The transfer function of a first order RC lowpass filter is:
| The transfer function of a first order RC lowpass filter is:
A. <span class="math-tex">\(\frac{1}{{sRC}}\)</span>
B. R + sC
C. 1 + sRC
D. <span class="math-tex">\(\frac{1}{{\left( {1 + sRC} \right)}}\)</span>
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
The Low pass filter is shown below
The capacitive impedance will be:
\(X_c=\frac{1}{s C}\)
Applying voltage division rule, we get the transfer function as:
\(\frac{{{V_0}}}{{{V_i}}} = \frac{{\frac{1}{{sC}}}}{{\frac{1}{{sC}} + R}} \)
\(\frac{V_0}{V_i}= \frac{1}{{1 + sRC}}\)
Observations:
- The circuit consists of a series resistor and a shunt capacitor.
- This circuit passes low frequencies of the input and attenuates the high frequencies because the reactance of the capacitor C decreases with increasing frequency.
- At very high frequencies, the capacitor acts as a virtual short circuit and the output falls to zero.
- Hence it is called a low pass filter circuit.
