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Spice algorithms: conductance or capacitance?

Discussion in 'CAD' started by ldg, Sep 17, 2003.

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  1. ldg

    ldg Guest

    Does anyone know why most simulators are still based on conductance
    rather than capacitance and charge? I know Berkeley went conductance
    initially, but it seems that capacitance would have some advantages.

    For instance, I've been told that singularity issues don't happen with
    a capacitance based algorithm in that the time step is in the
    numerator rather than the denominator of the equation. Is this so?

    Also, from what I've been told, Saber is capacitance based.

    What are the advantages and disadvantages of each algorithm (short

  2. Larry,
    The usual trade-offs are between using a Norton equivalent
    vs Thevenin equivalent for capacitances and then whether to
    integrate an expression for the non-linear capacitances or
    have an expression of the charge and compute the capacitance
    as something symbolically differentiated from this charge
    expression. Two different issues.

    Most simulators solve for [V] in [G][V]=. There, on Norton
    vs Thevenin, Norton is good for capacitances for large time
    steps but causes singularities at short timesteps since the
    conductance goes infinate at short time steps. Since you have
    to be able to solve DC, you end up needing a Norton equivalent
    for capacitances so that matrix isn't singular. By the same
    token, inductors are done as Thevenin so that the DC solution
    can be found. I you didn't use [G][V]= but [R]=[V],
    then you'd use Thevenin for capacitances and Nortons for inductors.
    Since each Thevenin equivalent has an internal node, the matrix
    becomes larger[I think you'd also have to hack out some
    MBA(Modified Branch Analysis)]So [G][V]= makes a smaller
    matrix if you have more capacitances than inductors and need
    to solve DC. I'm guessing this is what you mean by a
    conductance-based simulator.

    Note that if you include the devices' series resistances, then
    you prevent the singularity for capacitances at short timesteps
    and can also use a Norton equivalent for inductors. Both of
    these also reduce the circuit matrix by one row and column
    and is a method used in LTspice, but it requires one to write
    integrators than can integrate the series resistance as
    an intrinsic part of the pure reactance. This is a technique
    I developed and haven't seen others duplicate. I know the
    academic SPICE codes don't have anything like it but I don't
    know if simulators like Spectre or Saber do.

    As far as charge vs capacitance, charge is the way to go, since
    the solution won't wander off conservation -- if you can get an
    expression for the charge. But, this issue is usually not
    too important unless you are doing something like designing
    DRAM cells because of the floating gates.

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