Hello, and welcome to Part 3 of the TI Precision Labs on Op Amp Stability. The previous videos discussed the types of issues that op amp stability can cause in production systems, how to identify stability issues in the lab, and a review of Bode plots and stability theory. This video will explain how to perform open loop SPICE simulations to obtain the rate of closure and phase margin of op amp circuits. Please be sure you've completed the lectures and problem sections for Op Amp Bandwidth 1 through 3 before proceeding. 

The AOL, 1 over beta, and loop gain curves required for rate of closure and phase margin measurements cannot be obtained from a circuit in a standard closed loop configuration. To generate these curves, the feedback loop of the amplifier needs to be opened up or broken. Then a small signal source is used to excite the high impedance side of where the loop was broken. Measurements can then be taken at the op amp inverting input, Vfb, and output, Vo, which will be used to derive the desired curves. 

However, simply breaking the feedback loop of a circuit will not produce correct simulation results. Without a proper DC bias, the output will saturate to one rail or the other, reducing the performance of the output stage. As shown here, the op amp output is near the positive rail, resulting in erroneous AOL and loop gain curves. 

To properly generate the open loop curves in SPICE, the circuit being simulated must have a closed loop feedback path at DC while being open for all AC frequencies. The circuit at the top left shows the desired DC Circuit, where the L1 switch is closed, and the C1 switch is open. A closed loop circuit at DC allows the output to be biased to a proper DC operating point, commonly mid-supply. 

The circuit at the bottom left shows the desired AC circuit, where the L1 switch is open and the C1 switch is closed. With the loop open for AC frequencies, the stimulus can be applied to generate the open loop curves. Thankfully, there's a straightforward way to create a circuit that meets both the DC and AC criteria using the ideal properties of SPICE components. 

Switch L1 is replaced with a 1 terahenry inductor, and switch C1 is replaced with a 1 terafarad capacitor. At DC, L1 is a short and C1 is an open circuit, providing a proper DC operating point. For all AC frequencies, L1 is an open circuit and C1 is a short, resulting in the proper open loop AC connections. Therefore, here is the recommended open loop SPICE circuit configuration for op amp circuits. 

The feedback loop is broken between the op amp output and the feedback elements. The AC signal source is injected into the feedback network and measurements are taken at the output, Vo, and the feedback node, Vfb. With the feedback loop broken as shown, the equations for generating the desired curves are as follows. Loaded AOL equals Vo divided by Vfb. 1 over beta equals 1 over Vfb. Loop gain equals Vo. 

Several common circuits ready for open loop simulation are provided here. These circuits can be used to review where to break the loop in many common circuit configurations. For proper stability analysis, any output loads must remain directly on the output of the op amp, and should not be placed on the other side of the inductor. Doing so would remove the effects that the output load has on the op amp output. 

Before checking the AC behavior of the circuit, a quick check of the DC operating point should be performed. Simply click Analysis, DC Analysis, Calculate Nodal Voltages to do this. The Vfb voltage should roughly equally the input offset voltage, or Vos of the op amp, while Vo should show Vos multiplied by the closed loop gain. 

Once you verify the DC operating point of the circuit, performing an AC transfer characteristic analysis over the op amp bandwidth. Click Analysis, AC Analysis, AC Transfer Characteristic to do this. Set the start and end frequencies and then press OK to run the simulation. The results for the Vo and Vfb probes will be displayed after the simulation is complete. 

To add the desired curves for open loop analysis, click the Post Processor button in the Result window. Then write the proper equations for AOL and 1 over beta in the line editor, name them, and then create the curves. A new curve can be added for loop gain, but since it equals Vo, which is already displayed, this is not necessary. 

Please note, the text editor will not allow the entry in the New Function Name box to begin with a number or have special characters. Therefore, 1 over beta or 1 beta are not allowed. We recommend to use Beta1 for the 1 over beta curve name. 

Here's what the results will look like with the new curves added. The next steps will format the results to make them easier to view. Click View, then Show/Hide Curves. Select only the curves Vo, AOL, and Beta1. Then double click the x-axis and y-axis to bring up the Set Axis window. Change the x-axis to a logarithmic scale with eight divisions, a lower limit of 1 hertz, and an upper limit of 10 megahertz. Then change the y-axis to a linear ndB scale with nine divisions, a lower limit of negative 40 dB, and an upper limit of 120 dB. 

The final step is to measure the phase margin on the curves. First, place the cursor on the loop gain curve and then type 0 into the y text box to set the cursor to fc frequency. Then either place the second cursor on the loop gain curve to directly measure the loop gain phase, or as shown here, click the Legend button and place it on the screen to display the magnitude and phase of all of the visible curves at fc. The phase margin is the phase of loop gain at fc, which is 87.7 degrees in this example. 

In summary, this video described the methods to break the loop of standard op amp circuits and perform open loop AC analysis. The next video will review indirect methods to test for op amp stability, including transient and AC transfer function measurements and simulations. Thank you for your time. Please try the quiz to check your understanding of this video's content.