# Inverting & Non-Inverting Amplifiers

## INVERTING AMPLIFIER

A inverting amplifier provides the same function as the common emitter and common-source amplifiers. The schematic diagram for an inverting amplifier is shown in Figure (a).

Observe that the offset and D.C. voltages have been left off of these circuits for simplicity. These connections are generally the same for all circuits using the same type of OP-AMP.

The input signal is applied to the inverting (minus) input. The (-) input produces a 180^{o} phase shift between input and output signal. The non-inverting (plus) input is grounded and is common to both the input and the output.

Negative feedback (degenerative) is coupled from the output back to the input through the feedback resistor (R_{f}). The ratio of Ri to R_{f} will determine, the circuits voltage gain voltage gain for this circuit can be calculated using the formula.

A_{v} = R_{f} / R_{i}

This formula can be derive as follows:

The input and feedback current are algebraically added as point G. it is also called summing point. Hence it is assumed to be zero or at ground potential the specific term used for this point is virtual ground.

I_{1} = V_{in} / R_{1}

And I_{2} = -V_{out} / R_{f}

Note that negative sign is because of negative feedback current.

By using Kirchhoff’s current law

I_{1} + (-I_{2}) = 0

Because I_{1} and I_{2} are combining at point G.

I_{1} – I_{2} = 0

(V_{in} / R_{1}) – (-V_{in} / R_{f}) = 0

(V_{in} / R_{1} ) + ( V_{out} / R_{f}) = 0

V_{in} / R_{f} = V_{out} R_{f}

R_{f} / R_{1} = V_{out} / V_{in}

V_{out} / V_{in} = R_{f} / R_{1}

Voltage gain = V_{out} / V_{in} = R_{f} / R_{1}

A_{v} = R_{f} / R_{1}

Equation shows that closed loop gain of the inverting amplifier depends on the ratio of two external resistors R_{1} and R_{f}.

### Virtrual Ground

The term virtual ground can be easily understand by using Figure (a).

This figure employs negative feedback with the help of resistor R_{f} which feeds a portion of output in to input.

The concept of virtual ground arises from the fact that input voltage V_{in} at the inverting terminal of the OP-AMP is forced to such a small value that for all practical purposes, it may be assumed to be zero. Hence point G is essentially at ground voltage and is referred to as virtual ground.

Note that it is not actually ground as shown in Figure (b). The terminal which is connected to ground is non-inverting (+) trminal.

Virtual ground can also be described as "A node which is at zero potential with respect to ground, but not physically ground.

The input and feedback current are algebraically added at point G.

## NON-INVERTING AMPLIFIER

The schematic diagram for a non-inverting amplifier shown in Figure (b) output of this circuit is in phase with the input. Notice that the input is applied to the non-inverting (+) input while the feedback is applied to the inverting (-) input.

A resistor R_{1} is connected from the inverting input to the common circuit between input and output. The non-inverting input is always used when we do not want the signal to the inverted.

Feedback is applied to inverting input through resistor R_{f} which is connected to R_{1} and the OP-AMPs inverting input. The ratio of these resistors (R_{1} and R_{f}) has an effect on the circuit gain. Voltage gain can be calculated using the formula.

A_{v} = (R_{1} + R_{f}) / R_{1}

Or A_{v} = 1 + (R_{f} / R_{1})

This equation can be derived as follows:

Voltage across R_{1} is the input voltage

V_{in} = IR_{1}

The output voltage is applied across the series combination of R_{1} and R_{f} therefore,

V_{out} = voltage across R_{1} + voltage across R_{f}

V_{out} = I.R_{1} + I.R_{f}

V_{out} = I (R_{1} + R_{f})

V_{out} / V_{in} = (1(R_{1} + R_{f})/ IR_{1})

A_{v} = (R_{1} + R_{f}) / R_{1}

A_{v} = 1 + (R_{f} / R_{1})

### Alternative Method:

In this figure the current through two resistor is I_{1} and I_{2}.

The voltage across R_{1} is V_{out} and across R_{f} (V_{out} – V_{out}).

I_{1} = V_{in} / R_{1} ------------------(1)

And I_{2} = (V_{out} – V_{in}) / R_{1} ----------------(2)

Using KCL to point G(virtual ground). We have

I_{2} + (-I_{1}) = 0

From equation (1) and (2)

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