Inverting Amplifier 2.5 2000/08/08 2004/08/10 08:13:11.993 GMT-5 Don Johnson dhj@rice.edu Carol Bettoney carolrb@alumni.rice.edu Don Johnson dhj@rice.edu inverting amplifier Inverting amplifier.

opamp The top circuit depicts an op-amp in a feedback amplifier configuration. On the bottom is the equivalent circuit, and integrates the op-amp circuit model into the circuit.

The feedback configuration shown in is the most common op-amp circuit for obtaining what is known as an inverting amplifier. R F R out R out G R F 1 R out 1 R in 1 R L 1 R 1 R in 1 R F 1 R F v out 1 R v in provides the exact input-output relationship. In choosing element values with respect to op-amp characteristics, we can simplify the expression dramatically. Make the load resistance R L much larger than R out . This situation drops the term 1 R L from the second factor of . Make the resistor R  smaller than R in , which means that the 1 R in term in the third factor is negligible. With these two design criteria, the expression () becomes R F R out R out G R F 1 R 1 R F 1 R F v out 1 R v out . Because the gain is large and the resistance R out is small, the first term becomes 1 G , leaving us with 1 G 1 R 1 R F 1 R F v out 1 R v in If we select the values of R F and R so that ≪ R F G R , this factor will no longer depend on the op-amp's inherent gain, and it will equal 1 R F . Under these conditions, we obtain the classic input-output relationship for the op-amp-based inverting amplifier. v out R F R v in Consequently, the gain provided by our circuit is entirely determined by our choice of the feedback resistor R F and the input resistor R . It can even be less than one, but cannot exceed the op-amp's inherent gain and should not produce such large outputs that distortion results (remember the power supply!). Interestingly, note that this relationship does not depend on the load resistance. This effect occurs because we use load resistances large compared to the op-amp's output resistance. Thus observation means that, if careful, we can place op-amp circuits in cascade, without incurring the effect of succeeding circuits changing the behavior (transfer function) of previous ones; see this analog signal processing problem.