## Design of output transformers

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DESIGN OF OUTPUT TRANSFORMERS

Radio amateur and amateur radio operator of Poland, Year 24, December 1974, No. 12.

Low-frequency tube amplifiers, especially with higher power, are still built by radio amateurs. The output transformer is the most difficult element to design and manufacture. This is evidenced by inquiries and requests for help in the calculations sent to the editorial office. The basic principles of designing transformers intended to be made in amateur conditions presented here briefly should satisfy the wishes of interested readers.

The principles of designing low-frequency transformers in amateur conditions are slightly different from those used in industry. First of all, it is determined approximately what core is needed for the designed amplifier. Then a more or less suitable core is searched for, and after it is acquired, further winding calculations are made. After establishing approximate data as to the necessary winding wires, wires with diameters similar to the selected ones are purchased and only then the number of turns of individual windings is finally determined.

The basic relationships linking the phenomena in a transformer result from the following formula:

*E _{tr} = 6,28⋅f⋅n⋅Q⋅B⋅10^{-4}* (1)

where:

- E
_{tr}- the amplitude of the reverse-electromotive force induced in the primary winding, approximately equal to the amplitude of the supplied voltage [V], - f - frequency [Hz],
- Q - core cross-section [cm
^{2}], - n - number of turns of the winding,
- B - the highest induction value in the core [T].

The value of the reverse electromotive force is related to the alternating voltage of the final amplifier stage and results from the power and operating resistance. The highest and the lowest frequency of the passband results from the assumptions. The highest allowable induction value in the core should not exceed 0.6T. For Hi-Fi amplifier transformers, it is recommended to take 0.4T. Two unknowns remained in the formula given: the core cross-section (Q) and the number of turns (n). We determine the core cross-section approximately from the formula:

where:

- P
_{wy}- the output power of the amplifier.

As far as possible, we aim to build a transformer with a large core cross-section, which will allow to reduce the number of turns in the windings. This is important both due to the undesirable leakage inductance of the transformer and the degree of difficulty of its manufacture. In transformers composed of sheets with holes for fastening bolts, it is necessary to check that the core cross-section near the bolts is not smaller than that of the main column.

The simplified transformer substitute circuits are shown in Fig. 1. At the lowest frequency, the influence of the inductance of the transformer primary winding, which is connected in parallel to the appropriate amplifier load, should be taken into account. In most cases, it is the necessity to obtain a sufficiently large value of this inductance that determines the number of turns of the primary winding. At medium frequencies (1000Hz is assumed), only the winding resistances play an important role. At high frequencies, the influence of the leakage inductance is noticeable, the value of which depends on the number of turns, the transformer winding scheme and its quality. This inductance, in combination with the inter-winding capacitances, creates a low-pass filter limiting the transformer bandwidth..

Fig. 1. Simplified equivalent transformer diagrams.

a - equivalent circuit for the lowest frequencies,

b - equivalent circuit for medium frequencies,

c - equivalent circuit for great frequencies (treble and ultrasound).