# kt/c noise of sample and hold

#### Ans5671

##### Member level 2
I am trying to simulate the KT/C noise of a sample and hold. The Fs = 500MHz with a tracking time of 250ps.
How does the tracking time and sampling speed impact the noise.
What beat frequency do I need to choose in pss 500MHz or 2G(1/2*Tracking time)?

Also, the KT/C noise is not matching the theoretical number. Why?

#### sutapanaki

Your beat frequency is commensurate with the sampling frequency, that's the periodicity in your circuit.
As for the discrepancy with the theory - different sampling circuits will have different noise. It is kT/C only for simple switch and C circuit. Try to increase the max frequency bandwith for the pnoise simulation. Stop when the noise does not change anymore.

#### AMS012

##### Full Member level 4
You should be able to match the simulated noise number exactly to the kT/c value. Different sample and hold circuits will not have different noise unless you have more than one sampling operation taking place.

#### sutapanaki

For sure different S/H circuits will have different amount of kT/C noise. S/H circuits that use amplifiers or bufferes will have multiples of kT/C factors.

#### AMS012

##### Full Member level 4
Sutapanaki, I guess you are talking about the excess noise from gamma factor of the MOS that changes the integrated noise from kT/C to kT/Cm * gamma. If you assume gamma = 1, you should always see kT/C noise as the output integrated noise of any S/H circuit. It is the source of noise and the noise equivalent band width that matter.

#### sutapanaki

Sutapanaki, I guess you are talking about the excess noise from gamma factor of the MOS that changes the integrated noise from kT/C to kT/Cm * gamma. If you assume gamma = 1, you should always see kT/C noise as the output integrated noise of any S/H circuit. It is the source of noise and the noise equivalent band width that matter.

kT/C is the noise of a resistor and capacitor or in our case a switch resistance and capacitor. Rarely anyone uses this simple kind of S/H unless we are talking about low resolution converters, but in low resolution converters noise is perhaps not the primary issue. A more complicated S/H than this will have also more noise. It is not physical to assume excess factor of 1 in this case. Murphy says it's too good to be true.

#### AMS012

##### Full Member level 4
Agree with you, Sutapanaki. Especially when working in lower technology nodes like finfet and all, it's not correct to assume gamma of 1. I was just trying to see if I am missing anything else.

#### crutschow

The interesting thing about KTC noise is that, although it's caused by resistance in the circuit, the resistance value does not appear in the noise equation.
But "T" is the temperature of the resistor, and the noise is independent of the capacitor temperature.

#### sutapanaki

The interesting thing about KTC noise is that, although it's caused by resistance in the circuit, the resistance value does not appear in the noise equation.
But "T" is the temperature of the resistor, and the noise is independent of the capacitor temperature.

It gets much deeper than that when we consider physical reasoning about the kT/C noise. Some people like to use equipartition theorem to explain it all but it boils down to basic physical phenomena and thermodynamics.