RC-Differentiator : Lab Report

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.


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

VLab Observations Obtained:

Calculations:


For example, a case has been taken and the required parameters value is being noted down below:
1. Input Wave:   Sinusoidal.
2. Amplitude:  10.6V
3. Frequency:   10Hz
4. Output Voltage:   950mV
5. Phase Difference:   -88⁰




Calculation



• 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.



Result:


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



Precautions:



1. Connections should be verified before clicking run button.
2. The frequency should be in the range to observe the correct differentiated output.