Circuit Simulation

what devices are there?

Sparse Tableau Analysis (STA)
- KCL, KVL, BCR, incidence matrix

Nodal Analysis
1. A * i = 0
2. A * f(v) = 0
3. A * f(transpose(A) * e) = 0

Device stamps: filling in matrix A values by input inspection

Modified Nodal Analysis (MNA)

Is an ODE always solvable analytically?

DAE system: d/dt q(x(t)) + f(x(t)) + b(t) = 0
- x: unknowns; q(): charges/fluxes; f(): resistive; b(t): inputs

GE
- pivoting
- partial O(n), complete O(n^2)
- numerical stability problem
- O(n^3) complexity

LU factorization
- forward + backward substitution
- sparsity maintainance


Other topics: sensitivity analysis and noise analysis

* proving linearity of functions

Newton-Raphson Method
- assumptions:
- heuristics for solution
- step size
- initial condition
- (prove) quadratic convergence
- what are NR weaknesses?
- convergence
- abstol, reltol, and residual
- e ~ mV (10^-3), i ~ uA (10^-6)



Transient Simulation (DAE and ODE treatments)
- Lipschitz condition (existence and uniqueness)
- LMS: (FE, BE, TRAP) and their stability
- local truncation error
- how to choose step size based on truncation error
- global error
- Gear's Method

Smoothing
- step() function using tanh()


AC Analysis
DC Analysis
Transient Simulation