GB396084A - Wave filter circuits - Google Patents

Abstract

396,084. Impedance networks. CAUER, W., 35, Friedlõnderweg, G÷ttingen, Germany. Oct. 29, 1931, No. 30049. Convention date, Dec. 6, 1930. [Class 40 (iii).] Specification 350,498 describes filters which are so dimensioned as to yield prescribed image-impedance and attenuation characteristics with a minimum number of impedance elements. The symmetrical forms of these filters are equivalent to filters made up of bridge sections having pairs of opposite arms whose impedances are respectively 31 and 32 and the invention described in the former Specification consists in choosing the values of #(3132) and #(31/32) from a set of tables given in the Specification, the following being a typical value: m(#2+#<2>a)#(#<2>+#<2>-1)/(#<2>+#<2>-a)#(#<2>+#<2>1); #<2>+#<2> = o,# is 2# times the frequency, and the remaining quantities are arbitrary parameters, #1 and #-1 being the cut-off frequencies while #a, #-a are frequencies corresponding to poles or zeros of 31 and 32. For certain non-dissipative band-pass filters Fig. 1 shows #(3132) on a logarithmic scale against #, where #=(2#-#1-#-1)/(#1+#-1). It shows only the positive halves of the curves, the rest of the Figure being a mirror image reflected in YY<1> for even Cauer classes and comprising reciprocally related curves for the odd classes. The curves c, d, e, f, corresponding to successively higher classes (i.e. to greater numbers of filter elements) lie successively closer to the line 001 for which #(3132) = R, where R is the terminal impedance of the filter. Each curve oscillates between maxima and minima which are numerically equal for that curve ; it is then said to exhibit " Tschebyscheff behaviour," and the invention consists in choosing the parameters (i.e. resonances and anti-resonances) of a filter in relation to the data of a given problem so that the filter shall exhibit such behaviour. The value of log H, corresponding to the distance OQ, is determined by the degree of uniformity which has to be attained up to the limit represented by K. The remaining data relate to the attenuation curves outside the transmission band, and examples of such curves are given in Fig. 2, where the attenuation A1 (a function of #(32/31) for a band-pass filter) in nepers is plotted against # for the right-hand part of the' complete diagram, when # > 1. There is a symmetrical set of curves for the corresponding part where #<-1. Curves 1 .. 6 relate to Cauer's filter-classes 1 .. 6, which are distinguished by the numbers of elements which they contain. To each pair of lines PP<1>, QQ<1>, Fig. 1, there corresponds a line of minimum attenuation RR<1>, Fig. 2, and the curves shown are so chosen that they touch this line except in their left-hand branches. These branches cut the line at different abscissµ, the abscissa OK3 being shown for curve 6 ; and the permissible size of the distance OK3 is a further datum of the problem. The Specification gives examples of the manner in which the Tschebyscheff parameters are to be calculated, and refers to published work in which the theory is extended to dissipative networks.