DVOR VHF omnidirectional range
the doppler signal encodes station identifier, i(t), optional voice, a(t), navigation variable signal in c(t), , isotropic (i.e. omnidirectional) component. navigation variable signal a3 modulated (greyscale). navigation reference signal delayed, t+, t−, electrically revolving pair of transmitters. cyclic doppler blue shift, , corresponding doppler red shift, transmitter closes on , recedes receiver results in f3 modulation (colour). pairing of transmitters offset equally high , low of isotropic carrier frequency produce upper , lower sidebands. closing , receding equally on opposite sides of same circle around isotropic transmitter produce f3 subcarrier modulation, g(a,t).
t
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t
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a
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−
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r
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c
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sin
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2
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sin
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cos
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g
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f
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i
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cos
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m
d
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cos
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f
c
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cos
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{\displaystyle {\begin{array}{rcl}t&=&t_{+}(a,t)-(r/c)\sin(2\pi f_{n}t_{+}(a,t)+a)\\t&=&t_{-}(a,t)+(r/c)\sin(2\pi f_{n}t_{-}(a,t)+a)\\e(a,t)&=&\cos(2\pi f_{c}t)(1+c(t))\\&+&g(a,t)\\c(t)&=&m_{i}\cos(2\pi f_{i}t)~i(t)\\&+&m_{a}~a(t)\\&+&m_{n}\cos(2\pi f_{n}t)\\g(a,t)&=&(m_{d}/2)\cos(2\pi (f_{c}+f_{s})t_{+}(a,t))\\&+&(m_{d}/2)\cos(2\pi (f_{c}-f_{s})t_{-}(a,t))\\\end{array}}}
where revolution radius r = fd c / (2 π fn fc ) 6.76 ± 0.3 m .
the transmitter acceleration 4 π fn r (24,000 g) makes mechanical revolution impractical, , halves (gravitational redshift) frequency change ratio compared transmitters in free-fall.
the mathematics describe operation of dvor far more complex indicated above. reference electronically rotated vast simplification. primary complication relates process called blending .
another complication phase of upper , lower sideband signals have locked each other. composite signal detected receiver. electronic operation of detection shifts carrier down 0 hz, folding signals frequencies below carrier, on top of frequencies above carrier. upper , lower sidebands summed. if there phase shift between these two, combination have relative amplitude of (1 + cos φ). if φ 180°, aircraft s receiver not detect sub-carrier (signal a3).
blending describes process sideband signal switched 1 antenna next. switching not discontinuous. amplitude of next antenna rises amplitude of current antenna falls. when 1 antenna reaches peak amplitude, next , previous antennas have 0 amplitude.
by radiating 2 antennas, effective phase centre becomes point between two. phase reference swept continuously around ring – not stepped case antenna antenna discontinuous switching.
in electromechanical antenna switching systems employed before solid state antenna switching systems introduced, blending by-product of way motorized switches worked. these switches brushed coaxial cable past 50 (or 48) antenna feeds. cable moved between 2 antenna feeds, couple signal both.
but blending accentuates complication of dvor.
each antenna in dvor uses omnidirectional antenna. these alford loop antennas (see andrew alford). unfortunately, sideband antennas close together, approximately 55% of energy radiated absorbed adjacent antennas. half of re-radiated, , half sent along antenna feeds of adjacent antennas. result antenna pattern no longer omnidirectional. causes effective sideband signal amplitude modulated @ 60 hz far aircraft s receiver concerned. phase of modulation can affect detected phase of sub-carrier. effect called coupling .
blending complicates effect. because when 2 adjacent antennas radiate signal, create composite antenna.
imagine 2 antennas separated wavelength/3. in transverse direction 2 signals sum, in tangential direction cancel. signal moves 1 antenna next, distortion in antenna pattern increase , decrease. peak distortion occurs @ midpoint. creates half-sinusoidal 1500 hz amplitude distortion in case of 50 antenna system, (1,440 hz in 48 antenna system). distortion amplitude modulated 60 hz amplitude modulation (also 30 hz well). distortion can add or subtract above-mentioned 60 hz distortion depending on carrier phase. in fact 1 can add offset carrier phase (relative sideband phases) 60 hz components tend null 1 another. there 30 hz component, though, has pernicious effects.
dvor designs use sorts of mechanisms try compensate these effects. methods chosen major selling points each manufacturer, each extolling benefits of technique on rivals.
note icao annex 10 limits worst case amplitude modulation of sub-carrier 40%. dvor didn t employ technique(s) compensate coupling , blending effects not meet requirement.
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