Time-constant control analysis of microwave differentiators

A model describing the time constant of a wide-band microwave differentiator is presented. The time constant combined with the amplitude response dictates the circuit behaviour of a microwave differentiator. By representing the formulations of differentiators in the discrete-time (or Z) domain, the authors implement the differentiators with equal-length transmission lines. The approach method consists of discrete signal processing techniques, transfer functions in the Z domain and optimisation algorithms. Three differentiators with different time constants and frequency bands are built and tested. The experimental results are in good agreement with theoretical values.