An Alternative Approach to Bode’s Noise Theorem

Bode's noise theorem is an efficient way of determining the total noise in passive, linear RLC networks. This theorem has been traditionally derived in the frequency-domain using contour integration. We present an alternative (and more intuitive) derivation of Bode's theorem. Our technique works in the time-domain and exploits energy conservation. Finally, we apply our technique to determine the autocorrelation function of the noise at the output of the network.

I. Introduction

A circuit designer is often required to evaluate the total integrated noise in electrical networks with linear passive components. The first (and perhaps the most common) network in which the total noise is evaluated is the humble RC-network shown in Fig. 1(a). Fig. 1.

(a) First and (b) second-order RC-networks.