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.