Inverting Amplifier

Op-Amp inverting amplifier.

The above diagram is an inverting amplifier. The difference between the inverting amplifier and the non-inverting amplifier is that the locations of the input and ground are swapped.

For the inverting amplifier, the non-inverting input of the op-amp is connected to ground (0 volts). Since the op-amp will make its output voltage whatever it takes to make to inverting input equal to the non-inverting input, the inverting input will also be at 0 volts. With the inverting amplifier, the inverting input of the op-amp often called a virtual ground. This is because, under normal operation the inverting input will always have a potential of 0 volts. However, this is called a virtual ground for a reason. A fault in the feedback network, of an unexpectedly high input voltage can make it impossible for the op-amp to put a voltage on its output that will make the input voltages equal. In that case the voltage at the inverting input will not be 0 volts. You cannot use the virtual ground as a circuit ground.

In the above example, each resistor is 1k. The left side of R1 has the input voltage and the right side is always at 0 volts. Therefore, the voltage across R1 will always be equal to the input voltage. That is 2 volts in this illustration. R2 has the same resistance as R1 so it must have the same voltage as R1. We start at +2 volts and lose 2 volts across R1, then lose 2 more volts across R2. This means the output voltage must be -2 V. 

Notice that when the resistors are equal, the output voltage is equal to the input voltage but of opposite polarity. For example, if the input is +2 volts the output will be -2 volts. If R2 has double the value of R1, the output voltage will be twice the input voltage. Therefore, the voltage gain of the inverting amplifier is equal to the ratio of the feedback resistors but of reversed polarity. You do not add 1 to the ratio of the resistors to find the gain of the inverting amplifier.

Circuit with resistor to compensate for current flowing internally between inputs.

Occasionally, you my see a resistor between the non-inverting input and the ground. In some applications the circuit may be sensitive to tiny currents that flow into the inverting input and back out the non-inverting input to ground. A resistor at the non-inverting input equalizes the voltage drift caused by such currents. The compensation resistor should be equal to the combined values of R1 and R2 calculated in parallel.

AC operation

Like the non-inverting amplifier, when there is a mix of AC and DC at the input, the voltages are thought of as if they are treated separately. For example, if you have 3 V_p-p centered on +2 V DC, and the gain of the inverting amplifier is 2, the output will be 6 V_p-p centered on -4 V DC. The DC output has the opposite polarity to the DC input. However, there is no concept of polarity with AC. Therefore, the AC component has no polarity label.