COUPLING TO A DEVICE ON A PRINTED CIRCUIT BOARD INSIDE OF A CAVITY Chatrpol Lertsirimit (1) , David R. Jackson (2) , Donald R. Wilton (3) , and Danilo Erricolo (4) (1) University of Houston, Dept. of ECE – Houston, Texas, 77204-4005 USA. Email: lertsirm@mail.uh.edu (2) As (1) above, but Email: djackson@.uh.edu (3) As (1) above, but Email: wilton@uh.edu (4) University of Illinois at Chicago, Dept. of ECE. – Chicago, Illinois, 60607-7053 USA. Email: erricolo@ece.uic.edu Abstract: An efficient method for calculating the coupling of an exterior electromagnetic signal to a device on a printed circuit board inside of a cavity is considered for a wire penetrating an aperture in the cavity and making contact with the trace on the printed circuit board. Results are presented in both the frequency and time domains, and the case of a damped sinusoidal pulse is considered in some detail. It is shown analytically how the properties of the signal should be chosen to maximize the maximum induced voltage at the device, and this is confirmed by simulations. INTRODUCTION Many electronic systems are housed inside of metallic enclosures (cavities) that often have apertures. In many cases, wires or cables pass through one or more apertures and terminate inside the cavity, often ending on a printed circuit board (PCB). The system is illuminated by an incident wave, such as a plane wave. The voltage at the device port for this type of problem is calculated here in the frequency domain using an efficient “hybrid” method that separates the analysis of the PCB from that of the cavity [1]. This method, although approximate, accurately captures the different types of system resonances such as external cavity, wire, and internal cavity resonances. The device port is assumed to be open-circuited (or terminated in a linear load). The system considered here is thus linear (at least up to the time of the device failure). With this assumption, the system response in the frequency domain can be used with the Fourier transform to find the time-domain response at the device port due to an incident time-domain electromagnetic plane wave. For the special case of a damped-sinusoidal plane-wave pulse, an analysis is given to show how the parameters of the pulse should be chosen to maximize the peak output voltage at the device port. TIME DOMAIN ANALYSIS A time-varying incident plane-wave pulse and the output voltage at the device port are related by a linear, time-invariant, continuous-time system. The system consists of the feed wire, the cavity, the PCB trace, and any linear loads that terminate portions of the PCB trace before it arrives at the device port of interest (which is assumed here to be open-circuited). Figure 1 shows a particular system used for the results. The PCB substrate is actually replaced by air in this figure for simplicity, corresponding to a transmission-line wire that is 1 mm above the bottom of the cavity. The time variation of the incident plane wave is assumed to be a damped sinusoidal pulse, having the form ( ) ( ) ( ) sin bt s pt Be tut ω − = , (1) where u(t) is the unit step function, s ω is the radian frequency of the carrier signal, and b is the decay parameter of the pulse. The parameter b is related to the quality (Q) factor of the pulse by 2 s s b Q ω = − . The Q s of the signal is inversely related to the bandwidth of the pulse. The relative bandwidth in the frequency domain is defined from the –10 dB bandwidth limits ω + and ω − , and is given approximately as ( ) / / 3/ R s s s BW Q ωω ω ω ω + − =Δ = − = .