Op Amp Model - Level 3
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2nd Gain Stage
OPMODEL3_2ND_GAIN_STAGE.CR Download the SPICE file
Unfortunately, for particular combinations of slew-rate, first-pole frequency and open-loop gains, the Intermediate Op Amp Model just can't handle it. The spreadsheet coughs up a negative number for RE1 and RE2 making it impractical. So what's the fix? Normally all of the gain comes from the same stage that models the first pole frequency and slew rate. But, what if we split the gain into the two stages, by adding another gain stage? This additional stage also comes with a key ingredient - a voltage clamp to set the slew-rate. This additional degree of freedom makes any combination of slew-rate, pole frequency and gain possible. A spreadsheet below helps you arrive at the component values. If you wish, take a quick refresher tour of the Intermediate op amp Model.
For this op amp model, there are several key characteristics.
OVERALL VOLTAGE GAIN
From differential input to output buffer, you can write the gain as
The Intermediate Model works only if it passes the following test:
For combinations of high slew-rate and first pole frequency, the test returns a NO. As a result, RE1 and RE2 become negative and we put the model out with the trash. However, an additional gain stage and voltage clamp transforms this model into a useful one.
GAIN AND SLEW-RATE LIMITING
How did slew-rate limiting work in the Intermediate Model? Essentially, the clamping (or limiting) action was accomplished by the differential pair. Normally the pair's bias current I1 is split between the two transistors. However, when the input is overdriven, all of I1 flows into one transistor only. This maximum current I1 is delivered to capacitor CP1 via G1 limiting the rate at which it could charge.
However, our new model places the limiting action in the additional gain stage. Zener diodes DZ1 and DZ2 clamp the voltage to a maximum of VCLAMP = VD_ZENER + VD_ON. This maximum voltage produces a peak current in G1 and slew-rate limit of
The only trick is choosing a gain KV for this additional stage. With too little gain, the limiting action of the differential amplifier will clamp V(15) before the VCLAMP voltage. So you need enough gain KV for the clamp diodes kick in first. A few iterations with the spreadsheet may be needed to get the gain high enough.
The overall gain of the op amp model (open-loop gain) is given by
OP AMP COMPONENT VALUES
A few simple calculations and your model is ready.
OPEN-LOOP RESPONSE Let's take a look at the open-loop response of the SPICE file OP3_2ND_GAIN_STAGE.CIR. VS drives the positive input; R1 = 1 Ω grounds the negative input.
Run an AC Analysis and plot the output V(3). How does the op amp model perform? Is the low frequency gain equal to AOL_DC = 100k V/V? To get a better view, change the Y-Axis Settings to a log scale. Does the output fall to 0.707 of maximum at fp1 = 2000 Hz? And finally, does the output drop to unity at fu = 200 MHz?
CLOSED-LOOP RESPONSE Time to strap some feedback around our op amp model and check its response to a step input.
For a non-inverting amplifier with unity gain, remove R1 by adding a "*" at the beginning of its statement and add R2 = 1 Ω by removing the "*" at the beginning of its statement. VS generates a 1 V step input voltage. Run an Transient Analysis and plot the input V(1) and output V(3).
CIRCUIT INSIGHT How does the model's slew-rate limit measure up to the expected 40 V/μs? To check it, see if the output ramps to 0.4 V in 10 ns, which represents the same slew-rate limit. During the slewing action, take a look at the clamping action at V(15) of the model. Although inside the subcircuit, your display program should let you plot voltages within a subcircuit.
HANDS-ON DESIGN Suppose your asked to create a model of the following op amp:
Run the parameters of this op amp (or any other op amp you choose) through the Excel spreadsheet. You should be able to create a SPICE model for the basic behaviors of most op amps.
Take a quick refresher tour of the
Intermediate Op Amp Model.
Download the file or copy this netlist into a text file with the *.cir extension.
OPMODEL3_2ND_GAIN_STAGE - OPAMP MODEL WITH 2ND GAIN STAGE.CIR * * SIGNAL SOURCE VS 1 0 AC 1 PWL(0US 0V 0.01US 1V 100US 1V) * * POWER SUPPLIES VCC 10 0 DC +15V VEE 11 0 DC -15V * *R1 0 2 1 R2 2 3 1 XOP 1 2 3 10 11 OPAMP3 RL 3 0 100K * * OPAMP MACRO-MODEL 3 - ADDITIONAL GAIN STAGE * * IN+ IN- OUT VCC VEE .SUBCKT OPAMP3 1 2 81 101 102 Q1 5 1 7 NPN Q2 6 2 8 NPN RC1 101 5 151.7 RC2 101 6 151.7 RE1 7 4 100 RE2 8 4 100 I1 4 102 0.001 * * ADDED GAIN STAGE GV 100 15 6 5 0.001 RV 15 100 200K * CLAMP FOR SLEW-RATE LIMITING DZ1 15 16 DZENER DZ2 100 16 DZENER * * GAIN, FIRST-POLE AND SLEW RATE G1 100 10 15 100 0.0005 RP1 10 100 1MEG CP1 10 100 79.6PF * *OUTPUT STAGE EOUT 80 100 10 100 1 RO 80 81 100 * * INTERNAL REFERENCE RREF1 101 103 100K RREF2 103 102 100K EREF 100 0 103 0 1 R100 100 0 1MEG * .MODEL NPN NPN(BF=50000) .MODEL DZENER D(BV=5.7V IS=1E-14 IBV=1E-3) * .ENDS * * ANALYSIS .TRAN 0.001US 0.2US .AC DEC 5 1HZ 1000MEGHZ * * VIEW RESULTS .PRINT TRAN V(3) .PRINT AC V(3) .PROBE .END
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