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這是小弟寫的文章 編講義用的 歡迎高手同行找碴:( W4 i% Y! @; @5 G W
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This section highlights the importance of an accurate pre-determined DC compact model.\cite{dc!!!}* b0 E. q/ u4 b
For compact model developers, extraction of the DC parameters always needs to be carried out before the extraction of AC ones.
8 B3 E6 {9 N# r$ j& I1 zFor devices measurement, DC measurement has to be carried out before AC measurement.
3 a* ^) c3 I9 ?; G9 t C7 y: o0 [' Y( pFor modern IC designers, DC analysis needs to be carried out before AC analysis.\cite[4.6.4]{smith!}* ~) i$ _6 u' L" ~5 u; t
For SPICE-like simulators, DC simulation also needs to be swept first and then follows by AC simulation.\cite{nlz!}
' R% ]$ G& F0 S: U) vFrom the device-level perspectives,
1 Z7 \1 r6 d! Q5 M% sa set of equations which describe the terminal characteristics of DUT are written in a compact model.
9 Y3 B9 |1 U, xThe equations are solved by SPICE-like simulators.; {) M6 t: e" Z# O
The procedure of establishing equations, describing device's electrical characteristics, in a compact model
) ~/ i: z- `% N: r8 o- c# Mand have them solved by SPICE-like simulators is termed as: Device Characterization.
c, z. {$ ~) ?The fully Characterizations are treated by two independent steps:7 u6 u9 A9 ]! z
(1)DC Characterization or DC parameters extraction+ n1 K9 l4 r2 \4 i
(2)AC Characterization or AC parameters extraction
- m4 f2 g( c9 l% c+ e( E: HCharacterizing a nonlinear electronics component always begins with0 {! N' D* v* }# \
DC characterization and follows by the AC characterization.4 ~+ D5 q! u3 M& g0 {9 D
Because the AC model is origined from the linearization of the DC model at an indicated operating point.+ ^! x- X- s# `6 p7 x5 y- r( ~% c2 s
Accordingly, accuracy is highly required in DC characterization because of its piority in the procedure of parameter extraction ./ b8 C _9 w4 Z: ]( Z3 T
! [9 Z6 ]8 s; F/ x, g- kFrom the circuit-level perspectives,,$ G# j; u0 t1 A5 m% k; N
Circuit analysis refers to solving a circuit with KVL and KCL.
) d& ?6 G. U7 E; a' HTo be more specific, it means solving out nodes voltages and branches currents of each element in a circuit.
' o- v0 x) p0 u& AAs the source of stimulus can be systematically separated into DC sources and AC sources,! h" ~! V9 b k! G
the unknown/solutions of the circuit are also separated into DC part and AC part.& ^( K. u! b. D
Analyzing a circuit is treated in two independent meansA)DC analysis (B)AC analysis& J+ Z& ]: Z6 M2 l, I/ S
The separation between DC analysis and AC analysis greatly simplified a complex circuit./ Q1 ?* K' ]2 }2 l; d
DC analysis is being carried out before AC analysis.
% Y. U: p$ ?/ i. c {- xDC analysis determines the Q-point, including each node voltage and branch current.
- D% J$ K6 i! p L( H E: sAC analysis gives the frequency response, including bandwidth and gain.( m- ^9 ~" E3 E4 c* r
Before performing AC Analysis, the DC operating point needed to be calculated from DC analysis first.8 k( j& \" E, [2 a( N
This is to construct a linear small-signal model for the nonlinear component.! q: \; V5 [& O8 l* V% i1 Z
So, the small signal (AC) response is highly dependent upon the presetting (DC) bias condition .
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. u, c, N9 O6 ]3 _6 mDC simulation in analog SPICE-like simulator, aims for computing the equilibrium points,
0 I( [: q3 l6 s$ M4 ?+ D0 Iwhich are the calculated DC node voltages and DC branch currents in a circuit.
8 O6 [6 N Q! q" v) W3 f) `# W. eThey are the DC solutions of the DC equivalent equation/circuit.6 @! f3 R( @! k& L8 n- B! c6 Q* l* [' _
A circuit will only reach its equilibrium if its stimulus is off3 p8 [; i' t0 ~
and the independent sources are remain constantly employed.
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3 O# E# S, ]: e( {: T$ r+ HThere is an important reason why a given electronics circuit always
; M0 u7 |, P: O* Fneed to be reduced into a DC equivalent circuit (large-signal model)
4 P, L( Z. d% u+ Aand followed by an AC equivalent one(small-signal model).
B. N# j8 S' e" {3 uIt has to do with the present of an active component in the circuit.1 p) ?$ {' g1 B; m% Z9 n- M
The active component is a nonlinear element.So, it will have to be linearized.
7 l0 b% d5 ^( i6 B- b. [The employment of active elements, like transistors, make the circuit a nonlinear algebra system.
3 {1 ~, n5 A0 ]# dNormally, the nonlinear equation can only be solved by means of iterative methods,
& ?+ D/ T: s; {& }, msuch as Newton-Raphson algorithm \cite{nlz!}. This algorithm transforms the solutions$ B9 D" j: Z) z8 H5 j) V
of the nonlinear equation into a sequence of linear equation.
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