Solution Process

Basic Assumptions in Q3D Extractor

All electromagnetic phenomena, including capacitance and inductance effects, are described by Maxwell 's equations. These relate the electric field to the magnetic field in the presence of materials described by electric permittivity ε, conductivity σ and magnetic permeability μ.

In differential frequency-domain form, Maxwell 's equations are:

and

ρ denotes the density of free charges, j is the imaginary unit, and .

Q3D is based upon a simplification of Maxwell 's equations called the quasistatic approximation: it is assumed that the size of the structure to be analyzed is small compared to the wavelength at the maximum frequency of interest. A general rule of thumb is that the size of the structure should be less than one tenth of a wavelength. The wavelength is inversely proportional to frequency. In most printed circuit, IC and packaging materials it is approximately 15 cm at 1 GHz, and 1.5 cm at 10 GHz. This assumption allows Q3D to solve very complicated structures in an efficient way.

For structures that are larger than one tenth of a wavelength, a full-wave field solver (one that considers the two-way coupling between the electric and magnetic fields, such as HFSS) should be used. The full-wave solver will ensure that all electromagnetic phenomena are modeled, but may be more time-consuming to run than Q3D.