Maximum Output of Telephone Transformers

Abstract

If Z₁ is the impedance of the source, Z₂ the impedance of the load, L_p the complex self-inductance of the primary, L_s the complex self-inductance of the secondary of the transformer, M the complex mutual inductance between the primary and the secondary, R_p and R_s the'resistance of the primary and the secondary respectively the transformer constants may be expressed by L_p and other four constants p, κ, A_p, A_s as follows.
L_s=p²L_p
M=p^κL_p
R_p=A_pL_p
R_s=p²A_sL_p
where p is the ratio of transformation, κ the coupling coefficient, A_p and A_sthe complex damping constant of the primary and the secondary respectively. Assuming the slope of L_p, L_s and M to be equal, the ratio of transformation to give maximum output is
p=√|Z₂(Z₁/jωL_p+1-jA_p/ω)|/|Z₁(1-jA_s/ω)+jωL_p{(1-jA_p/ω)(1-jA_s/ω)-κ²}|……(14)
From this basis, the design theory of the maximum output transformer is given.