Analyzing Operational Amplifier Circuits with MicroCapEE210 – Circuits and SystemsTony RichardsonIt is relatively easy to simulate operational amplifier circuits using MicroCap. The inverting amplifier shown in Figure 1 will be used as an example.+––++vo–viRf = 10 kΩRi = 1 kΩRo =2 kΩFigure 1: An Inverting AmpliferThere is not a MicroCap model that is exactly equivalent to the ideal op amp, but we can easily build a model based on the equivalent circuit shown in Figure 2.+––+v1v2vov1v2vo–vd+RiA vdRoFigure 2: An Op Amp and An Equivalent CircuitThis equivalent circuit does a very good job of modeling an op amp in DC or low-frequency circuits. An even simpler equivalent circuit can be obtained by letting Ri be infinite and Ro be equal to zero. This simpler equivalent circuit is shown in Figure 3.+––+v1v2vov1v2vo–vd+A vdFigure 3: Simplified Equivalent Op Amp ModelFigure 4 shows the MicroCap simulation of the inverting amplifier circuit in Figure 1. This simulation uses the simplified model in Figure 3 with open-loop gain A = 2 × 105.10/09/07 Page 1 of 4Figure 4: Simulation using Simplified Op Amp ModelNotice that the output voltage in the simulation is -9.999 V which is nearly the same as the ideal op amp theoretical value of -10 V. The input differential voltage vd is -49.997 μV. The ideal op amp value is 0 V.Instead of building op amp models using dependent sources, it is much easier to use the MicroCap supplied op amp models. Just click on the op amp icon in the component menu toolbar. After placing the op amp in the circuit, the window shown in Figure 5 will appear. (The bottom of this window has been intentionally cropped.) In this window we select the particular op amp model that we want to simulate. In Figure 5 the LM741A has been selected from the menu on the right side of the window.The values in the bottom half of the window are parameters of the particular op amp selected. We will only discuss the LEVEL parameter. In the windows the LEVEL parameter has been set to 1, the default value is 3. When LEVEL is 1, a simple model that uses a voltage-controlled current source with a finite output resistance and open loop gain is used. This is similar to the model shown in Figure 2. This model will produce results that agree well with calculations based on the ideal op amp. More importantly, it does not adequately model the behavior of a real op amp at high frequencies or if the op amp is in saturation. Simulation results are shown in Figure 6. Again there is good agreement between theoretical results using the ideal op amp and simulation results.The LEVEL 3 model provides the most accurate results. It models positive and negative slew rates, finite gain, AC and DC output resistance, input offset voltage and current, phase margin, common mode rejection, unity gain bandwidth, three types of differential input, and realistic output voltage and current limiting. Simulation results are shown in Figure 8. Again there is good agreement between simulated and theoretical results.10/09/07 Page 2 of 4Figure 5: MicroCap Op Amp Model Selection WindowFigure 6: MicroCap Simulation Using the LEVEL 1 Model10/09/07 Page 3 of 4Figure 7: MicroCap Op Amp Model Selection WindowFigure 8: MicroCap Simulation Using the LEVEL 3 Model10/09/07 Page 4 of