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An inverting amplifier is a circuit involving the use of an amplifier, often an operational amplifier, which is configured such that the output is 180° out of phase with the input. That is, if a positive input increases the subsequent negative output decreases and vice versa. A schematic diagram of an inverting amplifier is shown in Figure 1.1.

An inverting amplifier differs from the voltage follower by having one input connected to common. This eliminates the common-mode rejection error allowing for a more straightforward relationship between gain and resistance. Higher gain is achieved at the expense in the gain accuracy.^[1]

The R_f resistor allows some of the output signal to be returned to the input. Since the output is 180° out of phase, this amount is effectively subtracted from the input, thereby reducing the input into the operational amplifier. This reduces the overall gain of the amplifier and is dubbed negative feedback.^[2]

The inverting amplifier uses negative feedback to stabilise voltage gain. Negative feedback is achieved by bringing a fraction of output signal to inverting input of an op-amp thereby reducing the gain, increasing the frequency, and improving the stability.^[3]

Gain

The gain of the amplifier is determined by the ratio of R_f to R_in. That is:

$A=-{\frac {R_{f}}{R_{in}}}$

The presence of the negative sign is merely a convention indicating that the output is inverted. So, for the sake of example, say R_f is 10,000 Ω and R_in is 1,000 Ω. Then the gain would be -10000Ω/1000Ω, which is -10.

The final gain is negative. To get a positive gain, you can use the output of an inverting amplifier as an input to a second inverting amplifier, or you can simply use a non-inverting amplifier.^[4]

Now take the instance where R_f has infinite resistance. In this case, it would act as if the feedback loop had been removed, and the gain would be infinite. In reality, infinite gain cannot occur. The maximum obtainable gain is limited by the properties of the operational amplifier. For one, the integrated circuit limits the gain, but the major limiting factor is the power supply. The input voltage (or current) cannot exceed the maximum output of the power supply. Should this limit be reached, no further amplification occurs, and the amplifier is said to be saturated. This is often the purpose for which these amplifiers are included in a circuit.

A third possibility which should be considered is that in which both resistors possess the same resistance, i.e. R_f=R_in. In this case, the gain is -1. Thus the input and output are the same magnitude, only the output is 180° out of phase with respect to the input. The term used to described this situation is unity gain. These circuits are called voltage followers, because the output simply “follows” the input. Voltage followers can be used when a signal inversion, but not additional amplification is needed. Voltage followers can also act as buffers to prevent the loading of subsequent parts of a circuit.^[5]

Notes

^ ^ Malmstadt, Enke and Crouch, Electronics and Instrumentation for Scientists, The Benjamin/Cummings Publishing Company, Inc., 1981, ISBN 0-8053-6917-1, Chapter 5. pp 118.
^ Basic Electronics Theory, Delton T. Horn, 4th ed. McGraw-Hill Professional, 1994, p.342-343.
^ http://www.antonine-education.co.uk/Electronics_AS/Electronics_Mod2/Topic_2_5/topic_5__the_inverting_amplifier.htm
^ http://people.ee.duke.edu/~cec/final/node46.html
^ Basic Electronics Theory, Delton T. Horn, 4th ed. McGraw-Hill Professional, 1994, p.342-343.

[1] Malmstadt, Enke and Crouch, Electronics and Instrumentation for Scientists, The Benjamin/Cummings Publishing Company, Inc., 1981, ISBN 0-8053-6917-1, Chapter 5. pp 118.

[2] Basic Electronics Theory, Delton T. Horn, 4th ed. McGraw-Hill Professional, 1994, p.342-343.

[3] ttp://www.antonine-education.co.uk/Electronics_AS/Electronics_Mod2/Topic_2_5/topic_5__the_inverting_amplifier.htm

[4] ttp://people.ee.duke.edu/~cec/final/node46.html

[5] Basic Electronics Theory, Delton T. Horn, 4th ed. McGraw-Hill Professional, 1994, p.342-343.

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	An '''inverting amplifier''' is a circuit involving the use of an [[amplifier]], often an operational amplifier, which is configured such that the output is 180° out of phase with the input. That is, if a positive input increases the subsequent negative output decreases and vice versa. A schematic diagram of an inverting amplifier is shown in Figure 1.1.		An '''inverting amplifier''' is a circuit involving the use of an [[amplifier]], often an operational amplifier, which is configured such that the output is 180° out of phase with the input. That is, if a positive input increases the subsequent negative output decreases and vice versa. A schematic diagram of an inverting amplifier is shown in Figure 1.1.