TRANSFORMERS A Simplified Analysis of the Broadband Transmission

Bell Laboratories (Retired) and Consultant T his paper presents an easily understood analysis of the transmission line transformer (TLT). It also includes some history and the author's suggestion for the future of these devices. It is hoped that future device development and application will be encouraged. The TLT transmits the energy from input to output by a transmission line mode and not by flux-linkages as in the conventional transformer. As a result the TLT has much wider bandwidth and higher efficiencies than its conventional counterpart. With proper core materials and impedance levels of 100 ohms or less, bandwidths of about 100 MHz and effi-ciencies approaching 99% are possible today when matching 50 ohms up to 100 ohms and 50 ohms down to about 3 ohms. Future research and development, especially with impedance ratios less than 4:1, should make TLTs operate at much wider bandwidths. The TLT and conventional transformer have two models used in their analysis. The low frequency models are similar, usually containing an inductive impedance in parallel with the input impedance. The high frequency model of the conventional transformer consists of a distributed capacitance in parallel with the leakage inductance. The TLT in turn contains a configuration of transmission lines in the high frequency model. Therefore, the conventional transformer model only requires a background in circuit theory, while the TLT requires both circuit and transmission line theory. The TLT first appeared upon the scene in 1944 in a classic paper by George Guanella in the Brown Boverie Review. The title of his paper was " Novel Matching Systems for High Frequencies " [1]. The second classic paper was written by Clyde Ruthroff at Bell Labs and was published fifteen years later in the Proceedings of the IRE. His paper was named " Some Broadband Transformers " [2] and introduced the 1:4 unbalanced-to-unbalanced transformer (unun). Guanella's basic designs were balanced-to-unbalanced (balun) transformers. They consisted of transmission lines connected in a parallel/series arrangement. They are the basis for the later " equal-delay " TLTs. Ruthroff on the other hand, applied the input voltage to part of the output, which has been known as a " Bootstrap Effect. " His transformers usually added a delayed voltage to a direct voltage therefore a cancellation effect took place limiting the high frequency response. Guanella's goal was to develop a balun to match the balanced internal impedance of a push-pull vacuum-tube amplifier of 960 …