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| =Steady-State= | | =Small-signal analysis= |
| | | *[[Sinusoidal Steady State Analysis]] |
| =Transient=
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| =Frequency domain=
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| ==Sinusoidal Steady State Analysis==
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| Consider the symbolic representation of the 3 device equations: Poisson, electron and hole continuity equations.
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| [[File:Dev_eqn.png|200px]] | |
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| The dot term represents the time derivative component of the electron and hole electron continuity equations.
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| Sinusoidal Steady State Analysis (S3A) solves the device equation system in the frequency domain as a steady state perturbed by an infinitesimal signal. The small signal assumption allows linearization of the device around the DC bias point. The corresponding Jacobian takes the symbolic form: | |
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| [[File:matrix.png|300px]]
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| which is a 3Nx3N matrix (for 3 solution variables and N nodes). Notice the imaginary frequency dependent components in the electron and hole rows corresponding to the time derivative dot term in the continuity equation.
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| The matrix equation now takes a form slightly different to the steady-state form JX=B.
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| [[File:matrix_eqn.png|130px]]
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| where J remains the steady-state Jacobian at the desired DC-bias point, D is now a diagonal matrix with zeros for Poisson rows and ω=2πf for diagonal elements of continuity rows. Both are 3Nx3N matrices. X is solution vector and B is boundary condition vector.
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| For computational reasons(i.e. seperating real and imaginary terms), the matrix system takes the following 6Nx6N form
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| [[File:final_matrix_eqn.png|200px]]
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| where XR and XI are real and imaginary components of the solution variables.
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| ====Examples====
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| ==== Examples ====
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| device
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| contact name=VSS voltage supply=$bias acreal
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| contact name=VSS voltage supply=0.0 acimag
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| device freq=100
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