Inverting Operational Amplifier – Inverting Op Amp

In this lecture, we are going to discuss the Inverting Operational Amplifier. We will discuss the operation of inverting Op Amp, derivation of the closed-loop voltage gain of inverting operational amplifier, and input and output resistance.

There are three basic op-amp configurations:

1. Inverting operational amplifier
2. Non-inverting operational amplifier
3. Buffer amplifier or Voltage follower

Note that the inverting operational amplifier configuration discussed in this section, we assume that the used operational amplifier in this section is ideal.

Inverting Operational Amplifier

The circuit diagram of an inverting operational amplifier is shown in the figure below.

The signal which is to be the amplifier is applied at the inverting (-) terminal of Op-amp.

The amplified output signal will be 180⁰ out of phase with the input signal.

In other words, the output signal is inverted. Therefore this amplifier is known as the inverting operational amplifier.

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Also Read: what is Op-amp? |Block diagram of op-amp

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Operation of Inverting Op Amp

The signal to be amplified (V_s) has been connected to the inverting terminal via the resistance R₁. The other resistor R_F, connected between the output and inverting terminals is called the feedback resistance. It introduced negative feedback.

The non-inverting (+) terminal is connected to the ground.

As the op-amp is an ideal operational amplifier, its open loop voltage gain A_v = -∞ and input resistance R_i = ∞.

The input and output voltage waveforms are shown in the below figure. Output is an amplified and inverted version of the input signal V_s.

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Also Read: What is CMRR? | Common Mode Rejection Ratio

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Closed Loop Voltage Gain of Inverting Op Amp

• Looking at the figure of the inverting amplifier, we can write that,

\mathbf{V_0 = \left | A_V \right | \times V_d }

\therefore \mathbf{V_d = \frac{V_0} {\left | A_V \right |}}

Where A_v = open loop voltage gain of Op-Amp

• As we know A_v of an open loop Op-amp is ∞.

\therefore \mathbf{V_d = \frac{V_0} {\infty } = 0}

But, V_d = V₁ – V₂

∴ V₁ – V₂ = 0

• As the non-inverting (+) terminal is connected to the ground, V₁ = 0. Sp from above equation V₂ = 0. Thus V₂ is as ground potential.

• Since the input resistance R_i = ∞, the current going into the Op-amp will be zero. Therefore the current I that passes through R₁ will also pass through R_F as shown in the figure. As voltage V₂ = 0, the input voltage V_s is the voltage across R₁ and the voltage across R_F is the output voltage.

• The input voltage, V_s is given by,

V_s = I R₁

And the output voltage V₀ is given by,

V₀ = – I R_F

• Closed loop voltage gain \mathbf{A_{VF} = \frac{V_0}{V_s}}

Substituting the expression for V₀ and V_s, we get

\boxed{\mathbf{A_{VF} = - \frac{IR_F}{IR_1} = -\frac{R_F}{R_1} }}

Note: The negative sign indicates that there is a phase shift between te input and output voltages.

From the above equation, we can draw the following important conclusions:

1. The value of closed-loop voltage gain A_VF does not depend on the value of open-loop voltage gain A_v.
2. The value of A_VF can be very easily adjusted by adjusting the values of the resistor R_F and R₁. generally, the feedback resistor R_F is a potentiometer to adjust the gain to its desired value.
3. The output is an amplified inverted version of an input.

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Also Read: Ideal Differential Amplifier

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Ideal Closed Loop Characteristics of Inverting Op Amp

We have already obtained the value of the ideal closed-loop voltage gain on inverting operational amplifiers. Now let us obtain the ideal closed-loop input resistance and output resistance values of inverting op-amp.

Closed loop input resistance R_iF

Referring to the above figure, we can conclude that the input resistance R_i is the resistance seen by the source V_s. Since V₂ = 0 due to the virtual ground concept.

R_i = R (between point A and GND)

R_iF = R₁

Note: This shows that the input resistance of the inverting operational amplifier with ideal op-amp is equal to only R1, (instead of ∞). This is the biggest disadvantage of inverting configuration.

Closed loop output resistance R_oF

Referring to the above figure, we can write that,

R_oF = 0

This is because the output resistance of an ideal op-amp i.e. R₀ = 0

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FAQs on Inverting Op Amp

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