Assume that the fm radio station wants to transmit a stereo

Question

1. Consider the approximate form of a NBFM signal and the diagram used to generate this approximate NBFM signal. Let the message signal be a single-tone and given by:

m(t) = A_mcos(ω_mt) = 14cos(2Π x 10²t) Volts.

The modulation index E is

(A) β = 0.0223 (B) β = 0.00322 
(C) β = 0.0332 (D) β = 0.00223

2. Consider a voltage-controlled oscillator (VCO) using an LC tank and producing an FM signal based on having its capacitance, C, vary linearly with the message, m(t) , as follows:

C = C₀[1-km(t)] with km(t) << 1.

The carrier frequency of the FM signal available at the output of the VCO is equal to 95 MHz. Determine the value of k if the VCO-produced FM signal turned out to have a bandwidth equal to 180 kHz computed using Carson's rule.

The message, m(t), is assumed to have 15 kHz band- width and maximum amplitude value equal to 2 Volts.

(A) k = 0.879 x 10^-3V^-1  (B) k = 0.789 x 10^-3V^-1

(C) k = 1.789 x 10^-3V^-1  (D) k = 1.879 x 10^-3V^-1

3. Consider the approximated form of a NBFM signal :

V_NBFM(t) = A_c(cosω_ct) - βA_csin(ω_mt)sin(ω_ct).

Let β = 0.1 and determine the maximum deviation of the envelope of V_NBFM(t) from A_c of the NBFM signal.

(A) 0.1 A_c (B) 0.005 A_c (C) 0.001 A_c (D) 0.004 A_c

4. The bandwidth allowed for the transmission of an FM radio signal is 200 kHz, Assume that the FM radio station wants to transmit a stereo message signal of bandwidth equal to 52 kHz. Determine the maximum value of the message signal. Use k_f = 4000 (V.s)^-1

(A) 15 Volts (B) 10 Volts (C) 12 Volts (D) 18 Volts