Transmission Line Transformers
An RF transceiver often requires impedance transformation, power splitting, or transformation from a balanced to an unbalanced (balun) transmission line. Such circuits appropriate to the RF range are described in this chapter. The subject matter of Chapter 3 was impedance transformation. This subject is taken up here again, but now with more careful attention given to the special problems and solutions required for RF designs. The discrete-element designs described previously can be used in RF designs with the understanding that element values will change as frequency changes. The alternative to discrete-element circuits are transmission line circuits. The classical microwave quarter-wavelength transformer can be used up to hundreds of gigahertz in the appropriate transmission line medium. However, at 1 GHz, a three-section quarter-wavelength transformer would be a little less than a meter long! The solution lies in finding a transformation structure that may not work at 100 GHz but will be practical at 1 GHz.
The conventional transformer consists of two windings on a high-permeability iron core. The flux, ϕ, is induced onto the core by the primary winding. By Faraday’s law, the secondary voltage is proportional to dϕ/dt. For low-loss materials, the primary and secondary voltages will be in phase. Ideal transformers have perfect coupling and no losses. The primary-to-secondary voltage ratio is equal to the turns ratio, ...