Analog Modulation

Conventional AM: power and efficiency

• $$s(t)=A_c\big[1+\mu\cos\omega_mt\big]\cos\omega_ct$$

  $\mu=A_m/A_c$ = modulation index

• $$\mu=\dfrac{A_{\max}-A_{\min}}{A_{\max}+A_{\min}}$$
• $$P_t=P_c\left(1+\dfrac{\mu^2}{2}\right),\qquad P_c=\dfrac{A_c^2}{2}$$
• $$\eta=\dfrac{\mu^2}{2+\mu^2}\ \Rightarrow\ \eta_{\max}=33.3\%\ \text{at}\ \mu=1$$
• $$\mu_t=\sqrt{\mu_1^2+\mu_2^2+\cdots}$$
• $$\text{BW}=2f_m$$

  same as DSB-SC

DSB-SC, SSB and VSB

• $$s_{\text{DSB}}=A_cm(t)\cos\omega_ct,\qquad \text{BW}=2W$$

Angle modulation: FM and PM

• $$s(t)=A_c\cos\!\big[\omega_ct+2\pi k_f\!\!\int^t\!\! m(\tau)d\tau\big]\ \ \text{(FM)}$$

Noise performance and the superheterodyne receiver