The design method of integral operation circuit is introduced in detail

This paper introduces the design of integral operation circuit .

Characteristic analysis of integral operation circuit

The figure below shows the basic inverse integral operation circuit with the integrated operational amplifier as the core component , Input voltage uI Via resistance R Add to the inverting input of the operational amplifier ,C Is the feedback capacitance , Introduce voltage parallel negative feedback ,R‘ To balance the resistance ,uO Is the output voltage .

Input signal uI Is the duty cycle q=50%、 The magnitude is ±Um、 The period is T The output signal is triangular waveform , The input and output signal waveforms are shown in the figure below .

The circuit principle is analyzed as follows . By ideal op amp's virtual short 、 The concept of virtual break and virtual ground of circuit , Establish the circuit equation

Solution （1） The general expression of the integral operation relationship is

Circuit time constant

When the integrating circuit enters the steady state , capacitance C The initial voltage on the is not zero , For convenience , On the circuit 0≤t≤T During the analysis and discussion of definite integral . stay 0～T/2 period , Input signal uI=UIm、 capacitance C The initial voltage on the is +UOm, By the type （2） Yes

By the type （7） You know , By choosing the time constant RC The numerical , It can make the amplitude of output voltage UOm And the amplitude of the input voltage is UOm＞UIm、UOm=UIm And UOm＜UIm3 One of the relationships . Because the maximum output voltage of the integrated operational amplifier is close to the power supply voltage ±VCC The finite value of , Therefore, the amplitude of the output voltage of the integral operation circuit UOm Satisfy

Input resistance of inverse integral operation circuit

To prevent integral saturation or cutoff caused by integral drift , Often a resistor is connected into the circuit RF（ The figure below ）.

Integral operation circuit to prevent integral saturation or cut-off

But access RF It will divert the charge and discharge current of the capacitor , This leads to integral error , To reduce the error , Generally, it should meet

Usually selected

Design of inverse integral operation circuit

Design of inverse integral operation circuit , It is known that the input duty cycle of the input terminal is 50% The frequency or period of a rectangular signal T、 amplitude ±UIm、 Amplitude of output voltage ±UOm And input resistance RI, determine RC Component parameters of integrating circuit . The design steps are ：

By the type （8） Determine the time constant of the circuit , By the type （9） Determine the resistance R, Then solve the capacitance C The numerical .

Design examples ： Design an inverse integral operation circuit , The frequency of the signal of the input rectangular wave is known f=1kHz、 amplitude UIm=±2V, Amplitude of output voltage UOm=±8V, Input resistance RI=10kΩ, Power supply voltage of operational amplifier ±VCC=±12V.

The design process is as follows .

UOm=±8V,±VCC=±12V, Satisfaction （9） Linear operating conditions .

By the type （8）, The time constant of the circuit

Multisim10 The simulation software simulates, analyzes and verifies the designed inverse integral operation circuit ［7,8］, The simulation circuit constructed is shown in the figure below . Where the input signal uI Is the duty cycle q=50%、 amplitude UIm=±2V、 frequency f=1kHz（ cycle T=0.001s） Rectangular wave , The dual trace oscilloscope is used to observe the input signal uI And the voltage at both ends of the capacitor uC Waveform of .

Integral operation simulation circuit

The simulation waveform is shown in the figure below , Among them, from top to bottom is the input rectangular wave signal uI、 Voltage at both ends of the capacitor uO Waveform of . Move the two cursor pointers to the voltage uO The peak of the waveform - Peak position , Peak of output voltage can be read - The peak value is 15．727V, Then the amplitude of the output voltage UOm=15．727V/2=7．8635V, Slightly smaller output voltage value of theoretical design , The capacitance can be appropriately reduced C The capacity of . From the figure 5 It can be seen that , The output voltage waveform is a triangular waveform with good linearity .

Simulation waveform of integral operation circuit