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# AC gain at very low frequency vs. DC gain ?

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#### BillQ

##### Junior Member level 1
For an amplifier simulation

I run a DC sweep analysis and got the DC transfer curve Vout vs. Vin, then I can calculate the gain A from the slope of the transfer curve

I also run an AC analysis and plot directly the gainB=Vout/Vin.

For B at very low frequency, the amplifier should also operate at near DC condition. But the two values A and B(f~0) are completely different

I am wondering these two are just completely different analysis, AC refers to the small signal gain, but DC refers to the large signal gain. So maybe I should no compare them at all. Is my understanding correct?

Just now I also checked the ac output voltage in magnitude.

Its voltage is even several KV, but my supply voltage is limited to 3.3V

Does it mean that I don't need to care about the AC output magnitude, but only the resulted ratio Vout/Vin in the AC simulation

A DC sweep analysis will show quite a different gain from a very low frequency gain value from an ac analysis. Stepping through the DC transfer curve, you move from (static) small-signal to large-signal gain, moreover the DC operating point(s) - due to full DC feedback - will be shifted quite a lot from the original OP.

An AC analysis, however, linearizes the circuit around a fix OP (calculated by an automatic previous and independent DC analysis), and so runs a true small-signal analysis. Doesn't matter whatever your AC input voltage is (µV, mV, V, or even kV), only the ratio of Vout/Vin counts and will always be the same, due to the linearization of the circuit. The unit voltage (1V) is just a practical value, because then the Vout value directly corresponds to the gain.

So you cannot compare the 2 gain values. If "DC gain" is mentioned, always the very low frequency small-signal value from an AC analysis is referred to.

melkord

Points: 2

### melkord

Points: 2
DC analysis can be small signal or large signal depending on how large a portion of the transfer curve you look at. AC at LF should be the same as small signal DC.

Are you sure they are operating under the same bias conditions?

You mention several kV in the AC analysis - where do you get a voltage from? AC analysis just gives gain.

Keith

### BillQ

Points: 2
Generally, both gain values should be similar. So something seems to be wrong, either in your analysis setup or the circuit.

You don't need to care for the magnitude in AC analysis, but have to care for correct bias. In case of an amplifier with strong
non-linearity near the bias point, e.g. due to cross-over distortions, the AC analysis may be misleading.

AC analysis just gives gain.
Depends on the tool. With PSPICE, you connect an AC source and get output voltage, may be µV or kV.

### BillQ

Points: 2
FvM said:
AC analysis just gives gain.
Depends on the tool. With PSPICE, you connect an AC source and get output voltage, may be µV or kV.

Clearly kV is nonsense. It is really gain expressed as volts per volt, relative to a 1V input voltage which in reality is an infinitely small input voltage - not 1V.

Keith

### BillQ

Points: 2
keith1200rs said:
Clearly kV is nonsense. It is really gain expressed as volts per volt, relative to a 1V input voltage which in reality is an infinitely small input voltage - not 1V.
May be in your simulator, but neither in SPICE, HSPICE, PSPICE, nor in SPECTRE. Due to the linearization of the circuit in AC analysis, the magnitude of the input/output voltages doesn't matter (s. the explanation in one of the answers above). You might also check Ken Kundert's book ("The Designer's Guide to Spice & Spectre") about this topic.

erikl said:
keith1200rs said:
Clearly kV is nonsense. It is really gain expressed as volts per volt, relative to a 1V input voltage which in reality is an infinitely small input voltage - not 1V.
May be in your simulator, but neither in SPICE, HSPICE, PSPICE, nor in SPECTRE. Due to the linearization of the circuit in AC analysis, the magnitude of the input/output voltages doesn't matter

I never said the magnitude of the input/output voltages did matter. I said that to refer to them as voltages is a nonsense. They are gains.

Keith

I don't think I am describing anything different to you. What you describe as 'linearization' I view as the small signal response to an infinitely small input signal.

Keith

keith1200rs said:
I said that to refer to them as voltages is a nonsense. They are gains.
Keith
I don't think this is quite correct. With AC analyses you can add noise (analysis), which in general (also) depends on frequency. Hence parts from your output voltage may stem from the amplified stimulus, other parts from (internally) added (and varyingly amplified) noise contributions. So I think it does make sense to calculate with voltages primarily, and then calculate the gain from the voltages (estimating, or having measured the noise contribution before, so knowing its contribution). That's probably why all these before mentioned simulators really operate with the given stimulus voltage magnitude.
erikl

Yes, the noise analysis deals with real voltages and applies the small signal gain to them. It doesn't alter the fact that if you have a 1kV output in an AC analysis it means you have a gain of 1000, not a 1kV output.

Keith

keith1200rs said:
Yes, the noise analysis deals with real voltages and applies the small signal gain to them. It doesn't alter the fact that if you have a 1kV output in an AC analysis it means you have a gain of 1000, not a 1kV output.

Keith
Very true, fortunately ;-) Fully agree! erikl

This relates to the real circuit, of course. The simulation result may still attach a voltage of such magnitude to the output.

yes they are gain,not the really magnititude of the output.or you may kill someone with an opamp

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