Circuits and YOU!

So we have our basic components, Capacitors, inductors and resistors. We also have semiconducting components such as diodes and transistors. If you read my other blog you also know about microcontrollers. Operational Amplifiers or op-amps for short, are in their own league. At its heart an op amp provides a voltage gain to a potential difference on its inputs. However, when you begin to do some analysis and creative placing of components, you realize op-amps do so much more.

An op-amp typically has 5 inputs:

+ : The non inverting input
- : The inverting input
V+: Positive rail supply voltage (not shown)
V-: Negative rail supply voltage (not shown)
V_out: Output Voltage

Operation

As said earlier, the op-amp is a simple device, it applies a voltage gain on the voltage difference between the + and - pins. Gain is denoted by A and is typically around the scale of 10^6. Now, this might be a little confusing, does this mean the op-amp will output 10^6 volts when a 1 volt difference is applied across the + and - pins? No, you are bound by the positive rail and negative rail supply, you can never surpass those.

So if that's the case, wont a few millionths of a volt cause the op amp to go completely to one rail? This is true however we must make a few idealized assumptions about op-amps so that we can properly analyze op-amps and once we do that we can understand what feedback is.

The idealization and analysis of an op-amp

The best way to go about analyzing an op-amp is to break it up into two parts:

The input: The input of the op-amp are the inverting and non-inverting inputs, here we make our first assumption. The resistance between these two points is infinite. This means that no matter what voltage is on either pins no current flows between the two points. This is our second assumption, no current flows into or out of the input pins.

The output: Taking our idea on how the op-amp works we get the following formula:

We can turn the Vout pin into a dependent voltage source (i.e. it is a voltage source which is dependent on a voltage somewhere else in our circuit) going through a resistor. The output voltage is governed by the equation above.

Our final assumption is that, this resistor is 0 ohms.

Our ideal op-amp

Taking our four assumptions:
-Resistance between + and - pins is infinite
-No current flows into the + and - pins
-Vout = A*Vin
-Output resistance is zero

After we make these assumptions we get the following circuit

Now what?

A simple amp using feedback

Now the greatest power an op-amp has is its ability to use feedback to create some neat effects.

Lets say we input a voltage to the + terminal and then have a resistor from the output feedback to the - input.

Analysis

Lets start off by reminding ourselves of our assumptions, We know that the resistance is infinite between the inverting and non-inverting inputs and because of that no current flows. Because of that, the + and - pins are held at the same potential.

So lets look at our circuit. We see that the output voltage is hooked up in a voltage divider configuration with the - input. We recall for a voltage divider that:

or that....

Taking our original formula

We find for this circuit

This circuit represents controllable gain, which is extremely useful.

Many basic signal amplifiers work off of this very practical circuit.

Where do we go from here?

Operational amplifiers have many other applications to signal processing beyond just a simple controllable gain circuit.

Many other uses of op amps include:

-Signal Buffers (Zero gain amp circuit)
-Summers
-Differentiators
-Integrators
-Oscillators and Waveform Generation
-Much more!

We'll be going over uses of op amps as we use them.

A Step back

In the LDR post i posted about how you could use an operational amplifier to get more precise triggering of the LED light. Ill go over this briefly.

If you apply a voltage to the inverting input and another to the non inverting:

If V+ > V- the output will be the positive supply rail.

If V- > V+ the output will be the negative supply rail.

Thus if we hook up the LDR to the + terminal (in a divider configuration) and apply a voltage the the - input (via a divider or voltage source) we can get a binary output from the LDR sensor.

Formula sheet

Ideal Op amp:

Non-inverting amplifier output voltage: