US 2533239 A
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A. W. GENT ET AL JIMPEDANCE TRANSFORMER FOR COAXIAL LINES 2 Sheets-Sheet l L//ve @me 129 N5@ Filed Jan. 5, 194e ER troy www5,
Dea, mi, E950 A. w. GENT Erm. 2,533,239
IMPEDANCE TRANSFORMER FOR coAxIAL LINES Filed Jan. 5, 1946 2 Sheets-Sheet 2 Patented Dec.. 12, y, 1950 UNITED STATES PATENT OFFICE IMPEDANCE TRANSFORMER FOR CQAXIAL LIN Alfred Walter Gent and Peter John Wallis, London, England, assignors, by mesne assignments, to international Standard Electric Corporation, New York, N. Y., a corporation of Delaware Application January 5, 1946, Serial No. 639,290 In Great Britain November 16, 1944 section 1, Public Law 69o, August s, 1946 Patent expires November 16, 1964 4 Claims.
the inner or outer conductors having different diameters.
Hitherto when joining two coaxial lines of diiferent impedances and therefore of different transverse sectional dimensions, it has been usual to insert between the two lines a third length of line of uniform cross-section and substantially an odd number of quarter wave lengths long at the operating frequency. The characteristic impedance of the inserted quarter wave-length section is chosen to be the geometric mean of the impedances of the two lines between which it is inserted. A conspicuous feature of this arrangement is that there is necessarily a step in the size of at least one of the conductors at each end of the inserted section.
It is one object of the present invention to provide an impedance matching section for trans forming the impedance of a coaxial conductor transmission line by transforming the diameter of at least one of the conductors gradually so that there are no discontinuous steps in conductor size anywhere.
This object is attained in accordance with the present invention by a section of coaxial transmission line having conductors whose diameters at one end are equal to the diameters of the conductors of said line and decrease or increase gradually in the direction of the desired conductor change to the other end of the said section so that there are no discontinuous steps in conductor size anywhere, and said section having an electrical length equal to an integral number of half-wavelengths at the operating freu quency.
In practice, coaxial cables are usually ernployed for wide frequency bands and it is usually not suflicient to match a coaxial conductor transmission line as regards the impedance at one frequency only by an impedance transformer. It is another object of this invention to provide a coaxial section impedance matching trans former for transforming over a wide band oi' yfrequencies the impedance of a coaxial conductor transmission line to a line of another impedance. This object is attained in accordance with the present invention by providing a section of tapered coaxial conductor transmission line, having conductor diameters at one end equal to the diameters of the conductors of the line to Awhich said section is connected, said section conductors tapering in opposite directions with such tapers as to produce on said transmission line unity standing wave ratio at the mid band operating frequency and having an electrical length equal substantially to an integral number of half-wave-lengths at said mid-band frequency.
Another object of the invention is to provide an impedance transformer for transforming over a wide band of operating frequencies the impedance of a coaxial conductor transmission line to a given impedance coaxial conductor transmission line having one conductor of predetermined diameter. Such a transformer according to this invention comprises two series connected sections of tapered coaxial transmission line, one of said sections having conductor diameters at one end equal to the diameters of the conductors of the line to which said section is connected, said section conductors tapering in opposite directions with such tapers as to produce on said transmission line unity standing wave ratio at the said mid-band operating frequency and having an electrical length equal substantially to an integral number of halfwave-lengths at said mid-band frequency, and the other section having conductors tapering in the same direction from the dimensions of the conductors at the junction of said two sections to the dimensions of the conductors of the line of known impedance having a conductor of known diameter.
If the outer or inner conductors of the two transmission lines to be coupled have the same radius it is `thus desirable to taper both conduce tors of the coupling section impedance transformer in opposite ways from the diameters o' the conductors of one transmission line for a half-wave-length of the said mid-band frequency and then in the same direction tothe diameters of the conductors of the other transmission line.
The invention will be further described in connection with the accompanying drawings in which:
Figs. l to 6 each show in longitudinal section an impedance transformer according to the present invention connecting together two coaxial conductor transmission lines of different conductor radial dimensions.
Fig. '7 shows' several curves used in the description and Fig'. 8 shows a curve of Fig. 7 extended to greater limits than in Fig. 7.
Referring to the drawings, in Fig, 1 are shown two coaxial conductor lines indicated as line I and line 2. The outer conductors 3, 4 of these two lines have different diameters as also the inner conductors 5, 6, and hence the lines have different characteristic impedances Z1 and Zz respectively. These lines I and 2 are coupled by a coaxial line impedance transformer 1, 8 whose outer conductor 9 tapers from the larger conductor 3 to the smaller conductor 4 and whose inner conductor l tapers in the reverse direction from the larger conductor 6 to the smaller conductor 5. Such a general arrangement, however, does not provide a good impedance match between the lines l and 2.
If e is the impedance at 8 looking into the line l, it can be shown that the additional impedance z1=z-Z1 is a fluctuating function which tends to zero for a given Z1-Zz as the length e of the section tends to infinity. Furthermore, it can be shown that whether one or both conductors of the section '1, 8 is or are tapered, the added resistance 1', is substantially zero when e is substantially equal to an integral number of halfwave lengths of the operating frequency and at these values of e the added reactance :z: is also a minimum. Hence to transform a coaxial transmission line to one of diiferent characteristic irnpedance, the optimum length of connecting section to use is one whose electrical length is an integral number of half-wave-lengths at the operating frequency. Although the reactance X can be brought to a minimum by the use of a connecting section an integral number of half-wave lengths long, it cannot be brought to zero if only one of the conductors is tapered. To make the reactance zero, it is necessary to taper both c'onductors in a uniquely determinate way, as will be explained hereinafter.
Usually, it is not sufficient to match impedances at a spot frequency, but it is required to have as good a match as possible over an appreciable band of frequencies.
As a criterion of goodness of match the standing wave ratio set up in the line l on the left of the drawings Figs. 1 to 6. the inner and outer conductors having radii RiRs resspectively, by the introduction of the matching section will be considered. The standing wave ratio 0 for any standing wave is the ratio of the maximum root mean square voltage measured at the voltage antipodes to the minimum root mean square voltage measured at the voltage nodes. It is well known from usual line theory that if a line of characteristic impedance Zo is terminated in an impedance R-l-fiX, the standing Wave ratio 0 satisfies the equation It will be observed that 0 is a function only of the ratio R/Zo and X/Zo and does not depend on the absolute values of R and X. It can be shown that z-Z1 remains unaltered if both Z1 and Z2 are increased while their difference remains unchanged, but the standing wave ratio which depends upon a/Z1 will approach nearer to unity.
The input impedance Zin to a quarter wave transducer, is given by:
where e is the length of the transducer, vand i. is the wave-length of the operating frequency. Thus the standing wave ratio which is a function only of Zin/Z1 is in turn a function only of Z2/Z1, and is thus the same for any pair of coaxial lines which have the same ratio of characteristic impedances Z2/Z1.
This makes a perfectly general comparison with the quarter wavelength stepped uniform line transducer difficult, although it is always simple to compare any particular case in which Z1 and Z2 are given.
As an example, the case Z1=120 ohms, 22:70 ohms, has been worked out for the quarter wave and three quarter wave stepped uniform line, see curves A and B, Fig. 7; for the tapered line with unchanged outer conductor, see curve C, Fig. 7; and for the doubly tapered line of optimum taper, see curves D and E, Fig. 7. The standing wave ratio 0 is plotted against 1re/A where in the cases of curves A, B, C, D, E, Fig. 7 respectively. A more extended graph of curve E, Fig. 7, is given in Figure 8.
One or two points about these curves should be observed. In the rst place it will be seen that the frequency band width regarded as a percentage of the central frequency remains unchanged when an optimum double-tapered section is increased from l/gl to )1 see curves D and E. This is in contrast to the stepped uniform line transducer, where an increase in length from 1/4l to 3A1k, curves A and B, reduces the bandwidth by a factor of 3. Another point to notice is that when only one of the conductors is tapered, the other remaining unchanged, curve C, it is impossible to achieve unity standing wave ratio. This is because the reactance cannot be made to vanish. However, the curve C of standing wave ratio against wavelength in this case is very flat, and for large enough departures from the central frequency the curve C crosses the curve A for the quarter wave stepped uniform line and thereafter lies below it. Thus for very wide band applications the singly tapered line is preferred to the stepped uniform line, for although the standing wave ratio is worse than for the stepped uniform line at the centre of the band, if the band is wide the standing wave ratio will be better at the edges of the band than for the stepped uniform line. Of course, if there is no objection to the slight extra trouble of tapering both conductors, curves D and E, the optimum doubly tapered line is better both at the centre and edges of the band, and is much to be preferred.
In designing the matching section the two impedances Z1 and Z2 between which to match and the size of either one or both of the lines will be known.
If only the size of the Z1 line, say R3, is known. then, of course, R1 is obtained by the well-known relation Z1=60 loge R3/R1. If there is no restriction on Rz and R1 and R2 are chosen such that Rl-R,
where R1 and R3 are the radii of the inner and outer conductors of one line, impedance Z1, and R2, R4 the radii of the inner and outer conductors of the other coaxial line of characteristic impedance Z2.
If, however, R2 is known then R5 and Re (are first found) such that:
R1 Re where Re and Re are the radii of the inner and outer conductors at the other end of the tapered section. This will give g- Z3/60 RFQ We then taper the inner and outer conductors from radii R5 and Re to the radii R2 and R4, with Ris-Re In Figure 2 of the drawings is shown a case where the inner conductors of the two lines I and 2 to be coupled have different diameters as well as the outer conductors. The impedance transformer comprises two series connected sections the conductors having at their common connecting point, equal dimensions. One of the sections, in this case, the section II connected to the line I has the optimum length of one half the wavelength of the mid-band frequency the diameters of the conductors at the end of the section I3--I4 being determined as hereinbefore described so that lea e E The conducto-rs of the other section I2 are then tapered up from dimensions of R5 and Re at the connecting plane I3I4 to dimensions R2 and R4 respectively such that Thus if R2 or R4 is known, the other is determined accordingly.
It is still advisable to match in this fashion even if it is required to have R2=R1, R4=R3. That is, a conductor is not run straight through, even if the radius of one of the output conductors is the same as that of one of the input conductors. This procedure produces a lmnp on the inner conductor or a constriction in the outer conductor as shown in Figures 3 and 4 respectively.
In the embodiment shown in Fig. 3, the inner 1 'conductors of the two lines I and 2 have the same diameters, but the outer conductors have different diameters. In Fig. 4 the outer conductors have the same diameters but the inner conductors have different diameters. As in the case of Fig. 2, the sections II are given the optimum length of half a wave-length of the mid-band frequency but the section I2 may be of any convenient length.
It might be convenient mechanically to start from the low impedance and use a divergent cone initially as shown in Figs. 5 and 6.
The embodiments shown in Figs. 5 and 6 are the reverse cases of those shown respectively in Figs. 3 and 4. In all these Icases, it will be observed that in the section I I having the optimum length of half wave-length the inner and outer conductors taper in opposite directions while in the section I2, the inner and outer conductors taper in the same direction. The lengths of the sections I2 are shown as being different in all four cases, sin'ce there is no restrictive condition on this length.
There is nothing to choose between the arrangements shown in Figs. 3 and 4 or 5 and 6 from electrical considerations.
The lengths of the tapered sections, in which the tapering is in the opposite sense in the two conductors, may be of course made an integral number of half wave-lengths long, but there is tor 6.,. little to be gained by using more than one half wave-length. In the sections where the tapering is in the same sense in the two lines, i. e. where mere scaling up or down is carried out, there is no restriction to half wavelength sections. These latter sections may be of any length.
What is claimed is:
l. An impedance matching section for transforming over a wide band of operating frequencies the impedance of a coaxial conductor transmission line to the impedance of another coaxial conductor transmission line comprising a section of tapered coaxial conductor transmission line having conductor diameters at one end equal to the diameters of the conductors of one of the lines to which said section is to be connected, said section conductors tapering in opposite directions and having an electrical length equal substantially to an integral number of half wave-lengths at the mid frequency of the operating band, said section conductors further tapering in the direction to the diameters of the other line to which the section is to be connected.
2. An impedance matching transformer for transforming over a wide frequency band the impedance of a coaxial conductor transmission line to a given impedance coaxial conductor line having one conductor of predetermined diameter comprising two series connected sections of tapered coaxial transmission lines, one of said sections having conductors tapering in opposite directions andhaving an electrical length equal substantially to an integral multiple including unity, of one half wave-length at the mid-frequency of the operating band and the other section having conductors tapering in the same direction from the dimensions of the conductors at the junction of said two sections to the dimensions of the conductors of the line to which said other section is to be connected.
3. An impedance transformer for transforming over a wide frequency band, the impedance Z1 of a coaxial conductor transmission line to the impedance Zz of another coaxial conductor transmission line of which the diameter R2 or R4 of the inner or outer conductor is known, comprising two series connected sections of coaxial transmission line, one of said sections having conductors tapering in opposite directions to diameters R5 and Re at the common junction point of the two sections from the end of said transmission line of impedance Z1 so that Re/R5=e""2/6o and having a length substantially equal to an integral multiple including unity of half a wave-length at the mid-band operating frequency, and the conductors of the other section tapering in the same direction from R5, Re to the diameters R2, R4 of the inner and outer conductors respectively of the other transmission line in such manner that R2/R5=R4/Rs.
4. An impedance matching section for transforming the impedance Z1 of a coaxial conductransmission line having conductors of diameters R1 and R3 to an impedance Z2 of another coaxial conductor transmission line having conductors of diameters R2 and R4 by transforming the diameters of the inner and outer conductors respectively, comprising a section of coaxial transmission line having conductors whose diameters at one end are equal respectively to R1 and R3 and which taper in opposite directions to diameters R5 and Re respectively, said section having an electrical length equal to an integral number of half wave lengths at the REFERENCES CITED Operatmg frequency the (hamsters R5 R6 being The following references are of record in the such that file of this patent:
Ro 626 r UNITED STATES PATENTS l) E: e Number Name Date t v 1,841,473 Green Jan. 19, 19132 and a second section of coaxlal transmisslon line 1,932,443 Clavier Octl 21I 1933 having conductors Whose diame ers a one end OTHER REFERENCES are equal respectively to Rs and R6 and which 10 taper to diameters R2 and R4. Microwave Transmission Design Data, Pub- ALFRED WALTER GENT. lication No. 23-80 by Sperry Gyroscope Co., Inc., PETER JOHN WALLIS. Manhattan Ridge Plaza, Brooklyn 1, N. Y.