Patent GB-477209-A (GB)
Title: Separating filter for oscillating electric currents
IPC: H03H7/01
Filed: 1936-04-17
Abstract: 477,209. Impedance networks. CAUER, W., and BRANDT, W. April 17, 1936, No. 11056. [Class 40 (iii)] The principles described in Specifications 350,498*, 396,084, and 430,003 are extended to the design of separating-filters having three or more pairs of terminals. The product of the open-circuit impedances or short-circuit admittances for each pair of pairs of terminals is approximately equal to the product of the terminating resistances or conductances in the attenuation range, while the ratios of these quantities are approximately equal in the pass range. Forms of separator. The separators may be forked ; for instance two channels may pass between the main terminals (0), Figs. 5a, 5b, and the two subordinate pairs of terminals (1), (2), and in such a separator the filter sections q<1>, q<2> may be connected in shunt as in Fig. 5b or in series as in Fig. 5a. Three or more series-connected sections may form a closed ring, Fig. 6a, so that a channel exists between each pair of terminals and each other pair, or a similar arrangement of shunt-connected sections may be adopted, Fig. 6b (not shown). Instead of the ring being closed as shown in Fig. 6a, it may be open so as to give a pair of subordinate or one-channel terminals at each end, Figs. 7a, 7b (not shown). The theory is generalized to deal with separators having any number of pairs of terminals. Theory of forked separator having a main or multi-channel pair of terminals (0) and n pairs of subordinate or single-channel terminals (1) ... (n). The equations relating the voltage Zs at the sth pair of terminals to the currents Jt at all the pairs of terminals, where t = 1 ... n, contains coefficients Zst which are of the dimensions of an impedance, and the complete set of such coefficients can be arranged to form a matrix ; alternatively a matrix of admittances Yst can be postulated. The terms Zss, Ztt are the open - circuit impedances for the channel (s, t), and according to the invention Zss, Ztt#=Rs.Rt in the attenuation range while Zss/Ztt#Rs/Rt in the pass range, where Rs, Rt are the terminating impedances ; or a corresponding relation may hold for the short-circuit admittances Yss, Ytt. Such a matrix is formed in accordance with prescribed conditions as to the type and quality of the filter channels, and the appropriate physical embodiment of the matrix is then deduced. The design is carried out in three steps. (1) The pass ranges for the channel between the main terminals (0) and each subordinate pair of terminals (t) are prescribed ; they correspond to attenuation ranges for all the other channels. Between the pass ranges and attenuation ranges for each channel there are transition regions, and the limiting frequency which theoretically separates a pair of adjacent ranges may be taken as the geometric mean of the limits of the transition region in which it lies. (2) Certain attenuation functions qt, one for each channel (o, t), are determined. Each quantity qt is a function of frequency ; it is imaginary in the pass range of the channel (o, t) and real in the attenuation range. When the attenuation approaches infinity, qt approaches 1, and the poles and roots of qt have to be chosen so that qt may not differ from 1 by more than a prescribed amount in the attenuation range. In the pass range of channel (o, t) the product of all the remaining functions q, other than qt, must fulfil an analogous condition. In the transition regions lying between pass and attenuation ranges these conditions are not fulfilled, but the limits of the transition regions are prescribed and are data in the problem to be solved. Further conditions are that, in order that the number of requisite circuit elements may be minimized, the functions q must have the minimum number of roots and poles that will satisfy the above conditions, and for this purpose the functions q may be derived from the Tschebyscheff functions described in Specifications 396,084 and 430,003. Table II of the present Specification shows how to choose the class number of the functions q and to construct these functions in terms of the pulsatance # when the appropriate Tschebyscheff function, expressed in terms of the normalized pulsatance #, has been selected from Table I of the Specification ; # is a function whose form has to be chosen according to a rule. The use of Tschebyscheff functions brings it about that the roots and poles which are common to the open-circuit impedances or short-circuit admittances in the pass range become more closely spaced as the limiting frequency is approached, and each of such poles is paired with a pole of the transmission loss in such a way that the product of the pair of poles is equal to the normalized attenuation limit. (3) As the third step, the matrix of impedance coefficients Zst (or admittance coefficients Yst) has to be set up. The requisite matrix is given in equation (13) of the Specification; Zot is of the form, #{ RoRt(qt<SP>2>-1)} where Ro, Rt are the terminating resistances at terminals (o) and (t), and Ztt is of the form Rtqt<SP>2>/#q. The quantities Z so obtained are functions of A, where #=j# and # is the pulsatance. They are next expanded in partial fractions, as described in Specification 430,003 and illustrated in equation (23) of the present Specification. A network having a class-3 low-pass channel (0, 1) and a class-1 high-pass channel (0, 2) is shown in Fig. 10a. Similar treatment of an admittance matrix gives the inverse network, Fig. 10b (not shown). The Specification gives other simple examples of networks according to the invention, Figs. 11 to 14 (not shown), and numerical calculations for a particular case, Figs. 12a, 12b (not shown).