# Two stage amplifier small signal analysis

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#### mvj Dear All,

In the analysis of a two stage amplifier, we simply multiply the small signal gain of the first stage with the small signal gain of the second stage. Since the output signal from the first stage is already ampified, the input to the second stage is no longer a small signal, in such a case how can we simple assume the total gain as the product of the two small signal gains?

Best Regards,
M.

#### FvM

##### Super Moderator
Staff member Since the output signal from the first stage is already ampified, the input to the second stage is no longer a small signal
This is just an arbitrary conclusion. You can either perform small signal analysis, neglecting any nonlinearities. Or transient analysis, harmonic balance, whatsoever and consider non-linear behaviour. The decision doens't depend on the number of stages, however.

• syeda amna

### syeda amna

Points: 2

#### KerimF As long a signal passes linear devices from input to output, the system can be analyzed properly by what is known as "small signal analysis". It doesn't matter if the signal is 1mV or 1000V.

#### mvj consider non-linear behaviour

As long a signal passes linear devices from input to output, the system can be analyzed properly by what is known as "small signal analysis". It doesn't matter if the signal is 1mV or 1000V.

Thank you very much for the replies!!

If we consider a two stage amplifier such as the miller compensated amplifier, the first stage would have a gain of gm(r01||r02). Now when the input signal is amplified by such amounts of gain the swing of the output from the first stage would be high. This means that the input to the second stage is not a small variation about a DC bias level. Since the input to the second stage is varying over a wide range, will it not effect the parameters of the device ( such as gm and r0) there by contsantly varying the gain of the second stage greaty. Now such contineous change in gain should result in great amounts of non-linearity in the final output but that does not seem to be the case when the amplifier is actually simulated. May I know why this is so.

#### KerimF Please note that even 1mA current may not be suitable for the small signal analysis if it drives a forward diode between 0V and Vd. Hope you got the point.
The subject here is about linear and non-linear behaviour only of the elements in the analyzed circuit.
So you are totally right that if for some reasons (by increasing the input voltage, for example) a part of the circuit is no more linear as expected then the result of the analysis will be, in turn, not accurate.

• mvj

### mvj

Points: 2

#### LvW Thank you very much for the replies!!

If we consider a two stage amplifier such as the miller compensated amplifier, the first stage would have a gain of gm(r01||r02). Now when the input signal is amplified by such amounts of gain the swing of the output from the first stage would be high.
................

What means "high"? Remember that the input voltage for an opamp with an open-loop gain of 100 dB may be as low as 1E-5 volts. The output is 1 volt and will certainly be within the linear range of the transfer characteristic of the amplifier.

• mvj

### mvj

Points: 2

#### jardila

##### Junior Member level 2 Hi,

A High gain in an opamp means that this circuit can amplify smaller
signals than other one with less gain. In other words, High gains
in an opamp limits the amplitud for the input signal.
Look the following simple example:

1. I have an opamp with Gain=100V/V and a Voltage output swing = 1V.
Then, I can put in the input, a signal amplitud as high as 1/100=10mV.

2. Now, the opamp's gain is increased to 20000V/V with the same topology
(probably because I optimized my design ). In this case, for the
Voltage output swing of 1V, the maximum amplitud for the input signal
is only 50uV!. If we have two stages, we can allocated a gain of 500V/V
for the first stage and 40V/V for the second. Then, the maximum signal
amplitud at the input of the second stage is (50uV)x(500V/V)=25mV.

This value probably will be a small variation around the DC bias
of the second stage.

This example show us, that we must be careful with the amplitud for the input
signal in order to maintain the linearity of the system.

Regards,

PD: Excuse me for my bad english • mvj

### mvj

Points: 2

#### jaxrobinson

##### Newbie level 5 Yes you can just multiply the outputs of first signal and the second signal signal together to get the perfect result.

#### leo_o2 For small-signal analysis, both input and output signal are supposed to be infinitesimal.

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