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Operational Amplifier (OP-AMP) – Formulas and Equations

Operational Amplifier (OP-AMP) Formulas

Operational Amplifier (OP-AMP) - Formulas and Equations

Operational Amplifiers:

Inverting Amplifier:

Inverting Amplifier

The following terms are used in the formulas and equations for Operational Amplifies.

  • Rf = Feedback resistor
  • Rin = Input Resistor
  • Vin ­­­= Input voltage
  • Vout = Output voltage
  • Av = Voltage Gain

Voltage Gain:

The close loop gain of an inverting amplifier is given by;

gain of an inverting amplifier

Output Voltage:

The output voltage is out of phase with the input voltage that is why it is known as the inverting amplifier.

Summing Amplifier:

Summing Amplifier

Output Voltage:

The general output of this given circuit above is;

Summing Amplifier

Inverted Amplified Sum of Input Voltage:

if the input resistors are same, the output is a scaled inverted sum of input voltages,

If R1 = R= R3 = R= R

Inverted Amplified sum of input voltage

Summed Output:

When all the resistors in the above given circuit are same, the output is an inverted sum of input voltages.

If Rf = R1 = R= R3 = R= R;

Vout = – (V+ V2 + V3 +… + Vn)

Non-Inverting Amplifier:

Non-Inverting Amplifier

Terms used for Non-Inverting Amplifier formulas and equations.

  • Rf = Feedback resistor
  • R = Ground Resistor
  • Vin ­­­= Input voltage
  • Vout = Output voltage
  • Av = Voltage Gain

Gain Of Amplifier:

The total gain of non-inverting amplifier is;

Non-Inverting Amplifier

Output Voltage:

The output voltage of non-inverting amplifier is in-phase with its input voltage and it’s given by;

output voltage of non-inverting amplifier

Unity Gain Amplifier / Buffer / Voltage Follower:

If the feedback resistor in removed i.e. Rf = 0, the non-inverting amplifier will become voltage follower/buffer.

Unity gain amplifier

Differential Amplifier:

Differential Amplifier

Terms used for Differential Amplifier formulas.

  • Rf = Feedback resistor
  • R= Inverting Input Resistor
  • R= Non Inverting Input Resistor
  • Rg = Non Inverting ground Resistor
  • Va ­­­= Inverting Input voltage
  • Vb ­­­= Non Inverting Input voltage
  • Vout = Output voltage
  • Av = Voltage Gain

General Output:

the output voltage of the above given circuits is;

Differential Amplifier

Scaled Differential Output:

If the resistor Rf = Rg  & R= R, then the output will be scaled difference of the input voltage;

Scaled Differential Output

Unity Gain Difference:

If all the resistors used in the circuit are same i.e. Ra = R= R= R= R, the amplifier will provide output that is the difference of input voltages;

Vout = V– Va

Differentiator Amplifier

Differentiator Amplifier

This type of Operational Amplifier provides the output voltage which is directly proportional to the changes in the input voltage. The output voltage is given by;

Differentiator Amplifier

Triangular wave input => Rectangular wave output

Sine wave input => Cosine wave output

Integrator Amplifier

Integrator Amplifier

This amplifier provides an output voltage which is the integral of the input voltages.

Integrator Amplifier

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