EXPERIMENT 9 Problem Solving: First-order Transient Circuits I. Introduction In transient analyses, we determine voltages and currents as functions of time. Typically, the time dependence is demonstrated by plotting the waveforms using time as the independent variable. PSPICE can perform this kind of analysis, called a Transient simulation, in which all voltages and currents are determined over a specified time duration. To facilitate plotting, PSPICE uses what is known as the PROBE utility, which will be described later. As an introduction to transient analysis, let us simulate the circuit in Figure 1, plot the voltage v C (t) and the current i(t). Figure 1. The inductor and capacitor parts are called L and C, respectively, and are in the ANALOG library. The switch, called SW_TCLOSE, is in the EVAL library. There is also a SW_TOPEN part that models an opening switch. After placing and wiring the switch along with the other parts, the Schematics circuit appears as that shown in Figure 2. Figure 2. PSPICE schematic To edit the switch s attributes, double-click on the switch symbol and the ATTRIBUTES box in Figure 3 will appear. Deselecting the Include Non-changeable Attributes and Include ELEC 2110 Experiment 9 1 of 9
System-defined Attributes fields limits the attribute list to those we can edit and is highly recommended. The attribute tclose is the time at which the switch begins to close, and ttran is the time required to complete the closure. Switch attributes Rclosed and Ropen are the switch s resistance in the closed and open positions, respectively. During simulations, the resistance of the switch changes linearly from Ropen at t = tclose to Rclosed at t = tclose+ttran. When using the SW_TCLOSE and SW_TOPEN parts to simulate ideal switches, care should be taken to ensure that the values for ttran, Rclosed, and Ropen are appropriate for valid simulation results. In this example, we see that the switch and R1 are in series; thus, their resistances add. Using the default values listed in Figure 3, we find that when the switch is closed, the switch resistance, Rclosed, is 0.01 Ω, 100,000 times smaller than that of the resistor. The resulting series-equivalent resistance is essentially that of the resistor. Alternatively, when the switch is open, the switch resistance is 1 MΩ, 1,000 times larger than that of the resistor. Now, the equivalent resistance is much larger than that of the resistor in Figure 1. Figure 3. Switch ATTRIBUTE box Each component within the various Parts libraries in PSPICE has two or more terminals. Within PSPICE, these terminals are called pins and are numbered sequentially starting with pin 1, as shown in Figure 4 for several two-terminal parts. The significance of the pin numbers is their effect on currents plotted using the PROBE utility. PROBE always plots the current entering pin 1 and exiting pin 2. Thus, if the current through an element is to be plotted, the part should be oriented in the Schematics diagram such that the defined current direction enters the part at pin 1. This can be done by using the ROTATE command in the EDIT menu. ROTATE causes the part to spin 90 counterclockwise. In our example, we will plot the current i(t) by plotting the current through the capacitor, I(C1). Therefore, when the Schematics circuit in Figure 2 was created, the capacitor was rotated 270. As a result, pin 1 is at the top of the diagram and the assigned current direction in Figure 1 matches the direction presumed by PROBE. If a component s current direction in PROBE is opposite the desired direction, simply go to the Schematics circuit, rotate the part in question 180, and re-simulate. ELEC 2110 Experiment 9 2 of 9
Figure 4. Pin numbers for common PSPICE parts. To set the initial condition of the capacitor voltage, double-click on the capacitor symbol in Figure 2 to open its ATTRIBUTE box, as shown in Figure 5. Click on the IC field and set the value to the desired voltage, 0 V in this example. Setting the initial condition on an inductor current is done in a similar fashion. Be forewarned that the initial condition for a capacitor voltage is positive at pin 1 versus pin 2. Similarly, the initial condition for an inductor s current will flow into pin 1 and out of pin 2. Figure 5. Setting the capacitor initial condition. The simulation duration is selected using SETUP from the ANALYSIS menu. When the SETUP window shown in Figure 6 appears, double-click on the text TRANSIENT and the TRANSIENT window in Figure 7 will appear. The simulation period described by Final time is selected as 6 milliseconds. All simulations start at t=0. The No-Print Delay field sets the time the simulation runs before data collection begins. Print Step is the interval used for printing data to the output file and has no effect on the data used to create PROBE plots. The Detailed Bias Pt. option is useful when simulating circuits containing transistors and diodes, and thus will not be used here. When Skip initial transient solution is enabled, all capacitors and inductors that do not have specific initial condition values in their ATTRIBUTES boxes will use zero initial conditions. ELEC 2110 Experiment 9 3 of 9
Sometimes, plots created in PROBE are not smooth. This is caused by an insufficient number of data points. More data points can be requested by entering a Step Ceiling value. A reasonable first guess would be a hundredth of the Final Time. If the resulting PROBE plots are still unsatisfactory, reduce the Step Ceiling further. As soon as the TRANSIENT window is complete, simulate the circuit by selecting Simulate from the Analysis menu. Figure 6. The ANALYSIS SETUP window. Figure 7. The TRANSIENT window. When the PSPICE simulation is finished, the PROBE window shown in Figure 8 will open. If not, select Run Probe from the Analysis menu. In Figure 8, we see three sub-windows: the main display window, the output window, and the simulation status window. The waveforms we choose to plot appear in the main display window. The output window shows messages from ELEC 2110 Experiment 9 4 of 9
PSPICE about the success or failure of the simulation. Run-time information about the simulation appears in the simulation status window. Here we will focus on the main display window. To plot the voltage, v C (t), select Add Trace from the Trace menu. The ADD TRACES window is shown in Fig. 9. Note that the options Alias Names and Subcircuit Nodes have been deselected, which greatly simplifies the ADD TRACES window. The capacitor voltage is obtained by clicking on V(Vc) in the left column. The PROBE window should look like that shown in Figure 10. Before adding the current i(t) to the plot, we note that the dc source is 10 V and the resistance is 1 kω, which results in a loop current of a few milliamps. Since the capacitor voltage span is much greater, we will plot the current on a second y axis. From the Plot menu, select Add Y Axis. To add the current to the plot, select Add Trace from the Trace menu, then select I(C1). Figure 11 shows the PROBE plot for v C (t) and i(t). Figure 8. The PROBE window. ELEC 2110 Experiment 9 5 of 9
Figure 9. The ADD Traces window. Figure 10. PROBE plot of the capacitor voltage. ELEC 2110 Experiment 9 6 of 9
Figure 11. PROBE plot of v C (t) and i(t). Exercises Your report must include ALL circuit diagrams, with all variables clearly labeled, and ALL calculations must be clearly shown. In addition, you will need to capture plots for the various exercises and include them in your lab report. 1) The switch in the circuit below has been opened for a long time and is closed at t = 0. Calculate i 0 (t) for t > 0. Plot i 0 (t) versus time using Matlab and include the plot in your report. Now simulate this circuit using PSPICE and plot i 0 (t) versus time. Include this plot in your report as well. ELEC 2110 Experiment 9 7 of 9
2) The switch in the circuit below has been closed for a long time and is opened at t = 0. Calculate i 0 (t) for t > 0. Plot i 0 (t) versus time using Matlab and include the plot in your report. Now simulate this circuit using PSPICE and plot i 0 (t) versus time. Include this plot in your report as well. 3) The switch in the circuit below has been closed for a long time and is opened at t = 0. Calculate v 0 (t) for t > 0. Plot v 0 (t) versus time using Matlab and include the plot in your report. Now simulate this circuit using PSPICE and plot v 0 (t) versus time. Include this plot in your report as well. ELEC 2110 Experiment 9 8 of 9
4) The switch in the circuit below has been opened for a long time and is closed at t = 0. Calculate v C (t) for t > 0. Plot v C (t) versus time using Matlab and include the plot in your report. Now simulate this circuit using PSPICE and plot v C (t) versus time. Include this plot in your report as well. ELEC 2110 Experiment 9 9 of 9