Alford2
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1941 (4) Some of the coupled networks which have been discussed have been very useful in solving certain practical problems. Most of these practical applica- tions so far have been made at high frequencies be- tween about 5 megacycles and 140 megacycles. Below 5 megacycles these networks become rather large and somewhat unwieldy. Above 140 megacycles there has not been much need as yet for solving the particular type of problems for which these networks are most suited. Broadly speaking, there are two types of service for which coupled networks of the transmission line type are particularly well adapted, (a) filters and (b) im- pedance transformers. (a) Coupled Network Filters. A coupled section is a very simple and efficient rejec- tion-type filter which transmits every frequency but those to which the section is resonant. When the sec- tion is coupled loosely, that is when s is small, the vm rn — & Fig. 20—A coupled-section band-pass filter. rejected band is narrow. When the network is coupled tightly, the rejection band is relatively broad. Since the bands of rejection occur when the section is 3A, 3, etc., long it is clear that these bands are very far apart so that a section of this kind can generally be used to reject just one frequency without disturbing any other. A coupled section when connected as shown in Fig. 20 acts as a band-pass filter which transmits only the frequencies to which the section is tuned and rejects all others. Again, as in the previous case, the bands at which the section is in tune are very far apart so that in practice a filter of this type may often be employed to transmit just one frequency, others not coming within the scope of the frequencies used, or rejected by other elements in the circuit. When using the ar- rangement of Fig. 20 it is ordinarily convenient to select the points at which the line is connected to the section in such a way that this line from the transmit- ter is matched at the frequency which is passed by the network. Several transmitters operating at differ- ent frequencies may be connected to the same antenna, each through its own section, so that all can deliver their power into the line simultaneously without inter- fering with each other. When the frequencies to be delivered simultaneously to the same antenna are separated by 6 per cent or so, it is best to employ two stages of filtering. Fig. 21 illustrates a two-stage filter Alford: Coupled Networks in Radto- Frequency Circuits 69 of the kind used to feed three frequencies into the same antenna. In this figure the sections are in the same plane with the transmission line rather than be- low it. This particular form is more convenient from the practical point of view and also greatly reduces the radiation resistance of the sections and thus reduces Fig. 2I—A group of two-stage coupled-section filters used in feeding the same antenna from three 50-kilowatt high-frequency trans- mitters simultaneously. This picture was taken in 1938 at Mackay Radio and Telegraph transmitting station at Palo Alto, California. the loss. The value of s to be used, when the spacing of the line is Ay, the spacing of the section conductors is Ay, and the spacing between the plane of the line and the plane of the conductors is D, may be calcu- lated from the following formula: 60 /D? + 3(Ai + As)? S = — log. Zo VD? + 4(Ai — 2)? (59) in which go is the surge impedance of the line, not of the section. (b) Coupled Sections as Impedance Transformers. The coupled networks may be employed as trans- formers as shown for example in Fig. 17 in which a coupled section is used to eliminate the standing waves along a transmission line. This application is based on the reciprocity law for standing waves which has al- ready been stated elsewhere.> In accordance with this law any network with zero dissipation which is capable of producing standing waves along a transmission line may be used to eliminate them. While no passive net- work is free of all losses the transmission-line networks in general and coupled networks in particular have such small losses (unless abused) that this law may be applied to them without appreciable error. When this law is used the calculations which were made in con- nection with Fig. 14 become directly applicable to Fig. 17 and the position of the section with respect to the standing waves as well as the required reactance X may be readily predicted. 8 A, Alford, “High frequency transmission line networks,” Elec. Comm., vol. 17, pp. 301-312; January, 1939.