3 - University of Minnesota Duluth
EE 3235 Electronics II
|Experiment # 8 |
Understanding pole compensation
Note: (1) You need to use the lab material and circuit from lab 7.
(2) Some Important Background Information is attached at the end of the lab.
3. Dominant Pole Compensation
Next, you will compensate the amplifier as shown in Figure 3.
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Figure 3. Dominant Pole Compensated Feedback Amplifier
First, using your measured component values, derive an expression for A(s), which is the open-loop transfer function for your based amplifier in Figure 3 from Lab7.
Then determine the feedback coefficient β for the feedback amplifier in Figure 3 (you may need to check Lab7 as well for that purpose and you should get β=0.1, as 1/ β is about equal to the closed-loop DC gain).
Subsequently, based on the measured magnitude plot and phase plot from Lab 7 for the base amplifier, determine the dominant pole frequency so that a 45 degree phase margin is achieved (Note that if your phase measurement starts from 180 degrees at DC, then subtract the phases by 180 degrees to make sure it starts from 0 degrees at DC).
After you obtain the dominant pole frequency, compute the value of Cx Measure the value of Cx and wire it (using the closest available standard value) into the circuit between terminals x and y, as shown in Figure 3.
Now apply a square wave to the input at a level low enough to prevent distortion on the output. Sketch Vout(t), and record the input level(s) as well as the steady state value of output voltage and the first and second (+ and -) peaks. Also, measure the ringing period and the time from the point at which the output begins to change to the first peak.
Now, check the sensitivity of the amplifier closed loop gain to the open loop gain by temporarily changing R2 in Figure 1 to 20 K (a 100% change) and measuring the closed loop gain.
4. Dominant Pole Compensation with Zero Cancellation
A slightly more complex compensation scheme is illustrated in Figure 4. As detailed in the background material for this experiment, compute the required values of Rx and Cx. Using the nearest available standard values (measure them!), wire the circuit of Figure 4, and repeat the measurements outline in Section 3.
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Figure 4. Zero Cancellation Compensation
Change the fixed resistor Rx to a variable one (with a potentiometer or decade box) and repeat the above measurement after adjusting Rx for optimum performance, that is minimum overshoot consistent with smallest ringing and fastest rise time. Now make Cx variable (use a decade capacitance box) and simultaneously adjust Rx and Cx for optimum performance.
5. Cadence simulation
Simulate your circuit in Figure 3 and 4 in Cadence. Compare with your measure results. Note that now you need to do also transient analysis in addition to AC analysis. Also, for transient analysis, as discussed in class, it is preferred to give a pulse with a time-duration of 50 to 100 times of 0.35/B, where B denotes the bandwidth (the closed-loop bandwidth). What is the bandwidth B for the closed-loop amplifier? (B is the dominant pole frequency you derived before, why?).
Cadence tips
1) Use VSIN from AnalogLib for AC/frequency analysis (note that AC amplitude is set to 1 V)
2) Use VSOURCE from AanlogLib for transient analysis (select PULSE for type and set the pulse properly).
3) Use dB20( ) calculator statement if you want to convert the gain into dB format (to do that click Output in the analog design window, select setup, give a name for gain, type in dB20(VF(“/Vout”) supposing you denoted your output voltage by Vout, and finally click ok). Note the simulation results will give you the gain in terms of dB instead of the numerical value.
4) Similarly, use phase( ) calculator statement if you want to find phase of the output, note that you need to subtract 180 to get the actual phase.
Feedback Amplifier Compensation: Background Material
Dominant Pole Compensation with Pole/Zero Cancellation
Let the uncompensated base amplifier gain function A(s) of this experiment be given in the general format shown in equation (1) bleow:
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In that equation, note the third OpAmp stage has the DC/low-frequency gain equal to – R0/R6 (assuming that the input voltage of the third OpAmp stage is the voltage across C3).
Now add-on of the compensation circuit of shown in Figure 4 results in the third OpAmp stage circuit shown in Figure 5. You should analyze this circuit and convince yourself that its transfer function is H(s) shown below
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Where
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Figure 5. Third Stage Circuit with Zero-Canceling Compensation Network.
Then, the gain function of the overall based amplifier with the add-on compensation circuit becomes:
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Where Ao, (1, (2, and w3 are the same parameters as those in equation (1). The procedure now is to adjust Rx and Cx such that (z = (1. This removes the pole at (1, and the remaining gain function can be compensated by using (0 as a dominant pole relative to (2, which is larger than (1. Therefore, (0 can be larger than is the case with simple dominant pole compensation. You can estimate the Rx and Cx using the following two equations:
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