Operational Amplifier (OP-AMP) – Formulas and Equations

Electrical Technology

Operational Amplifier (OP-AMP) Formulas

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Operational Amplifiers:

Inverting Amplifier:

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

R_f = Feedback resistor
R_in= Input Resistor
V_in= Input voltage
V_out = Output voltage
A_v = Voltage Gain

Voltage Gain:

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

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:

Output Voltage:

The general output of this given circuit above is;

Inverted Amplified Sum of Input Voltage:

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

If R₁ = R₂= R₃ = R_n= R

Summed Output:

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

If R_f = R₁ = R₂= R₃ = R_n= R;

V_out = – (V₁+ V₂ + V₃ +… + V_n)

Related Post: Negative Feedback Amplifier Systems

Non-Inverting Amplifier:

Terms used for Non-Inverting Amplifier formulas and equations.

R_f = Feedback resistor
R = Ground Resistor
V_in= Input voltage
V_out = Output voltage
A_v = Voltage Gain

Gain Of Amplifier:

The total gain of non-inverting amplifier is;

Output Voltage:

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

Unity Gain Amplifier / Buffer / Voltage Follower:

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

Differential Amplifier:

Terms used for Differential Amplifier formulas.

R_f = Feedback resistor
R_a= Inverting Input Resistor
R_b= Non Inverting Input Resistor
R_g = Non Inverting ground Resistor
V_a= Inverting Input voltage
V_b= Non Inverting Input voltage
V_out = Output voltage
A_v = Voltage Gain

General Output:

the output voltage of the above given circuits is;

Scaled Differential Output:

If the resistor R_f = R_g& R_a= R_b, then the output will be scaled difference of the input voltage;

Unity Gain Difference:

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

V_out= V_b– V_a

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;

Triangular wave input => Rectangular wave output

Sine wave input => Cosine wave output

Integrator Amplifier

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