Noise Calculation with the Equipartition Theorem Method?

[mike_ech]

Anybody know how calculate the noise with equipartition theorem method?

For a simple RC one order filter. The noise charge across the capacitor is Q. we have 1/2*k*T=1/2*C*(Q/C)^2

For a more complicated network as below. Can you help me on how to calculate the total noise charge or voltage across all the capacitors? Can I use equipartition theorem?

 

[Aaron Barnard]

The equipartition theorem states that the energy of a system is equally distributed among the degrees of freedom of the system. In other words, for a system with N degrees of freedom, each degree of freedom will have an energy of 1/2kT.

In this case, you need to calculate the number of degrees of freedom in the circuit. This is done by counting the number of independent capacitors and resistors in the network. For example, if there are three capacitors and two resistors in the network, then there are five degrees of freedom.

Once you have the number of degrees of freedom, you can use the equipartition theorem to calculate the total noise charge or voltage across all the capacitors. The total noise charge is equal to the number of degrees of freedom times 1/2kT. So, if there are five degrees of freedom, then the total noise charge will be 5*1/2kT.

Hope this helps!