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What is a feedback resistor and capacitor? Why are they are used in amplifier circuits?

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To understand why they are needed you first need to understand the basics of the opamp. There are a few simplified rules that you can use to help you solve any opamp circuit:

  1. The opamp will adjust Vout in attempt to make the + input equal to the - input. So when trying to solve for the voltage out, you should set the voltage at the + terminal equal to the voltage at the minus terminal. You don't actually know what this voltage is, so you just have to assign it a variable.
  2. No current flows in or out of the + or - terminals.

If you apply these two rules to your circuit you will find that you can use any other standard circuit analysis method to solve your circuits.

It turns out that you can get some very basic equations for specific configurations, but they all are derived from circuit analysis combined with the rules I mentioned.

If you have a specific configuration that you are having a hard time understanding how it operates, feel free to post a schematic of it and we can help explain it.

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Feedback can be used in any kind of amplifier circuit, not just in op-amp circuits. Feedback can be achieved by any component or network that will deliver a portion of the output signal back to the input; resistors and capacitors and networks built from them just happen to be common choices.

Feedback can be either positive or negative. Positive feedback adds to the input in such a way that an increase in the output signal will reinforce the input signal, producing in turn still more output. Negative feedback has the opposite effect, tending to cancel out the input and reducing the output.

Negative feedback decreases the gain of an amplifier, so what good is it? The usual reason for using negative feedback is to improve the frequency response of an amplifier. Suppose that, without the feedback network, the amplifier does a better job at amplifying some frequencies than others. By adding negative feedback, the stronger response to these favored frequencies results in more negative feedback, which reduces the output at those frequencies. The overall gain is lowered, but the payoff is that it essentially levels the amplifier's frequency response over a wide range of frequencies.

Positive feedback is less common, but has uses. Positive feedback increases the gain of the amplifier, and an old (early 20th century) radio design employed positive feedback for just that purpose. The problem with positive feedback, however, is that when the gain of the amplifier combined with the loss in the feedback network gives you a 'loop gain' of 1 or more, your amplifier turns into an oscillator.

Feedback can exist in an amplifier whether it's intentional or not. Parasitic capacitance can couple outputs back to inputs, as can magnetic coupling. If there happens to be a frequency at which these un-intentional feedback paths can result in a loop gain over 1, a circuit that is intended as an amplifier can quickly turn into an oscillator at that frequency. It's often the case that a feedback network is added to the amplifier just to counteract the effects of parasitic feedback.

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Resistors and capacitors are used with amplifier circuits to shape the bandwidth of the response to ensure stability. Most amplifier circuits have large bandwidth capabilities, necessitating external limitation to guarantee a predictable response.

Control theory dictates that a closed-loop system (which an amplifier with feedback can be considered to be) needs to have certain gain and phase criteria to be considered unconditionally stable (i.e. never oscillating).

Generally, in a negative feedback system, if there is positive gain with no phase shift, you end up with an oscillatory response. This is generally bad news for amplifier circuits.

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Traditionally in both tube and transistor amplifiers negative feedback is used to prevent the amplifier from oscillating.

Similarly an oscillator stage can be built from a basic amplifier circuit by simply adding some positive feedback and having a tuned output circuit.

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