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| =Small-signal analysis= | | =Small-signal analysis= |
| *[[Sinusoidal Steady State Analysis]] | | *[[Sinusoidal Steady State Analysis]] |
| Sinusoidal Steady State Analysis is typically used to carry out small-signal analysis for extracting capacitance, transconductance, current-gain and cut-off frequencies. Even without energy balance/hydrodynamic model, accurate results can be obtained up to several GHz.
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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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| device
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| contact name=VSS voltage supply=1.0 acreal
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| contact name=VSS voltage supply=0.0 acimag
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| device freq=100
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| First device does a steady-state solution at previously provided bias point.
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| Setting "real" supply to unity would be recommended as response is linear (also convenient for obtaining conductance directly from current).
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| Small-signal of 100 Hz is applied at the chosen contact.
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| For a highly doped resistor, consider just electron current.
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| set Re_cur ([contact name=VSS sol=Elec flux acreal])]
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| set Im_cur ([contact name=VSS sol=Elec flux acimag])]
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| As expected for low resistance, real current Re_cur will be high and imaginary current Im_cur due to capacitive component will be extremely low.
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