-invariant filters and multipliers, as explained in [26,27].…”

“…To calculate the filter 𝑄 𝑘 ( 𝑗𝜔), the channel frequency response 𝐻 𝑚 ( 𝑗𝜔) should be measured in advance. In this paper, a series of sinusoidal signals with different frequencies are used to measure channel frequency responses, which have been widely utilized in previous works [24,26,27,29]. A sufficiently large number of frequency points within the test frequency band are selected, and the frequency response is determined based on the relationship between the output and input of each channel.…”

“…The proposed approach in this paper is similar to [27], but we use Hadamard transform instead of complex exponential modulation to further simplify the signal processing and the computation. The calibration strategy in [24] and [29] also do not use modulators, which they replace with interpolators and data selectors, respectively. Additionally, although a 4-channel TIADC system is used for the analysis in this paper, the proposed method can be extended to systems with other channel numbers, except that it is important to note that the Hadamard matrix corresponding to the number of channels of the system must be present, e.g., 2, 4, 8, etc.…”