Exploitation of Spurious Coupling in Metal Enclosures for Oscillator Design S. Held # , T. Bolz * , and K. Solbach # # University Duisburg-Essen, Duisburg, 47057, Germany * IMST GmbH, Kamp-Lintfort, 47475, Germany Abstract— Modeling of spurious coupling between a circuit and its metallic enclosure in a circuit simulator is an important feature. Especially simulating circuits with nonlinear components will benefit greatly from this, because these components can typically not be simulated in the field simulator directly, but require artificial ports inside the calculation domain. It will be shown in this paper, that these ports introduce erroneous coupling results, if misplaced or misorientated. This is validated by separating the coupling effects from the normal circuit response by introducing an impedance coupling network into the circuit simulator. This makes modeling of electromagnetic coupling inside the circuit simulator possible and provides fast and accurate results, as will be shown by example of a cavity embedded oscillator. Index Terms— Cavity resonators, Electromagnetic coupling, Modeling. I. I NTRODUCTION To accurately simulate circuits influenced by resonant cavity modes along with nonlinear (e.g. transistors) components, one uses a full-wave solver together with a circuit simulator. Artificial ports are introduced at the location of the nonlinear device. This distributed passive structure is solved by the (linear) full-wave solver and s-parameters are exported. The circuit simulator may now employ for example harmonic balance simulation while incorporating the former results as a black box data item. This is proven to be a powerful and accurate concept to tackle such circuits. However, problems arise if the metallic enclosure possesses resonant modes in the analyzed frequency range. The artificial ports will couple energy into the modes and therefore distort the behavior of the circuit. Modeling of the resonant modes directly inside the circuit simulator solves this kind of problem. Furthermore, it speeds up the simulation, because lengthy full-wave solver runs are not needed anymore. At first, this paper examines the behavior of artificial ports in a free-space environment and inside a cavity. Then a method is introduced, which models the resonant modes of the cavity in terms of a circuit model. To prove the validity of the network representation, a cavity embedded oscillator is designed. Finally the measured response of the prototype is compared to the simulation. II. PORTS Let’s consider two simple 50 Ω microstrip lines separated by a 4 mm gap and fabricated on top of a laminate with ε r = 3.55 (h = 0.51 mm). The following discussion assumes a 100 Ω resistor is mounted across the gap. To model the described circuit in a full-wave solver, one needs to define artificial ports to connect the resistor (there also exist methods to directly embed lumped components, but the general approach is to use ports). In setup one (Fig. 1), the artificial port is introduced across the gap, parallel to the substrate surface. This seems to be the natural way to connect a lumped element and is in accordance with the physical connection. In setup two, two ports are needed each with a connection from the end of the gap to the ground plane, i.e. perpendicular to the surface of the substrate. This model allows for a two port lumped element in contrast to setup one. Active devices and other general two-port elements are embedded into full-wave simulations using this technique. Data item Data item Setup one Setup two port port port Network representation Network representation 1 Ref 1 Ref 2 MSL 2 MSL 1 MSL 1 MSL 2 Fig. 1. Different port configurations. As long, as free space conditions apply, both approaches give similar results (see Fig. 2). This is no longer true, if the microstrip line is placed inside a cavity. Now, the direction of the current (flowing through the ports) affects the coupling to the resonant modes of the cavity. This differing behavior is seen in Fig. 3. At resonance ( f = 4.518GHz) both curves deviate from each other. The orientation of the introduced artificial ports has a significant influence on the transmission coefficient S 21 . III. METHOD To understand coupling effects in a cavity, these effects have to be separated from the circuit response. In this paper a 3D extension of [1] is used for this purpose. The mutual coupling between the circuit and the resonant modes inside the metal enclosure are modeled by introducing the impedance coupling network depicted in Fig. 4.