Introduction to operational amplifiers

Practical op amp model

Practical operation amplifier model.



In an ideal operational amplifier (op amp), the value of rd is considered to be infinite when in actual fact the resistance is around 10MΩ. This value is dependent on the variety of omp amp and generally increases with price. The higher the value of rd, the better.

This same premise also applies to the open-loop gain. It’s value in an ideal op amp is also considered to be infinite, when in actual fact it is around 10M.

ro however is the inverse, as in an ideal op amp it is 0Ω and a typical practical value is about 10Ω,


Using the above formula the following can be derived:

V difference formula

The difference between the voltage on the inverting input and the non-inverting input is equal to the output voltage divided by the gain.

Now assuming ideal values for the gain (infinite), its value can substituted in and the formula can be rearranged.

V difference formula (values)

Any value divided by infinity is equal to zero, therefore:

V difference formula (simp)

Looking back at the original formula, the following can be deduced:

Vout_formula (2)

Vout_formula (3)

Substitute in the value for Vd:

Vout_formula (4)


Vout_formula (5)

In addition to this, two more values can be stated when using ideal values.

The value of rd is infinite, therefore no current is flowing into the inverting or non-inverting terminals (Ip = 0A and In = 0A).

The output impedance is 0Ω.




Schmitt Triggers

A Schmitt trigger has one input and one output. It sets the output to one of two states depending on the voltage at Vin. Because of the nature of inverting op amp set-ups, the outputted signal will be inverted. When Vin goes below a certain voltage (the lower switching threshold), Vout goes high. When Vin goes above a certain voltage (the higher switching threshold), Vout goes low.

Schmitt Trigger

Because Schmitt triggers have an upper and lower switching threshold, they’re much better at cleaning up noisy signals than a single switching threshold. This is because with a single threshold, the noisy signal will jitter between each side of the threshold, causing it to  trigger multiple times.

Non-Inverting Amplifier

A Non-inverting amplifier increases the amplitude of a signal. Its input resistance is that of the op amp itself (infinite in an ideal op amp), which makes it perfect for amplifying small signals, that can provide very little current on their own.

One thing to note quickly. The output can never be higher than the positive supply voltage, or lower than the negative supply voltage.

Non-inverting amplifier

Non-inverting amplifiers however, can only provide a minimum gain of one. This means the output will always be at least the same value as the voltage on Vin. Its gain can be calculated by using the following formula:

Inverting Amplifier

An inverting amplifier increases the amplitude of a signal. But due to the fact that the signal is fed into the inverting input, the output signal will be inverted. However, unlike Non-inverting amplifiers, they can have a gain of less than one.

One thing to note quickly. The output can never be higher than the positive supply voltage, or lower than the negative supply voltage. This means that for an inverting amplifier to work you need the negative supply pin to have a voltage below ground (e.g -6v).

Inverting amplifier

In inverting amplifiers, the gain can be calculated by dividing Vout by Vin. In addition to this, the same figure can also be acquired by dividing the feedback resistance by the input resistance ( feedback resistance = Rf, Input resistance = R1) . However, because the output is inverted, the value of the feedback resistance needs to be inverted too. From all of this, we can deduce the following equations:


If two inverting amplifiers are used in series, the inversion can be rectified. A schematic and equation is shown below to demonstrate this.

Inverting amplifiers in series

The gain of the first op amp is calculated:




Then the gain of the second op amp:


Now assuming that Vin = 0.5v, the output of the first op amp would be the following:

Finally, with -5v being inputted into the second op amp, the output will be once again positive:


Therefore the total gain of the circuit is 10, meaning that the inversion has been rectified.

Operational Amplifiers

Op Amps (Operational Amplifiers) are composed of two inputs, an output, and positive and negative power supply pins.

Op Amps can be used in many different set-ups, among them being: Voltage Comparators, Inverting and Non-inverting amplifiers, Summing amplifiers, and Difference amplifiers.

In Op Amps, the voltage of the output is dependent on the voltages of the two inputs. If the Inverting input is higher, the output will be the same as the negative supply. If the Non-Inverting input is higher, the output will be the same as the positive supply.

Pins 2, 3, 4, 6, and 7 are the only pins which need to be connected to the circuit in order to use the Op Amp.

LM741 Operational Amplifier actual viewop amp schematic