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Exercise Problems · Q5

Q.A modulating signal 10 sin(2π × 10³t) is used to modulate a carrier signal 20 sin(2π × 10⁴)t. Find the

(a) modulation index
(b) percentage modulation
(c) frequencies of the sideband components and their amplitude
(d) bandwidth of the modulated signal.
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[!TLDR]

With Vm=10 VV_m = 10\ \text{V}, Vc=20 VV_c = 20\ \text{V}, fm=1 kHzf_m = 1\ \text{kHz} and fc=10 kHzf_c = 10\ \text{kHz}, the index is 0.5 (50 %), the sidebands are at 9 kHz and 11 kHz (5 V each) and the bandwidth is 2 kHz.

From the modulating signal 10sin⁡(2π×103t)10\sin(2\pi\times10^{3}t): Vm=10 VV_m = 10\ \text{V}, fm=103=1 kHzf_m = 10^{3} = 1\ \text{kHz}. From the carrier 20sin⁡(2π×104t)20\sin(2\pi\times10^{4}t): Vc=20 VV_c = 20\ \text{V}, fc=104=10 kHzf_c = 10^{4} = 10\ \text{kHz}.

  1. Modulation index: ma=VmVc=1020=0.5m_a = \dfrac{V_m}{V_c} = \dfrac{10}{20} = 0.5.
  2. Percentage modulation: 0.5×100=50%0.5\times100 = 50\%. …
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