## Communication Systems

# Amplitude Modulation, Production and Detection of Amplitude Modulated Wave

- During PHASE MODULATION, the phase of the CW (carrier wave) is changed in accordance with the amplitude variations of the signal.
- The extent to which the modulation is to be taken up is called the modulation factor (m
_{a}) - \tt m_{a} = \frac{Amplitude \ change \ in \ carrier \ wave}{Amplitude \ of \ unmodulated \ CW}
- If a carrier wave is modulated by different audio waves to different strengths then the effective modulation factor is given by \tt \sqrt{m_{1}^{2} + m_{2}^{2} + ....}
- Carrier Wave power \tt P_{c} = \frac{V_{c}^{2}}{2R}
- Power of each side band \tt P_{1} = \frac{m_{a}^{2} V_{c}^{2}}{8R}
- Total power of side bands \tt P_{s} = \frac{m_{a}^{2} V_{c}^{2}}{4R}
- Total power carried by modulated wave \tt P_{T} = \frac{V_{c}^{2}}{2R} + \frac{m_{a}^{2} V_{c}^{2}}{4R} = \frac{V_{c}^{2}}{2R} \left[\frac{2+m_{a}^{2}}{2}\right]
- Fractional power carried by the side bands \tt \frac{P_{S}}{P_{T}} = \frac{m_{a}^{2}}{2 + m_{a}^{2}}
- \tt \frac{P_{C}}{P_{T}} = \left(\frac{I_{c}}{I_{t}}\right)^{2}
- \tt \frac{P_{S}}{P_{T}} = \frac{m_{a}^{2}}{2 + m_{a}^{2}} = \frac{1}{3}
- \tt \frac{P_{C}}{P_{T}} = \frac{2}{2 + m_{a}^{2}} = \frac{2}{3}
- y(t) = BV
_{m}sin ω_{m}t + BV_{c}sin ω_{c}t + \tt \frac{CV_{m}^{2}}{2} + \frac{V_{c}^{2}}{2} - \frac{CV_{m}^{2}}{2} \cos 2 \omega_mt - \frac{CV_{c}^{2}}{2} \cos 2 \omega_{c}t + CV_{m}V_{c }cos (ω_{c}− ω_{m})t − CV_{m}V_{c}cos (ω_{c}+ ω_{m})t - Detection:

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1. Power in Amplitude Modulation waves Power dissipated in any circuit, P = V^{2}_{rms}/R. Hence,

Carrier power, P_{c} = \frac{(E_{c}/\sqrt{2})^{2}}{R} = \frac{E_{c}^{2}}{2R}

2. Total power of Amplitude modulation wave,

P_{t} = P_{c} + P_{sb} = \frac{E_{c}^{2}}{2R}\left[1 + \frac{m_{a}^{2}}{2}\right]

3. A sinusoidal carrier wave can be represented as *c*(*t*) = *A _{c}* sin (ω

_{c}

*t*+ Φ)