Question

m (+) -0.3 1.3 -0.2 10.2 0.4

Suppose that we have a sinc-function message signal m(t) as shown in the figure. We perform AM modulation with a carrier frequency of 10π krad/s and with a proper DC shift so that envelope detection can be used for demodulation.

Which one of the resistor values below is suitable to use with a 1nF capacitor for proper envelope detection?

(See the "Hints" part at the end of the Reference Sheet for the range of RC)

URGENT !!! I JUST NEED TO ANSWER. I DO NOT NEED STEP-BY-SEP SOLUTION

220M ohms

1M ohms

47k ohms

390 ohms

30M ohms.

Answer 1

The condition for proper envelope detection is    $\frac{1}{fc} \leq RC\leq \frac{1}{fm}$ .

where; fm - frequency of message signal

           fc - frequency of carrirer signal.

Given that,

          $\omega$ c - 10$\pi$k rad/sec

         2$\pi$fc = 10$\pi$k   $\Rightarrow$ fc = 5k Hz.

from the graph, fm = 10Hz.

$\frac{1}{5k}\ \leq RC\leq \frac{1}{10}$   $\Rightarrow$$\frac{1}{(5k)(1n)}\leq R\leq \frac{1}{10(1n)}$

200kΩ<R< 100ΜΩ

From the given options,

$30M\Omega$ is the resistance value for proper envelope detection.