CC BY
37
Peculiarities of signal formation of the autodyne short-range radar with linear frequency modulation
Noskov, V. Y.1, Ignatkov, K. A.1, Chupahin, A. P.1, Vasiliev, A. V.2, Ermak, G. P.2, Smolskiy, S. M.3
1Ural Federal University, Ekaterinburg, Russia 2O.Ya. Usikov Institute for Radiophysics and Electronics, Kharkiv, Ukraine 3National Research University "Moscow Power Engineering Institute", Moskow, Russia
E-mail: noskov&oko-ck.ru
Research results of signal formation peculiarities in autodyne sliort.-range radars with linear frequency modulation by non-symmetric saw-tooth law are presented. Calculation expressions for autodyne signals are obtained in the general case of arbitrary delay time of reflected emission. Temporal and spectral diagrams of autodyne signals are defined in the cases when its period duration is much more than the delay time of reflected emission, as well as for cases when this inequality is not satisfied. Experimental investigations are performed using the autodyne oscillator on the Guim diode of 8mm-range. which is electronically controlled in frequency by the varicap.
Key words: autodyne: autodyne signal: autodyne response: short-range radar: frequency modulation: Gunn-diode oscillator
Introduction
Autodyne short range radars with frequency modulation (FM ASRR) have fonnd wide application as guard sensors, anti-collision sensors for transport vehicles. measuring devices for car motion in hump yards, detectors of point-work occupation and railway crossings and many others fl 5] duo to construction simplicity and low cost of the transceiver device. Operation principle of these devices is based on the so-called "autodyne effect", which consists in oscillator parameter variations under influence of reflected emission [5]. These variations registration in the form of autodyne signals and their further processing provide a possibility to obtain information about reflecting object and its relative motion parameters.
A large number of publications is devoted to peculiarities of FM ASRR autodyne signal formation, in which different mathematical models and impact function representations for proper reflected emission are used. In earlier publications, which were mainly issued in the period of autodyne theory coming into being, the impact function was represented by variable load, which varies with a frequency of the signal formed [G]. In later publications, this function was described by the equivalent current (or voltage) source having the relative frequency offset caused by emission FM and by reflected radio-signal delay [5.7 9]. Within the limits of described approaches, the oscillation frequency and amplitude are
changing with the differential frequency and the output signals become harmonic result of these variation detection.
In publications of the recent time, the presence of anliarmonic distortions [10, 11] at investigation of FM ASRR signal in the millimeter wavelength range. The phase delay of reflected emission was assumed
as a
basis of the model, which takes into consideration this phenomenon. At that, it was shown that signal distortions are caused by autodyne frequency variations, which canse nonlinearity of the reflected emission phase incursion. Nevertheless, solution of equations with retarded argument in known publications was obtained for the first approximation only, which is valid under condition, when the delay time t of reflected emission in much less than the period Ta of formed autodyne signal. In the actual conditions, at large values of frequency deviations and the high FM operation speed, which is typical for millimeter-wave range, this inequality may be violated1. For snch conditions of FM ASRR functioning, peculiarities of autodyne response formation did not consider in known publication.
To develop the promising FM ASRRs and its reasonable applications, it is undoubtedly necessary to have a knowledge about signal properties under mentioned conditions. Therefore, the goal of this paper is obtaining the general solution of the system of retarded equations for the single-circnit autodyne FM oscillator. Then, on the base of this solution, we are going to
1For example, in Smm-range, in typical situation of 500 MHz frequency deviation [4], the frequency modulation by non-symmetric
saw-tooth law equaled to 10 kHz and the distance to the object 75 m, the delay time r is 0.5 • 10-6 sec, and the autodyne signal period
ta is equal to 0.4 • 10"6 sec.
examine peculiarities of autodyne response formation at different FM parameters and distances to the radar object for the non-symmetric saw-tooth FM law. Partially. this task were discussed in reports [12 14].
1 Initial expressions for signal analysis
A system of differential equations linearized in the vicinity of steady-state mode for small relative variations of the oscillation amplitude a and frequency x f°r single-circuit oscillator, which is under impact of the proper reflected (from the radar object) emission, has a view [12.15]:
(Qp/^cav)(da/dt) + aa + ex = T~(t, tcos S(t, t), (1)
fia + Qlx = -T(t,T sin S(t,T ),
(2)
where Ql, ucav are the loaded Q-factor and the cavity-natural frequency, relatively; a, ^^d ft are dimensi-onless parameters defining the oscillator increment slope, non-isodromity and non-isochronity, relatively; 'q = Qh/Qex, Qex is an efficiency and the external Q-factor of the oscillating system; V(t,T) = ro[A(t,T)/A(t)], S(t,T) = ^(t) — ^(t,T) are the modulus and the phase of the instantaneous reflection factor reduced to the oscillator output; r0 is the emission damping factor in amplitude at its propagation to the object and back; A(t), A(t,T^d ^(t), ^(t,T) are oscillator amplitudes and phases in the current moment t and from the system pre-history (t — t ); t = 21/c, where I is a distance to the reflecting object; c is the speed of emission propagation.
At FM by means of the bias voltage variations across the varicap, both frequency and ''parasitic" amplitude modulation (PAM) occur:
u(t) = wo + AuFM (t) = wo[1 + mFM fmod(t)], (3) A(t) = Ao[1 + aAM CO] = Ao[1 + aAM fm„d(t)], (4)
where mpM = Aupm/^o and mAM = AA am Mo are coefficients of frequency (FM) and amplitude (AM) modulation, relatively; AwFM, AAam are maximal deviations of oscillation amplitude and frequency from the steady-state values Ao and wo due to oscillation modulation; fmod(t) is the normalized modulating function having the Qmod frequency. The quasi-static solutions of the first approximation [16] of the equation system (1), (2) with account (3), (4) for relative variations of the amplitude a(t, t) and absolute frequency variations w(t, t) of FM ASRR have a view:
a(t, t) = mAM fmod(t) + T(t, t)Ka cos[S(t, t) — (5)
u(t, t) = wo {1 + mAM fmod(t) - T(t, t)La
sin[S(t,T )+ 0]}:
where Ka, La are coefficient of autodyne amplification and the frequency deviation; ^ = arcXim(p), 0 = arctan(7) are angles of phase shift; p = e/Ql, 1 = are coefficients of oscillator non-isodromity and non-isochronity, relatively.
To obtain expressions describing the autodyne response in the general case of arbitrary ratio of reflected emission delay time t and Ta period, we use the known approach to analysis of systems with delay, which is developed for the case of usual (without FM) autodyne signal description in [15]. Its sense consists in expansion of functions A(t,T) and ^(t,T) of retarded impact into Taylor series over the small parameter ratio of delay-time t and the current time t. At that, we assume that functions (5), (C) have no breaks over all time interval for autodyne response formation. In addition, here we exclude from consideration the transients in reverse zones of the modulating functions taking into account fulfillment of the strong inequality t << 2n/Q.mod. Then, taking above-mentioned into consideration, expressions for D(t, t) mid S(t,T) in ( ), ( ), as functions of normalized (dimensionless) delay times Tn = uot/2-k and the modulating function tn
Qmodt/2-K, have the view:
T(t ni )=ro 1 + 2^rnYoKa-
m \
Y, (-1)mXm(rn) sin[S(tn, rn) - ^ + em(rn)] (7)
m=0 J
5(tn,Tn) = 2nTn + nBFM fmod(tn)-
M
- CpbY (-i)mxm(rn ) sin[ô(tn, Tn) + e + em(rn)]
m= 0
(8)
where rn = r/Ta is the parameter of normalized (with the respect to the autodyne signal period Ta) distance to reflecting object; Bpm = AFpmt is the parameter of !'FM base" defining the number of signal periods being stacked over the modulating function period at fixed reflecting object, when Tn is fixed; AFpm = A^pm/2-n is the frequency deviation expressed in Hz; Cps is the feedback parameter of the autodyne system; Xm(rn), Qm(rn) are amplitude values and phase shifts of m-th terms (m = 0,1,...,M) of series in equations ( ) and (8):
^m (rn )
(2Krn)2mv?4(m + 1)2 + (2nrn)2
2(m + 1)(2m + 1)!
Qm(rn) = — arctan
(9)
(m + 1)
Autodyne variations of oscillation amplitude T0Ka are usually very small: T0Ka << 1. Therefore, we can neglect by the second term in large parenthesis
a
of (7). Such an approximation in the autodyne system mathematical model supposes an account the phase delay only of the reflected emission. At that, we note that known solutions for the autodyne response following from (7) (9), are obtained in the first approximations assuming m = 0. Account of series terms of higher order in these expressions, as it will shown later, allows taking into consideration also the dynamics of phase variation $(tn, Tn) at any ratio on delay time r of reflected emission and the autodyne signal period Ta.
In this connection, the further analysis of the autodyne response will be examined without first terms in ( ), ( ) for r(t,r) = r0. Then, expressions for normalized maximal values of variations of amplitude and frequency in the form of the amplitude (AAC) (tn ,Tn) and frequency AFA Xn (tn ,Tn) characteristics of the autodyne, have the vews:
an(tn,rn) = a(tn,rn)/rKa = cos[5(tn,rn) - ^], (10) Xn (tn ,rn ) = x(tn ,rn )/r La = - sin[£ (tn ,Tn ) + 0]. (11)
Solution of the transcendent equation (8) under condition of its smoothness when Cfb < 1 can be obtained by the successive approximation method. This solution in the form of the autodyne phase characteristic (APC) S(tn,rn) has a view:
5{tn ,rn) = 5{tn ,rn )(o)-
M
- Cfb Y, (-!)mX™(r™) ^, )(1) + 0 + (rn)-
m=0 M
-CFB Y(—i)mXm(rn) sin[5(tn,rn)(2)+e+em(rn)-...
m=0 M
m=0
2 Numerical analysis autodyne response
of the
FM ASRR signals are usually registered in the power source circuit of the UHF oscillator (the autodetection signal) or by means of oscillation amplitude variations detection. Both variations of the amplitude in the form of AAC an (tn) and of the autodyne current frequency in the form of AFC Xn (tn) give the contribution in these signal formation. To clarify the peculiarities of FM ASRR signal formation, we use the following mathematical form of the normalized modulating function fmod (tn) [ ] f°r the non-symmetrical modulation law:
2
fmod (tn) = - arctan
'K
tan i^T-)
(13)
(a)
(b)
— CfbY ( — ■l)m(r-) sinß(tn, rn)(k) + 0+Qm(rn)]...
...]] (12)
(c)
(d)
Fig. 1. Time diagrams of APC formation 5(tn), their derivatives d5(tn)/dtn, AAC an(tn) (curve 1) and AFC Xn (tn) (curve 2) calculated at various values of normalized distance rn\ rn = 0 (a), rn = 0.5 (b), rn = 1 (c) and rn = 1.5 (d)
Calculation results of the time diagrams of APC 5(tn) and its normalized derivatives d5(tn )/dtn characterizing the variation speed of the reflection emission phase incursion, as well as AAC an(tn) and AFC Xn(tn) fulfilled according to (10) (12) with account of (13) for different normalized distances rn, are presented in Figure . Spectral diagrams an(Fn) and Xn(Fn) of signal characteristics calculated at previous values of oscillator
2These characteristics are determining in autodyne signal formation, therefore, they are referred as signal characteristics in the theory of autodyne systems [15].
where indices in parenthesis near terms 5(tn ,rn) denote the approximation order; S(tn,rn)0,1,...,k = 2nrn +
kBFM fmod (tn )■
The zero approximation, when we take into consideration the first term only of the sum in ( ) ö(tn ,rn), corresponds to the linear phase characteristic, which is typical for homodyne SRR. The further approximations insert nonlinearity in the function, which is the autodyne system attribute. Therefore, the main attention below in research fulfilled will be focused on revealing of ASRR signal peculiarities under conditions, when the Cfb parameter is commensurable with 1.
parameters and normalized distances rn (see Figure l,a-d), are presented in Figure 2. In the future, at analysis on autodyne characteristics, we shall call as "operation zones" (beginning for the first, where 0 < rn < 1) the segments of normalized distance rn, which are multiplies to integer numbers.
I i i i i
0.8 -
t? 0.6 -
£ 0.4 - -
0.2 - I A A A A
0
10
15
fn
20 25 30
(a)
(b)
1 0.8 - lili
g 0.6 -
£ 0.4 -
0.2 -
0 Ii lili
10
20 25 30
(c)
on, and the peak height of the normalized derivative d5(tn)/dtn essentially decreases. The anharmonic distortion degree of A AC and AFC diagrams, and accordingly, the level of higher harmonic components, significantly decrease. This tendency is especially noticeable in the first operation zone, where 0 < rn < 1. In the case of rn = 1, 2,..., as well as at Cfb << 1 AFC and AAC have practically the sine view as for homodyne FM ASRR.
For more obvious representation of functions obtained, we use the generalized parameter — the total harmonic distortion (THD) factor characterizing the distortions of quasi-periodic oscillations. Calculation results of THD as a function of the normalized distance rn, are presented in Figure for different Cfb-
(d)
Fig. 2. Spectrograms an(Fn) and Xn(Fn) calculated for normalized distances rn = 0 (a), rn = 0.5 (b), rn = 1 (c) and rn = 1.5 (d)
Hereinafter, if there is not the special reservation, calculation of the time diagrams are performed at 9 = 1, ^ = 0.2, BFM = 5 Cfb = 0.8, k = M = 50, rn = 0. We note that the number of series terms in (7), (8) and approximations of fc-order in ( ), which were taken in calculations, ensure the convergence of calculation results in the ranges rn < 5 and Cbf < 0.98.
From analysis of time and spectral diagrams presented in Figures l,a and 2,a, we see that results obtained for rn = 0 correspond to research results, which were performed in [10, 11] only for the first approximations (t << Ta). In other cases, as we see from diagrams in Figures l,b-d and 2,b-d, with growth of the normalized distance rn, their view essentially varies. So, for example, the APC time diagram 5(tn) approaches to linear functi-
Fig. 3. Plots THD(rn) calculated for Bfm = 5 and
CFB = 0.4 (curve 1) and for Cfb = 0.8(curve 2)
From plots in Figure 3, it is seen that the most distortions of the FM ASRR signals are observed in the region of small rn of the first operation zone. At Cfb =0.8, THD in this zone achieves about 40%. With further transition into operation zones of higher order, signal distortions essentially decrease achieving the minimal values at the normalized distances rn, which are multiplies of integer numbers (rn = 1, 2,...).
Returning to examination of calculation results presented in Figure 2, it is necessary to note a presence of DC components ao(Fn) and %o(Fn) in spectrograms of Figure 2a,b,d. A presence of the DC component %o (Fn) in the oscillator response on frequency variation Xn (tn) indicates to some offset of the average oscillation frequency under influence of the reflected emission. Therefore, these components deserve attention at studying FM ASRR signals. Their account may be required, for instance, at signal processing, the noise immunity analysis, etc.
Calculation results of relative levels of DS components ao (rn) and %o (rn) depending on the normalized distance rn at Cfb =0.8 for the autodyne responses an (tn) and Xn(tn) are presented in Figure .
From curves in Figure 4 we can see that in the first operation zone of the FM ASRR at large values of Cfb ~ 1 the DC component level may have values, which is commensurable with signal amplitudes. In zones with higher order, we may neglect by influence of DC components. It is necessary to note that for Cfb << 1 ,
DC components in the output signals of FM ASRRs are practically absent.
1 0.8 0.6 0.4 0.2 0 \
\
>
0 0.5 1 1.5
2.5 3
(a)
(b)
damping of "oscillations" in dynamic phase variations A5dd is here observed.
Plots of AFC Xn(tn) and A A C an(tn) are presented in Figure 6 for the case of rn = 2.^d Cfb = 5.
0.5
« -0.5
-1
A 1 \ * 1 \ ' \ \ A *' ! \ * \ \ %
\l 2A 1 \ 1 \ % 1
;y I \ i \ \I
( \ • * \ J' i \ J'
Fig. 4. Plots of a0(rn) (curve 1) and x0(rn) (curve 2) calculated for Bfm = ^d Cfb = 0.8
To understand of the character of dependences obtained, let us introduce the concepts of equivalent feedback parameter Ceq of the autodyne system and the angle of dynamic displacement of phase A5dd of the autodyne response: Ceq = CfbKdf and A5dd = S(rn) — 5(rn = 0). Here Kdf = Z^m=o(—1)mXm(rn) is the "dynamic factor" of feedback included in ( ) and ( ); 5(rn), 5(rn = 0) are phases of the instantaneous reflection factor obtained for the current value of rn and for its zero value, relatively. Calculation results for functions Kdf(r„^d A5dd (rn) are presented in Figure , at that, for A5dd(rn) two curves are obtained: for non-isochronic (curve 1) and for isochronic (curve 2) oscillator.
0.1
0.2
t„
0.3 0.4
Fig. 5. Plots of the dynamic feedback factor Kdf (rn) (a) of FM ASRR and phase displacement A5dd (rn) (b) of signals versus the normalized distance rn to the reflected object: 8 = 1 (curve 1), 8 = 0 (curve 2)
From the curve Kdf(rn) (see Figure a) we see that with growth of rn in the first operation zone, where 0 < rn < 1, to value of Kdf and, hence, the equivalent parameter Ceq decreases practically by an order. Then, with growth of rn, the value of Ceq asymptotically damps with slight growths in the middle part of the operation zones of higher order, where rn > 1.
Dynamic phase variations A5dd of signal characteristics, which influence on the distortion character, which is well seen from comparison of curves of Figures la and b, with growth of rn in the first operation zone are also maximal. At rn = 1, there is the first minimum of this value, which is determined by the 8 parameter, characterizing of oscillator non-isochronous property (see Figure b). with further growth of rn, the asymptotic
Fig. 6. Time diagrams of AFC Xn(tn) (curves 1) and A AC an (tn) (curves 2) formation calcu lated at Cfb = 5 and rn = 2.5
As we see from plots in Figure 6, in spite of the fact that Cfb > 1, the autodyne response in higher operation zones of FM ASRR is smooth and has not jumps and breaks. At that, the distortion level of quasi-harmonic characteristics equals to 31%.
Results obtained here seem to be contradictory to the habitual representations [10,llJ and have quite explainable physical sense. For its understanding, it is enough to take the simplified model of representation of interaction process of the autodyne with the proper reflected emission, which can be described by the steps method [17J. From this model it follows that with shortening of the radio-pulse relative duration (this is equivalent to growth of normalized distance), a number of partial reflections decreases during the time period of the radio-pulse action. This leads to reduction of equivalent feedback parameter Ceq of the autodyne system and, hence, the signal distortion level. When rn achieved the unity (rn = 1
and formation of practically harmonic autodyne variations is provided, which is shown by the above-described analysis.
3 Results of experimental investigations of FM autodynes
Experimental investigations of FM ASRR were performed with the oscillating module on 8mm-range Gunn diode in the structure of the autodyne radar developed for monitoring of point-works occupation in hump-yards [2 4]. The autodyne oscillator of this sensor was made on the base of the Gunn diode AA727A and the varicap 3A637A-6 in packaged implementation. Output power is 25 mW, the central frequency is 36.5 GHz. The UHF oscillator provides the frequency tuning of 500 MHz in the mode of linear FM. The FM law is the non-symmetric saw-tooth, the modulation frequency is 10 kHz. The antenna is horn-lens type with the pattern width 6 x 6 degrees.
The autodyne signal was extracted in the power source circuit of the Gunn diode with the help of the wideband current transformer. After filtering and amplification, it passes on the analog-to-digital converter of the digital signal processor (DSP) TMS320F2808 from Texas Instrument of the processor unit. In this unit, functions of modulation voltage formation, digital signal processing and communication interface RS-485 with the personal computer.
Figure 7 shows the signal spectrograms obtained from the corner reflector (a) and from the wall of five-floor building (b). The corner reflector with effective dispersion area near 10 m2 was mounted at the distance I = 3 m (delay time t = 2 ■ 10-8 sec) from the ASRR antenna aperture. The building wall was situated at distance I = 60 m (t = 4 ■ 10-7 sec). Signal amplitudes (Us) in both cases were practically the same. The converted signal frequency in the first case was about 100 kHz (Ta = 1 ■ 10-5 c), a to btopom - 2 MFu (Ta = 5■ 10-7 c).
I, m l m
(a) (b)
Fig. 7. Spectrograms of signals converted by the autodyne obtained from the corner reflector (a) and from the wall of 5-fioor building (b)
In the first case (see Figure Ta), we see in spectrograms the noticeable level of second and third harmonics typical for anharmonic distortions of the autodyne signals. In the second case, higher harmonic components are practically absent. From comparison of obtained spectrograms presented in Figures 7a,b and 2a,c, we see their qualitative agreement. Thus, obtained experimental data confirm the adequacy of above-developed mathematical model for analysis and calculation of FM ASRR signal and spectral characteristics.
Conclusions
Peculiarities of FM ASRR signal formation are considered for the non-symmetric saw-tooth law in the general case of arbitrary ratio of delay time t of the reflected emission and the autodyne signal period Ta. At description of signal properties, the new concepts of the normalized distance rn to reflected object, the equivalent feedback parameter Ceq of the autodyne system and the angle of phase dynamic displacement ASDD of the autodyne response.
From analysis of the fulfilled research results the important conclusion follows that FM ASRR signal
frequency in the whole range of distances to the radar object corresponds exactly to the frequency of the converted signal obtained in the case of the homodyne system [5].
In the first operation zone, at small distance to the reflected object, where the strong inequality rn << 1 is true, and hence, t << Ta, the analysis results obtained are agreed with results of previous researches. In this zone, at CFB ~ 1, significant distortions of autodyne signals and spectrum enrichment are observed, which require of its account in devices for signal processing.
With growth of normalized distance rn, the value of equivalent feedback parameter Ceq of the autodyne system essentially decreases while the angle of phase dynamic displacement ASdd of the autodyne response after significant variations in the first operation zone has got the steady-state value in the further zones. This approaches APC S(tn) to the linear function and essentially decreases the anharmonic distortion degree of AAC an(tn) and AFC Xn(tn). This feature is especially noticeable in the first operating zone if rn ^ 1. In the case, when rn is the multiple of the integer number (rn = 1,2,...), AAC an(tn) and A FC Xn(tn) have practically the sine view.
Signal analysis results obtained in this paper develop and expand results of known researches fulfilled in publications [15,18] in the part of FM oscillator account as well as fulfilled in [10, 11] in the part of account (in the autodyne model) of dynamics of phase variation of reflected emission at its propagation to the object and back. Revealed regulations of signal formation in FM ASRR have rather general character, therefore, obtained results, as we think, can be used at signal calculation of autodyne systems made on the base of semiconductor laser modules [19-21].
Acknowledge
The present paper is prepared in accordance with an Agreement on scientific-technological cooperation between UrFU and IRE XASU, as well ctS clt financial support of Russian Federation Government, order Xo 211, contract Xo 02.A03.21.0006.
References
[1] Armstrong B.M., Brown R., Rix F. and Stewart J.A. C. (1980) Use of Microstrip Impedance-Measurement Technique in the Design of a BARITT Diplex Doppler Sensor. IEEE Transactions on Microwave Theory and Techniques, Vol. 28, No. 12, pp. 1437-1442. DOI: 10.1109/TMTT.1980.1130263
[2] Varavin A.V., Vasiliev A.S., Errriak G.P. and Popov I.V. (2010) Autodyne Gunn-diode transceiver with internal signal detection for short-range linear FM radar sensor. Telecommunication and Radio Engineering, Vol. 69, No. 5, pp. 451-458. DOI: 10.1615/TelecoiriRadEng.v69.i5.80
[3] Ermak G.P., Popov I.V., Vasilev A.S., Varavin A.V., Noskov V'.Ya. and Ignatkov K.A. ("2012) Radar sensors for hump yard and rail crossing applications. Telecommunication and Radio Engineering, Vol. 71, No. 6, pp. 567-580. DOl: 10.1615/TelecomRadEng.v71.i6.80
[4] Noskov V'.Ya., Varavin A.V., Vasiliov A.S., Ermak G.P., Zakarlyuk N.M., Ignatkov K.A. and Smolskiy S.M. (2016) Modern hybrid-integrated autodyne oscillators of microwave and millimeter wave ranges and their application. Part 9. Autodyne radar applications. Uspekhi souremennoi radi-oelektroniki, No. 3, pp. 32-86. (in Russian).
[5] Komarov l.V. and Smolskiy S.M. (2003) Fundamentals of short-range FM radar. Norwood: Artech House, 289 p.
[6] Hinman W.S. and Brunetti G. (1946) Radio Proximity-Fuze Development. Proceedings of the IRE, Vol. 34, No. 12, pp. 976-986. DOl: 10.1109/.IRPRUG. 1946.233235
[7] Takayama Y. (1973) Doppler signal detection with negative resistance diode oscillators. IEEE Transactions on Microwave Theory and Techniques, Vol. 21, No. 2, pp. 89-94. DOl: 10.1109/TMTT. 1973.1127929
[8] .Jeilbrd P.A. and Howes M.S. (1985) Modulation schemes in low-cost microwave held sensor. IEEE Transaction of Microwave Theory and Technique, Vol. 31, No. 8, pp. 613-624. DOl: 10.1109/TMTT.1983.1131559
[9] Votoropin S.D. and Noskov V'.Ya. (2002) Analysis of operating regimes of EHF hybrid-integrated autodynes based on the Gunn micro power mesa planar diodes. Russian Physics Journal, Vol. 45, No. 2, pp. 195-206. DOl : 10.1023/A:1019664300993.
[10] Votoropin S.D., Noskov V'.Ya. and Smolskiy S.M. (2008) An analysis of the autodyne eilect of oscillators with linear frequency modulation. Russian Physics .Journal, Vol. 51, No. 6, pp. 610-618. DOl: 10.1007/sll 182-008-9083-5
[11] Votoropin S.D., Noskov V'.Ya. and Smolskiy S.M. (2009) Modern Hybrid-Integrated Autodyne Oscillators of Microwave and Millimeter Range and Their Applications. Research of Autodynes with Frequency Modulation. Uspehi souremennoi radioelektroniki, no. 3, pp. 3-50. (in Russian).
[12] Noskov V'.Ya., Vasiliov A.V., Ermak G.P., Ignatkov K.A. and Chupahin A.P. (2016) Mathematical model of FM autodyne radar. Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW), 2016 9th International Kharkiv Symposium on, A-25, pp. 1-4. DOl: 10.1109/MSMW.2016.7538101
[13] Noskov V'.Ya., Vasiliov A.V., Ermak G.P., Ignatkov K.A. and Chupahin A.P. (2016) Main expressions for analysis of signals and noise of autodyne FM radar. Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW), 2016 9th International Kharkiv Symposium on, A-9, pp. 1-4. DOl: 10.1109/MSMW.2016.7538019
[14] Ignatkov K.A. and Vasiliov A.V. (2016) Signals of the autodyne FM radar for mm-wavelength range. Microwave & Telecommunication Technology (CriMiCo), 2016 26-th International Crimean Conference, Vol. 10, pp. 2139-2145.
[15] Noskov V'.Ya. and Ignatkov K.A. (2013) Autodyne signals in case of random delay time of the rellected radiation. Telecommunication and Radio Engineering, Vol. 72, no. 16, pp. 1521-1536. DOl: 10.1615/TelecomRadEng.v72.il6.70
[16] Noskov V'.Ya. and Ignatkov K.A. (2014) About applicability of quasi-static method of autodyne systems analysis. Radi-oelectronics and Communications Systems, Vol. 57, No. 3, pp. 139-148. DOl: 10.3103/S0735272714030054.
[17] Noskov V'.Ya. and Ignatkov K.A. (2013) Dynamics of autodyne response formation in microwave generators. Radi-oelectronics and Communications Systems, Vol. 56, No. 5, pp. 227-242. DOl: 10.3103/S0735272713050026
[18] Noskov V'.Ya. and Ignatkov K.A. (2013) Dynamic features of autodyne signals. Russian Physics .Journal, Vol. 56, No. 4, pp. 420-428. DOl: 10.1007/slll82-013-0051-3
[19] Giuliani G, Norgia M, Donati S. and Bosch T. (2002) Laser diode self-mixing technique for sensing applications. .Journal of Optics A: Pure and Applied Optics, Vol. 4, No. 6, pp. 283-294. DOl: 10.1088/1464-4258/4/6/371
[20] Sobolev V.S. and Kashcheeva G.A. (2008) Self-mixing frequency-modulated laser interferometry. Optoelectronics, Instrumentation and Data Processing, Vol. 44, No. 6, pp. 519-529. DOl: 10.3103/S8756699008060058
[21] Usanov D.A., Skripal A.V. and Astakhov E.l. (2014) Determination of nanovibration amplitudes using frequency-modulated semiconductor laser autodyne. Quantum Electronics, Vol. 44, No. 2, pp. 184-188. DOl: 10.1070/QE2014v044n02ABEH015176
Особливост! формування сигнал!в авто-динних радюлокатор!в 1з лшшною частотною модулящэю
Носков В. Я., Ггиатков К. А., Чупа:ан А. П., Васильев А. С., брлшк Г. П., Смолъсъкий С. М.
Представлен! результати досл1джеш> особливостей формуваппя спгпал1в автодишшх систем ближпьо! ра-дюлокацп мктаметрового д!апазопу з липйпою частотною модулягцею по песиметричпому пилкопод1бпому закону. Отримаш вирази для розрахупку автодишшх сигпал1в в загалыюму випадку довольного часу зашзшоваппя взбитого випромшюваппя. Побудовапо тимчасов! 1 спектральш д!аграми автодишшх сигиал1в для випадшв, коли трива-л!сть 1х перюду зпачпо бглыне часу зашзшоваппя взбитого випромшюваппя, а також для випадшв, коли така пер1вшсть по викопуеться. Експеримептальш досл1джеппя викопаш 1з застосуваппям генератора па дюд! Гаппа 8мм д!апазопу довжшш хвиль, електричпо керовапого по частот! варикапом.
Клюноаг слова: автодш: автодшший сигнал: автодип-ппй в!дгук: система ближпьо1 радюлокацп: частотна мо-дулягця: генератор па дюд! Гаппа
Особенности формирования сигналов автодинных радиолокаторов с линейной частотной модуляцией
Носков В. Я., Игнатков К. А., Чупахин А. П., Васильев А. С., Ермак Г. П., Смольский С. М.
Представлены результаты исследований особенностей формирования сигналов автодинных систем ближней радиолокации с линейной частотной модуляцией по несимметричному пилообразному закону. Получены выражения для расчёта автодинных сигналов в общем случае произвольного времени запаздывания отражённого излучения. Построены временные и спектральные диаграммы автодинных сигналов для случаев, когда продолжительность их периода значительно больше времени запаздыва-
ния отражённого излучения, а также для случаев, когда данное неравенство не выполняется. Экспериментальные исследования выполнены с применением генератора на диоде Ганна 8-мм диапазона длин волн, электрически управляемого по частоте варикапом.
Ключевые слова: автодин; автодинный сигнал; авто-динный отклик; система ближней радиолокации; частотная модуляция; генератор на диоде Ганна
