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

26 Chapter 2: Nonlinearity at the ADC’s Front-End
transferred to the output using switch M 3 . Therefore, V out is equal to the capacitor
voltage at the end of the tracking phase. Using samples of the input and output voltage
at the end of the tracking phase we can write the relation between discrete-time
samples of V in and V out with the following equation
2 dVout
( k)
Vin
( k)
= Vout
( k)
+ ( a0 + a1V
out
( k)
+ a2Vout
( k)
+ ...) ×
(2.8)
dt
This equation is written based on the assumption that R 1 can be approximated as a
static nonlinear function of V out . From equation (2.6), we know that R 1 is a nonlinear
function of V in and V top . In a sampling network with sufficiently large bandwidth, V top
and V C track the input closely and differ by a weakly nonlinear term that is determined
by the respective RC product and the signal derivative. Therefore, the resistance of M 1
can be approximated by a nonlinear static function of V C and therefore V out (k).
In the above equation V in is modeled as a nonlinear function of V out with memory,
where nonlinearity only comes from R 1 and is a static function and memory is all
included in the derivative and is a linear function. Separating these two effects in our
distortion function helps us simplify the correction filter as will be discussed in detail
in Chapter 3.
2.4 Nonlinearity in the input circuit
As mentioned in Section 2.2, second-order non-idealities at the input driving
circuit of the ADC can add more dynamic nonlinear errors to the system. Figure 2.19
shows a complete schematic of the front-end of the ADC including flip-around trackand-hold
amplifier, package parasitics and the input driving circuit including a
transformer for converting single-ended to differential signal. The input driving circuit
can alternatively include buffers, differential amplifier or other kind of drivers, but the
general form of nonlinearity in all of them is the same and will not change the analysis
in this section.