Question

A diode detector is used to detect an amplitude modulated wave of $60\%$ modulation by using a condenser of capacity $250$ $\text{pico farad}$ in parallel with a load resistance $100\text{kilo}\text{ohm}$. Find the maximum modulated frequency which could be detected by it.

• A. $5.31\text{kHz}$
• B. $10.62\text{MHz}$
• C. $10.62\text{kHz}$
• D. $5.31\text{MHz}$

Answer 1

The correct option is C $10.62\text{kHz}$


Given: $\mu =0.6,R=100k\Omega ,C=250\times {10}^{-12}F$

Frequency, $f=\frac{1}{2\pi \mu \tau }$
For a combination of resistance and capacitance, $\tau =RC$
Therefore, frequency can be given as:
$f=\frac{1}{2\pi \mu RC}$

$\tau =RC=100\times {10}^3\times 250\times {10}^{-12}\text{sec}$
$=2.5\times {10}^7\times {10}^{-12}\text{sec}$
$=2.5\times {10}^{-5}\text{sec}$

The higher frequency which can be detected with tolerable distortion is
$f=\frac{1}{2\pi \mu \tau }=\frac{1}{2\pi \times 0.6\times 2.5\times {10}^{-5}}$
$=10.61kHz$

Hence, option $\left(B\right)$ is correct.