Power Electronics

# Program Streamlines Power Converter Simulation

To meet the need for a simple Windows-based circuit-simulation program, a new software package called Power Circuits 101 is available for modeling electrical and electronic circuits. The software overcomes certain limitations of existing simulation programs, which are larger and more complex. Although such programs are fine for testing a production design, they are cumbersome to use during the concept stage.

Power Circuits 101 consists of two programs, Linear Circuits 101 and Transient Circuits 101.[1] Entering a circuit in these programs is like building a breadboard circuit. The circuit is entered into a formatted net list and then activated.

The linear program computes node and component voltages for dc and ac models, as well as gain and phase versus frequency (Bode) plots. The transient program produces graphic waveforms of circuit operation, while simulating both fixed- and variable-frequency switching circuits, such as power converters. The program allows ac, dc and pulse generators to run simultaneously. The resulting plots of multicycle operation then display the overall response of a circuit. At the same time, the cycle-by-cycle waveforms can be observed.

Because the linear and transient programs are not SPICE-based, complex-analysis modes needn't be selected. The linear program's method of solution is a common routine. The transient method employs routines developed by the writer. Generally, convergence isn't a problem because the computations don't diverge from the correct solution. The exception is for a circuit with positive regeneration and a loop gain greater than one. However, the program detects this condition and allows the user to correct the circuit or use a smaller time step to lower the loop gain.

These general-purpose programs are optimized for the development and analysis of power converters. As a demonstration, a discontinuous current converter circuit is modeled here. This converter isn't high in efficiency, but it has other attractive features: It's short-circuit proof, compact and can go from no output to full output and back in one cycle.

### Circuit Analysis

Fig. 1 shows the results of modeling a discontinuous current converter. The program in use, Transient Circuits 101, demonstrates a discontinuous converter in a closed-feedback-loop configuration. The converter runs with an 80-kHz clock, while the load is switched from 10% to 90% at a 1-kHz rate. The left plot is the converter output current, and the Node 10 referred to here is the output node of an ammeter. The right plot is the output voltage measured across the output filter C1.

In these plots, the units are normalized to microseconds, microFarads and microHenries. Under the view menu, the graph data can be scanned. In this case, the data shows the output voltage peak-to-peak regulation is less than 0.5 V or 0.7%. The “average” in the graph title indicates that this is a plot of the average value for each cycle. The plots show averages of data taken over 80 cycles.

Viewing Fig. 1, the lower right grid contains the circuit net list. Similar to a spreadsheet, the white box at its top left is a text box for editing this grid. The blue box at top center contains prompt information and changes as the grid boxes are selected. The left grid contains the Parameter information that controls the program operation. This grid has its own edit box at the top.

In Fig. 1, the onscreen features include a normal Windows menu bar at the top, a title block for the user to identify the application, and an automatic printing of the file name and path. In addition, a Components menu provides a quick list of the program's model parts and access to the part descriptions.

On completion of a program run, the stored data contains the point-to-point capacitor voltages, inductor currents and user-selected node voltages of the last cycle along with average values for the whole run. These values can be viewed by selecting them in the Graph A and Graph B menus without rerunning the program. The data can then be saved into a comma-delimited file for further graphing and analysis in a spreadsheet program.

Fig. 2 shows the basic converter circuit being modeled. (Note that schematic capture isn't included in the program.) The input is a half-bridge inverter but could have been a full bridge just as well. Transformer saturation with a full bridge isn't a problem, as the inductor L1 forces balance of the transformer magnetizing current. L1 limits current flow and acts as a no-loss impedance between the input inverter and the output rectifier. The rectified output is a relatively high-impedance current source; thus, the filter capacitor C1 is directly across the rectifier output.

The model switches used in this schematic are normally open and frequency controlled by the program clock. Their set parameters are cyclic time period, percent of cycle duty and percent of cycle delay.

The goal here is to design a converter that will provide 7 A at 70 V. The program's opening window gives the user a choice of programs and some information to help in the selection. At this point in the analysis, the transient program is needed. Selecting Transient Circuits 101 on the opening window brings up the program.

Fig. 3 shows the data entry of the circuit in Fig. 2 and the resultant plots. The program has run 240 cycles, starting with the output filter capacitor at 0 V. The cycle-by-cycle inductor current is displayed in the left graph and the output voltage versus time in the right graph. The inductor value L1 is adjusted here by trial and error to produce the 70-V output with dead space between half cycles to allow for regulation.

The voltage plot is close to a simple RC time constant. This shows that the converter has a simple output characteristic that can be modeled as a voltage source and series impedance, or a current source and parallel impedance. The latter is the writer's choice.

To analyze the operating parameters of this converter, a pulse width modulator (PWM) drive and some test voltage sources have been added to the circuit (Fig. 4.)

The modulator is made up of the V1 Ramp generator and logic components U3 through U7. The Ramp generator and the PRF generator are separate, but they are set to the same frequency in the circuit net list. The power switches U1 and U2 are a program feature to simplify modeling. They eliminate the need for run time-consuming drive circuits. The switch inputs are a logical AND. Also, the inputs are isolated from the circuit. Logic nodes start at number 51 and are computed in a separate routine — not with the main network.

The Fig. 4 model measures the change in output current for a change of input voltage. From this data, current gain is calculated. Furthermore, the model measures the change in output current for a change of output voltage, using this data to calculate the circuit's output impedance.

In this example, the V2 REF is set to 6.9 V, while the Vdc Out is set to 70 V. When the program is run, the output current at meter M1 is 7 A. Next, the V2 REF input signal is increased from 6.9 V to 7.3 V and the program is rerun. The output current increases by 0.7 A, giving a gain of 1.75 A/V. Subsequently, the input voltage is reset to 6.9 V and the Vdc Out voltage is changed to 73 V.

After running the program again, output current has decreased by 0.8 A. Allowing for the parallel load impedances, the output impedance is 3.7 Ω. With this gain and impedance information, a linear model can be developed for a gain and phase versus frequency study.

Fig. 5 shows the linear model. The converter is modeled by a voltage-dependant current source, GCONV, and its shunt output impedance, RZ Out. Capacitor C1, the load resistor and a 10-to-1 resistor feedback divider make up the load. A feedback amplifier and ac drive voltage complete the open-loop circuit.

Next, the Transient program is closed and the Linear Circuits 101 program is opened. Although the format of this window is similar to that of the transient program, this program is different in its offering of six operating modes: dc, ac, frequency dB, frequency polar, gain dB and gain polar.

The dc and ac modes compute all the node voltages and component voltages in one run. The ac mode is for a single frequency. The frequency dB and frequency polar modes plot a single-node voltage and phase over a set range of frequencies. Finally, the gain dB and gain polar modes plot the gain and phase between any two node points over the same range of frequencies.

Fig. 6 shows the linear program window in the gain dB mode. The circuit list is entered with the usual prompts and component menu aide. In the parameter grid, “>” characters indicate the required inputs. The reference node is selected as 1. The gain is the voltage at Output Node 3 divided by the voltage at Input Node 4. The remaining inputs set the frequency range and number of plot points.

To run the program, enter the Run menu or press F8. The graph will appear as in Fig. 6, except the phase will be starting at 180 degrees because of the negative feedback requirement. Selecting “Invert Phase” in the Options menu will switch the phase data 180 degrees for viewing as lead-lag information.

At this point, the feedback amplifier gain and the size of the output capacitor C1 and high-frequency roll off capacitor C2 are selected. Resistors R3 and R4 set the overall low-frequency gain in this example at about 35 dB. The output capacitor C1 sets the first break point followed by the C2 break point.

This converter operates at a clock frequency of 80 kHz. Therefore, the gain curve should cross the 0-dB line typically at or lower than the clock frequency divided by 10 (8 kHz). At the 0-dB crossover, the corresponding phase shift should be between -90 degrees and -135 degrees. The curve shown in Fig. 6 meets these criteria, so the model is ready for a closed-loop transient test.

An in-depth study of the circuit's gain and output impedance would show that these values change at different operating points. However, the gain and output impedance track each other so the initial break point will vary; this will result in only small changes in the 0-dB crossover frequency.

Fig. 7 shows the schematic for the model used in the closed-loop transient test. In the load circuit, the values of resistors R1 and R2 have been lowered to make a 10% load. The RLOAD value is an 80% load and is switched in and out by a frequency-controlled switch. The frequency for the switch is set to 1 kHz with a 50% duty cycle.

A Zener diode has been added to the output of the op amp to prevent overcharging of C2 during periods when the circuit is out of regulation. An overcharge would delay the regulation recovery.

The transformer used in this model is an ideal transformer with no magnetizing current or leakage inductance. With a real transformer, the leakage inductance is in series with inductor L1 and becomes part of the circuit. No switching losses are caused by leakage inductance, making this circuit suitable for high-voltage applications where leakage inductance can be high. The inductance of L1 is often lowered to compensate for the transformer leakage.

Fig. 1 is the culmination of this exercise, showing the circuit's fast output current response to an 80% 1-kHz load change. Moreover, this circuit demonstration shows the flexibility of the transient program in that multiple-cycle frequency operations can be modeled. The limits of the Power Circuit 101 programs are only those of the engineer's imagination.

Even systems with multiple couplings between inductors can be modeled with this package. Some simulation programs discourage such systems because they produce incorrect computations even when seemingly correct coupling factors are selected. However, in the Power Circuit 101 package, a routine is included for testing mutual-coupling coefficients so transformers with more than two coils can be safely modeled.

### References

• This program package is distributed by e/j Bloom Associates Inc. Visit www.ejbloom.com for more information.