# Inverting Op-Amp and the Concept of Virtual Ground

### Inverting Op-Amp Configuration:

As discussed in the previous article, the op-amp is a very high gain differential amplifier. In the open-loop configuration, the typical gain of the op-amp is 105 to 10 Fig. Operational Amplifier

Because of high open-loop gain, even for a small differential input between the two terminals, the output of the op-amp will get saturated. Fig. Voltage Transfer Curve of Operational Amplifier

To use the op-amp as an amplifier, it needs to be operated in the linear region. In the open-loop configuration, the linear input range is very limited. For example, if the saturation voltage of the op-amp is ±10V and open-loop gain is 106 then the differential input range over which the op-amp will operate in the linear range is limited to ± 10 μV. (Saturation Voltage / open-loop gain).

To use the op-amp as an amplifier over a wider input range, somehow its gain needs to be controlled. It is possible to control the gain of the op-amp with negative feedback.

As shown in the figure, in the inverting op-amp configuration, a fraction of output is feedback towards the input side using the feedback resistor Rf and the input is applied at the inverting input terminal through resistor R1. Fig. Inverting op-amp configuraiton

In this configuration, it is possible to control the gain of the op-amp using feedback resistor Rf and resistor R1.

### Concept of Virtual Ground in Operational Amplifier

Ideally, the concept of the virtual ground is applicable when the op-amp is ideal and it is used in the linear range with negative feedback. But for practical op-amps also, since the open-loop gain of the op-amp is very high (105 to 106), this concept is still applicable.

According to this concept, when the op-amp is operated with negative feedback (in the linear region), both inverting and non-inverting op-amp terminals will be at the same potential. When non-inverting op-amp terminal is grounded then the inverting terminal will also act as gound. Although the inverting terminal is not actually grounded, it acts as a virtual ground.

Let’ understand the concept of virtual ground with inverting op-amp configuration.

With negative feedback, assuming op-amp is operating in the linear region, the output of the op-amp can be given as

Vo = Ao x (V+ – V-) = Ao x Vd

V+ is the voltage at the non-inverting input terminal

V- is the voltage at the inverting input terminal

Ao – Open loop gain of the op-amp

For one practical op-amp, let’s say the open-loop gain of the op-amp is 106  and with negative feedback output voltage is 10V.

∴ Vd = 10V / 106 = 10 μV

∴ V+ – V- = 10 μV

with the negative feedback, the voltage difference between the two op-amp terminals is merely 10 μV.

For ideal op-amp, if the open-loop gain is considered as infinite then Vd = 0 or V+ = V-

It shows that when the ideal op-amp is operated with negative feedback, both inverting and non-inverting terminals will be at the same potential. If a non-inverting op-amp terminal is grounded then the inverting terminal will also act as a virtual ground.

### Op-Amp output in inverting configuration (and derivation) Fig. Inverting op-amp configuration

For deriving the output of the op-amp, first, let’s consider the op-amp is ideal. For the ideal op-amp, the input impedance is infinite and no current is flowing into op-amp terminals.

And with the negative feedback, the concept of virtual ground can be applied. Since the non-inverting terminal is at the ground potential, the inverting terminal will also act as a virtual ground. (The voltage at node A will be zero)

Applying KCL at node A,

I1 = I2

⇒ (Vin – VA)/ R1 = (VA – Vo)/Rf

Since VA = , Vin /R = -Vo /Rf

⇒ Vo = -(Rf / R1)*Vin

As per the expression, by controlling the feedback resistor and resistor R1, it is possible to control the gain of the op-amp. Moreover, there is a negative sign in the output expression.

e.g if the input is 1V DC and gain of the op-amp is 5, then the output of the op-amp in the inverting configuration is -5V.

In the next article, the non-inverting op-amp configuration will be discussed.