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Operational Amplifier Equations For Circuit Design

Introduction

An operational amplifier (op-amp) is an analogue circuit block that takes a differential voltage input and produces a single-ended voltage output. How to solve op-amp circuits? Look at the following op-amp equations by several main operational amplifier applications circuit.

An operational amplifier has two input pins and one output pin. Its applications in a host of different circuits where their attributes of gain, input impedance, output impedance, differential input and so on. The major op-amp formulas used to calculate are shown as follow:

Voltage Follower

Fig 1. Voltage Follower
Note: Buffer High Impedance Signal and Low Impedance Load

 

In-phase Op-Amp

Fig 2. In-phase Op-Amp
Note: In-phase Signal Amplification

 

Reversed-phase Op-Amp

Fig 3. Reversed-phase Op-Amp
Note: Amplify and Invert Input

 

Voltage Subtractor, Differential Amplifier

Fig 4. Voltage Subtractor, Differential Amplifier
Note: Amplify the voltage difference and suppress the common-mode voltage

 

Voltage Adder

Fig 5. Voltage Adder
Note: Summation of Adding Voltage Values

 

Low-pass Filter, Integrator

Fig 6. Low-pass Filter, Integrator
Note: Limit Signal Bandwidth

 

High-pass Filter, Differentiator

Fig 7. High-pass Filter, Differentiator
Note: Eliminate DC, Amplify AC Signal

 

Differential Amplifier

Fig 8. Differential Amplifier
Note: Drive Differential Signal to Analog-to-Digital Converter From A Differential or Single-ended Signal Source

 

Instrumentation Amplifier

Fig 9. Instrumentation Amplifier
Note: Amplify the Low-Level Difference Signal and Suppress the Common Mode Signal

 

Single-State Op-Amp Noise

Fig 10. Single-State Op-Amp Noise

Note:
RTO NOISE=NG×RTI NOISE
RTI=Converted to the Input
RTO=Converted to the Output

 

Decibel Formula (equivalent impedance)

Decibel Formula (equivalent impedance)

 

Johnson-Nyquist Noise Formula

Johnson-Nyquist Noise Formula

 

Ohm's Law (DC circuit)

Ohm's Law (DC circuit)

 

Closed-loop Frequency Response (voltage feedback amplifier)

Fig 11. Closed-loop Frequency Response (voltage feedback amplifier)

 

Resistance Formulas

Resistance Formulas

 

Reactance_Formulas_13baa8cfa2fbf9c5304ec946faeded509eb03ea7.jpg

Reactance Formulas

 

Impedance Formulas (in series)

Impedance Formulas (in series)
Note:
RL in series
RC in series
LC in series
RLC in series

 

Voltage and Impedance Formulas (parallel connection)

Voltage and Impedance Formulas (parallel connection)

 

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