Analyze Inverting Op Amp Circuits

An inverting amplifier takes an input signal and turns it upside down at the op amp output. When the value of the input signal is positive, the output of the inverting amplifier is negative, and vice versa. Here is an inverting op amp. The op amp has a feedback resistor R₂ and an input resistor R₁ with one end connected to the voltage source.

The other end of the input resistor is connected to the inverting terminal, and the noninverting terminal is grounded at 0 volts. The amount of amplification depends on the ratio between the feedback and input resistor values.

Because the noninverting input is grounded to 0 volts, you have

For ideal op amps, the voltages at the inverting and noninverting terminals are equal and set to zero. The inverting terminal is connected to a virtual ground because it’s indirectly connected to ground by v_P.

Apply Kirchhoff’s current law (KCL) to Node A to get the following:

Simplify the equation with the following constraints for an ideal op amp:

The constraints make the KCL equation simpler:

You wind up with the following relationship between the input and output voltages:

Again, the amplification of the signal depends on the ratio of the feedback resistor R₂ and input resistor R₁. You need only external components of the op amp to make the signal way bigger. The negative sign means the output voltage is an amplified but inverted (or upside down) version of the input signal.

For a numerical example, let R₂ = 10 kΩ and R₁ = 1 kΩ. In that case, the inverted output voltage v_O is ten times as big as the input voltage v_S. In nothing flat, you just made a weak signal stronger. Nice work — you deserve a raise!

Resistors should be around the 1 kΩ to 100 kΩ range to minimize the effects of variation in the op amp characteristics and voltage sources.