Transfer functions of a transformer at different values of coupling coefficient

The low‐ and mid‐frequency model of the transformer with resistive load is analysed for different values of coupling coefficients. The model comprising of coupling‐dependent inductances is used to derive the following characteristics: voltage gain, current gain, bandwidth, input impedance, and transformer efficiency. It is shown that in the low‐ and mid‐frequency range, the turns ratio between the windings is a strong function of the coupling coefficient, i.e., if the coupling coefficient decreases, then the effective turns ratio reduces. A practical transformer was designed, simulated, and tested. It was observed that the magnitudes of the voltage transfer function and current transfer function exhibit a maximum value each at a different value of coupling coefficient. In addition, as the coupling coefficient decreases, the transformer bandwidth also decreases. Furthermore, analytical expressions for the transformer efficiency for resistive loads are derived and its variation with respect to frequency at different coupling coefficients is investigated. It is shown that the transformer efficiency is maximum at any coupling coefficient if the input resistance is equal to the load resistance. Experimental validation of the theoretical results was performed using a practical transformer set‐up. The theoretical predictions were found to be in good agreement with the experimental results.