# Amplification and bias point

I'm completely new to microelectronics, so please be forgiving. Let's say I have the following circuit:

I have two fundamental questions:

1. Can the amplified voltage exceed the power supply voltages or might it cause any trouble?
2. In this multistage amplifier (I know that it is a poor design but the question is conceptual), how can I use a small signal model for the second stage if the initial signal is amplified to be much larger? How can I assume that Q2, for example, can be analyzed with a small signal model?

I know that these two questions are kind of foolish but I'm looking to settle these conflicts going through my mind.

• If you got rid of stage 3 and stage 4, your questions would still apply but then you'll get half the number of grumbles about how poor a design this is and, you might just attract someone nice who can answer you. It's probably not a great idea to ask these questions with a severely flawed circuit. In fact, why bother showing a circuit because, on the face of it, your questions apply generally. Dec 22, 2021 at 16:48
• Are you still working on the "mid band Gain=71[db] [3548.13] Rin=50 ohm Rout=50 ohm f_3db_low = 8kHz f_3db_high = 800 kHz" amplifier? (I'm still wondering how you can have a spec with a gain specifying 6 decimal digits of precision.)
– jonk
Dec 22, 2021 at 17:12
• You are rightly concerned about signal voltage swing. Where emitter resistor >> collector resistor, voltage swing is limited. A simulator doing AC analysis assumes your design is linear: it may claim that output voltage is 80V with Vac=20mV. If you switch to transient analysis with a sinusoidal Vac, you should check that output voltage is still sinusoidal, and not clipped. Reduce Vac until it is sinusoidal. What is required is a linear gain near 4000. So if you reduce Vac to say: 10uV, then output would be 40mV. Dec 22, 2021 at 17:40
• Why do you ask for a small-signal model for Q2? What is your intention? Do you hope that such a model will improve your knowledge? Remember: Such a small-signal model is nothing else than a visual verification of the well-known small-signal relations which describe the transistor function.
– LvW
Dec 22, 2021 at 17:42

Not sure what you mean be 'amplification voltage', but in this circuit, if the input V exceeds the supply, nothing more serious than distortion will occur.

If the input is extremely large, you would have to worry about power dissipation in the resistors and damage to the input NPN (above 6 V input because of VBE breakdown).

The circuit won't be able to generate an output higher than the supply.

A small signal model is applicable when the changes caused by the signal don't significantly affect the operating characteristics of the components (transistors). In the limit, this is an arbitrary small signal; anything else will cause distortion in the circuit.

For hand calculations, you might consider that signal swings more than 10 % of the bias current will cause detectable distortion; swings of 50 % of the bias current will cause easily observable (e.g. on an oscilloscope or simulation waveform) distortion of sinusoids or other waveforms.

Distortion can be mitigated by negative feedback -- your amplifier doesn't have any overall feedback. This amplifier has an extremely (unnecessarily ?) large amount of gain at AC (because of the bypass capacitors across the emitter resistors). Without any overall feedback, this amplifier will have distortion and clipping even with inputs of 1 mV. It could be complex to use negative feedback with this amplifier because of the large number of internal stages (and their associated poles and zeros).

The gain of each stage is approximately the collector load resistance divided by (26_mV/emitter_current); so the 1st stage gain is about 17).

Can the amplification voltage exceed the power supply voltages or might it cause any trouble?

It won't exceed the power supply voltages. However, if your small-signal model predicts that the voltage exceeds the rails, then you're well outside the range where your small-signal model is applicable. In reality, your amplifier will have saturated, which is a phenomenon that a linear small-signal model cannot describe or model adequately.

In this multistage amplifier (I know that it is a poor design but the question is conceptual), How can I use a small signal model for the second stage if the initial signal is amplified to a a much larger, How can I assume that Q2 for example can be anaylyzed [sic] with a small signal model.

You will have to check and see with your intended signal range. If your input signal is small enough that the input of the second stage is also a small signal, then you can. If not, then you cannot use that model, and your amplifier is likely saturating anyway.

It's worth noting that this is an open-loop amplifier. If you had negative feedback from the output back to the first stage, then as long as the output doesn't saturate, you can usually consider all stages in small-signal.

However, with four stages, a feedback amplifier can have severe instabilities due to negative phase margin if the poles and compensation are not carefully considered.

I will answer only the first part of your first question because it is very fundamental and deserves special attention:

Can the amplified voltage exceed the power supply voltage...?

The answer is simple: The amplified voltage cannot exceed the supply voltage because it is a part of the latter.

Literally speaking, the "voltage amplification" is not an amplification; it is an attenuation. It is just a clever trick with which we get an output voltage that is proportionally higher ("amplified") than the input voltage. How is this done?

Amplifier stages are "voltage dividers" controlled by the input voltage and powered by a higher (supply) voltage. They are implemented by so-called "active elements" (transistors) which in fact are voltage-controlled "resistors".

So, when the small input voltage slightly varies, the output voltage significantly varies from zero to the supply voltage… but no more... The output voltage stays between the input voltage and supply voltage; it is higher than the input voltage and lower than the supply voltage.