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.
Figure 1. | The transfer function for a second-order recursive digital filter has coefficient values that yield a lowpass, highpass, band-reject, or bandpass-transfer function. |
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 A_{S} are the coefficients of the denominator polynomial of the transfer function, and the B_{S} 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, f_{S}, relates to the transmission-line delay as t = 1/f_{S}. 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:
Figure 2. | In 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. |
In this case, the transmission-line delay is 1/6000 = 166.67 µsec. If you additionally specify an impedance, Z, of 1 Ω for the transmission line, then the parameters for the transmission line are Z_{0} = 1 Ω, 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.
Figure 3. | In this PSpice simulation, the digital bandpass filter uses transmission lines as delay lines. |