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(%i1) load("/home/vcaeken/Desktop/rfMaxima.mac")$

Result

MESFET Notebook

http://qucs.sourceforge.net/docs/MESFET.pdf
(See also: "A MESFET Model for Use in the Design of GaAs Integrated Circuits", Walter R. Curtice,
IEEE Transactions on Microwave Theory & Techniques, Vol. 28, No. 5, May 1980, pp. 448-456)

1 Curtice MESFET Model Parameters

Name: description [Unit]

Vto: pinch-off voltage [V]
Beta: transconductance parameter [A/V^2]
Alpha: saturation voltage parameter [1/V]
Lambda: channel length modulation parameter [1/V]
B: doping profile parameter [1/V]
Qp: power law exponent parameter
Delta: power feedback parameter [1/W]
Vmax: maximum junction voltage before cap. limiting [V]
Vdelta1: capacitance saturation transition voltage [V]
Vdelta2: capacitance threshold transition voltage [V]
Gamma: DC drain pull coefficient
Nsc: subthreshold conductance parameter
Is: diode saturation current [A]
N: diode emission coefficient
Vbi: built-in gate potential [V]
Bv: gate-drain junction reverse breakdown voltage [V]
Xti: diode saturation current temperature coefficient
Tau: transit time under gate [s]
Rin: channel resistance [Ohm]
Fc: forward-bias depletion capacitance coefficient
Area: area factor
Eg: bandgap voltage [eV]
M: grading coefficient
Cgs: zero-bias gate-source capacitance [F]
Cgd: zero-bias gate-drain capacitance [F]
Cds: zero-bias drain-source capacitance [F]
Betatc: Beta temperature coefficient [%/DegC]
Alphatc: Alpha temperature coefficient [%/DegC]
Gammatc: Gamma temperature coefficient [%/DegC]
Ng: subthreshold slope gate parameter
Nd: subthreshold drain pull parameter
ILEVELS: gate-source current equation selector
ILEVELD: drain-source current equation selector
QLEVELS: gate-source charge equation selector
QLEVELD: gate-source charge equation selector
QLEVELDS: drain-source charge equation selector
Vtotc: Vto temperature coefficient [V/DegC]
Rg: gate series resistance [Ohm]
Rd: drain series resistance [Ohm]
Rs: source series resistance [Ohm]
Rgtc: gate series resistance temperature coefficient [1/DegC]
Rdtc: drain series resistance temperature coefficient [1/DegC]
Rstc: source series resistance temperature coefficient [1/DegC]
Ibv: gate reverse breakdown current [A]
Rf: forward bias slope resistance [Ohm]
R1: breakdown slope resistance [Ohm]
Af: Flicker noise exponent
Kf: flicker noise coefficient
Gdsnoi: shot noise coefficient
Tnom: device parameter measurement temperature [DegC]
Temp: device circuit temperature [DegC]

(%i2) Vto:-1.8$
%beta:3e-3$
%alpha:2.25$
%lambda:0.05$
B:0.3$
Qp:2.1$
Delta:0.1$
Vmax:0.5$
Vdelta1:0.3$
Vdelta2:0.2$
Nsc:1$
Is:1e-14$
N:1$
Vbi:1.0$
Bv:60$
Xti:0$
%tau:1e-9$
Rin:1e-3$
Fc:0.5$
Area:1$
Eg:1.11$
M:0.5$
Cgs:0.2e-12$
Cgd:1e-12$
Cds:1e-12$
Betatc:0$
Alphatc:0$
Gammatc:0$
Ng:2.65$
Nd:-0.19$
ILEVELS:3$
ILEVELD:3$
QLEVELS:2$
QLEVELD:2$
QLEVELDS:2$
Vtotc:0$
Rg:5.1$
Rd:1.3$
Rs:1.3$
Rgtc:0$
Rdtc:0$
Rstc:0$
Ibv:1e-3$
Rf:10$
R1:10$
Af:1.0$
Kf:0.0$
Gdsnoi:1.0$
Tnom:26.85$
Temp:26.85$

2 MESFET Equations

2.1 DC Equations

Boltzmann's constant [J/K]
Electric charge [Coulombs]

(%i52) kB:1.3806503e-23$
q:1.6e-19$

(%i54) TK(Temp):=Temp+273.15$
TnK(Tnom):=Tnom+273.15$
Tr(Temp,Tnom):=TK(Temp)/TnK(Tnom)$
Vt(Temp):=kB*TK(Temp)/q$
Gmin:1e-12$

(%i59) Is(Temp):=Is*exp(Xti/N*ln(Tr(Temp,Tnom))-(Eg/N/Vt(Temp))*(1-Tr(Temp,Tnom)));

Result

For V_GS<-Bv+50*Vt

(%i60) I_GS(Temp,V_GS):=-Is(Temp)*(1+exp(-(Bv+V_GS)/Vt))+Gmin*V_GS;

Result

For -Bv+50*Vt<=VGS<-5*Vt

(%i61) I_GS(Temp,V_GS):=-Is(Temp)+Gmin*V_GS;

Result

For V_GS>=-5*Vt

(%i62) I_GS(Temp,V_GS):=Is(Temp)*(exp(V_GS/(N*Vt))-1)+Gmin*V_GS;

Result

For V_GS-Vto>0

(%i63) I_DS(V_DS,V_GS):=%beta*(V_GS-Vto)^2*(1+%lambda*V_DS)*tanh(%alpha*V_DS);

Result

2.2 Charge Equations

(%i64) Q_GS:Cgs*V_GS$
Q_GD:Cgd*V_GD$
Q_DS:Cds*V_DS+%tau*I_DS$

3 IV Curves

(%i67) kill(V_DS,V_GS);

Result

(%i68) wxplot2d([I_DS(V_DS,Vto),I_DS(V_DS,-1.5),I_DS(V_DS,-1),I_DS(V_DS,-0.5),I_DS(V_DS,0)],
    [V_DS,0,10],
    [legend,false],
    [xlabel,"V_DS [V]"],
    [ylabel,"I_DS [A]"],
    [style,[lines,3,11]],
    [style,[lines,3,11]],
    [style,[lines,3,11]],
    [style,[lines,3,11]],
    [style,[lines,3,11]],
    [gnuplot_preamble,"set grid"])$

Result


Created with wxMaxima.