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Operational Amplifiers - Ideal Circuits

posted 10 Jun 2012, 05:57 by James Gibbard   [ updated 15 Jul 2013, 08:20 ]
If you are not familiar with op-amps it might be worth reading the first two articles in this series: Operational Amplifiers - Basic Concepts and Operational Amplifiers - Negative Feedback

Ideal op-amp rules
In the last article in this series it was shown that op-amps have a very large gain; when looking at ideal op-amps this gain is considered to be infinite.  When put in a negative feedback configuration this infinite gain effectively means that the op-amp will drive the output to what ever value is necessary to make the voltage difference between the two inputs (V+ and V-) equal to zero. 

In addition to infinite gain two further assumptions are made when thinking about ideal op-amps. Firstly the input impedance of the amplifier's inputs is assumed to be infinite. This means that no current enters the op-amp's input terminals. In reality a small bias current is drawn. Secondly the output impedance of the op-amp is assumed to be zero. This means that the load connected to the op-amp's output terminal has no effect on the output voltage of the op-amp. In reality the output impedance of an op-amp is small but greater than zero. 

The three rules are summarised below: 
RULE 1: The op-amp will drive the output so that the voltage difference between the two inputs is zero.
RULE 2: No current is drawn by the op-amp's inputs.
RULE 3: The output load does not affect the op-amp's output voltage.

Using the three rules we can develop several ideal op-amp circuits. The two most common op-amp circuits are the inverting amplifier and the non-inverting amplifier.

Non-inverting amplifier
The non-inverting amplifier applies a positive gain to the input. The configuration of a non-inverting amplifier is shown in figure 1 below.
Non-inverting amplifier
Figure 1

The gain of the amplifier can be calculated using the three idea op-amp rules. It can be seen that the resistors R1 and R2 form an potential divider between Vout and GND. The output of the potential divider is at the negative input of the op-amp (called VA in figure 1). From this we can say that:

non_invert_eq

For example setting R2 to be 9 kohms and R1 to 1 kohms would give a gain of 10. It should be noted that the gain can not be set below 1 in this configuration. If R2 is a short circuit and R1 is an open circuit then the gain is 1. This called a buffer amplifier and was shown in the previous article. 

Inverting amplifier
The inverting amplifier applies a negative gain to the input. The configuration of an inverting amplifier is shown in figure 2 below.
inverting_op-amp
Figure 2

The gain of the circuit can be calculated by performing Kirchhoff's current law (KCL) at the negative input to the op-amp. 

inverting amplifier equations

Since R2 and R1 are positive values the gain will always be negative. 

Differential amplifier
A differential amplifier amplifies the difference between the two input terminals of the op-amp. The configuration of a differential amplifier is shown in figure 3.
d
Figure 3

The output of a differential amplifier can be calculated as follows:
Differen

If the resistors are set so that Rg/R2 = Rf/R1 then equation 10 cancels down to:

differential amplifier equation
Summary
This article has covered three ideal op-amp circuits, the non-inverting amplifier, the inverting amplifier and the differential amplifier. Methods to calculate the gains of each of these circuits have been shown. 
  • By using negative feedback the closed loop gain of the op-amp can be set.
  • Ideal op-amp circuits assume that the gain and input impedance are infinite and the output resistance is zero.
  • The ideal op-amp rules combined with traditional circuit techniques can be used to calculate the gain of an op-amp circuit.
The next article will cover several further idea op-amp circuits. 

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