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Operational Amplifiers - Basics concepts

posted 9 Jun 2012, 08:37 by James Gibbard   [ updated 15 Jul 2013, 03:12 ]
What is an op-amp? 

Operational amplifiers or "op-amps" are a very common electrical component found in a huge range of electrical devices.

An op-amp is a differential amplifier with a very high gain. Each op-amp has two inputs; a non-inverting input (V+) and an inverting input (V-). The output of the amplifier V(out) is the difference between the voltages at the two inputs, multiplied by the open loop gain. The image below shows the typical circuit symbol for an ideal op-amp.

ideal_opamp

The output of an ideal op-amp is given by the equation: 
open_loop_eq
(Where Av is the open loop voltage gain of the amplifier)

A typical op-amp has an open loop voltage gain of greater than 100,000. With such a high gain even a small voltage difference between the V+ and V- inputs will cause the output voltage to be very large. For example if V+ = 2.1V and V- = 2.0V the output voltage would be:
V(out) = (2.1 - 2.0)*100,000 =  10,000V.

This is just an ideal calculation, a real op-amp cannot simply produce an infinitely high voltage; the output voltage is limited by the op-amp's power supplies. The image of the op-amp below now includes the connections for the op-amp's power supplies.

power_opamp
Op-amps typically have two power supplies; a positive power supply Vs+ and a negative power supply Vs-. The power supplies are usually set to be equal in value but inverted in polarity, for example Vs+ = +12V and Vs- = -12V. NB: In some cases the negative power supply is connected to ground, this is called a single supply op-amp.

When the op-amp tries to output a large voltage, for example 10,000V, the output saturates at (nearly) the supply voltage.

Since the gain of the op-amp is so high the following assumptions can be made:

In case you are not familiar with the notation, the = sign with the ~ above it means roughly equal to. This is used because not all op-amps can drive the output all the way to the supply rails. The reasons for this will be covered in more detail in a later article.

What happens when V+ = V- ? Ideally the output of the amplifier should be 0V. In the real world, slight imperfections in the op-amp will cause a small voltage offset between the V+ and V- inputs. As we have already seen even a small voltage difference will cause the amplifier to saturate at one of its power supply rails. Information on offsets and other "non-ideal" behaviour of op-amps can be found here.

When used in this manner the op-amp is acting as a comparator. A comparator simply compares two voltages and outputs either a HIGH or LOW signal depending on whether V+ is greater than V- or vice versa.

Op-amp comparator example

In this example a sine wave  is fed into the V- input of the amplifier, while the V+ input is held at a fixed voltage.

The sine wave has an amplitude of 4V peak to peak and is offset so that it is centred around 2.5V. The fixed voltage at the V+ input is set to 2.5V. The supply voltages are set so that Vs+ = 5V and Vs- = 0V.

The circuit below shows the set up for the test. LTSpice was used to simulate the circuit. It is available to download for free here.

The plot below shows the input (Green trace) and output (Blue trace) waveforms of the op-amp.
Click image to expand

It can be seen that the output of the amplifier is a square wave with an amplitude of 5V. At the start both V+ and V- are equal therefore V(out) is 0V (this is an idea simulation). As the voltage of the sine wave increases the voltage at V- becomes greater than at V+ which is fixed at 2.5V. Due to the high gain the amplifier tries to set a negative output of 1000's of volts, however since Vs- is set to 0V the output becomes saturated at 0V. As the voltage of the sine wave reduces to lower than 2.5V, the voltage at V+ becomes greater than V-. The amplifier now tries to set a positive output of several 1000's of volts, however since Vs+ is set to 5V the output becomes saturated at 5V.

It should be noted that dedicated comparator ICs are available that offer better performance and stability when compared to an op-amp in this application. For more information on the limitations of real world op-amps click here.

Summary
This article has covered the basics of op-amps and the use of op-amps in an open loop configuration (I.e. without any feedback).
  • Op-amps are differential amplifiers with a very high gain.
  • When used in an open loop manner the output of the amplifier will almost always saturate at the positive or negative power supply rails.
  • An op amp in open loop configuration can be used as a comparator.

The majority of op-amps applications rely on feedback to accurately set gain and other parameters. The next article will look closely into closed loop op-amp circuits.


Click here to proceed to the next article in the series: Operational Amplifiers - Negative Feedback

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