US2507692A - High-frequency impedance transformer for transmission lines - Google Patents

Description

gral multiples thereof so as to convert the pure resistance afforded by the transformer in accordance with the invention to some other desired value.

In order that the invention may be clearly understood and readily carried into effect it will now be more fully described with reference to the accompanying drawings, in which:

Figure l illustrates diagrammatically a transformer in accordance with one form of the invention,

Figures 2 and 3 illustrate diagrammatically transformers in accordance with the form f thev invention shown in Figure -l associated with further sections of transmission line for converting the pure resistance to a desired value,

Figure 4 illustrates the application of the invention to the coupling of aA coaxial line circuit to awave guide, Y

Figure 5 illustrates diagrammatically the coupling of two waveguides by a coaxial line circuit,

Figure 6 illustrates diagrammatically an impedance transformer comprising a section of waveguide, and

Figure '7 illustrates diagrammatically a modication of the arrangement shown in Figure 6.

Referring now to Figure l of the drawings which illustrates the invention as applied to a transformer comprising a section of coaxial line,

the reference numeral. 8 indicates a section of coaxial line feeding a complex impedance A-l-gB indicated by the reference numeral 9. In order to make the complex:impedance appear to be a substantially non-reactive or pure resistance at the end of the transmission line 8 an impedance transformer is inserted between the line 8 and the impedance 9 indicated at I0 composed of a further section of coaxial transmission line the length and the characteristic impedance Zo of the section I0 and the complex impedance 9 are so related to one another that .of the complex impedance; Where the length of the section I0 is equal to n odd eighth-wavelengths then when 'n is l, 5, 9 etc., the value of the pure resistance is given by the expression and when n is 3, 7, ll etc., the value of the pure resistance is given by the expression M-B M M+B where M is the modulus of the complex impedance. Y j Y If the valueof the substantially pure resistance afforded by the transformer is not of the required value, then it is possible to employ, in conjunction with the transformer, a further section of a transmission line effectively equal to one-quarter of a wavelength or odd integral multiples thereof so as to convert the pure resistance afforded by the transformer in accordance with theiinvention to some other4 desired value. u. Figure 2 'ofk the drawings illustrates the introduction of such a quarter wavelength section Il between the section I0 and vthe complex impedance 9, whilst Figure 3 of the drawings illustrates the introduction of the quarter Wavelength section II between the line 8 and the section I0. In the latter case, assuming that the complex impedance A-i-y'B is transformed by the transformer I9 to a pure resistance R and it is desired to convert the pure resistance R to another pure resistance R', for example, in order to provide an impedance match with the line 8, then the characteristic impedance Zo of the 'quarter wavelength section II is given by Whilst the invention is capable of a wide variety of uses, it is of particular importance in matching a coaxial cable to a wave guide. Heretofore when it has been desired to effect an impedance match between a cable and a waveguide, such has been accomplished by connecting the coaxial cable to a probe projecting into the waveguide. To effect an impedance match two requirernents have-to be satisfied. Firstly, the resistive component of the guide impedance as seen from the end of the 4coaxial cable must be made equal to the characteristic impedance of the cable, and, secondly, the reactive component of the guide impedance as seen from the end of the coaxial circuit must be made zero. Usually, in order to satisfy these requirements the length of the portion of the probe which projects into the guide is adjusted so that the resistive component is of the required value which usually leaves a large reactive term which is then tuned out by varying the position of a tuning piston associated with the waveguide. It has been found that it is even sometimes necessaryrto employ additional tuning plungers. On account ofthe number of adjustable elements that it isrnecessaryrto employ in such an arrangement the latter is not only complicated to adjust but the impedance match is liable to be disturbed 4by mechanical shock. Furthermore, the matching of a cable to a, waveguide in this manner necessitates an accurate balance tok be made between two relatively large reactances and hence any small change, in the operative wavelength which changes either or both'of the two opposing reactan'ces usually results in the two reactances becoming unequal giving rise to a relatively large residual freaGtance. Thus the arrangement described affords only a satisfactory impedance match over a relatively narrow frequency band.

Figure 4 of the drawings illustrates the invention as employed to obtain an impedance match between a coaxial cable I2 and a waveguide I3. One end of the waveguide I3 is closed by a conductor I4 which may be permanently fixed in position as distinct from the adjustable piston employed in the prior arrangement above referred to and the coaxial cable is connected toa probe I5 projecting into the waveguide, the probel also being rigidly fixed in position in any suitable manner and disposed at a desired position with reference to the closed endof the guide. The probe I5 'may comprise a projecting portion of ens-ancona the centre@ conductor of the, coaxial cablefthe; outer vconductor' of whichv is connected to` the" waveguide, as shown. Thel impedance at the: point where the probe passes intothe waveguide vdetermined by any of the well known means and"T in general, this impedance will be complex not equal to the characteristic impedancelof the coaxial cable. In order to lconvert the com-.- plex impedance into` a substantially pure resistance a transformer in accordancewith the invention is employed which, as shown, comprises a sleeve I6 surrounding the probe I5 or centre conductor and insulated therefrom, said sleeve being-preferably one-eighthof a wavelength'long. The characteristic impedance of the transmission line formed by the sleeve I6 and the portion of the probe l5 or centre conductor surrounded thereby is made equal to the modulus of the complex impedance. This transformer wi1lj convert the complex impedance to a pure resistance Rand: if it isf necessary to convert the pure resistance R.' t'o aI value equal to the characteristic impedance of the-coaxial cable in order properly to terminate the'coaxial cable, then a further transformer effectively equal in length to one-quarter of a wavelength is then inserted between the cable -l3 and-the -transformer in accordance with the invention, the characteristic impedance of the qnarter-wave transformer being made equal rto whereZo is the characteristicimpedance of the coaxial cable.v The quarter-wave transformer, as shown, comprises a sleeve I1 surrounding yand insulated Yfrom the centre conductor of the coaxial cable and it may be convenient in practice to form the sleeves I6 and' Il integrally with one another, the sleeves iitting within-.and being connected to the outer conductor of the cable, as shown. The construction described will provide an impedance match between a coaxial cable and a waveguide which is of a rigid nature and -requires no adjustment after being initially correctly assembled. If desired the space between the centre conductor and said sleeve may be lle'd'with solid insulation and it'will thereforebe appreciated that the physical lengths of the vtransformers may be different from their electrical lengths depending upon the dielectric constant oij'the insulation employed.

"It will be appreciated from the abovethatan impedance match can be obtained whatever is the length of the portion of the probe l5 Which projects into the waveguide and furthermore, the

match can be obtained whatever the position of' the probe relatively to the closed end of the wave.- guide. This is advantageous since it is possible thereby to make the arrangement less susceptible to' changes of operating frequency. As stated above, the magnitude of the complex impedance as seen through the transformer according to the invention when employing a transformer effectively 4equal to one-eighth of a wavelength long, is equal to M +B Mv 'FB and if B is small compared with A, that is to say, about one-fifth or less, the expression reduces approximately to A+B. Hence, if the length of the probe is adjusted together with the position ofithe closed end of the guide so that thewaveguide'impedance has its two components A and B varying with frequency in such a wayv that the Stunfoffthe twois constant, thenvthe impedance quencies in such a wayv that 4the* sum of'thetwo' componentsfis constant'. Hence, such anarrange-- ment will afford an impedance'inatch over arelfa tively'wide frequency range.

If desired, two` sections of waveguide may beV connected together by a length of coaxial' cableeach end of`which is matched to itsassociated? waveguide by thev construction describedk with reference Ato Figure 4. Figure 5 illustrates such an arrangement, the reference Ynumerals I1 Vand L8 indicati-ng two sections of waveguide andltlie numeral I 9 a length lof coaxial cable. The coaxial cable `is provided with a rotatable joint 2G, such as the plug and socket joint described in the specification of British patent application No. y11,862/42, the provision of such a joint eri--V abling the two sections of waveguide to be rotated with respect to one another without the necessity of providing specially constructed joints in the waveguideA sections. Heretofore, when it has been desired to employ two sections of waveguide Vmounted 'for relative rotational movement' it has been usually necessary to provide special tuning plungers and to,maintain the distance between the two waveguide sections very small and of a fixed dimension. If the two sections of waveguide are coupled by meansr of 'a' coaxial cable as shown in Figure 5, the distance'betweenr the two waveguide sections can bemade ofv any desired length, since the coupling is afforded' by a coaxial cable which can be of any appropriate length without disturbing the impedance match. There vis also an added advantage that" the coaxial cable joiningthe two waveguides can be bent so as to negotiate corners or other obstructions. The dimensions of the coaxial cable should be chosen to afford a minimum losse but the dimensions must not besuch as to---permitV the propagation of unwanted modes.

The-invention can also' be appliedto` impedancetransformers lcomposed Aoi" sections of waveguide.

It is known that thegtheory of two-wire transmission lines, such as coaxial cables, can be applied to waveguides providing that inve-any given problem the guides have substantially the same physical dimensions and energy of the same mode is Vvtransmitted through'the guides; In the case of a two-wire transmission line the impedance at' any pointis defined as the ratio of voltage to the current at that point. In the case'of a waveguide, however, vthe impedance at any point is dened as ther ratio of the-transverse electric field'to the transverse magnetic field at that point.

`Suppose that irl-any guide `of `any form in crosssection there are three axes, 5c, y and a mutually at right-angles and that z is the axis along which propagation occurs, thenpthe `z :aharacteristic gimeu pedance Zo ofthe, guide is o, n Hr 'Hz these two ratios having the same value. ratio gives -the'samevalue at everypoint in the guide but is diiferent for each mode lof lthe energy transmitted.

VvFor waves (or transverse electric waves) the ratioibecomes M/Ao, where Mis thewavelength in air and M is the corresponding value in the guide. VFor E waves (or transverse magnetic waves) the ratio is where k is the dielectric constant of the material in the guide and the permeability of this material is assumed to be unity. Since M depends on the particular E or H mode being transmitted land lalso on the dimensions of the guide, it follows that the characteristic impedance of the guide is also a function of these quantities. In practice, however, energy of only one mode is propagated and since, as stated above, the two-wire theory only applies to waveguides when the physical dimensions of the latter rem-ain substantially constant, the problem of applying the present invention to waveguides is considerably simplied.

The guide most commonly employed is one of rectangular cross-section and in such a guide energy of the Rio mode is usually employed. With such -a form of guide and energy of the stated mode, the characteristic impedance of the guide is where a is the longer side of the cross-section of the guide. The ratio Ag 2a guide 2l feeding a hollow resonant cavity 22 ,5

which presents to the waveguide a complex impedance A-l-y'B. In order to convert the complex impedance into a substantially pure resistance a waveguide transformer 23 composed of a section of waveguide is inserted between the waveguide 2l and the cavity 22, the length and the characteristic impedance Zo of the section 23 and the complex impedance 22 being related to one another in accordance with Formula 1 heretofore referred to. The desired characteristic impedance of the section '23 is imparted by providing the section 23 with a suitable dielectric medium indicated at 24. Preferably, as in the transformer shown in Figure l, the length of the section 23 is equal to one-eighth of the operating wavelength, in which case the impedance Zo of the section 23 is made equal to the lmodulus of the complex impedance.

Theoretically, the desired impedance of the waveguide section can be attained by suitably choosing the dielectric medium within the guide section, but in practice, however, any material which is sufficiently loss free to be used in a guide has substantially unit permeability with the result that a complication may arise due to the fact that whereas a dielectric constant of unity is obtainable by using air and dielectric constants from about 2.5 to 100 can be obtained by using,

for example, polystyrene suitably loaded with titanium dioxide, there is no available suitable substance which affords a constant between unity and 2.5. If therefore any given problem requires a dielectric constant within the range of 1 to 2.5 or between zero and unity, the difculty can be overcome by employing two sections in series with dielectrics having constants which can be obtained with available dielectrics.

To simplify this problem the term can be assumed to be small compared with lc so that it is possible to write 377 Zur-Wi (3) If in any particular problem this simplification cannot be employed, then the Formula 2 referred to :above must be used. Assuming that the simplified formula can be employed, then it may be required to convert the complex impedance 2804-5100 yto a pure resistance. The modulus of this complex impedance is 297 ohms which requires k to be 1.61 which is within the range of dielectricV constants which cannot conveniently be obtained. To overcome this diiculty the transformer may employ two eighth wavelength sections arranged in series as shown in Figure 7, the first section 25 having a dielectric medium of dielectric constant k1 and the second section 26 a constant Icz. If the first section is terminated by the complex impedance, then the impedance seen through the two sections will be a pure reslstance providing that where Z2 is the characteristic impedance of one of the eighth wavelength sections and Z1 is the characteristic impedance of the other eighth wavelength section. It is thus possible by employing available dielectric mediums to provide eighth wavelength sections of waveguide having characteristic impedances of the required values to satisfy the Equation 3. For instance, in the example referred to above k1 may be equal to 4.6 giving a characteristicimpedance Z1 of 175 ohms in which case k2 will be required to be 2.5 so as to afford a characteristic impedance Z2 equal to 238 ohms.

Alternatively, instead of employing two eighth wavelength sections, it is possible to employ a quarter wavelength section and then an eighth wavelength section, the quarter wavelength section transforming the complex impedance to a suitable value to enable an available dielectric medium to be employed for the eighth wavelength section. In this case if Z1 is the charac teristic impedance of the quarter wavelength section and A-l-y'B is the complex impedance, then the impedance seen through the quarter wavelength section is Z12 AJ`Bl ALI-B2 The modulus of which is:

With such an arrangement it is then necessary to make the impedance of the eighth wavelength section equal to this modulus. It is preferred, however, to employ two eighth wavelength sections since, in this case, the overall length of the transformer is shorter and is less susceptible to changes in the wavelength of the transmitted energy.

If the pure resistance afforded by the section or sections of the transformer shown in Figure or 6 is not of the required value for impedance matching purposes, then it will be necessary as 'in the arrangements shown in Figures 2 and 3 to employ a further section oi' waveguide effectively equal to a quarter of a wavelength long to convert the pure resistance to the required value. Thus, in some cases it may be necessary to employ one or two eighth wavelength sections in association with a quarter wavelength section or a one-eighth wavelength section in association with two sections each of a quarter of a wavelength long. It may even be necessary in some cases to employ two quarter wavelength sections in series to perform the functions of the quarter wavelength section shown in Figures 2 and 3. This may be necessary on account of the fact that the dielectric constant required to give the quarter wavelength section the correct impedance is not available. If the rst quarter wavelength section has a dielectric constant k1 and the second section a dielectric constant of k2 and assuming that the characteristic impedance of the guide is inversely proportional to the square root of the dielectric constant as assumed above, then if the resistance produced by the eighth wavelength section is R and that this resistance is to be converted in order to match a guide impedance of Z0 it is necessary to arrange that Providing the ratio of Ici to k2 satisfies thisequation the individual values of the dielectric constants are immaterial so that it is possible to arrange for the constants to fall within the available range.

If desired, instead of matchinga coaxial cable to a waveguide by means of a probe associated with a transformer as described with reference to Figure 4 of the drawings, the necessary impedance match can be obtained by the use of a transformer or transformers associated with the waveguide as described with reference to Figures 6 and '7. Furthermore, it is not necessary in connection with the matching arrangement shown in Figure 4 for both transformers i6 and l'l to be associated with the probe since, if desired, one of these transformers can be associated with the waveguide. y

Although in the above description certain specific lengths of transmission lines and waveguide sections are referred to, it will be understood that equivalent multiple lengths can be employed.

What I claim is:

1. A wave transmission system including a wave guide, and an intercoupled coaxial cable, said guide and said cable being coupled by a probe connected to a conductor of said cable and projecting into said wave guide, at a fixed position along said guide, one end of said wave guide being closed, a sleeve having a length equal to one-eighth of the operating wavelength of said system, surrounding said probe and insulated therefrom, the characteristic impedance of the section of transmission line formed by said sleeve and said probe being equal to the modulus 10 of the complex impedance of said wave guide at the point of insertion of'said probe.

2. A wave transmission system including a wave guide intercoupled with a coaxial cable the intercoupling being effected by an extension oi' the central conductor of said cable projecting into said wave guide at a fixed position along said guide, one end of said wave guide being closed, a sleeve having a length equal to oneeighth of the operating wavelength of said system surrounding said central conductor and insulated therefrom` the characteristic impedance of the sect-ion of transmission line formed by said sleeve and said central conductor being equal to the modulus of the complex impedance of said wave guide at the point of insertion of said extension of said central conductor, and a further one-quarter wavelength matching section interposed between said coaxial line and said extension of said central conductor to match the impedance of said section of transmission line to said coaxial cable.

3. A wave transmission system including a wave guide and a coaxial cable coupled thereto, said coupling being constituted by a probe connected to a conductor of said cable projecting into said wave guide at a predetermined position along said guide, one end of said wave guide being closed, the length of said probe and the predetermined position being such that the two components of the wave guide impedance vary with frequency in such a manner that the sum of the two is constant, a sleeve having a length equal to one-eighth of the main operating wavelength surrounding said probe and insulated therefrom, the characteristic impedance of the section of transmission line formed by said sleeve and said probe being equal to the modulus of the complex impedance of said wave guide at the point of insertion of said probe.

4. A wave transmission system including a wave guide, and a coaxial cable coupled thereto the coupling comprising aprobe constituting an extension of the center conductor of said cable projecting into said wave guide at a predetermined position along said guide, one end of said Wave guide being closed, the length of said probe and the predetermined position being such that the two components of the wave guide impedance vary with frequency in such a manner that the sum of the two is constant, a sleeve having a length equal to one-eighth of the main operating wavelength surrounding said probe and insulated therefrom, the characteristic impedance of the section of transmission line formed by said sleeveand said probe being equal to the modulus of the complex impedance of said wave guide at the point of insertion of said probe, and a further one-quarter wavelength matching section between said coaxial line and said probe to matchv the impedance of said section of transmission line to the impedance of said coaxial cable.

JOHN COLLARD.

REFERENCES CITED The following references arerof record in the flle of this patent:

UNITED STATES PATENTS Number Name Date 2,125,597 White Aug. 2, 1938 2,207,690 Cork et al July 9, 1940 2,241,582 Buschbeck May 13, 1941 2,433,011 Zaleski Dec. 23, 1947

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