Inverting Amplifier

One of the basic amplifier configuration with operational amplifier as active element in the circuit is the inverting amplifier. The simple circuit configuration of the inverting amplifier is shown on Picture 1. Since the op amp takes no input current, the same current flows through R1 and R2. Because the non-inverting input is grounded, a virtual ground exist in the inverting input by virtue of the infinite gain and the negative feedback being used. Thus, for the input and output voltage we can write:

Vi = i x R1

Vo = -i x R2

So, according to these relations, the voltage gain (amplification) of this inverting amplifier is:

Av = Vo/Vi = -R2/R1

Picture 1: Inverting Amplifier with OP Amp


For our circuit configuration shown on Picture 1, the voltage amplification is Av = -5K/500 = -10. This amplification can also be measured from the wave forms of the input and output voltage signals shown on Picture 2. These plots are generated with transient simulation in LT Spice. The power supply voltages are V+ = 12 V DC and V- = -12 V DC. The input voltage has amplitude of +/- 100 mV at frequency of 500 Hz. The green color plot line is input voltage Vi wave form and the blue color plot line is the output voltage Vo wave form.

Picture 2: Input/Output voltage wave forms of the Inverting Amplifier with OP Amp


The input impedance of this circuit is Ri = R1. To find the output impedance, we can apply a test current source to the output and ground to Vi. Because of virtual ground, no current flows through R1. Since no current flows into the inverting input, the current through R2 must be 0 as well. Thus, independently of the test current, Vo remains grounded in the ideal op amp. Consequently the output resistance is ideally 0.