Radio broadcast .. (1922-30)

MEASUREMENTS ON BAND-PASS FILTER CIRCUITS By W. T. COCKING Radio Engineer, The Receptite Co., London. Mr. Cocking, an English engineer whose writings have frequently appeared in foreign publications, presents in this article the results of some quantitative measurements on band-pass filters with various types of coupling. Although simi- lar arrangements have been thoroughly analyzed mathematically there has been an unfortunate lack here and abroad of definite laboratory data. An article deal- ing with the mathematical considerations in the design of band-pass filter circuits was published in February, 1930, RADIO BROADCAST, pages 212-214. IN MOST present-day sets the tuning is car- ried out by a number of cascade tuned circuits, and, although it is easy to obtain very high selectivity in this way, it is not possible to obtain good fidelity as well, un- less a prohibitively large number of such circuits are used. The band-pass filter, either alone or in conjunction with a number of cascade tuned circuits, offers a solution of the problem, for, when its components have suitable characteristics it gives high values of selectivity without serious suppression of sidebands. In this article consideration will be given chiefly to the capacitatively coupled filter, as it is'usually far superior to the inductively coupled filter. Fig. 5 (A and B) shows two different ways of obtaining inductive coupling, and (c) the usual con- nections for a capacitatively coupled filter. Provided that the values of the compon- ents are suitably chosen, the results with both types of inductive coupling are ab- solutely identical; and they may be cal- culated from the same formula, equation (1) below, and this equation is also ap- plicable for capacity coupling. It is ac- curate only when both primary and sec- ondary circuits are identical; that is, the total primary circuit inductance must be equal to the total secondary circuit in- ductance, the total primary circuit ca- Sorne Definite Quantitative Figures on Capacitatively and Inductively Coupled Filter Circuits. Band Width as a Function of Circuit Constants. Characteristic Curves With Typical Circuit Arrangements. pacity must be equal to the total secon- dary circuit capacity, and the effective r.f. resistance of both circuits must be the same. (1) II • effective r.f. resistance in ohms of coil, when connected in circuit. L — total inductance in henries of primary circuit and also of secondary circuit, since both are identical. C = total capacity of primary circuit in farads and also of secondary circuit, since both are identical. E = voltage induced in series with primary circuit, e = voltage developed across secondary tuning condenser. e/E — gain of circuit. X =* reactance of coupling component, = <oM for mutual inductance coupling, = G)L for inductive coupling, = for capacitative coupling. |M At the frequency at which uL = 1/uc the formula reduces to— e/ . "^ c (2) one-half of that for the ordinary series- tuned resonant circuit. The usual simple formulas, depending upon the coefficient of coupling, k, for calculating the frequencies of the two peaks in the tuning curve of a filter are inaccurate, since they neglect the effect of the coil resistance. The peaks occur approximately at the two frequencies for which— R +X = ujL- (6) and it is obvious that the quantity e/E is greatest when— B.x (3) Substituting, we get— If*' 2R But for an ordinary series-tuned circuit— e/ . ^c (5) Hence the efficiency of the band-pass filter, with optimum coupling, is exactly but if R is high, the term 4 R 2 (o>L -1 /we) 2 in the denominator of equation (1) appre- ciably affects the peak frequencies, in some cases to such an extent that the curve becomes single peaked. At any one frequency it will be seen that capacity coupling gives exactly the same results as inductive, since at that one frequency the reactance of the cou- pling condenser is the same as that of the coupling inductance. The negative sign for capacity reactance makes no differ- ence to the numerical result, for where- ever X occurs in the denominator of equa- tion (1) it is always squared. The change of sign in the numerator merely indicates that the output voltages from the filter are in opposite phase in the two cases. Capacitative vs Inductive The difference between the two methods of coupling is important in the practical case, where a wide band of frequencies must be covered with a fixed value for the coupling component. It has been shown above, equation (3), that for the optimum coupling the reactance of the coupling K-C-OFF RESONANCE Fig. 1 KC- OFF RESONANCE Fig. 2 326 • • RADIO BROADCAST FOR APRIL