To design and simulate an Integrator circuit and observe output with different input waveforms. 

   Function generator, CRO, Regulated Power supply, resistor, capacitor, 741 IC, connecting wires. 

 

Integrator circuit design has been implemented on the virtual breadboard using following specifications:

·         Power Supply: +10v and -10v

·         Function generator: Selected wave with following specifications:

Frequency = 50Hz, 55Hz, 60Hz, 100Hz. 
Amplitude: 2V 
Duty cycle = 50%

·         Capacitor C: 1000nF

·         Resistor R₁: 1.369K

 

The circuit in fig 1 is an integrator, which is also a low-pass filter with a time constant=R₁C. When a voltage, V_in is firstly applied to the input of an integrating amplifier, the uncharged capacitor C has very little resistance and acts a bit like a short circuit (voltage follower circuit) giving an overall gain of less than 1, thus resulting in zero output. As the feedback capacitor C begins to charge up, its reactance X_c decreases and the ratio of Z_f/R₁ increases producing an output voltage that continues to increase until the capacitor is fully charged. At this point the ratio of feedback capacitor to input resistor (Z_f/R₁) is infinite resulting in infinite gain and the output of the amplifier goes into saturation. (Saturation is when the output voltage of the amplifier swings heavily to one voltage supply rail or the other with no control in between). The circuit design generate triangular wave providing square wave as input to the integrator. Hence, the integrator circuit generates integral output with respect to the input waveform. 

The integrator Circuit

 

1.     Connect the circuit as shown in the circuit diagram.

2.     Give the input signal as specified.

3.     Switch on the power supply.

4.     Note down the outputs from the CRO

5.     Draw the necessary waveforms on the graph sheet.

 

 

1.     Observe the output waveform from CRO. A square wave will generate a triangular wave and sine wave will generate a cosine wave.

2.     Measure the frequency and the voltage of the output waveform in the CRO.

3.     Calculate 

 

4.     Observe outputs of the integrator circuit using different input waveforms.

 

 

1.     After Clicking on Open function generator icon on the left of the Vlab live environment page, set the frequency, amplitude and the type of waveform on function generator.

2.     Select sine wave and then set frequency 50Hz

 

 

3.     Set the peak to peak voltage V_pp = 2v i.e. amplitude = 2v.

 

 

4.     Check graph

 

 

5.     Circuit has been designed on the virtual breadboard with the help of procedure.

 

 

6.     Then on clicking on Run icon, the output waveform generated and the input can be observed on the CRO. CRO web page can be opened using icon oscilloscope at top left on the live experiment page.

 

 

7.     Click on measure.Then one can observe options like source, select, measure.

 Click on source and select 4 i.e. the input wave.

 Click on select and select the parameter to be measured for example select frequency or amplitude.

 Click on measure to get the frequency and amplitude of the input waveform.

It comes out to be Frequency: 50Hz, amplitude: 2.06V

 

 

8.     Then check the phase difference between the input and the output wave. Follow the same steps as mentioned earlier. Select phase option and get the phase difference.

 

 

The phase comes out to be -92

 

 

9.     Now observe the amplitude of the output waveform generated.

 

 

The output voltage comes out to be 4.31V.

 

 

If input V_in = 2.09 sin (2*50*t)

Output of the integrator will be equal to 

 

 

Thus, 

 

 

 

 

Hence theoretically, output voltage should be 4.72V and phase difference between input outputs should be -90�.

Experimentally phase difference observed is about 92 and output voltage 4.31V. 

Table representing different output voltages and phase difference at different frequency input waveforms obtained theoretically and experimentally. 

Frequency	V0 (Theoretical)	Vo (Experimental)	Phase Diff (Th.)	Phase Diff (Pr.)
50	4.72	4.31	-90	-92
55	3.94	4.42	-90	-92
60	4.05	3.38	-90	-91.7
100	2.19	2.43	-90	-92

 

10.   Observe the output voltage and phase difference at different frequencies.

                                                                                                    

 

 

 

The integrator circuit design output waveforms have been studied.