In this work we present a microwaves circuit electromagnetic simulator. It is fundamentally based on the 3D self-consistent numerical solution of the Maxwell's equations and the macroscopic conservation equations derived from the transport equation of Boltzmann. It can include linear electrical elements. As an illustration, it is applied to the simulation of a microstrip transmission line and the Distributed IMPact ionisation and Avalanche and Transit Time (DIMPATT) diode.
II. ELECTROMAGNETIC MODELIGN OF ELECTRONIC CIRCUITSThe theoretical study of the operation of the microwave electronic circuits would ideally require the exact space-time solution of the Maxwell equations. This model is indeed capable of describing the interaction between electrical charges and the evolution of their distribution and motion at the origin of the electromagnetic field. The Maxwell equations are (1):In practice, when we consider the scale of dimensions of an electronic circuit, it is in general possible to split this circuit in sub-elements. The connection points between the different elements then constitute the nodes of the circuit. This feature makes this simplifying approach interesting is the fact that these elements may present a specific dynamic electrical behavior. Many of them present a linear behavior which does not require a physical description of their internal operation. They consequently can be described by means of a simple model.
A. Physical model oftransportFor semiconductor device modeling, we use the threedimensional system of macroscopic conservation equations constituting the drift-diffusion model. Indeed, the stationary approach of the carrier transport is justified for DIMPATT diodes operating up to 100 GHz. The model is composed of the continuity equations for the electrons and holes and the equations determining the conduction current densities (2):
B. Linear Lumped ComponentsIn the FDTD method, a lumped component is assumed to coincide with an E field component. Linear lumped components include elements such as short length of perfect conducting wire, resistor, capacitor, inductor and resistive voltage source. Associated with each lumped element is the I-V relation. A certain potential difference imposed across the lumped element will result in certain amount of current flowing ap --+ -= -div J + G -R at p (1) --+ aE--+ rotH = f>m-+ lc -+ ali rotE = -11-at