On the modeling of log-domain LC-ladder circuits

Log-domain filters are an intriguing form of current-mode circuits. They are universally regarded as externally-linear internally-nonlinear circuits in which each bipolar junction transistor operates in the forward-active mode at all times and acts as a static exponential non-linearity relating the collector current to the base-emitter voltage. This paper establishes sufficient conditions for the external linearity of single- ended and differential log-domain LC ladder circuits. However, differential log-domain LC ladder floating- capacitor circuits exhibit externally-nonlinear behaviour. Modeling the transistors as static non- linearities, the equations of these circuits are unable to describe their nonlinear behaviour. Simulations show the strong influence of parasitics on these dynamics.