# Infinite bandwidth of an ideal amplifier

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1. Mar 23, 2017

### Faiq

What is meant by the infinite bandwidth of an ideal amplifier? If some extreme frequency signals were to be input in an amplifier of limited bandwidth and in the ideal amplifier, what will be the difference in their outputs?

2. Mar 23, 2017

### Staff: Mentor

The limited bandwidth amplifier would not pass frequencies above the bandwidth. It would act like a low-pass filter.

3. Mar 23, 2017

### Faiq

Would that happen in the circuitry of the limited amplifier or because of some EM wave radiation due to high frequency kind of thing?

4. Mar 23, 2017

### Staff: Mentor

Not necessarily. Simple attenuation is most likely.

But your question is hard to answer because you did not specify which frequencies. Extremely high frequencies don't follow wires at all; we use waveguides, or lenses instead.

I think that I may be missing the real point of your questions. How do you think limited bandwidth works?

5. Mar 23, 2017

### Faiq

I think limited bandwidth works as a sampler like in ADC. The device will sample the voltage values at particular frequencies (which I presume is the bandwidth is) and will provide an output amplifying the sampled values. Thus if the bandwidth is infinite, the sampling frequency is infinite, and thus voltage is noted or more precisely processed at every point giving a perfectly amplified output.

6. Mar 23, 2017

### Staff: Mentor

Ah so, you think in the digital domain.

Try thinking pure analog such as this limited bandwidth amplifier.

.

7. Mar 23, 2017

### Faiq

We haven't been taught the circuit of amplifier till now. We just deal with its characteristics that's all. Was my analogy flawed at some level?

8. Mar 23, 2017

### Staff: Mentor

No, that's not the reason for the limited bandwidth of real amplifiers. But keep on asking good questions as you study -- asking good questions is one of the keys to learning well.

There are a couple of reasons for the limited BW. The first is easy to understand, and the second one requires a bit more explanation. The first reason is that in any real circuit, there will be some finite resistance and at least parasitic capacitance. This forms a lowpass filter that limits how the amplifier can respond as the input frequencies get higher and higher. You can try to minimize the parasitic capacitance and use low impedances (which increases power dissipation of the amp), but you can only get so far with that strategy.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/rclo.gif

The second reason is that in amplifiers that are used in closed-loop feedback circuits, it is important to ensure that the amplifier does not go unstable and oscillate under any conditions (unless you want it to, like in an oscillator circuit). This is often done with internal components that limit the bandwidth of the amplifier (especially with opamps). The goal of this bandwidth limiting is to ensure that the overall gain of the amp falls to <1.0 as the phase shift through the amplifier gets close to -180 degrees. If the phase shift through the amplifier and external negative feedback circuit reaches -180 degrees and the opamp still has gain >1.0 at that frequency, you will get oscillations and the circuit will not work as intended.

The keyword phrases for reading more about this on-purpose limiting of amplifier gain are: Dominant Pole Compensation of Opamps, and Phase Margin of Opamps.

http://cktse.eie.polyu.edu.hk/eie403/solution1-bode.jpg
http://cktse.eie.polyu.edu.hk/eie403/solution1-bode.jpg

Last edited: Mar 23, 2017
9. Mar 23, 2017

### Faiq

Last edited by a moderator: May 8, 2017
10. Mar 23, 2017

### Faiq

One thing I have to ask is the gain of amplifier equal to 1/sqrt{1+w^2R^2C^2}?

11. Mar 23, 2017

### Staff: Mentor

No, that was just for a simple RC lowpass circuit. Amplifier gain depends on the actual circuit used in the amp.

The amp circuit that @anorlunda posted in Post #6 has a gain equation that is moderately complicated, and it is a simple circuit!

12. Mar 23, 2017

### Faiq

Oh, so the formula varies for every circuit. Is there some kind of general formula?

13. Mar 23, 2017

### Staff: Mentor

It varies with each circuit, so there's not really a standard formula for the open-loop gain, other than the lefthand side of the gain equation is usually Vout/Vin.

14. Mar 23, 2017

### Faiq

Okay thank you very much