US3002166A - Inside-out attenuator for high-frequency coaxial lines - Google Patents

Description

Sept. 26, 196 B. o. WEINSCHEL INSIDE-OUT ATTENUATOR FOR HIGH-FREQUENCY COAXIAL LINES Filed Aug. 11, 1959 M n T T f m mm mW r x O. M N n w mt 3.36 E56 m m m w t BB EtmGmm u u u q q II N m 1 H, n 11 I 1 1 I m D ijnite htates poration of Delaware Filed Aug. 11, 1959, Ser. No. 833,041 2 Claims. (Cl. 333-81) This invention relates to coaxial attenuators for highfrequency electric waves, and has for its primary object the provision of such an attenuator having high powerdissipation capability and relatively wide band-pass characteristics.

One usual form of high frequency coaxial attenuator consists of a practically lossless outer conductor (a metal barrel) with a resistive inner conductor. The power handling capability of the attenuator would be greatly increased if the position of the barrel and resistive element were interchanged. The resistive element would then be the outside conductor of the attenuator, Where, because of its position and larger area, it can dissipate much more heat than when centrally located. It is apparent, however, that this interchange of position results in a poorly shielded attenuator. The outer electrical Wrapping of the attenuator will be the thin layer of resistive material which will be somewhat transparent to ambient fields, and will permit signal leakage in both directions. To overcome this difiiculty, it is necessary to shield the entire attenuator by means of a metal barrel outside the outer resistive element. This shield constitutes a third conductor and makes the inside-out attenuator vastly more complex than the usual form of highfrequency coaxial attenuator where there are only two conductors. Furthermore, the resulting air space between the attenuator and the outer shield is a relatively poor heat conductor and offsets some of heat-dissipating advantage of this type of construction, which will hereafter be referred to as inside-out attenuator.

It is a major object of the invention to provide an attenuator of the above-described type which is effective to dissipate a maximum amount of power, yet is effectively shielded, and which can be used over a Wide frequency range.

Another object is to provide a fixed attenuator of constant value comprising an element of the outer conductor of a coaxial line and having an external shielding and heat-dissipating member, yet having an extended frequency characteristic generally similar to a coaxial attenuator having a central attenuating element.

The specific nature of the invention, as well as other objects and advantages thereof, will clearly appear from a description of a preferred embodiment, as shown in the accompanying drawing, in which:

FIG. 1 is a longitudinal cross-section of an attenuator unit embodying the invention;

FIGS. 2 and 3 are schematic equivalent circuit diagrams of a conventional attenuator and of the attenuator of FIG. 1 respectively, used in explaining the theory of the invention.

FIG. 1 shows the attenuator assembly comprising a central conductor 2 and a coaxial attenuating element 3 in the form of a thin film of resistive material deposited or otherwise adhered to the interior surface of a ceramic tube 4 concentric with conductor 2. This film may be formed in any suitable known manner, e.g., as described in my copending application, Serial No. 671,098 filed atent G July 10, 1957, for High Frequency Attenuator, or it may Patented Sept. 26, 1961 of heat-dissipating conductive fins 7. The outer surface of tube 6 and fins 7 is preferably blackened for maximum heat dissipation.

The inner resistive film 3 extends out over the ends of tube 4 and-into intimate contact with a low resistance heavy film 8 fired or painted on as a heavy band of low resistance on the outer surface of ceramic tube 4 near each end thereof. A ring of metal wire, Wound in the form of a coiled spring is pressed into an annular recess 9 formed in each end of outer metal shield 6, to form a low-resistance contact between the attenuator and each end-cap 11, 11. The end caps and the central conductor 2 terminate in standard coaxial fitting i2 and 13, for example, male and female respectively, for connecting the attenuator to components of a standard coaxial high-frequency line. 7

In some oases, the attenuator may be permanently connected at one end to associated high-frequency equipment, and in that event only the free end need be provided with either a male or female standard coaxial connector as required.

The previously mentioned patent to Weber, No. 2,689,- 294, shows in FIG. 6 an attenuator element formed as part of the outer conductor of a coaxial cable. In this figure, an air space is shown between the attenuator element and the outer shield, which reduces the efficiency of heat dissipation, and which also undesirably restricts the frequency characteristic, as will be shown below. Furthermore, the outer shield must be conductively connected to the outer conductor of the coaxial line in which the attenuator is used, for adequate shielding, yet it must not short-circuit the attenuator if the latter is to perform its intended function. To solve this problem, Weber uses a quarter wave-length section in the form of sleeves 7c and 7d to connect his shield to the outer coaxial conductor. This restricts the effective use of the attenuator to the immediate region of the frequency for which the sleeve length is one-quarter of. the wavelength; in other words, this type of attenuator is not only relatively inefiicient as a heat dissipator, but also is practically restricted to a single frequency of transmission.

In order to understand how the present invention overcomes the problem of wide-band transmission, it is necessary to analyze in some detail the operation of such attenuators, using the method of distributed constants.

Considering first the normal type of attenuator, with the resistance material on the central conductor of a coaxial line, as shown, for example, in FIG. 5 of the abovementioned Weber patent; using the method of distributed constants, this line can be represented as shown in FIG. 2 of the present disclosure, where L, C, and R are the inductance, capacitance and resistance per unit length. Analysis of FIG. 2 readily yields the following equations:

p =(w LO+jwRC) V Eq. 3

The solution of which is )+(V-) Eq. 4

The arbitrary constants in the solution are V+ and V where V+ is the amplitude of the wave moving in 3 the +x direction and V is that of the oppositely moving wave. The propagation constant k is given by:

Let us designate R/wL as r. We will discuss its significance later. If r is small we can expand the square Notice that r is a dimensionless quantity. Its significance can be obtained by writing it as:

where we have recognized that L Z (The characteristic lmpedance) V LC (The wavelength) 0: (The velocity of propagation) From Equation 8 it is apparent that r is /21:- times the resistance per wavelength normalized to the characteristic impedance of the line, so that 21rr is the normalized resistance per wavelength. Thus, if the wavelength is short, and the resistance per unit length small, the first two terms in Equation 7 are sufiicient to designate k. In this case Notice that the real part of Equation 9 which represents the attenuation is independent of w. As 1' increases (at lower frequency) the next term to contribute to the attenuation from Equation 7 is Considering now the attenuator of the invention, the inside-out attenuator with the required shield can be represented by FIG. 3. From FIG. 3, one can readily deduce the following four simultaneous differential equations in four unknowns:

To most easily solve these equations, we will use the normal mode approach at once. That is, we will assume that r can be expressed in the form V e where k is the complex propagation constant, and Where V is the maximum value of V as a function of x or distance along the line, and that 1, V and 1 will then also have the same form, with the same value of k. With this assumption Making similar transformations for the other variable, we reduce the set of differential equations to the f0llowing set of algebraic equations:

If we use Equation 17 and Equation 18 to eliminate I and I in both Equation 15 and Equation 16 we will have Equations 19 and 20 each determine a ratio of V to V That is, we could divide each of these equations by V We would then have two equations with the single unknown V V We can thus use these two equations to solve for k. Clearly the equation which must be satisfied by k is Since this is a 4th degree equation in k (as can be seen by multiplying out both denominations) we expect in general 4 solutions. These will be two normal modes each of which can propagate in either of two directions.

The solution of Equation 21 can be accomplished readily by noticing that k does not occur to the first power. If we multiply out Equation 21, we will have only terms in k and k*. We can therefore consider it to be an ordinary quadratic equation in the variable k Proceeding in this manner one can in a direct way obtain the solution From Equation 22 one can easily obtain the formula for the propagation constant of the two normal modes. Clearly the plus sign will give one mode and the minus sign the other; then when calculating k from k the optional sign of the square root will determine the direction of propagation. Thus, complete information on the propagation characteristics of each of the normal modes is contained in Equation 22.

Having found the four permissible values of k, either of Equation 19 or 20 will sufiice to give the ratio of V to V for each k value. (The same result will be obtained for this ratio if a correct value of k is substituted in Equation 19 or in Equation 20.) Also, knowing the values of k and V and V Equations 17 and 18 can be used to find the currents. Thus Equations 17, 18, 22 and either 19 or 20 will suflice to completely determine the attenuator performance.

To illustrate the method and to identify the two normal modes, let us consider the case of very small R. The square root term in Equation 22 then becomes 5 If. the plus sign is selected 7 i k =w L C -jwRC Eq. 23

referring to Equation 5 and FIG. 3 we see that this is what we would expect if the signal propagated only in the inner space between the central rod and the resistive film. We have accordingly labeled this value of k obtained by using the plus sign k since for small values of R it has the propagation characteristics of the inner line (V and I Also, if we insert this value of k in Equation 19, we see that V /V 0. Equation 18 indicates that when V 0, I also. Therefore, this k mode corresponding to the sign in Equation: 23 is the one which shrinks into the inner line for small values of R, and will propagate as though the outer shield did not exist. Conversely, it can be demonstrated that if the minus sign is selected in'Equation 23 we will have a mode which for small R, shrinks into the space between the resistor and the outer shield and propagates as though the innermost conductor did not exist. For finite values of R, however, both normal modes will have some energy in both spaces and the propagation constants of each mode will depend on the parameters of both spaces. However, in general it is true that the k mode will have most of its energy in the inner space, and the k mode will be mostly in the outer, and the propagation constants will approach that of the space in which they are principally concentrated.

The preceding formulas give us the ability to calculate the normal modes in the attenuator, and some understanding of the configurations involved. However, as discussed in the introduction, these normal modes must be combined to fit the boundary conditions at the ends 'of the attenuator before the complete configuration of voltage and current in the attenuator is known. This procedure is simple only in the cases like that of very small resistance where each normal mode is essentially confined to single space. In general, having found the four possible modes for a particular attenuator at a particular frequency we must combine these modes before we can determine the attenuation or the VSWR. The particular combination of modes required to match the boundary conditions will be very frequency-sensitive, and will depend, of course on the length of the attenuator. However, in the practical cases which we will'consider it will turn out for several reasons that the mode combinations will not play a very significant part in determining the properties of the attenuator. These properties will be essentially those of the dominant mode.

Equations 9 and 10 give the first and second order high frequency approximations for the propagation characteristics of a normal attenuator. In order to understand the inside-out attenuator for purposes of optimization, we would like to find a similar high frequency approximation for its propagation constants. To do this, we need only expand the radical in Equation 22 making the assumption that The first order expansion gives Taking the plus sign for the radical in Equation 22 and using the above approximation gives We now recognize that the real part of the fraction cannot greatly affect the attenuation. Therefore We find the imaginary part ofthe fraction, continuing the sumption of Equation 24. We find j '1 2( 1 2) i da- 2 2? If we were to solve the k by using the minus signinstead of the plus, we will obtain exactly the same formula with the subscripts 1 and 2 interchanged and a minus sign instead of a plus inside the brackets.

Before analyzing Equation 27, let us examine the assumption mode in Equation 24. It is clear that it can only hold if L 0 is substantially difierent from L C That is, if the velocity of propagation in the inner and outer lines are different. This requires that one of the two lines be filled with dielectric or ferrite material. In the particular case selected for analysis the outer line is filled with ceramic of high dielectric constant.

Now let us analyze Equation 27 by comparing it with Equation 10. Note that in both cases the frequency dependent part of the attenuation depends on R /w Z in the same way. Forv the attenuator we are considering L C L C and C C Therefore the bracket in Equation 27' is less than 1, and the attenuation will be less than the high frequency limit. Further, if C C and L C L C Equation 27 becomes similar to Equation 10 with the exception of the factor of 8 in the denominator of Equation 10. Thus the droop in the frequency char acteristics for the inside-out attenuator will be 8x that for the normal attenuator if C C As C C this droop can be reduced to a value lower than that of the normal attenuator.

Construction of experimental attenuators shows that,

in accordance with the analysis given above, it is possible to design an inside-out attenuator which will have a reasonably flat bandpass characteristic comparable to a conventional attenuator (e.g., Equation 10), if the denominator in Equation 20 is made large, that is, if there is a large diiference between the dielectric constant of the ceramic tube and the air between the inner conductor 2 and the attenuator film 3, or a large diiference in propa-. gation velocity between the inner and outer lines which decouples them. If this difiierenee is made sufficiently large, the attenuation can be calculated without reference to the small k load.

Equation 27 contains most of the information necessary to permit optimizing the design of the attenuator. It is clear that the frequency characteristic of the attenuator will be perfectly flat (to the degree of approximation involved) if the quotient can be reduced to zero. Clearly R cannot be reduced without making the attenuator longer or of lower value. The denominator concerns the difference in the velocities of propagation in the inner and outer line. We wish to make this difierence as large as possible. This Will also help decouple the energy in the inner and outer lines as discussed previously. For a practical attenuator, L C =8.4L C this is a very substantial difference, and probably cannot be greatly improved. The remaining factor is the difference in the capacities. In practice, this can be brought close to zero. However, a few practical considerations are in order.

If we wish to maintain a 5.0 ohm input impedance, we require that so In %50 where r, is the radius of the resistive film and r, is the radius of the inner conductor. This requires that and This means that the capacity 0, must be Therefore, for a 50 ohm attenuator with a dielectric constant of 8.4 in the outer line, to make C =C we require a ratio of innermost to outermost diameters of 2.3 1lOO=2,500 which is hardly practical. Not only is this impractical, but it is probably not really the optimum arrangement because the formula used is in fact only an approximation.

However, if the inner diameter were changed from to A; inch, then r, should change to .288 inch. If the outer diameter remained 1 inch and the same dielectric were used, the capacity C would be 1 Q SAXEXIO The quantity C C would then be reduced to a value which readily gives a reasonable approximation to a flat frequency characteristic over a useful range, for example, 711 kilomegacycles in a practical attenuator.

It will thus be seen that the attenuator of FIG. 1 can be designed to pass a wide frequency band by virtue of the dielectric constant of the ceramic material 4 entirely filling the outer space, and this ceramic material is also useful in increasing the thermal dissipation because it is a better heat conductor than air. The chief other basic design consideration is the ratio of outer to inner conductor diameters, which must be kept sufiiciently high to give a reasonably fiat frequency characteristic as dis- 3.74 X 10' farads/ meter cussed above. While this involves some compromises in design considerations, it has proved possible to design inside-out attenuators of the kind here described, with highly satisfactory frequency characteristics over a wide band by substantially completely filling the outer space with a high-dielectric ceramic material having much better thermal conductivity than air, thus fulfilling the objects of the invention in a simple manner.

While the attenuator has been disclosed in a cylindrical configuration, it is not limited to such configuration, but may also be used in rectangular or other configurations, e.g., for use with wave guides, etc.

It will be apparent that the embodiments shown are only exemplary and that various modifications can be made in construction and arrangement within the scope of my invention as defined in the appended claims.

I claim:

1. A wide-band coaxial high-frequency attenuator unit for connection to a coaxial line, comprising a low-resistance central conductor, a tubular member of high-dielectric ceramic material of substantial thickness coaxially surrounding and spaced from said central conductor, a thin conductive film of relatively high resistance uniformly coating the interior surface of said tubular member and of a thickness which is negligibly small compared to the depth of the high-frequency current penetration, coaxial connector means having an inner terminal and a coaxial outer terminal, inner contact means connecting said inner terminal to one end of said central conductor, outer contact means connecting said outer terminal to one end of said thin conductive film, and a coaxial lowresistance outer conductive shield coaxially conductively connected to said outer terminal by a contact having a low effective impedance over a wide spectrum of frequencies comprising the full useful frequency range of the attenuator, said shield surrounding said metal film and spaced therefrom, the ceramic material of said tubular member substantially filling the space between said film and said shield to provide a propagation path between the film and outer shield having a difierent mode of propagation from the path between the central condoctor and film such that there is a sufliciently large difference in propagation velocity between the inner and outer paths to effectively decouple the metal film from the outer shield over a wide frequency band.

2. The invention according to claim 1, said ceramic material having a dielectric constant of at least 8.

References Cited in the file of this patent UNITED STATES PATENTS 2,197,123 King Apr. 16, 194.0 2,689,294 Weber Sept. 14, 1954 2,764,743 Robertson Sept. 25, 1956 2,831,047 Wadey Apr. 15, 1958 2,831,170 Pressel Apr. 15, 1958 2,844,791 Jacques July 22, 1958 2,900,557 Webber Aug. 18, 1959

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