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20 Formulas for Operational Amplifier Circuit Design

Author: Apogeeweb Date: 19 Sep 2019  5373

basic amp circuit

Ⅰ Introduction

Although there are many types of operational amplifiers, different amplifier circuits are suitable for interfacing with different types of sensors, but most complex amplifiers are built by combining operational amplifiers. In order to get good amplication effect, it is necessary to design the circuit of the amplifier. This paper will introduce 20 opamp formulas as a design reference.

Op Amp Formulas For Voltage Calculation


Ⅰ Introduction

Ⅱ Operational Amplifier Formulas

Ⅱ Operational Amplifier Formulas

In almost cases today, op amps are configured in different ways using a feedback network to “calculate” the input signal. There are 20 formulas used to calculate.

Figure 1. Voltage Follower

Note: Buffer High Impedance Signal and Low Impedance Load


Figure 2. In-phase Op Amp

Note: In-phase Signal Amplification


Figure 3. Reversed-phase Op Amp

Note: Amplify and Invert Input


Voltage Subtractor, Differential Amplifier Circuit

Figure 4. Voltage Subtractor, Differential Amplifier

Note: Amplify the voltage difference and suppress the common - mode voltage


Voltage Adder circuit

Figure 5. Voltage Adder

Note: Summation of Adding Voltage Values


As a Low-pass Filter, Integrator

Figure 6. Low-pass Filter, Integrator

Note: Limit Signal Bandwidth


High-pass Filter, Differentiator.png

Figure 7. High-pass Filter, Differentiator

Note: Eliminate DC, Amplify AC Signal


Differential Amplifier

Figure 8. Differential Amplifier

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


Instrumentation Amplifier

Figure 9. Instrumentation Amplifier

Note: Amplify the Low Level Difference Signal and Suppress the Common Mode Signal


Single State Op Amp Noise

Figure 10. Single State Op Amp Noise


     RTI=Converted to the Input

RTO=Converted to the Output


Decibel Formula (equivalent impedance)


Johnson-Nyquist Noise

Johnson-Nyquist Noise Formula



Ohm's Law (DC circuit)


Closed-loop Frequency Response (voltage feedback amplifier)

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


resistance formulas.png

Resistance Formulas


Reactance Formulas


Transformer (step-up or step-down ratio)


Impedance Formulas (in series)

Note: RL in series

RC in series

LC in series

RLC in series 


Voltage and Impedance Formulas (parallel connection)


Frequently Asked Questions about Operational Amplifier Circuit

1. How do you make an op amp circuit?

2. What is amplifier with example?
Amplifiers are usually designed to function well in a specific application, for example: radio and television transmitters and receivers, high-fidelity ("hi-fi") stereo equipment, microcomputers and other digital equipment, and guitar and other instrument amplifiers.


3. Why do op amps have two inputs?
Operational amplifiers have two power supply rails because they usually need to swing bipolar - output voltages that go either positive or negative in response to the normal range of input signals. ... Without the dual supplies the output signal would clip at the ground potential.


4. Which type of amplifier is best?
Class “A” amplifiers are considered the best class of amplifier design due mainly to their excellent linearity, high gain and low signal distortion levels when designed correctly.


5. Are op amps AC or DC?
The basic Op-amp construction is of a 3-terminal device, with 2-inputs and 1-output, (excluding power connections). An Operational Amplifier operates from either a dual positive ( +V ) and an corresponding negative ( -V ) supply, or they can operate from a single DC supply voltage.


6. Can op amp amplify both AC and DC?
Infinite – An ideal operational amplifier has an infinite frequency response and can amplify any frequency signal from DC to the highest AC frequencies so it is therefore assumed to have an infinite bandwidth.


7. Do op amps work with DC?
In principle, yes, you can amplify DC with an op-amp, subject to the constraints of the amplifier. Mainly, the amplified output voltage must be between the output limits of the op-amp. ... (A fraction of the final output of the power supply is fed back to the op-amp's negative input to regulate the overall circuit.)


8. How do you amplify DC current?
A transistor can be used to increase current. You'll have a low current path, from base to emitter in an NPN, and a higher current path from collector to emitter. The collector current will be a multiple of the base current if the circuit allows it.


9. What are the ideal characteristics of op amp?
Ideal op amps use no power, have infinite input impedance, unlimited gain-bandwidth and slew rate, no input bias current, and no input offset. They have unlimited voltage compliance.


10. What is slew rate of op amp?
Slew rate is defined as the maximum rate of change of an op amp's output voltage and is given units of volts per microsecond. Slew rate is measured by applying a large signal step, such as 1V, to the input of the op amp, and measuring the rate of change from 10% to 90% of the output signal's amplitude.

Ordering & Quality

Photo Mfr. Part # Company Description Package PDF Qty Pricing
ADA4895-1ARZ-R7 Company:Analog Devices Inc. Remark:General Purpose Amplifier 1 Circuit Rail-to-Rail 8-SOIC Package:8-SOIC (0.154"", 3.90mm Width)
In Stock:On Order
1000+: $2.62010
MCP607T-I-ST MCP607T-I-ST Company:Microchip Technology Remark:IC OPAMP GP 2 CIRCUIT 8TSSOP Package:8-TSSOP (0.173", 4.40mm Width)
In Stock:7357
2500+: $0.74000
1+: $0.98000
25+: $0.81000
100+: $0.74000
TLC2652M-8DG4 Company:Texas Instruments Remark:Zero-Drift Amplifier 1 Circuit 8-SOIC Package:8-SOIC (0.154"", 3.90mm Width)
In Stock:On Order
59+: $4.27237
TLE2022MLB TLE2022MLB Company:Texas Instruments Remark:General Purpose Amplifier 2 Circuit TO-99-8 Package:TO-99-8 Metal Can
In Stock:On Order
27+: $9.37000
LM324ADTBR2G LM324ADTBR2G Company:ON Semiconductor Remark:General Purpose Amplifier 4 Circuit 14-TSSOP Package:14-TSSOP (0.173"", 4.40mm Width)
In Stock:On Order
1+: $0.44000
10+: $0.38000
25+: $0.35480
100+: $0.26360
250+: $0.22308
500+: $0.21294
1000+: $0.15717
2500+: $0.14703
5000+: $0.13689
UA741MD UA741MD Company:STMicroelectronics Remark:General Purpose Amplifier 1 Circuit 8-SO Package:8-SOIC (0.154"", 3.90mm Width)
In Stock:On Order
TLC2274IPWR TLC2274IPWR Company:Texas Instruments Remark:General Purpose Amplifier 4 Circuit Rail-to-Rail 14-TSSOP Package:14-TSSOP (0.173"", 4.40mm Width)
In Stock:On Order
1+: $1.98000
10+: $1.77800
25+: $1.67760
100+: $1.34200
250+: $1.17424
500+: $1.14070
1000+: $0.90585
2000+: $0.87230
6000+: $0.83875
10000+: $0.82533
50000+: $0.80520
AD627AR-REEL AD627AR-REEL Company:Analog Devices Inc. Remark:Instrumentation Amplifier 1 Circuit Rail-to-Rail 8-SOIC Package:8-SOIC (0.154"", 3.90mm Width)
In Stock:On Order

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pinglun 3 comments

    • pingluntus
    • Willile on 2019/10/23 16:54:19

    Add something, the op amp can be simply viewed as a high-gain direct-coupled voltage amplifying unit with one signal output port, a non-inverting input, and an inverting put, which belong to high-impedance inputs. So non-inverting amps, inverting amps, and differential amps can be made based on these amplifying units.

    • pingluntus
    • Eills on 2019/10/28 13:45:51

    We should know the principle before calculations, the power supply mode of the op amp is divided into dual power supply and single power supply. For dual-supply op amps, the output can be varied across zero voltage and the output can be set to zero when the differential input voltage is zero. With a single-supply op amp, the output varies over a range of power and ground.

    • pingluntus
    • Comie on 2019/11/11 17:55:57

    The output signal of the operational amplifier is proportional to the difference between the signal voltages of the two inputs. In the audio segment: output voltage = A0 (E1-E2), where A0 is the low-frequency open-loop gain , E1 is the input signal voltage of the non-inverting terminal, and E2 is the input signal voltage of the inverting terminal.

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