Op-amp Ideal Inverting Amplifier

Ideal Inverting Amplifier

As the name suggests the output of such an amplifier is inverted as compared to the input signal. The inverted output signal means having a phase shift of 180^o as compared to the input signal.

So, an amplifier which provides a phase shift of 180° between input and output is called inverting amplifier.

The basic circuit diagram of an inverting amplifier using op-amp is shown in the Fig. 2.21.1 (a).

Derivation of closed loop gain :

As node B is grounded, node A is also at ground potential, from the concept of virtual ground, so V_A =0.

I = V_in – V_A / R₁

I = V_in / R₁ ... (2.21.1)

Now from the output side, considering the direction of current I we can write,

I = V_A – V_o / R_f

I = - V_o / R_f  …. (2.21.2)

Entire current I passes through Rf as op-amp input current is zero.

Equating equations (2.21.1) and (2.21.2) we get,

V_in / R₁ = V_o / R_f

The R_f / R₁ is the gain of the amplifier while negative sign indicates that the polarity of output is opposite to that of input. Hence it is called inverting amplifier.

The input and output waveforms are shown in the Fig. 2.21.1 (b).

Observations :

1. The output is inverted with respect to input, which is indicated by minus sign.

2. The voltage gain is independent of open loop gain of the op-amp, which is assumed to be large.

3. The voltage gain depends on the ratio of the two resistances. Hence selecting R_f and R₁, the required value of gain can be easily obtained.

4. If R_f > R₁, the gain is greater than 1.

If R_f < R₁, the gain is less than 1.

If R_f = R₁ the gain is unity.

Thus the output voltage can be greater than, less than or equal to the input voltage, in magnitude.

5. If the ratio of R _f  and R₁ is K which is other than one, the circuit is called scale changer while for R_f / R₁ = 1 it is called phase inverter.

6. The closed loop gain is denoted as A_VF or A_VCL i.e. gain with feedback. 

1. Sign Changer

In the ideal inverting amplifier if R_f ≠ R₁ then the gain is A_CL = -1 Thus the magnitude of output is same as that of the input but its sign is opposite to that of the input.

V_o = -V_in for R_f = R₁

This circuit is called sign changer or phase inverter.

2. Scale Changer

In the ideal inverting amplifier if R_f ≠ R₁ then the gain is ACL = -K where K = R_f/R₁. Thus the circuit is used to multiply input by a constant K called scaling factor.

V_o = -K V_in

Example 2.21.1 Determine the voltage gain of the op-amp circuit shown in the Fig. 2.21.2.

Solution: From the Fig. 2.21.2, R₁ = 10 k Ω, Rf = 47 k Ω

The circuit is inverting amplifier.

The gain is 4.7 and negative sign indicates phase shift i.e. inverting mode.

Example 2.21.2 A sine wave of 0.5 V peak voltage is applied to an inverting amplifier using R₁ = 10 k Ω, and R_f = 50 k Ω. It uses the supply voltages of ± 12 V. Determine the output and sketch the waveform.

If now the amplitude of input sine wave is increased to 5 V, what will he the output ? Is it practically possible ? Sketch the waveform.

Solution : For an inverting amplifier.

Gain = V_o / V_in = - R_f / R₁ = -50 / 10 = -5

 Now V_m = 0.5 V for the input hence,

(V_o)_m = (V_in)_m × Gain = 0.5 × 5 = 2.5 V peak

The input and output waveforms are inverted with respect to each other and are shown in the Fig. 2.21.3 (a).

Now V_m = 5 V for the input hence,

(V_o)_m = (V_in)_m × Gain = 5 × 5 = 25 V peak

But op-amp output saturates at ± 12 V i.e. at supply voltages used. So portion above ± 12 V and below - 12 V will be clipped off from the output. So 25 V peak output is not practically possible. The input and output waveforms are shown in the Fig.2.21.3 (b)

In both cases, there exists a phase shift of 180° between input and output

Review Questions

1. Draw the circuit of inverting amplifier using op-amp and derive expression for its gain.

May-04, 18, Marks 4

2. With the circuit diagram explain the operation of a scale changer.

3. An inverting amplifier using op-amp has R₁ = 10 kΩ and Rf = 47 kΩ. It is applied with 2 V peak to peak sine wave voltage waveform. An a.c. voltmeter is used between the output terminal and ground to measure output voltage. Calculate reading on the voltmeter. Assume supply voltages to be ± 12 V.    

[Ans.: 3.3234 V]