The operational amplifier is one of the most versatile and useful components in electronics. The op-amp can be used as an amplifier, attenuator, filter, mixer, comparator, integrator, oscillator, rectifier, peak detector, clipper, and more. So op amps are great building blocks for synth DIY.

An op-amp is a linear amplifier. It has a high bandwidth and can provide an enormous amount of gain. Generally, it comes with two inputs and one output.

**Non-inverting input**(+)

A signal on this input has the same polarity on the output**Inverting input**(-)

A signal on this input has the reversed polarity on the output

Most op amps operate on a dual power supply providing positive and negative voltage. The power pins are often omitted in the schematic symbol for an op-amp. So it’s just assumed that the op-amp is connected.

## Ideal op amp characteristics

To understand how an op amp works, it’s useful to know the general characteristics of an ideal op amp.

- Infinite open-loop voltage gain
- No current flows into the input pins (infinitely high impedance)
- Zero voltage offset (perfectly balanced)
- The output swings as wide from positive to negative as the supply rails provide (rail to rail)
- Zero noise
- Infinite bandwidth and infinite slew rate (extremely responsive)

In the real world, op-amps aren’t perfect but these rules help to understand how an op-amp circuit works.

## Open loop configuration

The circuit below contains an op-amp in open loop configuration. Without feedback, the gain is enormous. Whenever the signal at the non-inverting input goes through zero, the op amp swings its output to the corresponding power supply voltage (+/- 10V). So the sine wave input effectively becomes a square wave at the output.

This is effectively a comparator using ground as a reference.

This input sine wave swings from -5V to 5V. We can calculate the voltage at the output by using the formula below. In this case, the gain (Ao) is infinite, so the output voltage is also infinite. This means that the output will be as close to the power rail as the op-amp can get.

So let’s now look at the way to control this huge internal gain.

## Negative feedback to tame the beast

The op-amp needs external circuitry to do useful work by means of a feedback loop. Most op amp circuits use negative feedback. So this means feedback from the output back to the inverting input.

The circuit below is a buffer or **unity gain amplifier**. The op-amp tries to keep the voltage at both input pins the same by varying its output. Since there’s a direct feedback loop to the inverting input the circuit has a gain of 1. No amplification or attenuation, just what goes in comes out at the same level.

This circuit comes in handy when you want to separate one part of the circuit from another part. Since there is (almost) no current flowing in or out of the op-amp, there is no load that can disturb the circuit on the input side. In Eurorack buffered multiples work like this.

## The non-inverting amplifier

The circuit below is called a non-inverting amplifier because the output has the same polarity as the input. It adds a voltage divider in the negative feedback loop. Since the resistors have the same value, we know that the voltage on the inverting input must be half of the op amp’s output.

Now, this is where the amplification magic starts to happen.

This circuit has a gain of 2, so twice the voltage level at the output. Here’s how it works:

- Assuming we have 5V coming in at the non-inverting input
- 5V comes out of the output at first
- The voltage divider leaves half of that at the inverting output (2.5V)
- The op amp senses the voltage difference at the inputs
- The op amp tries to even out that difference by increasing its output to 10V
- The voltage divider leaves half of that at the inverting output (5V)
- The voltage levels at the inputs are equal now
- The desired side effect is that the voltage level at the output has doubled (amplification with a gain of 2)

A very powerful concept. We can calculate the gain like this (R2 is the 10k resistor at the output):

As we can infer from this formula, the non-inverting amplifier circuit can’t attenuate the signal. It can’t go lower than a gain of 1. We need an inverting amplifier to attenuate a signal.

## The Inverting Amplifier

This circuit is called an inverting amplifier.

Here, the polarity of the output (Vout) is the inverse of that of the input (V-).

This circuit has a gain of -2. Here’s how it works:

- Assuming we have 5V coming from our signal source
- Through the 10k resistor there’s 3.33V left at the inverting input
- The op amp senses the voltage difference at the inputs
- Going through the 20k resistor and to get to the desired ground level at the inverting input, the op amp must lower its output to -10V
- The voltage levels at the inputs are equal now
- The desired side effect is that the voltage level at the output has doubled (amplification with a negative gain of 2)

The inverting input becomes a virtual ground this way since the input signal and output of the op-amp even out to ground level.

We can calculate the gain of an inverting amplifier like this (R2 is the 20k resistor at the output):

Note that when R2 gets smaller than R1, the circuit attenuates the signal.

A few frequently used operational amplifier IC’s are IC741, TL071, and LM386. There’s much more to op amps, but these are the basics.

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