Differentiator

 Aim

  To design and simulate a Differentiator circuit.

  Components

Theory

   A circuit in which output voltage is directly proportional to the derivative of input is known as a differentiating circuit. A differentiating circuit is a simple RC series circuit with output taken across the resistor R.

In order to achieve good differentiation, the following conditions should be satisfied:

1. The time constant RC of the circuit should be smaller than the time period of the input wave.
2. The value of Xc should be 10 or more times larger than R at operating frequency.

   Let e_i be the input alternating voltage and i be the resulting alternating current. The charge q on the capacitor at any instant is

e_c

C e_c

e_c

   Since capacitive reactance is very much larger than R, the input voltage can be considered to be equal to the capacitor voltage with negligible

   error. i.e. e_{c =} e_i

e_i

Output Voltage, e_{o =} iR

e_i e_i

   Hence the output is proportional to the time derivative of the input.

  Procedure

  EDWinXP-> Schematic Editor: The circuit diagram is drawn by loading components from the library. Wiring and proper net assignment has been made.

  The values are assigned for relevant components.

  EDWinXP-> Mixed Mode Simulator: The circuit is preprocessed. The test points and waveform markers are placed in input and output of the circuit. GND net is set as reference net. The Transient Analysis parameters have been set. The Transient Analysis is executed and output waveform is observed in Waveform Viewer.

  Result

   The output waveform may be observed in the waveform viewer.