Toroidally-Wound Transmission Line Transformers with 1-to-4 Impedance RatiosAuthor: R.J.Edwards G4FGQ © 9th July 1998
This analysis applies to bi-filar wound transformers having an impedance step-up ratio of 1-to-4. The low impedance winding is always unbalanced to ground. The high impedance winding may be unbalanced, or balanced with grounded centre-tap. The winding consists of two insulated wires laid alongside each other to form a short balanced-pair transmission line. The twin line is wound round the ferrite core and becomes an RF choke insofar as longitudinal currents are concerned.
The choke isolates the output voltage of the line from its input. This permits the input of the line to be connected in series with its own output. At frequencies where line attenuation and phase shift are small, transformer output volts are twice input volts and the impedance ratio is therefore 1-to-4. At the LF end of its range it operates as an ordinary auto-transformer.
Line conductor loss increases as Sqrt(Freq) and is inversely proportional to Zo. But at HF it is advantageous to adjust line insulation thickness such that Zo equals half the transformer terminating impedance. This minimises reflection loss. The high frequency response is ultimately limited by line phase shift. At half wavelength the 180-degree phase reversal results in no transformer output volts. But performance is poor even when the line reaches 1/4-wavelength.
As with all transformers, the LF response is limited by the shunting effect of winding inductance. The source has to supply a watt-less magnetising current. Transmission loss will increase on any line between source and transformer input.
For broadband applications a compromise is necessary. For a given core size, if more turns are used to improve the LF response, line loss and phase shift will increase and the HF response will suffer. An increase in core permeability, Mu, will improve LF response but may result in greater hysteresis loss in the core. High Mu ferrites are associated with high core loss at the lower frequencies. In the range 1-to-50 MHz, values of Mu less than 250 are recommended.
The core is assumed to have a square cross section with well rounded corners to prevent damage to conductor insulation. The line should not be twisted but laid flat around the core. Small air spaces do not matter. Twin 18 or 16-swg speaker cable, or similar, will form a suitable line. Use the percentage of input power which is dissipated in the transformer as a guide to wire gauge.
Use a ring diameter large enough to allow space between turns. This minimises capacitance between adjacent turns of the line. The program allows for this. Overall transformer performance is displayed in terms of insertion loss with extra info on reflections and VSWR. Results are valid from 0.1 MHz up to a frequency where the line electrical length is 0.25 waves. For simplicity, hysteresis loss in the core is neglected. Transformers should not be run near saturation.
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