Fig.1 SAR ADC with input driver and reference buffer
Prior kT/C noise cancellation technique: The kT/C noise cancellation technique originates from the classic output series offset cancellation [5,6]. In [3], it is extended to a switched-capacitor amplifier which realizes the sampling noise reduction in an auto-zero manner. In [4], this technique is used in a SAR ADC. Comparing to [3], it reuses the SAR feedback to close the loop and only requires an open-loop amplifier. The SAR ADC with kT/C noise cancellation [4] is shown in Fig. 2. The sampling operation is divided into two phases, Φ1 sampling (from t0 to t1) and Φ2 sampling (from t1 to t2). During Φ1 sampling, the input signal is tracked on the DAC C1, together with the thermal noise from sampling switches. After Φ1 sampling, the sampling noise is frozen on C1. During the Φ2 sampling phase, it is amplified and stored on C2 through the amplifier. In this manner, the sampling kT/C1 noise is cancelled at the right side of C2. Considering the limited bandwidth of amplifier, the kT/C1 noise cannot be eliminated completely. The noise residue can be expressed as
\begin{equation} \overline{v_{ns1,res}^{2}}=kT/C_{1}\bullet e^{-2\Delta t/\tau}\nonumber \\ \end{equation}
where Δt is the time duration of Φ2 sampling, τ is the time constant at the output of amplifier.
To reduce noise, one way is to increase  Δt, but this can degrade the linearity of amplifier and even cause saturation because the input signal change during Δt is also amplified. To ensure linearity, the signal change at the amplifier input must be small. As a result, the input signal frequency is limited. Another way is to reduce the time constant τ by increasing amplifier bandwidth, but this is at the cost of increased power. Even if the power budget is sufficient, the bandwidth improvement will be eventually prevented by input transistor size of the amplifier. This is because the large input capacitance of amplifier exaggerates the ADC input-referred noise.
As analyzed above, for the ADCs with kT/C noise cancellation, the signal bandwidth is limited by the trade off between noise, amplifier bandwidth and linearity. The root cause of this issue is that the amplifier has to deal with the input signal change during Φ2 sampling phase.