Simple and accurate formulations are employed to represent discrete-time infinite impulse response (IIR) processes of first-order differentiator and integrator. These formulations allow them to be eligible for wide-band applications. Both first-order differentiator and integrator have an almost linear phase. The new differentiator has an error of less than 1% for the range 0-0.8π of normalized frequency and the new integrator has an error of less than 1.1% for the range 0-0.8π of normalized frequency.

In this paper, a new formulation of equal-length three-section open stubs having two zeros located on the unit circle and one zero at z=-1 (θ=π) in the Z-plane is presented. In particular, new filter configurations consisting of equal-length two-section open stubs, cascade lines, open stubs, and three-section open stubs are employed to emulate the discrete-time filters. To examine the validity of our formulation, we realized two discrete-time Chebyshev type II low-pass filters in the form of microstrip lines. The frequency responses of these two filters are measured to validate this new formulation.

A new formulation of equal-length asymmetric parallel coupled line (APCLs) having zero at z=-1 (θ = π) is employed to study band-stop filters. Such representations offer additional flexibility in the design of filter circuits through two extra variables. An optimization algorithm is used to tune the characteristic impedances of APCLs so that the transfer function of the signal line is close to the system function of an ideal prototype filter. Two band-stop filters are realized in the form of microstrip lines and their frequency responses are measured to validate this new formulation.