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examples/Educational/FRA/ReadMe.txt

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+                       Frequency Response Analysis
+
+These examples show to how to extract the small-signal, AC open-loop
+gain from time-domain, closed-loop simulations.  The technique is a
+subset of the method shown in ../LoopGain.asc and ../LoopGain2.asc.
+The method assumes that the input impedance of the error amplifier is
+infinite so that the loop gain can be computed solely by the voltage
+loop gain.
+
+The open-loop gain is computed from the closed-loop system by inserting
+a perturbing voltage source in the loop and measuring how well the
+perturbation is servoed out of the the loop via the feedback.  The
+open-loop gain is given by the ratio of complex voltages at either side
+of the perturbing voltage source.
+
+But since the SMPS macromodels are implemented as time-domain models
+that include detailed switching information but don't include
+continuous-time(average) equivalents, the complex voltage is determined
+from Fourier analysis of a time-domain sine wave perturbation.
+
+A script of .measure statements is used to perform the Fourier analysis
+and computer the open-loop response.  To use this script into your own
+SMPS design, follow these steps:
+
+1.  Place these .measure statements on your circuit as a SPICE
+    directive:
+
+     .measure Aavg avg V(a)
+     .measure Bavg avg V(b)
+     .measure Are avg  (V(a)-Aavg)*cos(360*time*Freq)
+     .measure Aim avg -(V(a)-Aavg)*sin(360*time*Freq)
+     .measure Bre avg  (V(b)-Bavg)*cos(360*time*Freq)
+     .measure Bim avg -(V(b)-Bavg)*sin(360*time*Freq)
+     .measure GainMag param 20*log10(hypot(Are,Aim) / hypot(Bre,Bim))
+     .measure GainPhi param mod(atan2(Aim,Are)-atan2(Bim,Bre)+180,360)-180
+
+2.  Insert a voltage source in the feedback loop under analysis.  Give
+    this voltage sourse the value SINE(0 5m {Freq})
+
+3.  Place a SPICE directive on the schmatic that defines Freq:
+
+     .param Freq=10K
+ 
+4.  Run a .tran command to see how long it takes your circuit to come to
+    steady state and then edit the .tran command so that data isn't saved
+    until this time.
+
+5.  Rerun the .tran command to do the analysis at the frequency defined
+    with the .param statement of step 3.
+
+6.  Execute menu command View=>SPICE Error Log to see the results of this
+    analysis.  The open-loop response magnitude is given by GainMag[dB]
+    and the phase is given by  GainPhi[<5B>].
+
+You can iterate the param Freq to zero dB.  That frequency is the loop
+crossover frequency and phase margin will be reported as GainPhi in the
+error log.
+
+You can set up a .step statement to sweep the parameter Freq.  Then you
+can plot the open-loop response be executing menu command
+View=>SPICE Error Log, and then right mouse clicking and executing menu
+command "Plot .step'ed .meas data"  Answer yes to the dialog that asks
+if LTspice should combine the real .meas data to complex data.  Then you
+can plot the quanity gain to get a Bode plot the open-loop response of
+the system.
+
+--Mike