PHASE METHOD OF DIRECTION FINDING

Direction finders (DFs) are used for exploration objects (EO) space coordinates finding. All of DFs (radio- technical radio-waves emitting or reflecting objects angle coordinates finders) and angle following radio-systems equalize signal coming direction with direction of normal to created by emission source wave front. Difference in direction finding methods and DF types comes from technical features of this normal orientation setting. DFs have the following high requirements in their parameters: reaction speed (direction finding ability by the shortest signal realization – by one impulse in limit), direction finding accuracy, resolution ability.

Phase method of direction finding based on phases difference of signals gotten by two equal antennas (A1 and A2 in the pic.1) spread on defined distance (base of d length). If distance between EO and DF base center is really high (R>>d) EO emitted wave front next to DF antennas system can be considered as plane one. Difference in signals distribution paths lengths from emission source to DF antennas A1 and A2 Δ=dsinφ (pic.1) leads to received by antennas signals s1(t) and s2(t) phases difference. Signals phases difference on main frequency ω0 and with true direction φ can be found from the following formula:

Δφ=ω0Δτ=ω0(Δ/c)=ω0(d/c)sinφ=2π(d/λ)sinφ   (frm.1),

where Δτ=Δ/c is a time delay between signals receiving times by spread antennas, c is a speed of light, λ is EO emitted wave length.

From frm.1 follows that true direction φ on emission source can be found as: φ=arcsin((cΔφ)/(ω0d)) (frm.2).

From frm.2 follows that for true direction on radio-locating system (RLS) finding it is necessary to find frequency ω0 and phases differences Δφ of signals received by spread antennas. But if DF will be of following type with ability of base turning and its parallel setting to coming wave front frequency can be unfound. In case of base tangency to coming wave front (case of base normality to direction of created by emission source wave), sinφ=Δφ=0 independently from signal frequency.

Arcsin() function in right part of frm.2 is controversial. That is why different true directions on emission source can appropriate to different found values of phases difference Δφ. To eliminate found true directions controversy antennas systems with different bases sizes are used.

Sometimes DFs find only true direction φ function value except value of true direction φ, for example function of direction cosine angle between DF base and direction on emission source. This angle adds φ to 90° that is why as it follows from frm.2:

cos(90°-φ)=(cΔφ)/(ω0d) (frm.3).

Method of base use for true direction finding has its great development in automatic dual-channel DF with turning antennas [1]. In modern radio-technical exploration systems such DFs are wide-spread and called as Doppler DF. Doppler DFs work in SW and USW wave diapasons. General simplified Doppler DF scheme is shown in the pic.2. In the pic.3 functional Doppler DF scheme is shown.

If RLS emits signal s(t) on ω0 frequency turning antennas output signals are the following: s1(t)=cos(ω0t-φ1(t))=cos(ω0(1-VR(t)/c)t);

s2(t)=cos(ω0t+φ2(t))=cos(ω0(1+VR(t)/c)t)   (frm.4),

where φ(t) is a signal phase changing over time because of antenna and emission source relative movement; VR(t) is this movement radial velocity – antenna movement on signal coming direction linear velocity vector projection equal to

VR(t)=Vcosα(t)=ΩRcosα(t)=ΩRcos(Ωt+φ)   (frm.5),

where α(t) is an angle instantaneous value between direction on emission source (true direction φ on exploring RLS) and turning antenna linear velocity vector V.

In frm.4 the following fact is taken into account: second antenna is turning in other direction and signal phase difference in this antenna has the same absolute value but other sign in comparison with first antenna. DF receivers RCV multiply oscillations from both of symmetrical antennas outputs. The result of such operation with accuracy of oscillating on 2ω0 frequencies components averaged in filters is the following:

S=s1s2=(1/2)sin(2ω0(VR/c)t) (frm.6) or together with frm.5

S=(12/2)cos((2ω0)/c)ΩRsin(Ωt+φ))  (frm.7).

This is a periodic angle-modulated oscillation. Oscillation spectrum contains turning antenna harmonics with known frequency Ω:

S=(1/2)n=0∑∞J2n+1(2(ω/c)ΩR)sin(2n+1)(Ωt+φ)   (frm.8),

where Jk(m) is a Bessel function of k order with argument of m=2(ω/c)ΩR=4πΩ((2R)/λ). With help of low-pass filter after multiplier first harmonic of this voltage always can be found S(1)=(1/2)J1(2(ω0/c)ΩR)sin(Ωt+φ) (frm.9)

and then with help of synchronous and in-phase with turning antenna oscillations formed by voltage reference VR device estimation of true direction φ* can be found as

φ*=arctg(Y/X)=arctg((S(1)sinΩt)/(S(1)cosΩt))≈arctg(sinφ/cosφ)=φ     (frm.10).

Approximation in frm.10 means that Y and X values are formed as the result of appropriate phase detectors PD output voltages averaging. During such averaging oscillations with double frequency 2Ω can be ignored.

Estimation of true direction φ* can be not found as arctg(Y/X) because this voltage can be just appropriately send to rejecting horizontal and vertical plates of oscillographic cathode ray tube. As the result the argument of illuminating display dot will be equal to estimation of true direction φ* – to emission source true direction φ.

Technically, in Doppler DFs, antennas are not turning but array ring of stable antennas situated in generatrixes of cylinder of R radius and in pairs periodically plugged to receiver input are used. Antennas commutation speed is equal to Ω. If DF contains multi-channel receiver true directions on different RLSs working on different main frequencies can be found. Modern Doppler DFs working in diapason from 20 MHz to 2 GHz and provide true direction accuracy no less than σφ<2° [1]. True direction accuracy is defined as RLS signal power as well as DF base 2R (to be more exact as (2R)/λ value).

Список литературы

1.     Вспомогательный источник для адаптированного перевода. Вартанесян В. А. Радиоэлектронная разведка. М.: Воениздат, 1991.

2.     Основной источник для адаптированного перевода. Радиоэлектронная борьба. Основы теории / А. И. Куприянов, Л. Н. Шустов. М.: Вузовская книга, 2011. – 800 с.: ил.