Patent GB-451527-A (GB)
Title: Electric wave filters
IPC: H03H7/01
Filed: 1935-05-28
Abstract: 451,527. Impedance networks. STANDARD TELEPHONES & CABLES, Ltd., 63, Aldwych, London.-(Norton, E. L. ; 15, Summit Street, East Orange, New Jersey, and Dietzold, R. L.; 51, 5th Avenue, New York, both in U.S.A.) May 28, 1935, No. 15511. [A Specification was laid open to inspection under Sect. 91 of the Acts. Dec. 10, 1935.] [Class 40 (iii)] The phase-lag caused by the insertion of a filter is made to vary linearly with frequency throughout the transmission region and in the neighbouring part of the attenuation region, account being taken of imperfect terminal matching. The critical frequencies of the line and cross arms are not necessarily coincident. In a low-pass lattice filter having line impedances jx1 and diagonal impedances jx2 and terminated by impedances equal to a constant resistance R, the design is carried out by means of two parameters y1, y2, which are defined thus, y1 = tan<-1> (X1/R), y2 = cot<-1> (-X2/R). If the insertion loss gamma=A+jB, the attenuation A== -log cos (y1 -y2) and the phase-change B = y1 + y2. The design starts from a desired phase characteristic 3, Fig. 3, which is linear throughout the transmission range and beyond it. The ordinates of curve 3 are B /2 and the abscissµ are f/fo where f is the actual frequency and fo the cut-off frequency. Since B = y1 + y2, curves 1 and 2, representing y1 and y2 respectively, are to be equidistant from curve 3 ; and since A, curve 4, is to be infinite at a frequency near the cut-off frequency, (y1 - y2) is to be equal to 90‹ at and above such a frequency, which is chosen to be 1À3fo. The attenuation A prescribed for the remainder of the range determines (y1 - y2,) and thence curves 1, 2 can be drawn. The poles and zeros of X1 must occur when y1 is a multiple of 90‹, and these critical frequencies serve to determine by Foster's theorem the arm X1 shown in Fig. 2 when one reactance element has been fixed. Such an element, viz. Lla, can be found from the desired gradient of curve 1 at zero frequency, where y1 = y2. X2 can be similarly determined, and the network corresponding to curves 3, 4 of Fig. 3 is thus found to be of the form shown in Fig. 2. The zeros and poles of X2 are not precisely coincident with the poles and zeros of X1, but for practical purposes the resulting multiband effect is swamped by the effect of the absence of matching. Corresponding to every pole of A is a reversal of the phase B of the kind shown where f = 1À3fo, Fig. 3. In another embodiment the critical frequencies are in arithmetical progression except that those next the cut-off frequency on either side of it are spaced from it by ¥ of the regular interval. The insertion loss gamma = # + #r + #i, where # is the image transfer constant, #r a similar constant representing the effects of the first reflection, and #i the interaction constant representing the effects of the remaining reflections. In the case of a low-pass lattice filter terminated by resistances R equal to the image impedance at zero frequency, and comprising line arms Za of the form shown in Fig. 6 and cross arms Zb of the form shown in Fig. 7, there are two critical frequencies f1, f2, Fig. 8, below the cut-off frequency fc, and two f3, f4 above it ; the former two determine the image transfer constant and the latter two determine the image impedance. In the transmission region #r and #i are negligible, while # amounts to a pliase-shaft of # between # and f and between f and f2. In order, therefore, that the phase-shift may be proportional to frequency, the critical frequencies f1, f2 must be linearly spaced, and the phase characteristic 12, Fig. 8, is thus obtained. In the attenuation band # is real and #i is negligible, so that the phase-shift is determined by #r, and by reasoning similar to the preceding the critical frequencies f3, f4 are determined to be similarly spaced, the resulting phase characteristic 13 being linear except for a change of #, such as a, Fig. 8, at each critical frequency. In the transition region between f2 and f3 there is a progressive phase change equal to # between f2 and fc due to # and a further progressive change equal to # between fc and f3 due to #r, with an abrupt change of - ¢# at fc due to #r. The net change of 3#2 indicates that the intervals f2 fc and fc f3 are to be ¥ of the remaining intervals. The phase-shift due to the interaction coefficient, shown at 14, is negligible except at fc, where it neutralizes the effect of the change of ¢# in #r. The values of the elements in Figs. 6, 7 are determined from the above frequencies, the value of R, and a further constant K1 which is deduced from the value of the image transfer constant at zero frequency in conjunction with the desired slopes of the curve 12. The infinite series of critical frequencies theoretically required beyond f4 may be simulated by one or two frequencies at extended spacings. Correction for dissipation. Dissipation in the elements disturbs the phase characteristic, particularly near the frequencies f3, f4, and for the purpose of correcting this effect, particularly in the transition region f2, f3, a lumped resistance may be added to Za or Zb so as to equalize their resistance components at f3 ; or alternatively the spacing of f2, fc, f3 may be slightly diminished ; or the constant terms which fix the zero-frequency values of the image impedance and transfer constant may be slightly adjusted. The above theory for low - pass filters may be extended to band - pass and highpass filters. Critical frequencies are evenly spaced except for the three-quarter spacing on either side of the cut-off frequencies, and in a band-pass filter the image impedance at the mean of the cut-off frequencies is equated to R.