Analytical expression for the equivalent input noise current spectral density of HBT distributed amplifier based optical receivers

In this paper we present the derivation of an analytical expression for the equivalent input noise current spectral density (EINCSD) of a combined p-i-n photodiode and HBT distributed amplifier (DA) based optical receiver. This expression takes into account the main HBT thermal and shot noise sources and also includes correlation effects between the latter. Noise from the DA idle port terminations and from the photodiode series resistance are also embodied within the expression. Derivation of the EINCSD expression is based on the analytical framework reported in our earlier publication which allows for incorporation of the effects of reflections from nonideal artificial transmission line (ATL) terminations. Accuracy of the derived expression is assessed by comparison with results from simulations and any discrepancies that arise are discussed. Practical ways in which the EINCSD expression can be utilised to aid the design of HBT DA based optical receivers are indicated