RLC-Network Based Circuits



RC-Differentiator : Case Study



Aim:


To study the characteristic of a capacitor as a differentiator.

Components required:


   Capacitor, Function generator, CRO, resistor, connecting wires.


Vlab Specifications Taken:


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


  • Function generator: Selected wave with following specifications:
Frequency = 10 Hz. (Any frequency <<1/R1C)
Wave type: Square, sinusoidal, triangular.
Duty cycle = 50%
Duty cycle = 50%
  • Resistor R1:1.562 K
  • Capacitor: 1000n


Theory:


A resistor-capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit. RC circuits can be used to filter a signal by blocking certain frequencies and passing others. The four most common RC filters are the high-pass filter, low-pass filter, band-pass filter, and band-stop filter. These circuits can also be used as a differentiator or an integrator.
RC circuit as a Differentiator Figure 1.shows the circuit for a capacitor as a differentiator. Consider an AC source with voltage vin(t), input to an RC series circuit. The output across the resistor is to be measured at low frequency i.e.



The capacitor has time to charge up until its voltage is almost equal to the source's voltage. Considering the expression for I (current), when



So





Now,





This is a differentiator across the resistor.


Figure 1.

Procedure:


  1. Connect the circuit as shown in the circuit diagram.
  2. Give the input signal as specified.
  3. Vary the amplitude and frequency of the input signal and also the type of the waveform (square, sine etc.). To verify the characteristic of a capacitor as a differentiator.
  4. Note down the outputs from the CRO
  5. Draw the waveforms on the graph sheet.


Observations:


  1. Observe the output waveform from CRO.
  2. Measure the frequency and the amplitude of the output waveform on the CRO.
  3. Check output voltage




Frequency of the output waveform will remain same and the output voltage can be calculated using above equation and can be compared with the observed value.

Observe outputs of the differentiator circuit using different input waveforms.

VLab Observations Obtained:


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

    2. Select sine wave on the function generator, click on the frequency button and then set frequency10Hz. (The frequency can be set to any value<<1000Hzi.e. 1/RC for this experiment)


    3. Click on the amplitude button and select the amplitude of the sine wave, for example 10V.


    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 screen. 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.


      8. 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.
      Similarly select source 1 to measure frequency or amplitude of the output wave form.
      The amplitude of input and the output wave is 10.6V and 950mV respectively and the frequency is 10Hz.
    8. Then check the phase difference between the input and the output wave. Select source 1 then select phase then select source 4 and click measure.



      9. The observed phase difference is 88o.

      Calculations:


      If input Vin = 10.6 sin (10t)
      Output of the differentiator will be equal to



      Hence theoretically, output voltage should be 1.039V and phase difference between input outputs should be 90o.

      Experimentally phase difference observed is about 88o and output voltage is about 1.0V.

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


    9. Observe the output voltage and phase difference at different frequencies and amplitudes with different wave type and verify the output.

      For example set the frequency and the amplitude to check the impulse wave at output when square wave has been given as input from the function generator.



      Set frequency and amplitude and observe the output.

      Result:


      The capacitor as a differentiator circuit is designed and studied successfully.

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