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Simple and accurate formulations are employed to represent discrete-time infinite impulse response processes of both first- and second-order differentiators in the Z-domain. These formulations, in conjunction with the representations of transmission-line elements in the Z-domain, lead to transmission-line configurations that are eligible for wide-band microwave differentiators. Both the first- and second-order differentiators in microstrip circuits are implemented to verify this method. The experimental results are in good agreement with simulation values.