Projection engineering (Sept 1929-Nov 1930)

Projection Engineering, Octooer, 1929 Page Representative circuits with transformers functioning at high frequencies. quency where «Li has become so great as to be inconsequent when considered in parallel with R. Thus: x = Zi/Zo at the low frequency, y = Zi/Zo at 1,000 cycles now . = (R2 j^Li)/(R2 + i"L,) X (Rp + R2 j«.'L,)/(R, + j«Li) 1 x'— 1 + [RP (R» + j«Li) /R» J«Li] R2 and y = pip ±lp ■+ Xt2 As was stated Zi/Zo = x/y so 1 Zi/Z. 1 + RP R2 (Rp + E») i <■> Li (J-3 + L5 = L6) Rp e C2 FIG. 10 Representative resonant circuit. Clearing the "j" term (rationalizing) Zi/Zo = '1 + Rp E2 "Li (Rp + E2) We might more simply consider the equivalent circuit to be as in Fig. 4 with R3 representing Rp in parallel with the transferred load resistance. Or Rp R2 R3 — then Rp -) R2 Zl/Zo=_ii^ z,/z, Rs + j^L, l.+ R? 1 j w Li Mt,)° and it may be seen that the primary inductance (Li) is the controlling fac tor in determining the "per cent turn ratio" at the low frequencies. At the high frequencies the problem is of a different nature. The leakage inductance of a transformer is a function of the coupling of the two windings and is a result of magnetic lines which fail to link the two windings. At low frequencies its effect is of negligible character, but at the higher frequencies it becomes a controlling factor in the design. The coefficient of leakage (V) bears the following relation to (K), the coefficient of coupling K= M V Li X U V = 1 — K2 and L3 and Lu in Fig. 5 are numerically L3 = Li V L, = L, V In Fig. 6 the load characteristics have been referred back to the primary in the relationship2. h A2 Rl Ls = R = A2 As shown before, <*>Li is negligible as paralleled with the transferred load at the higher frequencies and the equivalent circuit may be shown as in Fig. 7. Also, as before, we will proceed with B»/E as the criterion for perfect reproduction. At a chosen high frequency E2/E = Rp+R22+j.Le=X And at a mid-range frequency where «L8 is negligible in comparison Rp+R? E,/E = „ R2„ =y Rp + R2 x/y: 1 + x/y = j » Le Rp -+ R2 1 Msr&y O) Lc RP +R: ~V<4 (I)" and Ej/E x 100 is the "per cent turn ratio" as before. Note that Ls is the factor upon which the characteristic curve depends at the higher frequencies and that it must be kept low if the highfrequency response is to be maintained. In a given design the leakage inductance may always be reduced by decreasing the primary inductance with an attendant loss in the reproduction of the low frequencies. The problem to be taken up, in the second article of this series involves the mechanical design methods attendant upon re 2 See K. S. Johnson, "Transmission Circuits in Telephonic Communication." D. Van Nostrand Co. dueing L0 while keeping Li at its necessary value. In order to obtain the maximum efficiency, an impedance match (Rp = R2) is essential for the rule Rp/Rj = A2 holds good and must be kept in mind in the design. High-Ratio Transformers The essential difference between the transformers already considered and the high-ratio transformers ("line-totube," "tube-to-tube," etc.), lies in the attendant loads and in the fact that in a high-ratio transformer the distributed capacitances and load capacitances are far from negligible at the high frequencies, and in working out of comparatively low impedances the primary loading (Rt) may be of considerable moment. In Figs. 8 and 9 are the equivalent circuits comparable with Figs. 5 and 6 previously considered. (I_3+L5 = L6) Rp FIG.7 The equivalent of Fig. 6. The secondary load has been referred to the primary in the sense R2 = R;/A2 and the input impedance, except at the very low frequencies, will be „ R2 Rt R2 + Rt (wLi being so high as to be inconsiderable). Now and L4/A2 C2 = CVA2 Ci consists of the distributed capacitance of the transformer itself in parallel with the tube capacitance which will be c = c(g-f)+c(g-p)[i+sf|Va] RlI FIG. 8 Rp L3 L5 1 I e 1 Rti L< 10 0 0 C2_ Z | 1 1 p R2? FIG. 9 Equivalent circuits comparable to those of Figs. 5 and 6.