In classical circuit analysis, ideal OpAmp's generally have infinite open loop gain. However, in real life, OpAmp's open loop gain is finite and it introduces error in feedback systems, such as SC circuits. After a brief discussion on OpAmp finite open loop gain, two major sources of nonidealities will be discussed. The thermal noise coming from sampling action and the inherent OpAmp noise will be analyzed and referred to input to be used as a measure of the SC circuit performance.
Figure 1 shows an SC circuit with finite OpAmp gain in two phases of SC actions. During phase 1, the input signal is sampled onto both C
and C
; in phase 2, C is folded back to the output and the input is grounded. All the charge on C is transfered to C to form a 2x gain ( 
) for the SC circuit. However, if the OpAmp gain, A, is finite, the resulting gain will be
which means the requirement of 
. In general, a safe margin of 2x factor is taken into consideration; therefore, A is usually required to be at least 
.
Therefore, the A/D resolution determines the minimum DC gain for the OpAmp in the SC circuit, other parameters in the OpAmp for an optimal design will be briefly discussed in the following two sections.
C.3 Noise Contributors in SC Circuit
When the time varying input signal is sampled onto the sampling capacitor by the SC circuit, 
noise is sampled to the capacitor connected to the input of the OpAmp. (due to bottom plate sampling.) Its magnitude is
where 
is the input capacitance of the OpAmp. When the feedback is closed around the OpAmp, the sampled input and noise charges are transfered to C and create a V
. Assuming 
, the total noise charge sampled is
where 
is the feedback factor which equals to
Therefore, the input referred noise can be calculated by dividing the output noise by the gain square and is given by
In addition to 
noise in the SC circuit, the inherent OpAmp noise also contributes to the non-idealities. It's been shown in [3][12] that the input referred OpAmp noise variance is
C.4 Total Input-Referred Noise
Combing the two input-referred noise contributors from above, the total input-referred noise for SC circuit is given by
.