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UPRVUNL AE EC 2016 Official Paper

Option 4 : ω τ ≪ 1

EKT ME Full Test 1

2021

50 Questions
150 Marks
45 Mins

**Concept:**

**Differentiator is a circuit that is designed such that the output of the circuit is approximately directly proportional to the rate of change (the time derivative) of the input.**- A true differentiator cannot be physically realized, because it has infinite gain at infinite frequency. A similar effect can be achieved, by limiting the gain above some frequency.
- The differentiator circuit is essentially a
**high-pass filter.** - An active differentiator includes some form of the amplifier, while a passive differentiator is made only of resistors, capacitors, and inductors.
- A differentiator gives the
**derivative of input voltage**as output. - A differentiator using passive components resistors and capacitors is a high pass filter as shown in the circuit diagram.

- It acts as a differentiator only when the time constant is too small
**(ωτ<<1).** - The voltage at the output is proportional to the current through the capacitor. The current through the capacitor can be expressed as C (dv / dt).
- The output is taking across the resistor. So the
**output will be RC (dv / dt).**Thus differentiation of input takes place. - The circuit is called a differentiator because its effect is very similar to the mathematical function of differentiation, which means (mathematically) finding a value that depends on the rate of change of some quantity.
- The output wave of a differentiator circuit is ideally a graph of the rate of change of the voltage at its input. The output of a differentiator relates to the rate of change of its input, and that actually the actions of the
**high pass filter and the differentiator are the same.** - The differentiator output is effectively a graph of the rate of change of the input. Whenever the input is changing rapidly, a large voltage is produced at the output.
**The polarity of the output voltage depends on whether the input is changing in a positive or a negative direction.**