US2438915A - High-frequency terminating impedance - Google Patents

Description

April 6, 1948,

HIGH-FREQUENCY TERMINATING IMPEDANCE Filed July 30, 1943 2 Sheets-Sheet 1 W. w. HANSEN 2,438,915

INVENTOR W/L 4 64/14 M f/A/VSE/V ATTORNEY April-6, 1948. w.'w. HANSEN 2,433,915

HIGH-FREQUENCY TERMINATING IMPEDANCE Filed July 30, 1943 2 Sheets-Sheet 2 Patented Apr. 6, 1948 HIGH-FREQUENCY TERMINATING HHPEDANCE William W. Hansen, Garden City, N. Y., assignor to The Sperry Corporation, a corporation of Delaware Application July so, 1943, Serial No. 496,715.

Claims. (01. 178-44) The present invention is related to the art including high frequency energy conducting systems and it is more specifically related to devices for providing an energy sink or energyabsorbing termination for concentric transmission lines.

As the frequencies utilized in radio communication and radio control have increased, it has become necessary to use substantially enclosed, non-radiating energy conductors such as the well known concentric transmission line type. In many types of application of such energy conducting devices, it is necessary to provide a termination for the conductor which will avoid the production of reflected electromagnetic waves in the energy conducting system. Such reflected waves, of course, combine with the forward traveling energy and produce so-called standing waves which interfere with the proper functioning of other portions of the system by rendering the apparatus position sensitive; that is, the effects produced may depend upon the position at which the particular apparatus in question is connected to the energy conducting system. In addition, the powertransfer through the system may be materially reduced. It is desirable, therefore, to provide a terminating device which will be able to absorb whatever energy is flowing through the system without producing reflections or standing waves. Such terminating devices are also known as energy sinks or black bodies, since they absorb substantially all energy incident thereon without retransmittin an appreciable amount of such energy.

Accordingly, it is an object of the present invention to provide an improved form of terminating device for high frequency energy conducting systems.

It is a further object of the present invention to provide an improved high frequency terminating device for concentric transmission lines adapted to properly terminate such lines substantially without reflection or standing waves.

It is another object of the present invention to provide a practical and easily manufacturable form of such high frequency terminating devices.

It is still another object of the present invention to provide an improved form of concentric line terminating device which is substantially insensitive to variations in frequency and there- 2 fore may be utilized with a large number of widely varying operating frequencies.

It is a further object of the present invention to provide an improved form of energy sink or terminating device adapted for use at high power.

Other. objects and advantages will become apparent from the following specification and attached drawings in which Fig. 1 shows a longitudinal cross-sectional view of one form of the present invention,

Fig. 2 shows a similar longitudinal cross-sectional view of a more practical embodiment of the present invention adapted for easy manufacture, and

Figs. 3 and 4 show similar views of other forms of my invention.

As is well known, a suitable terminating device for a concentric transmission line must provide a substantially pure resistance equal to the characteristic impedance Z0 of the transmission line to be terminated. However, if an ordinary lumped resistance is inserted in the end of such a transmission line it will be found that, at the high frequencies with which such devices are used, the terminating resistance also usually displays a reactance which prevents matching of the device to the line. Also, with lumped high frequency resistances usually employed, it may be so small'as to have limited power handling capabilities.

According to the present invention, a terminating impedance is provided which presents a substantially pure resistance so that matching to the line is effected without frequency dependency and which can handle appreciable amounts of power. In the present instance, as seen in Fig. 1,the concentric transmission line to be terminated is represented by the outer conductor 1 I and the inner conductor l2. Joined to the inner conductor I2 is a rod l3 of resistance material having a diameter substantially the same as that of inner conductor l2 and forming a smooth continuation thereof.

The length of rod [3 is so chosen with relation to the resistivity thereof that the total re- -However, 2 should also equal terminating impedance, rod 13 is surrounded by a conducting member I4 which has an inner taper I6 of an exponential character, which will be shown more clearly below.

Thus, by the well known transmission line equations, the current and voltage relations at any point as along the tapered line of Fig. 1 may be written:

where z is the current, 1: is the voltage, is the, unit capacitance, l is the unit inductance, is'

theradian frequency, and a is the pureima'ginary /-1. If it be assumed that i=Ae 4 where A is a constant, e is the base of the Naperian logarithm, and 7c is aconstant to be determined, then Equation 1 becomes Thus, Equation 5'indicat'es that"; at point x,

e where Io isthe maximum value of current flowing'fin:theinnerIconductor, which can also be seen from (3) to"have constant magnitude but variable phase along the terminating impedance device.

Furthermore, as shown above, the impedance offered by the present terminating device is entirely independent of frequency, as is the characteristic impedanceZojthatis; this terrninating impedance is'substa'ntially a pure resistance. 'Accordingly the present device can be utilized for widely yary'ing ppe'rati ng' frequencies whilefstill the ratio, of voltage to current will be real'if'R is real, and'will be independent of frequency if k is a multiple of w. By selectingk=wl these conditions are satisfied, and then is the characteristic impedance at m. Substituting (4) and (6) in (2) %=Ae %+jkZA =(r FjwDAe 7 By equating the real components of ('7),

and therefore Z=r:c.

If the line H, l2 has a characteristic impedance Z0, then rL is chosen equal to Z0, and the device will serve as a proper frequency-independent termination.

As is well known, the characteristic impedance Z0 of a concentric transmission line su'ch as ll, 12 may be given by the following expression:

where be is the radius of the outer conductor of the line H, l2 and a is the radius of the inner conductor thereof. For a tapering or varying line such as l3, M, the correspond'ing"expression, which may be termed the characteristic impedance Z at a point of the line sectionpwill depend upon the position considered along the line. If we let the variable :0 represent the distance from the closed end of the device, as fshown in the diagram, to a point along the line being considered, and if bx isthe radius of the outer conductor at that point, then z=co 10g f 10 maintaining substantially perfect 'iinpeidance matching and. the optimum energy dissipating characteristics produced "by the "constant power dissipation along the length of the device,

The j device" oflliig l "is somewhat diificult to manufactureinfview of therequirement that the inner taper oifcorrductor'i 4 rnust be a substantiallyperfectfexponential curve; "However, a dejvice can be produced 'which performs substantially in the same manner as that of Fig 1,- which is rel ative ly easy to iabricate. Such a" device is shown in'Fig. 2 in which the outer conductor l t is roi'med 'as'i a' series'w f 'stepsgpreferably, each stepbeingfshortfcompared to one wave length at an operating frequency in the center of the yr qi sma b Q e V in length. These' sections"are ;made" to approxioperatingfrangeof requenciea Preferably these eighth" wave length or less mate neexppne fiatim of Fig. l by-choosing "a'constant 'r "ancesyary's y 'Ifhe 'ehange'm 1 characteristic impedance J from er ett f e i "refi onsfini a';

optimu rn value, =Withthis'yrelation'among the pr h f i ers iq um aging the characteristic impedstantially linearly alongthe device.

sive -section ee q tess t p i e ii n a t By" malgingl the mber of sections'frelatively ndered gnite} insensitive to erating irequencies' from the characteristicimpedances ofthe several sections, the over-all "effect "or fall thesections is substantially the same as theexponential' curve variation "o'fFig. 1.

"It" will be noticed "that t he devi'ce of Fig, 2 3 can be manufactured by relatively}simplemachining or drilling operations; The-center conductor may beheld infplace-by suitable set sr ew illbr may be pressed into the"end-"oFthe'outer conductor 14 or fixeddn any other de sired manner. The

other ma nu "resistivefconductor I3fmay"be suitably "supported by the "inn'enconductor i2,

' ner.

as fby means of' a 'suitable conducting peg arangernentillustr atedat'l 8 *or in any other-manbe imiderstciod' 'tiiat eemereoneuet l2 rt ed witliin coridulctor "I I by the usual in- 76"Siilating" spacers or'stub' liiie The inner conductor l3 may be formed as a solid rod or hollow cylinder of the proper resistivity, or may be formed as a resistance coating on an insulating form or rod.

While the above forms of the invention have been illustrated with the resistance incorporated in the inner member and the taper in the outer member, it is to be understood that these features may be reversed. Thus, in Fig. 3 a similar terminating impedance is illustrated in which the inner conductor is tapered and the outer conductor is uniform. As seen above, the essential criterion for the terminating device of the invention is that the characteristic impedance of the terminating device vary linearly from the value Z characteristic of the line lI-|2 to the value zero. For this purpose the ratio of the outer conductor diameter to the inner conductor diameter must vary exponentially.

In the device of Fig. 1, this exponential relation was obtained by a constant inner conductor and an exponentially varying outer conductor. In the device of Fig. 3, this relationship is obtained by a constant outer conductor diameter and varying inner conductor diameter. The essential relationship is defined by the following equation,

60 log -=a:r (11) from which is obtained the equation :2 a =be k 12 which indicates how the radius of the inner conductor must vary to provide the desired impedance relation.

In the device of Fig. 3, the outer conductor 14" is preferably made of resistance material or may have a surface coated with resistance material. The inner conductor I3" is preferably made of conductive material so that substantially all of the resistivity of the tapered line is produced by the outer conductor, the resistance of the inner conductor being negligible with respect thereto.

This device of Fig. 3 has an advantage over that of Fig. 1 in that the inner conductor I3" may be manufactured by a relatively simple machining operation, as by turning on a lathe. Also, the much larger area of the resistive element 14" and its location at the outside of the device permits better heat dissipation and use in higher power systems.

The device of Fig. 3 may be approximated in a manner similar to that shown in Fig. 2 by use of short stepped sections. This is shown in Fig. 4 where the inner conductor 13" is now formed of stepped sections such that the ratio of the radii of successive section-s remains constant. The length of the sections is again preferably less than one-eighth wave length. Here again, the outer conductor 14 is made the resistance member of the device.

The device of Fig. 4 is still more readily adapted for manufacture, since it is relatively simple to assure accurate machining of externally formed 6 cylindrical sections of member l3"' while the accurate machining of an exponential taper, as in Fig. 3 or Fig. 1, is relatively difficult.

Accordingly, I have provided a terminating impedance for a concentric transmission line which provides proper termination over a wide range of frequencies, which provides a desired uniform distribution of the power dissipation to avoid overheating of any local area, and which is relatively simple to manufacture and assemble. 7

Since many changes could be made in the above construction and many apparently widely different embodiments of this invention could be made without departing from the scope thereof, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

What is claimed is:

1. A high frequency terminating impedance comprising a section of concentric transmission line having a resistive inner conductor of uniform diameter and constant resistance per unit length, and an outer conductor formed of a series of sections, each section having a constant inner diameter and a ratio of the diameters of successive sections being constant;

2. A high frequency terminating impedance as in claim 1, wherein each of said sections has a length which is less than one-eighth wave length at the operating frequency thereof.

3. A high frequency terminating impedance comprising a section of concentric transmission line, one of whose conductors has a constant resistance per unit length and the other of whose conductors has an effective diameter varying in steps along said section, the ratio of the diameters of successive sections being equal.

4. Apparatus as in claim 3, wherein each of said steps has a length less than one-eighth wave length at the operating frequency of said device.

5. A high frequency terminating impedance comprising a section of concentric transmission line having an outer resistive conductor of uniform inner diameter and uniform resistance per unit length, and an inner conductor whose diameter varies in steps along the length thereof, said steps being selected to provide a constant ratio of successive step diameters along said section.

WI LIAM W. HAN- SEN.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,273,54'7- Von Radinger Feb. 17, 1942 1,926,807 Hansell Sept. 12, 1933 2,399,645 Latimer May 7, 19 6 2,409,599 Tiley Oct. 15, 1946 FOREIGN PATENTS Number Country Date 502,807 Germany July .22, 1930 Certificate of Correction Patent No. 2,438,915. April 6, 1948. WILLIAM W. HANSEN It is hereby certified that errors appear in the above nu mbered patent requiring correction as follows: In the grant, line 1, for William W.

Hensen reed William W.

, 7, Hansen; in the specification, column 3, line 43, equation 7, for 3; read 2%; same line, for Ae read Ad"; and that the said Letters Patent should be read with these corrections therein that the same may conform to the record of the case in the Patent fli-ce.

Signed and sealed this 15th day of June, A. D. 1948.

THOMAS F. MURPHY,

Assistant floflmissioner of Patents.

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