Analysis of the equal-delay transformer with non-commensurate constituent transmission lines

The effect of non-commensurate constituent transmission lines on the performance of the equal-delay topology for transformers and balancing networks is quantified. It is shown that when the load behaves as an isolated 2-terminal impedance or when the sum port connection is open-circuited to provide current balun operation, even a small difference in electrical lengths causes a complete nulling of the balanced output voltage and a concomitant open-circuit in the input impedance when the average electrical length of the lines is an odd integer multiple of 90°. This result is significant as it constitutes a major frequency limitation in the so-called Guanella topology. The special case of one of the transmission lines having zero length is then shown to be equivalent to the so-called bootstrap or Ruthroff topology, with the transmission null still occurring when the average electrical length of the lines is 90°.