A “Nyquist-Like” Noise Theorem for Linear Periodically-Switched RLC Networks

Nyquist, in his seminal paper published almost a hundred years ago, showed that the voltage noise spectral density of a one port consisting of resistors, capacitors and inductors is given by 4kT Re(Z(j2πf)) where Z(j2πf) denotes the driving-point impedance of the one port. In this work, we derive a result for one ports that consists of inductors, capacitors, resistors and periodically-operated switches. The derivation exploits power conservation and the properties of adjoint linear periodically time-varying (LPTV) networks.