Theory of intermediate and high injection noise in transistors

A theory is given of input, output, and cross-correlation of noise generators in transistors, operating at intermediate injection and at high injection. First, an approximate formula is derived for the carrier density spectra in a narrow quasi-neutral base. From this the noise sources in Z- and h-representation are derived, adding coherently the contributions of the junction voltages and the bulk drops. The open input noise voltage (for shorted collector) consists of ‘apparent junction noise’ which resembles in form the low injection result, plus current noise resulting from the conductivity-modulated impedance Z_bs in the longitudinal current path emitter-collector. This current noise has the form of amplified shot noise; it is partially correlated with the apparent junction noise. At the output the noise is represented by a short-circuit current generator (for open emitter) parallel to the collector admittance. It consists of a shot noise contribution which for intermediate injection is still close to the standard result, plus a quasi-thermal noise contribution due to the Early effect of the output admittance. A significant change is predicted for the cross correlation of the noise sources. This is caused by two effects; first there is no cancellation of thermal and shot noise contributions of the junction correlation noise, as for low injection and, secondly, input and output are related by the current noise of Z_bs. At very high injection only the latter remains and the correlation impedance is shown to be ≈ β_fZ_bs where β_f is the common emitter current gain. Several aspects of this theory are in fair agreement with intermediate injection noise measurements by Tong and van der Ziel.