Closed Loop Configuration of Op-Amp

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Closed Loop Configuration

When a part of output is fed back (given) to the input it is called closed loop configuration. It means that some kind of feedback is introduced in the circuit. In this article, following four circuits of closed loop configuration of Op-amp are explained.

  1. Inverting amplifier
  2. Sign changer
  3. Non-inverting amplifier
  4. Voltage follower

Inverting Amplifier

In this mode of an Op-amp, non-inverting terminal is grounded and the input voltage (Vin) is applied to inverting terminal through resistor Ri. The negative feedback is applied through resistor Rf from output to input.

For amplification feedback resistance must be greater than input resistance (Rf > Ri).

The circuit diagram for closed loop inverting configuration of op-amp (Inverting amplifier) is as follows.

closed loop configuration of inverting op amp,

Expression for Output Voltage

Let the voltage at point A and B is VA and VB respectively.

Applying Kirchhoff’s current law at point B,

{I_i} = \;{I_f}\;\;\;

\frac{{{V_{in}} - {V_B}}}{{{R_i}}} = \frac{{{V_B} - {V_O}}}{{{R_f}}}                                   …(1)

As node A is grounded. Considering Op-amp as ideal, node B is at virtual ground. (Always apply virtual ground concept to inverting configuration of op-amp.)

VA=VB=0

\therefore \frac{{{V_{in}} - 0}}{{{R_i}}} = \frac{{0 - {V_O}}}{{{R_f}}}

\therefore \frac{{{V_{in}}}}{{{R_i}}} = \frac{{ - {V_O}}}{{{R_f}}}

\therefore {V_O} = - \frac{{{R_f}}}{{{R_i}}}{V_{in}}                                       …(2)

This is expression for output voltage of closed loop inverting amplifier. The negative sign indicates that there is a phase shift of 180° between the input and output voltages.

Similarly, using above equation (2) the gain can be given as

Gain = \frac{{{V_O}}}{{{V_{in}}}} = - \frac{{{R_f}}}{{{R_i}}}

Here  \frac{{{V_O}}}{{{V_{in}}}}

 is closed loop gain for inverting Op-amp. Here negative sign indicates input is inverted at output. Hence it is called as inverting amplifier.

Output Waveform of Inverting Amplifier

output waveform of inverting op amp

Inverter or Sign-Changer

In a closed loop inverting amplifier if

Rf=Ri=R then

 

Gain = - \frac{{{R_f}}}{{{R_i}}} = - \frac{R}{R}

Gain = -1

The circuit diagram for Op-amp as an inverter is as follows. 

 

closed loop configuration of op amp, inverter, sign changer opamp circuit,

The output equals to input with 180° out of phase in inverter or sign changer.

inverter or sign changer waveform, closed loop configuration of op amp,

Non-Inverting Amplifier

In this mode of an Op-amp, the inverting terminal is grounded and the input voltage (Vin) is applied to non-inverting terminal through resistor Ri. The negative feedback is applied through resistor Rf from output to input.

For amplification feedback resistance must be greater than input resistance (Rf > Ri).

The circuit diagram for closed loop non-inverting configuration of op-amp (Non-inverting amplifier) is as follows.

Closed Loop Configuration of Op-Amp

Expression for Output Voltage

Let the voltage at point A and B is VA and VB respectively.

Applying Kirchhoff’s current law at point B,

{I_i} = \;{I_f}\;

 

\frac{{0 - {V_B}}}{{{R_i}}} = \frac{{{V_B} - {V_O}}}{{{R_f}}}          … (1)

 

Consider Op-amp as an ideal Op-amp. As node A is at potential Vin, the node B is also at same potential.

 

{V_A} = {V_B} = {V_{in}}

 

Hence equation (1) will be

\therefore \frac{{0 - {V_{in}}}}{{{R_i}}} = \frac{{{V_{in}} - {V_O}}}{{{R_f}}}

 

\therefore - \frac{{{V_{in}}}}{{{R_i}}} = \frac{{{V_{in}}}}{{{R_f}}} - \frac{{{V_O}}}{{{R_f}}}

 

\therefore \frac{{{V_O}}}{{{R_f}}} = \frac{{{V_{in}}}}{{{R_f}}} + \frac{{{V_{in}}}}{{{R_i}}}

 

\frac{{{V_O}}}{{{R_f}}} = {V_{in}}\left[ {\frac{1}{{{R_f}}} + \frac{1}{{{R_i}}}} \right]

 

\therefore {V_O} = {V_{in}}\left[ {\frac{{{R_i} + {R_f}}}{{{R_f}{R_i}}}} \right]{R_f}

 

{V_O} = {V_{in}}\left[ {\frac{{{R_i} + {R_f}}}{{{R_i}}}} \right]

 

{V_O} = {V_{in}}\left[ {\frac{{{R_i}}}{{{R_i}}} + \frac{{{R_f}}}{{{R_i}}}} \right]

 

\therefore {V_O} = \left[ {1 + \frac{{{R_f}}}{{{R_i}}}} \right]{V_{in}}           … (2)

 

This is expression for output voltage of a non-inverting amplifier.

There is no negative sign indicates that the output voltage and input voltage are in phase. As input voltage is not inverted at output, it is called as non-inverting amplifier.

Now, the gain of non-inverting op-amp can be obtained by using equation (2) as

 

Gain = \frac{{{V_O}}}{{{V_{in}}}} = 1 + \frac{{{R_f}}}{{{R_i}}}

 

Here  \frac{{{V_O}}}{{{V_{in}}}}  is closed loop gain for non-inverting Op-amp.

Output Waveform of Non-Inverting Amplifier

closed loop configuration of op amp,

Voltage Follower (Unity Gain Buffer)

When Ri=∞ and Rf=0 the non-inverting amplifier gets converted into voltage follower or unity gain amplifier.

The circuit diagram of Op-amp as an unity gain follower (Voltage follower) is as follows.

Closed Loop Configuration of Op-Amp

A circuit in which the output voltage follows the input voltage is called follower circuit.

For non-inverting amplifier,


Gain = \frac{{{V_O}}}{{{V_{in}}}} = 1 + \frac{{{R_f}}}{{{R_i}}}


As Rf=0 means no feedback is present

        Gain=1

Here output voltage will be equal and in phase with input voltage.

Closed Loop Configuration of Op-Amp
Inverting Amplifier and Sign Changer

For Video tutorials on Closed Loop Configuration of Op-Amp

Non-Inverting Amplifier and Voltage follower

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