Operational Amplifier (OP-AMP) – Formulas and Equations
Operational Amplifier (OP-AMP) Formulas
Operational Amplifiers:
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;
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 = Rn = R
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 = R2 = R3 = Rn = R;
Vout = – (V1 + V2 + V3 +… + Vn)
- Related Post: Negative Feedback Amplifier Systems
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;
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. Rf = 0, the non-inverting amplifier will become voltage follower/buffer.
Differential Amplifier:
Terms used for Differential Amplifier formulas.
- Rf = Feedback resistor
- Ra = Inverting Input Resistor
- Rb = 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;
Scaled Differential Output:
If the resistor Rf = Rg & Ra = Rb , 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. Ra = Rb = Rf = Rg = R, the amplifier will provide output that is the difference of input voltages;
Vout = Vb – Va
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.
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