Communications Formulas and Concepts

AMPLITUDE MODULATION

• AM Wave Vm V cos(ω c − ω m )t − m cos(ω c + ω m )t 2 2 where: Vc = maximum voltage of the carrier signal Vm = maximum voltage of the original modulating signal ωc = 2πfc = frequency of the carrier signal ωm = 2πfm = frequency of the modulating signal V (t ) = Vc sin ω c t + V m V max −V min = V c V max +V min where: m = modulation index Vmax = maximum peak-to-peak voltage swing of AM wave Vmin = minimum peak-to-peak voltage swing of AM wave m= AM wave equation in terms of modulation index

V (t ) = Vc sin ω c t + mVc mVc cos(ω c − ω m )t − cos(ω c + ω m )t 2 2

2 2 mt = m12 + m 2 + m3 ...... where: mt = total modulation index m1, m2, m3 = modulation index of signal having index 1, 2, 3 respectively

Power Savings a. Single Sideband (SSB) P + PC PS = LSB / USB Pt b. Single Sideband full carrier (SSBFC) P PS = LSB / USB Pt c. Two independent Sidebands P PS = C Pt • Tuned Radio-Frequency (TRF)AM Receiver TRF Design formulas 1 fr = 2π LC f Q= r BW where: Q = quality factor fr = frequency BW = Bandwidth Superheterodyne Receiver f si = f s + 2 f i where: fsi = image frequency fs = signal frequency fi = intermediate frequency α = 1+ Q2ρ 2 f image f f f ρ = si − s = − RF fs f si f RF f image where: α = image-frequency rejection ratio(IFRR) Q = quality factor of the circuit •

BW = 2 f m where: BW = bandwidth fm = modulating signal frequency • AM Power and Current V2 V2 V2 V2 Pt = carr + LSB + USB Pc = c R R R 2R 2 2 2 2 m Vc V m PLSB = PUSB = = m = Pc 8R 8R 4

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AM Bandwidth

 It  Pt m2 m2   =1+ =1+ I  2 Pc 2  c where: Pt = total transmitted power Pc = unmodulated carrier power It = total transmitted current Ic = unmodulated carrier current m = modulation index Note: The voltage should be in rms Amplitude Modulation with Multiple Signals  m2 Pt = Pc 1 + t   2   

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