PHY C21: Operational Amplifiers

In this chapter, we will take a look at one of the most widely used electronic devices: the operational amplifier (Op-Amp for short)!

  • Use of operational amplifiers as comparators
  • Properties of ideal op-amps
  • Graphs of input vs output voltage

What is an operational amplifier?
It is a type of integrated circuit which:

  • consists of transistors, resistors, & capacitors
  • can carry out multiple operations such as:
    • amplifying voltages
    • comparing 2 input voltages & providing a corresponding output voltage
    • acting as a switch dependent on the level of input voltage

A complete circuit diagram of an op-amp looks like this:

oh lordy that’s scary

…but we prefer to simplify it to this:

that’s better

Before explaining how it works, let’s take a look at its parts & properties:


Anatomy of an op-amp

User:Omegatron, CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0, via Wikimedia Commons
Inverting input (-)Potential at this input is labelled V
No current should flow into it (the op-amp may be damaged).
Non-inverting input (+)Potential at this input is labelled V+
No current should flow into it (the op-amp may be damaged).
OutputTerminal where an output voltage Vout is produced.

Output voltage depends on the difference between V+ & V (see below for a detailed analysis)

This terminal is usually connected across a load circuit to the ground.
Current can flow out of the output from either power supply.

Vout is LIMITED by the supply voltages (it cannot be higher than either supply)
Power supplyProvides voltage for the output.

There are 2 supplies to enable both (+) & (-) output voltages.

In this case, it can provide a maximum voltage of +6V or -6V.
Most op-amps operate with ±6V or ±9V.

If these don’t make sense yet, try reading how an op-amp works below first, then return here.


How does an op-amp work?
At its most basic use, an op-amp is a COMPARATOR.

What is a comparator?
A device which delivers an output depending on the difference between 2 inputs. It compares the 2 inputs.

Once an op-amp has a D.C. power supply, here’s how it operates:

Inverting input (-) & non-inverting input (+) are connected to
input voltages V & V+ respectively.
Op-Amp compares the 2 inputs.
IF V+ is LARGER than V:Output produces a POSITIVE voltage.

Vout = A0(V+ – V)

Since V+ > V,
V+ – V > 0
IF V+ is SMALLER than V:Output produces a NEGATIVE voltage.

Vout = A0(V+ – V)

Since V+ < V,
V+ – V < 0
IF V+ = V:Output produces NO voltage

Vout = A0(V+ – V)

Since V+ = V,
V+ – V = 0
BUT Vout is limited by the Vsupply
Vout CANNOT be larger than Vsupply
IF A0(V+ – V) > |Vsupply|,
THEN Vout = Vsupply

The sign of the Vsupply used depends on the sign of A0(V+ – V).

What’s this value A0?
Open-Loop Gain
or Amplification of the op-amp.
It is the measure of how many times the output voltage is greater than the difference between inputs.

IF Vout < Vsupply,

A0 = Vout/Vin

Vout = A0(V+-V)

What happens if A0(V+-V) exceeds the power supply?
The output voltage becomes SATURATED.
This means that it cannot increase above the power supply. In this case, we cannot calculate A0 using Vout/Vin.

Here’s a flowchart to summarise the working of an op-amp:


Properties of an IDEAL op-amp
These only apply to op-amps which are PERFECT – real-life ones don’t always have these properties!

Infinite input impedanceBoth inputs have infinite resistance.
No current flows through them into the op-amp.

This means that the potential supplied at an input will be the SAME as the voltage across the component that the input is connected in parallel to.
0 output impedanceThe output has 0 resistance.

It acts as a battery with no internal resistance, so the whole output voltage is seen across the load connected to the output.
Infinite open-loop gainWhen there is a very small input voltage, the output voltage will saturate.
This means that Vout is always saturated unless V+ = V

A0 is INFINITY, so:
Vout = Vsupply

Remember that the sign depends on which is larger:
Vout is + if V+ > V
Vout is – if V+ < V
Infinite bandwidthAll frequencies are amplified equally.

If an alternating voltage is input, then output will have the SAME frequency, but have an amplified amplitude.
All frequencies of alternating voltage are amplified this way by the same amount.
Infinite slew rateNo time delay between the moment the input is changed to the moment the output changes in response.
Output changes instantaneously as input is changed.

Using an ideal op-amp as a Comparator

Here’s an example of one application:

You can experiment with my circuit here on Falstad.com
Try change the temperature & see what happens!

When T > 25°C:

At high temperatures, Rs is low.
Above a certain temperature (25°C), it is less than 10kΩ
 
If Potential at A is larger than Potential at B,
a positive output voltage will be produced
This occurs when RS is less than 10kΩ

V+ is now at 3.264V
V- is now at 2.5V
In an ideal op-amp, open-loop gain is infinite.
Thus, Vout will be saturated at +Vsupply

Here, +Vsupply is +9V
The red diode is forward-biased, so it lights up. 

When T < 25°C:

At low temperatures, Rs is high.
Below a certain temperature (25°C), it is more than 10kΩ
 
If Potential at A is smaller than Potential at B,
a negative output voltage will be produced
This occurs when RS is more than 10kΩ
In an ideal op-amp, open-loop gain is infinite.
Thus, Vout will be saturated at -Vsupply
 
The blue diode is forward-biased, so it lights up. 

One last thing: what if the input voltage varies over time?

How does the output voltage of an op-amp vary?
Let’s look at 2 different examples, both with supply voltages of ±6V.

Non-ideal Op-Amp

Play around with the gain value (A) & supply voltage (V) to see how the graph changes:
https://www.desmos.com/calculator/rggxjmteee

For example:

  • Red: input voltage (V+ – V)
  • Blue: output voltage (Voutput)
  • In this case, Vsupply = ±6V
The blue function consists of curves until it reaches ±6V, where it becomes a straight line.

Play around with the input voltage function f(x), the gain (A), & the voltage supply (V) here:
https://www.desmos.com/calculator/8swps35j6
9

Ideal Op-Amp

Play around with supply voltage (V) to see how the graph changes:
https://www.desmos.com/calculator/uudt55bvg6

For example:

  • Red: input voltage (V+ – V)
  • Purple: output voltage (Voutput)
  • In this case, Vsupply = ±6V

The purple function consists of only straight lines.

Play around with the input voltage function f(x), the gain (A), & the voltage supply (V) here:
https://www.desmos.com/calculator/kmkbxqwcn2
This one took me 2 hours to write, hope it works!

One thought on “PHY C21: Operational Amplifiers

  1. Pingback: PHY C21: Outputs of Op-Amp Circuits – ProDuckThieves

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