David Báez-López, Department of Electrical and Computer Engineering, Ryerson University,

Toronto, ON, Canada; Edited by Charles H Small and Fran Granville -- EDN, 4/17/2008
Designers use PSpice mainly to simulate analog circuits. However, you can also simulate

digital filters with it. The main components in a digital filter are delay elements, adders,

and multipliers. Although you can implement adders and multipliers using operational

amplifiers, you can simulate a delay element with a transmission line. The transmission line

in PSpice is a long-forgotten element that can realize a delay of seconds.

For example, Figure 1 shows a second-order recursive digital filter. The transfer function

for this filter is:

where H(z) is the digital-filter-transfer function, z is the z-transform variable, the As

are the coeffieients of the denominator polynomial of the transfer function, and the Bs are

the coefficients of the numerator polynomial of the transfer function. You can obtain the

coefficient values with software available for filter design (Reference 1). The sampling

frequency, fS, relates to the transmission-line delay as t=1/fS. For example, a bandpass

digital filter with a 3-dB passband from 900 Hz to 1 kHz, a sampling frequency of 6 kHz, and

a Butterworth characteristic yields the following transfer function:

In this case, the transmission-line delay is 1/6000=166.67 µsec. If you additionally specify

an impedance, Z, of 1Ω for the transmission line, then the parameters for the transmission

line are Z0=1Ω, and t=166.67 µsec. Figure 2 shows the PSpice circuit. The VCVSs (voltage-

controlled voltage sources), E1 and E2, simulate voltage followers, and VCVSs E3 and E4 and

the resistors that connect to them simulate summers. Figure 3 shows the results of the

simulation.

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Reference
López, David Báez, “Windows Based Filter Design with Winfilters,” IEEE Circuits and

Devices, Volume 13, 1997, pg 3.