hi sutapanaki
I read your explenation but i don't understand.
you say:we have discrete noise samples and their spectrum is only in 0 to Fs/2 frequency range. I think we have after ph_1 a white noise.can explain your opinion?
you say:We know that the variance of that sequence of noise samples i.e. the noise power is equal to the variance of the continuous noise process before the sampler, which means it is proportional to kT/C. please introduce a reference for this. i can not approve it.
is below explenation right?
In ph1, KT/C noise is created( as you know the KT/C noise is sum or integral of noise spectral for white noise) . so i can say after ph_1 i have noise on across C capacitor with total value as KT/C.
In ph_2 , this broadband noise is sampled as the vin in across c is sampled. so with f0 frequency sampling, this noise is sampled and folded. these folded parts of principle spectrum of noise are added together so the contribution of KT/C is approximately zero after ending of ph_2.
thanks for reply
i am not english native,so excuse me if i can not declare clearly my meaning.
You have to try and imagine what happens in ph1 and ph2 of a S/H or in fact any switched capacitor circuit. In ph1 we track the input and then sample it at the end of ph1. Then, in ph2 the rest of the switched capacitor circuit grabs that sample and process it and produces the output at the end of ph2. So, from the point of view of the output and ph2, the circuit is really working with samples, not continuous time process i.e. it is a discrete signal processing. With respect to noise at the input - yes, there we have continuous time noise process, and when the input switch is closed during ph1, that continuous noise reaches the sampling cap but the moment we open the sampling switch we freeze a noise sample over the sampling cap. Or rather, we freeze noise charge sample. In ph2 that sample is transferred and redistributed to output cap. CT noise during ph2, from switches, amplifier, etc also gets sampled at the end of ph2.
Every time we sample a signal and take discrete points of that signal, like what ADC does when it converts the output of a S/H circuit, we work only in the frequency range from 0 to Fs/2 (Fs is the sampling frequency). This just comes from the periodic nature of discrete sine signals or complex exponentials. If a signal extends beyond Fs/2 it will alias back into that first Nyquist range (0 to Fs/2). In the case of noise, it is going to high frequencies, defined by the cut off of the input sampling R and C, but then upon sampling folds down into 0 to Fs/2 range. Parseval's theorem says that the power of signal in time domain is equal to the integral over all frequencies of its PSD. Also, in case of noise, it is an ergodic random process with 0 mean and then if we take samples of that process, basically just sequence of random numbers, the variance should be the same as if we had multiple realizations of the process and we sampled all of them at the same point in time and collected ensemble samples - these have the same variance. Variance is in fact power of noise. So, as a consequence, whatever is the power of the continuous time noise process, such is the power of the samples we take from that process. The continuous process has variance which is kT/C, and the discrete noise process also has variance that's kT/C. In the continuous case the kT/C is distributed in frequency from 0 to the noise BW of the circuit, something like 1/4RC. Because of aliasing, in discrete time that same kT/C power is distributed in 0 to Fs/2 because that's the only frequency range that exists in discrete time. But the spectrum of discrete noise is still white, which means uniform in that range, provided that withing the time period of 2/Fs we can fit more than 3 or 4 time-constants of the sampling network, which usually is the case in all practical circuits.