342 PHILIPS TECHNICAL REVIEW VOLUME26 Surface-wave transmission lines for microwave frequencies . I. The various types of transmission line 11. Applications of the dielectric line 621.372.826 In microwave techniques, the millimetre and submillimetre wavebands are coming to acquire a practical importance comparable to that at present occupied by the centimetre waveband. Components and measuring techniques for these extremely high frequencies are often a result of the marriage of known principles from transmission lines and optics. A special problem is the low-loss transmission of millimetre and submillimetre waves. There are various surface-wave transmission lines that can be usedfor this purpose. Since the transmission of the electromagnetic energy chiefly takes place in the space surrounding the line, not only the attenuation of these lines but also the radial extent of the field has to be taken into account. ' The dielectric line, on the basis of theoretical and practical results so far obtained, seems to be the most appropriate surface-wave line for transmitting electromagnetic energy in the . 1 mm wavelength range. I.-The various types of transmission line H. Severin In comparing various forms of transmission line the theoretical work showed to be the most promising. for electromagnetic waves with their practical applica- By way of introduetion a short summary is given bility in mind, two classes of problem must be taken of the properties of the conventional transmission into account. The first relates to the transmission pro- lines for high frequencies. For decimetre and centi- perties of the straight infinitely long line. Maxwell's metre waves coaxial cables and waveguides of rectang- equations have to be solved for the special boundary- ular cross-section are chiefly employed at present [11. values, giving the field configuration, the phase velo- The attenuation of these transmission lines increases city and the attenuation of the wave as a function with the square root of the frequency because the skin of guide dimensions and frequency. depth decreases with frequency [21, so that there are The second class of problem is of a more practical already considerable losses at centimetre wavelengths. nature. It concerns, for example, the possibilities of Since, on the other hand, the attenuation decreases exciting a certain mode, of matching various lines, of with increasing surface it can - to a certain extent - constructing components and measuring devices, such be reduced by enlarging the cross-section of the trans- as attenuators, directional couplers, slotted lines, etc.; mission line. This is one of the reasons for the pre- and also, for surface-wave lines, the method of mount- ferred application of waveguides for centimetre waves. ing and the avoidance of radiation losses at bends. The At a frequency of 10Gc/s-c-corresponding to a wave- theoretical and the practical problems are certainly of length of 3 cm - the attenuation of a standard copper equal importance in deciding which type of transmis- coaxial line without dielectric (outer conductor dia- sion line is the most favourable for a particular appli- meter 9.53 mm, inner conductor diameter 2.65 mm) cation. Nevertheless the theoretical problem can be said is 226 dB/km, whereas the attenuation of the standard to be of primary interest, because one cannot attempt copper rectangular waveguide for the 10 Gc/s fre- to treat the more practical questions until the trans- quency-band (inside dimensions 22.9 mm X 10.2 mm) mission properties are known. Part I of this paper is 96 dB/km. At a wavelength of 5 mm, the waveguide deals exclusivelywith the first class of problem, giv- for the 60 Gel» frequency-band (inside dimensions ing a survey of the various types of transmission line 3.76 mm X 1.88 mm) has an attenuation of 1300 dB/km. for surface waves. Part II follows with a survey of the In view of these attenuation values, the coaxialline more practical questions for the dielectric line, which and conventional waveguides are not suitable for longer distance transmission, because, with the pres- Prof. Dr. H. Severinçformerly a research worker at the Hamburg ent ,state of amplifier technique, the attenuation for laboratory of Philips Zentrallaboratorium GmbH, is IIOW Professor of High Frequency Techniques at the University of Bochum. sline transmission must be no greater than 3.5 dB/km. 1965, No. 11/12 SURFACE WAVE TRANSMISSION LINES, I 343 Even for short connections, e.g. antenna feeders, the magnetic field extends appreciably into the surround- attenuation is considerable, especially at high fre- ing space. In order to judge the applicability of these quencies. lines it is therefore not sufficient to know their atten- uation: the extent or the electro-magnetic field around The idea of increasing the conducting surface takes us from the line must also be known. A line supporting a wave the coaxial cable to the "Clogston-type" or "laminated cable" in which the inner and outer conductors consist of many concentric whose field extends considerably into the surrounding metallayers insulated from each other (31. If the thickness of the space is unsuitable for practical purposes, even if its individual layers is small c-ompared with the skin depth at the attenuation is extremely low. highest frequency to be transmitted, such a cable has a constant attenuation over a wide frequency range. In addition, the attenu- The single-wire transmission line (Sommerfeld line) ation is much smaller than that of a coaxial line of the same size. The laminated cable will perhaps find application as a broad-band The problem of propagating electromagnetic waves cable in the frequency range from 0.1 to 10 Mc/s, for example in along a single wire ("single-wire transmission line") carrier-frequency telephony or for television programme trans- was solved by Sommerfeld in 1899. Heinrich Hertz had mission, as soon as the difficulties of economic production are previously treated this problem without success. We overcome. know today that his experimental investigation failed For waveguides, increasing the conducting surface to reduce the losses leads to larger waveguide cross-sections. Apart from because of the large extent of the electro-magnetic being expensive, this gives rise to difficulties because of the sim- field around the wire. Because of the large field extent ultaneous excitation of unwanted higher-order modes, whose the surroundings, such as the laboratory walls, dis- number grows with increasing cross-section. The HOl-mode in turbed the field configuration. Theoretically 'Hertz circular waveguide proves to be superior to all other waveguide idealized the problem too much: he took the wire to modes because for equal attenuation it requires the smallest guide cross-section, and is thus accompanied by the smallest possible be infinitely thin and to have an infinite conductivity (J. number of unwanted modes. While for waveguide modes at high Sommerfeld's solution shows that in the limiting case frequencies the attenuation due to ohmic losses usually increases (J -+ 00 a surface wave along the wire cannot exist. with the square root of the frequency, the HOl-mode shows a For single-wire transmission line one can make the completely different behaviour: for this mode the attenuation same distinction as for waveguides between H- and approaches zero with increasing frequency. The ohmic losses in which either the magnetic field or the arise exclusively from circular wall currents due to the axial E-modes, H component of the magnetic field. Since the magnitude of the electric field E respectively has a component along the axial field component decreases with increasing frequency for direction of the wire. Sommerfeld's solution refers to all waveguide modes, the wall currents for the HOl-mode and the axially symmetrical E-mode, whose field is inde- hence the ohmic losses decrease with frequency. pendent of cp and consists of the components Er, Ez An immediate consequence of this behaviour is the fact that and Hrp if the wire coincides with the z-axis of a system in principle the attenuation at any frequency can be made as small as desired if the diameter of the waveguide is chosen large of cylindrical coordinates r, cp, z (fig. I). For all other enough (41. For example, at a carrier frequency of 50 Gc/s, E- and H-modes the major part of the field is inside the corresponding to a wavelength of 6 mm, an attenuation of about wire, as Hondros later showed. The attenuation of these 1.25 dB/km (13 % reduction in amplitude), which is typical for microwave links, is obtained by using a copper waveguide of 5 cm diameter. The following example illustrates the superiority of the HOl-mode for circular waveguide compared with the domi- nant Hll-mode. For the required attenuation of 1.25 dB/km the diameters required for the two modes at a frequency of 10 Gcl« are 11.2 cm and 43 cm respectively, and the number of possible modes is 40 for the HOl mode and more than 300 for the Hll-mode. The low attenuation ofthe surface wave transmission lines treated below is due to the fact that the electro- (11 w. Opechowski, Electromagnetic waves in waveguides, I and II,-Philips tech. Rev. 10, 13-25 and 46-54, 1948/49. - (2] The «skin depth" or "thickness of the equivalent conducting layer" is proportional to Itv! (f = frequency). For copper the skin depth atf = 1000 Mc/s is 2 X 10-3 mm. [31 A. M. Clogston, Reduction of skin effect losses by the use of laminated conductors, Bell Syst. tech. J. 30, 491-529, 1951. Fig. 1. Configuration of the transverse components Er and Hrp E. F. Vaage, Transmission properties of laminated Clogston of the electromagnetic field of the Sommerfeld wave.