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  3. Import a non-linear electro-thermal reduced-order model...

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Import a non-linear electro-thermal reduced-order model in SPECTRE ?

Herge
Herge over 10 years ago

The idea is the following : using a 3D finite-element tool, I  can generate a set of equations describing the electro-thermal behaviour of the on-chip  metal interconnections, as well as the bondwires and the package leads. In the end I get a large set of equations that describes the dynamic electro-thermal response of that "system".  This model can be reduced to a compacter representation that captures the essential dynamics (it has the same overall structure as the original model but a reduced size -- reduced order model )


This system of equations has the following structure  :

E*(dx/dt) = A*x + B*u + x*F*x + x * G * u

y = C*x+D*u

where x is a vector of state variable (voltages and temperatures), u is a vector of input variables (applied port voltages and temperatures as boundary conditions), y is a vector of output variables (port currents and thermal fluxes at the boundaries). A, B, C, D are the usual "system" matrices, F is a second order tensor, G also.

The question is : what is the best way to import the reduced order model (still having about 200 state variables, 20 inputs and 20 outputs) in SPECTRE ? 

(1) Can I misuse the NPORT model with option MATRIXFORM=YES ?  The idea would be to force to have all x listed along the original outputs in the y  vector, then compute the x(i) F(i,j) x(j) products using either a verilogA block or VCVS and reinject them as addtional u variables...

(2) Should I generate a VerilogA modue implementing the equations ? VerilogA can handle vectors as inputs and outputs, but no arrayed operations are available (as far as I am aware), so every equation must be spelled out explicitely (one can not write something like : matrixprod(A,x)).

(3) Any other suggestion ?

The motivation for doing this is that is to enable fast electro-thermal simulation of smart-power IC's "at system level", so that system architects can study various application-level scenarios (apply voltages and currents) and see how the thing heats and compute the impact on reliability.
Typically the IC model will consist on (a) the reduced electro-thermal model for the interconnect and the package, (b) core transistor models for key power devices (in VerilogA in order to have also thermal ports).

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