digital compensation of dynamic acquisition errors at the front-end of ...

22 Chapter 2: Nonlinearity at the ADC’s Front-End
2.3.2 Nonlinearity in the tracking phase
During tracking mode, the track-and-hold circuit of Figure 2.13 can be modeled
as an RC circuit. Ideally the capacitor voltage V C should track the input voltage;
however the finite switch resistance causes this voltage to differ from the ideal V out as
shown in Figure 2.9. The relation between V in and V c during tracking mode can be
modeled with the following equation
V
dVC
= Vin
− ( R1 + R ) C
(2.4)
dt
C 2
where R 1 and R 2 are switch resistances of M 1 and M 2 , respectively. R 2 is constant but
R 1 is a nonlinear function of the input voltage defined with the following equation
R1
= R1(
Vin
) =
µ C
n
ox
W
L
1
[ V −V
−V
]
DD
in
th
(2.5)
In the above equation, R 1 is a strong nonlinear function of the input voltage and
causes significant distortion in the sampled voltage on the capacitor. Therefore, it is
important to modify the circuit and make this resistance independent of the input
voltage. One common method for achieving a constant switch resistance is to use a
bootstrap switch structure [32] as shown in Figure 2.16. In this circuit, C boot is charged
first to V DD and is then connected across the gate and source terminal of the transistor.
This makes the V gs of the transistor constant during the tracking mode and makes the
impedance of the switch nearly independent of the input voltage.