Hi guys,
I want your suggestion regrding one system consisting of continuous filter and sampler system.Filter has a cutoff frequency to define the signal bandwidth and then this signal is sampled at a sampling rate.Basically sampler is track and hold circuit.so the for sampler noise simulation i do pnoise simulation but how to do this for whole system.Otherwise we can simulate them separately and the output noise spectrum of sampler will be shaped by filter response.First of all for sampler total noise we need to integrate upto cutoff frequency defined by filter, is this statement right???actually filter has a significant portion after cutoff,then upto what frequency i should integrate??can u guys suggest some solution...thanks

Hi,

The continuous-time filter noise can be estimated separately from that of the sampler, and then you can combine the 2 noise values. For the sampler, you correctly use the pnoise analysis.

As for what upper frequency limit to use for computing the noise from the continuous-time filter, you need to decide how much of the total noise falls in the signal band of interest for you.

There are several different scenarios and methods, all depending on your system definition, and the applicable bandwidth where noise is of interest to you.

If your sampling rate is much higher than the cutoff of the filter, then things are easy. Just take the signal band of interest to you (which is obviously less than the cutoff of the filter),

If you cannot ignore out-of-band noise in your system for some reason, then taking all the noise contained within the "noise bandwidth" of your filter is a good first guess. For a first-order lowpass filter, this is about (pi/2)*cutoff frequency.

The other extreme is to consider all the noise generated by your filter. This is typically limited and a function of the dominant capacitance (s) of your filter. Since noise simulations of continuous-time filters are trivial, this is very easy to do.

Regards,
Vivek

Hi Manodipan,

Once you have the CT filter noise component you could mathematically predict how much of that noise will show up at the output of your sampler (taking into account the limitations stated by Vivek according to the conditions that best fit your system):

- The autocorrelation of your CT filter noise will get multiplied by the modulation signal of your sampler: the TH circuit can be seen as an ideal sampler followed by a filter whose impulse response is a finite width square pulse. Therefore its power spectrum has a"sinc" shape.
Summarizing the TH circuit modulates (samples) and filters (with a sinc shape) the incoming noise.
- As a result of the modulation process, assuming your incoming noise is a stationary sthocastic process, the resulting output noise will be "cyclostationary" since it will be stationary over one period of your modulating signal. The output spectrum can be calculated by performing the multiplication of the incoming noise PSD and the modulating + TH filter transfer function Fourier transfoms.

- The outcome of this calculation will be the total output noise after going through the TH circuit. Right at this point is where you could add the noise contribution from the TH circuit to the already processed noise coming from the CT filter.

Obviously, the pnoise analysis will do all this math mess for you: the pnoise will take into account the CT filter noise modulation process when going through the TH circuit, and certainly the noise generated in the TH filter too. The output noise will contain both components.

As for your second question, you are correct: simply putting two switches in series doubles the RON and the equivalent total integrated noise will be KT/C. If you want the power up to a certain frequency just integrate up to that frequency the PSD of the filtered noise as you already suggested.

Sorry for the long answer.
Regards
Tosei

Hi manodipan,

when you have two Rs in series the calculation for the total integrated noise is the same as with just one R:

Each resistor contributes with 4KTR noise power. Therefore the total noise power is 4KT(2R), since the resistor noise can be modeled as an ideal (noiseless) resistor with a voltage noise source in series with it.
At the same time the time constant of the circuit will be (2R)C. Consequently the total integrated noise remains KT/C.

For the switches case if you have two of them in series and afterwards a capacitor the story is the same: you can treat the switches as 2R in series the same way as described above. Again the total integrated noise power is KT/C. That can be extended to N switches or resistors in series.
I´m not sure whether this addresses your question.

Finally, I´m not sure if I understand correctly your question regarding the sc filter: the input integrated noise will be dictated by the CT filter bandwidth as Vivek stated before. If you sample at a frequency higher than 2x such BW therefore you will not be foldbacking noise to the baseband and your baseband noise will simply be that one from the CT filter up to such bandwidth.

Hope his helps
Tosei

Hi Manodipan,

The KT/C total integrated noise is valid for a single pole system. Higher poles will show a different total integrated noise value. Now, if the last cap C from your set of switches in series is much larger than the diffusion cap of each of them, that can be approximated as a one pole system whose time constant is N*Ron*C.

Concerning the input referred noise of your sampler, I think it is better to refer it to the output since in that way you take into account the folding process of the sampler noise + potential folding of incoming noise if you are sampling at less than 2X the input noise BW.

Regards
Tosei