Q measurement and simulation for RF coils

Introduction: A widely used figure of merit in radiofrequency (RF) coil construction and testing is the Q or ‘quality factor.’ Q is a measure of the spectral selectivity of the coil, Q = f0/Δf , where f0 and Δf are the central frequency and bandwidth (FWHM) of the resonance, respectively. A narrow bandwidth (high Q) excludes more noise and results in better signal to noise ratio. Q is also related to the ratio of stored energy to the energy dissipated per cycle, giving an alternate definition of Q = ω0L/R. While the theory behind Q and what it means is well established, determining the best way to measure it for RF coils is not as clear. It is not always straightforward in practice. Considering how often coil Q is reported in the literature (i.e. for a new coil), there is surprisingly little literature on how to accurately measure Q. There are a variety of techniques to choose from (see, e.g. [1-3]). Also, simply connecting the coil to a measurement device such as a network analyzer (NA) (an instrument for measuring transmitted or reflected power as a function of driving frequency) perturbs the measurement by adding a load. In this case, a coupling coefficient, which compares the power dissipated externally to that dissipated internally, relates the loaded and unloaded Q (QL and Q0 respectively): Q0 = QL(1+κ). Note that the use of the terms ‘loaded’ and ‘unloaded’ Q in the theoretical literature is related to but distinct from the common use of these terms experimentally (where the load is a result of coupling to the anatomy or sample being imaged). This project is an initial attempt to compare several common methods of measuring Q with each other and with expected theoretical results. Matlab was used to model resonant circuit behavior by calculating complex impedance and the reflection coefficient. Several small square loop coils were constructed and characterized. Then the Q of each was measured using the various methods and the theoretical Q was computed.