TUTORIAL CHAPTER 4: AM MODULATION TRANSMISSION (ANSWER)
CALCULATION QUESTIONS (AM Modulation Fundamentals)
1. An AM wave has a peak modulation voltage, Vm of 1.5 V and a peak carrier voltage V of 4.0 V. Compute the modulation index, m, and percentage modulation index, M.
m = Vm / V = 1.5 / 4.0 = 0.375
M = m * 100 = 0.375 * 100 = 37.5%
2. An AM signal has the equation v(t) = [15 + 4 sin (44 x 10^3t)] sin (46.5 x 10^6t).
a. Find the carrier frequency.
b. Find the frequency of the modulating signal.
a. The carrier frequency is 46.5 MHz.
b. The frequency of the modulating signal is 44 kHz.
c. Find the value of the modulation index.
The modulation index cannot be determined from the given equation.
3. For an envelope with +Vmax = 40 Vp and +Vmin = 10 Vp, determine:
a. The unmodulated carrier amplitude.
b. The peak change in amplitude of the modulated wave.
c. The modulation coefficient.
d. The percent modulation.
a. The unmodulated carrier amplitude is Vc = (Vmax + Vmin) / 2 = (40 + 10) / 2 = 25 Vp.
b. The peak change in amplitude of the modulated wave is Em = (Vmax - Vmin) / 2 = (40 - 10) / 2 = 15 Vp.
c. The modulation coefficient is m = Em / Vc = 15 / 25 = 0.6.
d. The percent modulation is M = m * 100 = 0.6 * 100 = 60%.
4. For an unmodulated carrier amplitude Vc = 16 V and a modulation coefficient m = 0.4, determine the amplitudes of the carrier and side frequencies.
Vc = 16 Vp
Vusb = VIsb = Vc * m = 16 * 0.4 = 6.4 Vp
5. For a modulation coefficient m = 0.2 and a peak carrier power Pc = 1000 W, determine:
a. The sideband power.
b. The total transmit power.
a. The sideband power is Psb = Pc * m^2 = 1000 * 0.2^2 = 20 W.
b. The total transmit power is Pc + Psb = 1000 + 20 = 1020 W.
6. Describe the meaning of the following expression:
Carrier signal (volts)
Upper side frequency signal (volts)
Lower side frequency signal (volts)
The expression represents the voltages of the carrier signal, upper side frequency signal, and lower side frequency signal in an AM modulation system.