| (%i1) | load("/home/vcaeken/Desktop/rfMaxima.mac")$ |
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))); |
For V_GS<-Bv+50*Vt
| (%i60) | I_GS(Temp,V_GS):=-Is(Temp)*(1+exp(-(Bv+V_GS)/Vt))+Gmin*V_GS; |
For -Bv+50*Vt<=VGS<-5*Vt
| (%i61) | I_GS(Temp,V_GS):=-Is(Temp)+Gmin*V_GS; |
For V_GS>=-5*Vt
| (%i62) | I_GS(Temp,V_GS):=Is(Temp)*(exp(V_GS/(N*Vt))-1)+Gmin*V_GS; |
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); |
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); |
| (%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"])$ |
