# Introduction to Virtual Grounds and Virtual Shorts in Operational Amplifiers

Operational amplifiers are the workhorse of analog Electronic design. Since time immemorial, these humble devices have been used in everything from simple voltage followers to complex inverter designs. At CircuitDigest, we have discussed various op amp circuits and their applications. Today, we’re going to look at another interesting concept related to op amps called virtual grounds and virtual shorts. So, let’s dig a little deeper.

Author: Rajeswari

Operational amplifiers are the workhorse of analog electronic design. Since time immemorial, these humble devices have been used in everything from simple voltage followers to complex inverter designs. At CircuitDigest, we have discussed various op amp circuits and their applications. Today, we’re going to look at another interesting concept related to op amps called virtual grounds and virtual shorts. So, let’s dig a little deeper.

What are virtual grounds and virtual shorts?

Before going into the details, let’s take a look at the numbers given below. In panel (a), VA = the voltage at VB, this is because there is a short circuit between the VA and VB points. In figure (b), there is no connection (short circuit) between VA and VB. However, the voltage at VB = VA is still not connected to any other source, which means there should be a virtual connection between VA and VB, or VB equals VA due to some other virtual effect. This is an effect commonly referred to as a “virtual short circuit”.

Also, in Figure (c), even though VA is connected to a 5V source, due to some effect, if VA = VB = 0V (Gnd_PotenTIal) it means that this effect will be called “virtual ground”.

The details mentioned above may seem magical or impractical. However, basic op amp operation follows the above two concepts, and understanding the reasons behind it will help to understand the full op amp physics.

Basic operational amplifier rules:

The working mechanism of a basic op amp follows two important rules:

The voltages at the non-inverting and inverting inputs of an op amp should always be equal. Internal op amp design and output feedback resistors always tend to make them equal to maintain stable op amp operation.

According to the characteristics of op amps, op amps have high input impedance and low output impedance. Therefore, for ideal op amp operation, the current flowing through the input terminals of the op amp is assumed to be “zero”.

Virtual short circuit in op amps

The circuit below is a well-known non-inverting op amp topology with a 1V input and a gain resistor of R1 = R2 = 1KΩ. It has some defined equations in order to find the relationship between the input and output voltage relationship. Instead of using those defined formulas, we can apply basic op amp rules to find the output voltage.

According to rule – 1, the inverting input (-) voltage should be equal to the non-inverting (+) input voltage, V_Non_InverTIng = 1V for a given circuit. Like the non-inverting (+) pin, the inverting (-) pin is not connected to any dedicated voltage source, only the op-amp VOUT can bring the inverting (-) terminal to 1V.

So once the op amp is “powered up”, the internal parameters of the op amp work so that the inverting input voltage is equal to 1V, and as a rule, no current flows through the inverting pin. Since R1 and R2 become a voltage divider with VOUT as the source voltage, the output of the voltage divider should be equal to the non-inverting input voltage.

The output voltage changes from its previous state to a higher or lower voltage level such that V(+) = V(-). Here, since R1=R2 and both form a voltage divider combination, and VOUT = 2V such that (V+) = V(-).

Based on the following noninverting op amp gain equation:

So for a non-inverting op amp, the inverting pin voltage is equal to the non-inverting voltage without a direct short between the two terminals, and equal voltages on the two terminals occur through Virtual Concept, this effect is called a “virtual short circuit” op amp “.

Virtual ground concept in op amps

By applying rules 1 and 2 in the inverting op amp configuration below, the voltage at the inverting pin should be zero. However, the inverting pin (-) is connected to the 5V supply through R1. According to Rule 2, no current flows through the inverting (-) input, all current flows through R1 and R2. In order for V(-) = 0, VOUT must provide an offset voltage.

In the given circuit, the positive 5V is supplied to the inverting terminal through a 1K resistor, in order for the inverting terminal voltage = 0, VOUT should be -5V (due to R2 = 1K). If the value of R2 is modified, the internal structure of the op amp should also modify VOUT so that V(In-) = 0.

For inverting opamp configuration => V1/R1 = -VOUT/R2

In this inverting input configuration, the inverting input is always mentioned at “ground potential” (due to the non-inverting input ground potential), which is not directly connected to ground due to the internal function of the op amp. Even if the inverting input is powered by a 5V supply, the inverting terminal voltage is equal to “Gnd”, which is why it is called “virtual ground” or “virtual ground”.

Importance of virtual grounds and virtual shorts in op amps

Virtual ground and virtual short are two important parameters for examining any op amp circuit. Most op amp circuit derivations and transfer functions are formulated based on these two concepts and make circuit analysis simpler without considering the op amp’s input parameters.

The virtual ground and virtual short concepts only apply to “closed loop” op amp circuits. In an open loop or op amp used as a comparator, there is no feedback mechanism to control the matching between the inverting and non-inverting input voltages. So the op amp always operates in saturation mode and virtual ground, the virtual short concept doesn’t work. Under these types of conditions, designers should look at the “differential input” voltage limits to avoid op amp failure.

The virtual ground and virtual short concepts also fail under certain closed loop conditions when the output matching limits exceed the op amp’s Vcc and Vee supply ranges.

Examples of virtual ground and virtual short void conditions