Beyond the smith chart: A universal graphical tool for impedance matching using transformers

The topic of impedance transformation and matching is one of the well-established and essential aspects of microwave engineering. A few decades ago, when discrete radio-frequency (RF) design was dominant, impedance matching was mainly performed using transmission-lines techniques that were practical due to the relatively large design size. As microwave design became possible using integrated on-chip components, area constraints made L-C section matching (using lumped passive elements) more practical than transmission line matching. Both techniques are conveniently visualized and accomplished using the well-known graphical tool, the Smith chart.