Patent GB-534802-A (GB)
Title: Wave filter
IPC: H03H7/01
Filed: 1940-01-09
Abstract: 534,802. Impedance networks. STANDARD TELEPHONES & CABLES, Ltd. Jan. 9, 1940, No. 469. Convention date, March 9. 1939. [Class 40 (iii)] The design of filters to be used in groups for the separation of different frequency bands is complicated by the fact that the behaviour of the system as a whole is considerably affected by the characteristics of the individual 'filters in their attenuation ranges, particularly by the presence of zeros and poles of impedance in those ranges. According to the invention, such filters are designed so that the reactance or susceptance component of the image impedance or admittance, which is uniform over the pass range, is fixed at a certain minimum value determined by the resistance or conductance component. The mathematical theory of minimum reactance and minimum susceptance networks is analogous to that given in Specification 514,567 with reference to minimum phase shift network, and it is known that a certain contour integral relation, which is expressed in equation (4) of the present Specification, exists between the real and imaginary components of the image impedance or admittance, such that if either component is completely known the other can be calculated. It has been shown that the poles of impedance and admittance at real frequencies can be represented by anti-resonant and resonant circuits, and it follows that the remainder of the impedance or admittance function is realisable as a residual network whose impedance or admittance has no poles at real frequencies. It is evident that the reactance or susceptance of such a network cannot be reduced without alteration of the resistance or conductance. The prototype lattice filter shown in Fig. 6 has its series and diagonal branches Z 1 , Z, made up of a number of resonant circuits X 1 , X 3  ... Xm in parallel together with further impedances Xa, Xb. The circuits X 1 , X 3 ... X m , which are identical in the two branches, are resonant at frequencies in the attenuation range and mainly determine the image impedance. The impedances Xa, Xb, which may also consist of resonant circuits in parallel, have their critical frequencies within the pass range or at the cutoff and determine the image transfer constant. The requirement that the filter exhibits an attenuation peak at each zero and each pole of the image impedance enables the values of Z 1 , Z, to be calculated. A modified form which is sometimes useful exhibits attenuation peaks only at the zeros of the image impedance, so that Xa, Xb contain fewer elements. The identical branches X, ... Xm may be removed from the lattice and placed in shunt across the input and output terminals. If now the filter is terminated in its image impedance and the shunt branch across its input is removed, the conductance component of the driving-point admittance is unchanged, but the poles and zeros of the susceptance are eliminated, and the minimum susceptance network shown in Fig. 8 is obtained. A concrete example of complementary low-pass and high-pass filters of this type connected in parallel at their input ends is shown in Fig. 16. The conductance component of the input admittance is substantially constant, while the susceptance is substantially zero over the entire frequency range. When the cutoffs of the two filters are slightly spaced apart, the susceptance may be improved by the addition of a correcting circuit 37, 38 across the input terminals. The lattice networks just referred to may be developed into ladder-type structures, the low-pass form being shown in Fig. 17. If this network is bisected, each half will have at one end an image impedance equal to that of the original lattice and at the point of bisection an image impedance Zk of constant-k type. Additional sections having an image impedance Zk at both ends may be inserted between the two halves of the network or one half of the network may be replaced by sections of other types having an image impedance Zk at the junction point. Fig. 20 shows a combination of low-pass and high-pass filters which is equivalent to Fig. 16 without the susceptance-correcting circuit. In another form of prototype lattice filter, Fig. 22, the branches are made up of anti-resonant loops X<SP>1</SP> 1 , X<SP>1</SP> 3  ... Xlm in series together with further impedances X<SP>1</SP>a, Xlb, the image impedance being the inverse of that of Fig. 6, while the image transfer constant is the same. The identical loops may be placed in series at the ends, and the removal of those at the input end gives a minimum reactance network, Fig. 24 (not shown). The lattice networks may be developed into ladder-type structures analogous to that shown in Fig. 17 and having similar properties, and complementary filters of this type may be connected in series at their input ends, Fig. 27, to give a combination analogous to Fig. 20. Specifications 350,498 and 396,084 also are referred to.