# The method of determination of parameters of slow-wave systems

(57) Abstract:

The method of determination of parameters of slow-wave systems includes the excitation of the slow-wave system, short-circuited at the end, the microwave oscillations from the microwave generator in a given frequency range, the measurement of fixed f_{om}in this range, the determination of the coefficients of a slowdown in n

_{m}the measured frequencies by calculation and construction of the dispersion characteristics n=n(f) on calculated values of n

_{m}under this measure all frequencies f

_{om}successive resonances short-circuited at the end of the slow-wave system as dvukhpolosnykh to measure the real part of R

_{m}the input impedance of dvukhpolosnykh for each frequency f

_{om}measure around each frequency f

_{om}successive resonances top f

_{mV}and lower f

_{mn}the frequency at which the imaginary part of the input impedance of dvukhpolosnykh, respectively, X

_{m}(f

_{mV})=R

_{m}and X

_{m}(f

_{mV})=-R

_{m}determine the electrodynamic parameters of the slow-wave system at each frequency f

_{om}successive resonances, such as the following formulas. The technical result consists in the measurement of electrodynamic parameters sameday. 4 Il., 3 table. The present invention relates to the field of measurement technology, and more specifically to the field of measurements in microwave electronics. Can be used for measurements of electrodynamic parameters (EDP) uniform transmission lines (PL) electromagnetic waves (EMW), in particular helical slow-wave systems (SES).There is a method of measuring the dispersion characteristics (DF) slow-wave systems (CS) /1, page 265; 2, page 410/ includes excitation of CS, short-circuited at the end, SHF oscillations through the high-frequency measuring path (CHEAT) in a given frequency band, determining by means of the probe entered in the AP and movable along a CS neighboring points X

_{1m}and X

_{2m}minimum readings of the indicating instrument connected to the output of the probe at a given discrete frequencies f

_{m}within a given frequency band, determining the deceleration rate of n

_{m}at each fixed frequency f

_{m}according to the formula

< / BR>

where

_{om}the wavelength in free space corresponding to the frequency f

_{m},

_{om}= c/f

_{m}c = 310

^{8}m/s, and the construction of DF n = n(f) CS for calculated values.Device for measuring DF contains /2, page 410, Fig. 11.29/ generator microwave, vocalocity at the end of the AP, connected to the second output of the microwave generator, and connected in series probe entered in the AP, a detector section and indicating instrument.Dimension DF is produced as follows. Gather the scheme of measurements and excite CS fixed frequencies f

_{m}within a given frequency band. On each frequency f

_{m}using a probe to find and register the two neighboring points X

_{1m}and X

_{2m}minimum readings of the indicating instrument. Define

_{om}and I hope n

_{m}by the formula (I). Build DH n = n(f) on calculated values of n

_{m}.The disadvantage of analogue is the complexity of the measurements associated with the movement of the probe along the AP and check points X

_{1m}and X

_{2m}and significant error associated with the approval of the AP with the CHEAT to obtain the mode traveling wave in the entire specified frequency band.The closest in technical essence is chosen as the prototype of a method of measuring the deceleration rate in the cable /3, page 165/ includes excitation of microwave oscillations securechange from one end of the segment of the cable associated with the co-axial insertion-loop communication from the microwave generator in a given frequency range, the measurement and the register is as resonant frequencies according to the formula:

< / BR>

where m is the number of the resonance, m = 1,2,3..., C = 310

^{8}m/s, l

_{to}- cable length, m, f

_{m}the frequency of the m-th resonance, f

_{m-1}- previous frequency resonance, Hz.Device for measuring the deceleration rate contains /3, page 165, Fig. 7.1/ microwave generators, frequency connected to the first output of the microwave generator, connected in series attenuator, measuring standing wave ratio (VSWR), coaxial insert and the matched load connected to the second output of the microwave generator, and the monitoring cable, shorted at one end and a second end connected to the coaxial inserted through the loop due to the low connection.The measurement of the deceleration rate is produced as follows. Gather the scheme of measurements. Rebuild the microwave generator frequency to obtain first, second, etc. resonances at frequencies f

_{1}f

_{2},...f

_{m}record these frequencies. The presence of resonances in the cable is determined by the maxima of the CWS at these frequencies. Define n

_{m}on each frequency by the formula (2).The prototype partially addresses the lack of similar regarding approval before the mode traveling wave, however, has an error associated with fuzzy registration mediaremote the invention, is the task of measuring the EAF CS on a regular workplace in measurement mode input parameters shorted at the end of dvukhpolosnykh (DP).The technical result of the proposed solutions is the way of measuring EDP PL, including the AP, on a regular workplace in case of short circuit output PL by measuring the input resistance of the PL as dvukhpolosnykh.This technical result is achieved in that in the method of determination of parameters of slow-wave systems, including the excitation of the slow-wave system, short-circuited at the end, microwave oscillations from the microwave generator in a given frequency range, the measurement target frequencies f

_{om}in this range, the determination of the coefficients of a slowdown in n

_{m}the measured frequencies by calculation and construction of the dispersion characteristics n=n(f) on calculated values of n

_{m}what's new is that they measure all frequencies f

_{om}successive resonances short-circuited at the end of the slow-wave system as dvukhpolosnykh to measure the real part of R

_{m}the input impedance of dvukhpolosnykh for each frequency f

_{om}measure around each frequency f

_{om}successive resonances top f

_{mV}but X

_{m}(f

_{mV}) = R

_{m}and X

_{m}(f

_{mn}) = -R

_{m}determine the electrodynamic parameters of the slow-wave system at each frequency f

_{om}sequential resonance formula:

< / BR>

< / BR>

_{zm}=

_{om}n

_{m}(5)

< / BR>

< / BR>

< / BR>

< / BR>

where n

_{i}- the number of the serial resonance dvukhpolosnykh, m = 1,2,3,...,

_{om}the wavelength in free space, the corresponding m-th measured frequency f

_{om},

_{om}= c/f

_{om}c = 310

^{8}m/s, Q

_{om}- the quality of dvukhpolosnykh at frequency f

_{om}, l

_{sp}- set the length of the slow-wave system, m

_{zm}- phase constant of the wave propagation in slowing down the system at frequency f

_{om}, rad/m

_{om}- phase constant of the wave propagation in free space, rad/m

_{om}= 2/

_{om},

_{om}- constant attenuation of the wave in slow-wave structure at a frequency f

_{om}H

_{n/m}, Z

_{om}wave resistance slowing down the system frequency f

_{om}, Ohm, R

_{om}- set running resistance slowing down the system frequency f

_{om}, Ohm/m, L

_{0m}- inductance slows down the system at frequency f

_{om}, GN/m, C

_{0m}- linear capacitance slows the system frequency f

_{om}F/m

_{who I am for the argument f is the measured frequency fomsuccessive resonances dvukhpolosnykh.The set of essential features of the proposed solution allows to measure the EAF CS on a regular place in the measuring mode input characteristics shorted CS as dvukhpolosnykh.In Fig. 1 shows a block diagram of the measurement EAF CS on the proposed method, Fig. 2, 3, 4 - measured (solid line) and calculated (dotted line) deceleration rate n, the wave resistance Zoand constant attenuationorespectively (for two types of SES).Device for measuring the zdp CS by the proposed method Fig. 1, contains connected in series meter input impedance (CI) 1, 2 CHEAT and SES 3 located in the housing 4 and shorted at the end of the body 4.The EDP definition of CS on the proposed method produces the following way. Gather the scheme of measurements, for which the standard CS short circuit at the output and input CS is connected to the output of CHEAT IVS 1. Rebuilding IVS 1 frequency bottom-up, find the first f01the second f02third f03and so on up to fomfrequency in the specified frequency range at which the reactive part of the input impedance XI(fom) CS is equal to zero, Regis is these frequencies. Around each of these frequency fomfind and register upper fmeand lower fmnthe frequency at which the imaginary part of input impedance of the LC, respectively, Xm(fmV)= Rmand Xm(fmn) = -Rm. Calculated running resistance Romon each frequency fomany known method, for example, according to /4, page 132/. Expect ADTS CS by the formula (3) to (9), build the dispersion dependence a=a(f) each of the parameters, taking the argument f is the measured frequency fom.In order to confirm the feasibility of the proposed method and obtain a technical result made the layout for measuring the EAF CS of the proposed method. As IS and WCIT used industrial "Meter complex coefficients of the transmission P4-37 in the measurement mode of the input parameters (5). As the casing 4 used a cylindrical cavity of length Lp= 220 mm with an inner diameter of Dp= 120 mm as the AP used two SES mounted in the coaxial resonator using three dielectric rods of Plexiglas with a diameter of darticle= 8 mm and length larticle= 220 mmGeometrical dimensions of SES are tabliod) SES; dCR- diameter conductors SES; lsp- the length of the SES; N - number of turns (periods) in SES; rggeometric slow.The results of measurements and calculations according to formulas (3) - (9) are given in table. 2 for SES N 1 and table. 3 for SES N 2.In table. 2 and 3 denote: fom- the measured frequency of the serial resonance;omthe wavelength in free space corresponding to these frequencies; om- phase constant propagation electromagnetic wave in free space; nmthe deceleration rate at frequency fom; 2f =fmV- fmn- the bandwidth in the vicinity of the measured frequency fom; Rm- the real part of the input impedance at the frequency fom; Qom- figure of merit, calculated according to the formula (4);om- constant attenuation of EMW in SES at frequencies fom;zm- phase constant of propagation of EMW in SES at frequencies fom; Zomwave resistance SES at frequencies fom; Rom- linear resistance SES at frequencies fom; Lom; Com- inductance and capacitance at frequencies fom.In Fig. 2, 3, 4 shows the measured (solid line) and theoretically calculated (dotted line) coefficientsin and calculated EDP satisfactorily match, some discrepancies due to errors in fabrication and installation of SES in the body, as well as the inaccuracy of theory at low frequencies /4, page 112, Fig. IV. 2/.We show that the proposed method is a technical solution is implemented and allows to measure the EAFz,o, Zo, Loand CoCS.By definition, the deceleration rate is called the ratio /4, / 6/:< / BR>wherezandophase constant propagation of EMW in the AP and open space;oandzthe wavelength in free space and LC; c = 3108m/s; Uf- the phase velocity of propagation of EMW in the AP.From the formula (10) is immediately followed by the formula (5) descriptions:z=onz=o/n (11)From theory of long lines and slow systems known relation /4, page 128, 133, 6, page 298/:< / BR>< / BR>< / BR>< / BR>where zdefined in formulas (10) and (11);o= 2fofo- measured frequency; Z0wave resistance CS; Ro, LoCo- linear resistance, inductance and capacitance CS;zthe wavelength in the AP;o- constant attenuation, NP/mFrom the formula (15) yields the following formula (6) descriptions:< / BR>g>/BR>< / BR>The multiplicationz(11) at Zo(13) on the same frequency gives the formula (8) for Lodescriptions, and divisionzat Zoformula (9) for Codescriptions:< / BR>< / BR>< / BR>< / BR>Thus, if the measured resonant frequency fomand the quality factor QomCS at these frequencies and known linear resistance RomCS, then by the formulas (5) - (9) are defined EAFzm,om, Zom, LomComCS.We show that the quality factor QomCS can be measured in the measurement mode of the input parameters of CS as dvukhpolosnykh and that the frequency fomsuccessive resonances CS as dvukhpolosnykh mode KZ correspond to the resonance frequencies on the penetration characteristics of CS as a quadrupole.Let us return to Fig. 1 SES to the right of the section AA is a section of coaxial line short circuit, in which the inner conductor is spiral 3, and the outer cylindrical body 4. Cut the coaxial line short circuit is a side cross-section AA dvukhpolosnykh, the input impedance is equal to /6, page 329, formula (8.128)/:ZI(j) = Zothzlo(20)and for two-terminal device (PD) low-loss /the t complexity value; - the current angular frequency, = 2f , f - frequency, Hz; Zowave line resistance, Ohm; lo- the length of the line segment m;z=o+jz- constant propagation of EMW in line;oandzdefined in formulas (10) - (15).The input impedance ZI(i) = jXI() by the formula (21) is purely imaginary, the function is periodic with period changes from - to + on the period. Points on the frequency axisOO,OO,...,omoin which XI(omo) = 0 are the points of successive resonances DP mode KS;points on the frequency axiso2,o4,...,o2min which XI(o2m) = are the points of parallel resonances DP mode SC /6, page 322, Fig. 8.38/. Note that, firstly, on the frequency axis parallel and series resonances alternate, secondly, are separated from each other at equal frequency intervalso2m+1-o2m= o2m-o2m-1= /, = lo/Uf; lo- the length of the segment; Uf- the phase velocity of propagation of EMW in line, thirdly, on the segment of length lothe number of parallel and serial resonance endlessly, and fourth, on a segment of length loin a given frequency range F>fo2m+1-fo2mthem pointomconsecutive resonances. From the formula (21) shows that XI(om) = 0 at those points where tgzlo= 0 orzlo= m. From here get the ratio between the length laboutwavelengthzmin the line corresponding to the m-th frequency fomsequential resonance:< / BR>where m is the number of the serial resonance on the frequency axis, m = 1,2,3... .Thus, at frequencies fomsequential resonance length labouta multiple of an integer m half-wavezm/2 corresponding to these frequencies fom.From the formula (10)z=o/n and formula (22) yields the following formula (3) deceleration rate nmdescription< / BR>Examine input impedance (20) in the vicinity of the frequency of the serial resonanceom,omfor lines with low losseso1 andolo1. In this case, you can put thooloand the value of the second order of smallness thotgzlo0. Then the input impedance (20) DP is:< / BR>Putting in the formula (15) lo= mzm/2 for frequencies fomsuccessive resonances will get< / BR>Transform the function tgzloin (24) in okretnost is stata serial resonanceom= 2fom- detuning in the vicinity of a frequencyom,om< / BR>Followed as Let getWe substitute (25) and (26) in the original ZI(i) (24), we obtain< / BR>ZI(i) REKM(1+jEKM) (27)< / BR>Formula (27) represents the input impedance of the series resonant circuit on lumped elements LtoCto, Rtoin the vicinity of the resonance frequency /7, page 128, formula (7-17)/. Therefore, short-circuited coaxial line segment of length lo= lsp= mzm/2 in a neighborhood of the frequenciesomsuccessive resonances equivalent input resistance ZI(i) (27) a series resonant circuit on lumped elements LEKMCEKM, REKM/6, page 336, formula (8.140)/, whose resonant frequency , quality factor QOK= Qomthe resistance Rto= REKM= Zomm/2Qom, LEKMand CEKMequivalent lumped inductance and capacity. From this equivalence, it follows that the resonance properties of the short-circuited segment of the coaxial line of length lo= mzm/2 Fig. 1 in the vicinity of a frequencyom, omserial Rezo is inogo circuit on lumped parameters LtoCto, Rtoin the vicinity of the resonance frequency of the circuitOK,OK,OK=om. In particular, bandwidth 2toand the quality factor QOKsuch a circuit is determined by the normalized generalized resonance characteristic /6, pages 224 and 225 of the formula (7.7) and (7.10)/:< / BR>< / BR>where is the generalized detuning circuit; fOKresonance frequency of the circuit,OK= 2fOK;2to=in-n,2fto= fin-fn, inthe upper cutoff frequency of the correspondingin= +1,in= 2fin, nthe lower cutoff frequency, the correspondingn= -1,n= 2fn.Write the input impedance of II?W) (27) in exponential form< / BR>- amplitude-frequency characteristic (AFC);z() and phase-frequency characteristic (PFC), z() = arctan. Convert AFC - Z() as follows:< / BR>x is the imaginary part of the input impedance Z(i) ; R is the real part of the input impedance equal to the resistance Ro) at the resonant frequency.On the borders of the bandwidth of the pathin,n= 2fin,ngeneralized detuning /6, page 225, the formula (7.11)/. Therefore, on the borders of bandwidth UB>) corresponds to the upper boundary frequencyin= 2fin;Xn(n) - lower boundary frequencyn= 2fn, Ro) corresponds to the resonant frequency. This means that bandwidth 2to=in-n(or 2fto= fin-fn) series resonant on lumped elements in the vicinity of the resonance frequencyOK, OKand bandwidth 2m=mV-mn(or 2fm= fmV-fmn) is equivalent to a series resonant circuit in the vicinity of a frequencyomomsuccessive resonances short-circuited segment of the coaxial line of length lo= mzm/2 can be measured in the measurement mode only input parameters PD, namely in the mode of measuring the input impedance ZI(i) = R(1+j): need to measure the resonant frequencyomwhere = 0 and XI(om) = 0, the active component of Rm(om) the input impedance at this frequency, measure the top fmVand lower fmnthe frequency at which the imaginary part of the input impedance is equal to, respectively, XI(fmV)=Rmand XI(fmn) = -Rmto determine the bandwidth of equivalential (4).Let us return to the formula (21). By definition, the input resistance is called attitude /7, page 355/:< / BR>where is the voltage and current at the input of the DP (in the cross-section AA of Fig. 1). From (33) it is seen that the points of successive resonances XI(om) = 0 are those frequenciesomwhereWhen measuring the dispersion characteristics of the CS is often used resonance methods /8, pages 22-29/, in which the resonances is determined by the frequency ratio (CCP) in the mode of measuring flow parameters of a quadrupole. By definition CCP quadrupole (PE) name relationship /7, page 361/:< / BR>the voltage at the output of the PE; - the voltage at the input PE in cross-section AA of Fig. 1, coincides with the voltage of the DP in the formula (33). The resonance frequency of aopconsider the frequency at which K(op) _ or for lines with loss of Kop) = Kmax. From formula (34) shows that the resonance of entry CCP will be at those frequencies where . As in formulas (33) and (34) the input voltage is the same, we conclude that the frequency of the resonancesopin the AP by passing CCP coincide with frequenciesomsuccessive resonances CS as DP mode short circuit. This means that to measure the dispersion characteristics of CS instead resonance h is the resistance of CS as DP mode short circuit both frequencies are the same.Thus, the proposed method of determination of parameters of LC meet the conditions of patentability: meet the criteria of "novelty and inventive step, is a technical solution, technically implemented and has industrial applicability.Sources of information1. Taranenko H. I., Trokhimenko J. K. CS, Kiev, Nauka, 1965.2. Lebedev, I. C. Equipment and microwave devices. H. 1. Appliances microwave, M., Higher SHK. 1970.3. Fradin A. H., Ryzhov E. C. Measurement parameters AFD, M., Link, 1972.4. Silin P. A., B. N. Sazonov CS, M, Owls. Radio, 1968.5. P4-37. Measuring complex coefficients of the transmission. And TE. CO.400.245.THEN.6. Losev A. K. Linear radio circuits. M., High school. 1971.7. Atabay, I. the Fundamentals of circuit theory. Meters, Energy, 1969.8. Electromagnetic LC (method of measuring the electrical characteristics). M, Barongis, 1960. The method of determination of parameters of slow-wave systems, including Vozrojdenie slow-wave system, short-circuited at the end, the microwave oscillations from the microwave generator in a given frequency range, the measurement of fixed fomin this range, the determination of the coefficients zascitenim values of nm, characterized in that measure all frequencies fomsuccessive resonances short-circuited at the end of the slow-wave system as dvukhpolosnykh to measure the real part of Rmthe input impedance of dvukhpolosnykh for each frequency fommeasure around each frequency fomsuccessive resonances top fmband lower fmnthe frequency at which the imaginary part of the input impedance of dvukhpolosnykh, respectively, Xm(fmb)=Rmand Xm(fmb)=-Rmdetermine the electrodynamic parameters of the slow-wave system at each frequency fomsequential resonance formula< / BR>< / BR>zm=omnm,< / BR>< / BR>< / BR>< / BR>m - the number of the serial resonance dvukhpolosnykh, m = 1,2,3....,omthe wavelength in free space, the corresponding m-th measured frequency fomom= c/fomc = 3 108m/s, Qom- the quality of dvukhpolosnykh at frequency fom, lsp- the length of the slow-wave system, mzm- phase constant of the wave propagation in slowing down the system at frequency fom, rad/m om- phase constant of the wave propagation in free space, RA is B>om}wave resistance slowing down the system frequency f

_{om}, R

_{om}- set running resistance slowing down the system frequency f

_{om}, Ohm/m, L

_{om}- inductance slows down the system at frequency f

_{om}, GN/m

_{om}- linear capacitance slows the system frequency f

_{om}F/m

_{om}= 2f

_{om}f, f

_{om}in Hertz, and build the dispersion characteristics a=a(f), where a is any parameter as the argument f is the measured frequency f

_{om}successive resonances dvukhpolosnykh.

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