Resistance and capacitance minimization in low-pass RC ladder networks

Conditions are given for low-pass ladder networks that realize a voltage transfer function with minimum resistance and capacitance. In particular, it is shown that to minimize the weighted sum of resistance and capacitance, the open-circuit ladder is either symmetrical or antimetrical depending upon the structure considered. For either structure, the optimum ladder network follows directly from the prescribed voltage transfer function. Results are also given for low-pass ladders double-terminated in equal resistances and terminated in a resistor at the output.