Doppler Effect refers to the shift in the observed or perceived frequency of an electromagnetic or sound wave due to the motion of the source of the wave relative to the observer. The following equations apply. Sound Waves fo = fs [(v + w + vo) / (v + w - vs)] where fo = observed or perceived sound frequency (Hz) vo = velocity of observer (m/s) vs = velocity of source (m/s) v = velocity of sound in the medium (m/s) w = velocity of the wind in the direction of sound propagation (m/s) fs = frequency of the source (Hz) Electromagnetic Electromag netic Waves fo = fs (sqrt[(c + vr) / (c - vr)]) where fo = observed or perceived electromagnetic wave frequency (Hz) fs = frequency of the source (Hz) vr = velocity of source relative to the observer (m/s) c = speed of light in vacuum (3e8 m/s)
Below are some commonly used formulas for designing an antenna.
1) Length of Ideal Hertz Antenna L= λ /2 where L = length of the Hertz Antenna λ = wavelength
2) Length of Ideal Marconi Antenna L= λ /4 where L = length of the Marconi Antenna λ = wavelength
3) Power Received Received by a Hertz Antenna Antenna P = (PtGtGr λ2) / (16π2d2) where P = received power (W) Pt = transmitted power (W) Gt = gain ratio of transmitting antenna relative to an isotropic radiator Gr = gain ratio of receiving antenna relative to an isotropic radiator λ = wavelength (m) d = distance between antennas (m)
4) Effective Radiated Power
ERP = G x Pi where G = gain of transmitting antenna relative to an isotropic radiator Pi = input power (W)
AM is not an efficient way to modulate - much of its power is wasted. At least 2/3 of the power is used by the carrier signal, while the remaining power is split between the two equal sidebands. Percent Modulation M = [(Ec - Et) / (2Ea)] x 100% or M = [(Ec - Et) / (Ec+Et)] x 100% where M = % Modulation Ec = crest amplitude of the modulated carrier Et = trough amplitude of the modulated carrier Ea = average amplitude of the modulated carrier Sideband Power Ps = M2Pc / 2 where Ps = sideband power of an AM carrier, W M = %Modulation Pc = carrier power, W Total Radiated Power Pt = Ps + Pc where Pt = total radiated power, W Ps = sideband power, W Pc = carrier power, W
The following equations apply to FM. Percent Modulation M = [∆f / D] x 100% where M = % Modulation ∆f = change in frequency D = maximum frequency deviation, i.e., frequency deviation for 100% modulation Modulation Index Mi = fd / fa where Mi = modulation index fd = deviation frequency, kHz fa = modulating audio frequency, kHz
