Dissipation, resistance, and rational impedance matching for TEM and birdcage resonators

Using simple circuit parameters, mathematical expressions are given for the power dissipated by pure excitation of the principal mode of a Transverse ElectroMagnetic (TEM) or a birdcage resonator. From these, the Q, or quality factors are then derived for the TEM, and for the high and low pass birdcage. The drive point impedance is then expressed in terms of the Q and the element capacitance; and the synthesis of impedance matching networks by means of the Smith Chart is described, or in explicit detail for the discrete (or lumped) element TEM and the high pass birdcage, and in passing for the distributed TEM and the low pass birdcage. The limited applicability of a commonly used matching formula is noted. A complementary method of determining the drive point impedance by direct measurement is also given, along with corresponding Smith Chart calculations. All the proposed methodology is illustrated with respect to a pair of real world resonators—a discrete element TEM and a high pass birdcage—designed for proton imaging of the human head at 3.0 T. © 2002 Wiley Periodicals, Inc. Concepts in Magnetic Resonance (Magn Reson Engineering) 15: 177–188, 2002