Wiley
Member level 4
Re: a MoM question
Low frequency breakdown occurs when the capacitive part (scalar potential) of impedance matrix completely overwhelms the inductive part (vector potential) of the impedance matrix. We can split the impedance matrix into two parts: Z = Z_A + Z_Phi, where Z_A is the part of the impedance matrix due to the vector potential and Z_Phi is the part due to the scalar potential.
Z_A is proportional to frequency, but Z_Phi is inversely proportional to frequency. Not suprisingly, just like the impedance due to an inductor and a capacitor. At a certain frequency is Z_Phi is so much greater than Z_A, that numerically Z_Phi + Z_A = Z_Phi. Z_A is completely lost. Since we are solving a dynamic problem, both inductive and capacitive parts are important. However we have lost the inductive part and our impedance matrix becomes singular.
There are methods around this problem. Sonnet uses quad precision; you still have the fundamental problem, but the breakdown point is lowered by about seven decades. Ansoft Designer uses Loop/Tree, and I believe Momentum RF use Loop/Star.
Low frequency breakdown occurs when the capacitive part (scalar potential) of impedance matrix completely overwhelms the inductive part (vector potential) of the impedance matrix. We can split the impedance matrix into two parts: Z = Z_A + Z_Phi, where Z_A is the part of the impedance matrix due to the vector potential and Z_Phi is the part due to the scalar potential.
Z_A is proportional to frequency, but Z_Phi is inversely proportional to frequency. Not suprisingly, just like the impedance due to an inductor and a capacitor. At a certain frequency is Z_Phi is so much greater than Z_A, that numerically Z_Phi + Z_A = Z_Phi. Z_A is completely lost. Since we are solving a dynamic problem, both inductive and capacitive parts are important. However we have lost the inductive part and our impedance matrix becomes singular.
There are methods around this problem. Sonnet uses quad precision; you still have the fundamental problem, but the breakdown point is lowered by about seven decades. Ansoft Designer uses Loop/Tree, and I believe Momentum RF use Loop/Star.