SD Toolbox Reference |

kT/C Noise

Models the kT/C noise of a switched capacitor Cs.

Library

SD Toolbox.

Description

The kT/C Noise block models the kT/C noise of a switched capacitor Cs.

Thermal noise is caused by the random fluctuation of carriers due to thermal energy and is present even at equilibrium. Thermal noise has a white spectrum and wide band limited only by the time constant of the switched capacitors or the bandwidth of the operational amplifiers. The sampling capacitor Cs of a Switched-Capacitor (SC) Sigma-Delta modulator is in series with a switch, with finite resistance Ron, that periodically opens, thus sampling a noise voltage onto Cs. The total noise power can be found evaluating the integral

where k is the Boltzmann’s constant, T the absolute temperature and 4kTRon the noise power spectral density associated with the switch on-resistance. The switch thermal noise voltage eT (usually called kT/C noise) is then superimposed to the input voltage x(t) leading to

where n(t) denotes a Gaussian random process with unity standard deviation

The integrators or resonators of a SC Sigma-Delta modulator may include more than one SC input branch, each contributing to the total noise power. Each branch has to be modeled with a separate kT/C Noise block.

Parameters

- Sample Time: Period of the sampling signal in s (Ts = 1/fs, where fs is the sampling frequency)
- Sampling Capacitance: Value of the sampling capacitance Cs in F
- Absolute Temperature: Value of the absolute temperature in K
- Boltzman Constant: Value of the Boltzman constant k = 1.38x10-23 J/K
- Random Number Seed: Seed for the random number generator; different seeds among different blocks using the random number generator guarantee that the random sequences are uncorrelated

| White Noise | Jittered Sine Wave |