At lease two reactive elements are needed to match a lossless network to an arbitrary load. Yet two elements alone will not provide simultaneous control over the bandwidth and degree of match. Three-element matching networks, such as Pi- and Tee-networks, do provide additional control of the frequency response. In "Capacitor Pi Network for Impedance Matching," American Technical Ceramics (Huntington Station, NY) shows how to achieve a Pi configuration matching network without an inductor: by using a capacitor beyond its self-resonant frequency (i.e., when it has become inductive rather than capacitive).

The approach detailed in this five-page application note leverages the effective series inductance (ESL) of the series element in the Pi network. The design process relies on the broadband accuracy of the Modelithics (Tampa, FL) Global capacitor models. With three reactive components in the circuit model, there are at least two resonant frequencies: the series resonant frequency (SRF) and parallel resonant frequency (PRF). Above the resonant frequency, the capacitor acts like an inductor. The SRF generally sets the frequency limit on a capacitor's useful operating range. In this case, a capacitor is used as an inductor beyond its SRF to match a complex load to a real load.

The measured result is compared using both circuit simulation and method-of-moments (MoM) co-simulation. The substrate's properties, such as thickness, are key to obtaining a good correlation between the measured and simulated data. Another simulation is therefore included to compare the two substrates.

American Technical Ceramics, One Norden Ln., Huntington Station, NY 11746; (631) 622-4700, FAX: (631) 622-4728, Internet: www.atceramics.com