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Industrial Strength Simulation
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News:

Spectrum Software has released Micro-Cap 11, the eleventh generation of our SPICE circuit simulator.

For users of previous Micro-Cap versions, check out the new features available in the latest version. For those of you who are new to Micro-Cap, take our features tour to see what Micro-Cap has to offer.

 

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Stability Analysis

 

Stability analysis uses either the Middlebrook or Tian method to calculate the closed loop Gain Margin and Phase Margin. To use this method the user chooses a place in the circuit to insert a probe. The program breaks the loop at this probe point and measures the appropriate parameters needed in the calculation. To demonstrate the use of Stability Analysis we'll use the file, STABILITY.CIR. It looks like this:

Circuit to demonstrate Stability analysis



In this feedback amplifier we want to find the gain and phase margins. Press Alt+0 to select Stability Analysis. Press F2 to start the run and you'll see this:

Current Limit Test Circuit
The Gain Margin is measured at 45.87 dB and the Phase Margin at 87.38 degrees.

How does it work? The user inserts the probe component at any point in the loop. At the point of this probe, MC11 replaces the probe component with suitable voltage and current sources to measure closed loop voltage and current gains. During the run the variable Loop is stepped from 1 to 2 and the sources Vinj and Iinj take on these AC values:

if Loop==1 iol = 0 vol = 1
if Loop==2 iol = 1 vol = 0

The Tian method uses the following equation to determine the margins:

LoopGain = -1/(1-1/(2*(I(Vinj)@1*V(ol)@2-V(ol)@1*I(Vinj)@2)+V(ol)@1+I(Vinj)@2))

The equation in the LoopGain variable was derived from the Tian article. It uses the step selection operator @ to combine the waveform results from different steps. For example:

V(ol)@2 specifies the voltage at node ol during the second step of the simulation.

I(Vinj)@1 specifies the current through the source Vinj during the first step.

Together, the quantities V(ol)@1, V(ol)@2, and I(Vinj)@1 determine the variable LoopGain and its plot is examined to determine the gain and phase margins.

The gain margin is computed as follows:

Gain Margin = -dB(LoopGain) where Phase(LoopGain) equals -180.

The phase margin is computed as follows:

Phase Margin = 180+Phase(LoopGain) where dB(Loopgain) equals 0.

For those who would like to read more of the theory behind these methods, we recommend these references:

1) Tian Method: "Striving for Small-Signal Stability", Michael Tian, V. Visvanathan, Jeffrey Hantgan, and Kenneth Kundert, Circuits & Devices, January 2001.

2) Middlebrook Method: "Measurement of Loop Gain in Feedback Systems", David Middlebrook, International Journal of Electronics (volume 38, no. 4, pages 485-512, April 1975).

 
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