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# Micro-Cap v7.1.6 / RM

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 Title Vbe vs. Ic Purpose This screen estimates IS, NF, and RE. Input One or more pairs of Vbe and Ic values. Output Model values for IS, NF, and RE. Equations Vbe=VT•NF•log(Ic/IS)+Ic•RE Guidelines Use data from the VbeSat vs. Ic graphs. If unavailable, use typical values.
 Title Hoe vs. Ic Purpose This screen estimates the forward Early voltage, VAF. Input One or more pairs of Hoe and Ic values. Conditions The value of Vce. Output Model values for VAF. Equations Hoe = Ic / (VAF+Vce-0.7) Guidelines Use the Hoe vs. Ic graphs. If unavailable, use typical values.
 Title Beta vs. Ic Purpose This screen estimates the parameters, NE, ISE, BF, and IKF. These parameters model the low-current recombination and high-level injection effects that produce a drop-off in the forward beta. Input One or more pairs of Beta and Ic values. Conditions The value of Vce. Output Model values NE, ISE, BF, and IKF. Equations BF= f(Ic) = simulated tabular function of BF vs. Ic Guidelines Use the Beta vs. Ic graph. If unavailable, use typical table values.
 Title Vce vs. Ic Purpose This screen estimates NC, ISC, BR, IKR, and RC. These model the low-current recombination and high-level injection effects that cause reverse beta drop-off. The collector resistance is also estimated. Input One or more pairs of Vce and Ic values. Conditions The value of the Ic/Ib ratio used in the measurement. Output Model values NC, ISC, BR, IKR, and RC. Equations Vce = (simulated tabular function of Vce vs. Ic)+Ic•(RC+RE) Guidelines Use the Vce vs. Ic graphs. If unavailable, use typical table values.

257

 Title Cob vs. Vcb Purpose This screen estimates CJC, MJC, VJC, and FC. Input One or more pairs of Cob and Vcb values. Output Model values for CJC, MJC, VJC, and FC. Equations Cob = CJC/(1+Vcb/VJC)MJC Guidelines Use the Cob vs. Vcb graphs. Vcb is the value of the collector-base voltage and is always positive.
 Title Cib vs. Veb Purpose This screen estimates CJE, MJE, and VJE. Input One or more pairs of Cib and Veb values. Output Model values for CJE, MJE, and VJE. Equations Cib = CJE/(1+Veb/VJE)MJE Guidelines Use the Cib vs. Veb graphs. Veb is the value of the emitter-base voltage and is always positive.
 Title TS vs. Ic Purpose This screen estimates Tr, the reverse transit time value. Input One or more pairs of TS and Ic values. Conditions The value of the Ic/Ib ratio used in the measurement. Output Model value for Tr. Equations ar = br/(1.0+br) , af=bf/(1.0+bf) k1 = (1.0-af•ar)/ar , k2=(af/ar)•TF TS = ((Tr+k2)/k1)•ln(2.0/((Ic/Ib)/bf+1.0)) Guidelines Use the TS vs. Ic graphs. Use a typical value. If the typical value is unavailable, use an average of the min and max values.
 Title Ft vs. Ic Purpose This screen estimates TF, ITF, XTF, and VTF. Input One or more pairs of Ft and Ic values. Conditions The value of Vce. Output Model values for TF, ITF, XTF, and VTF. Equations vbe=VT•N•ln(Ic/ISS), vbc = vbe - Vce atf=1+XTF•(Ic/(Ic+ITF))2•e(vbc/(1.44•VTF)) tf =TF•(atf+2•(atf-1)•ITF/(Ic+ITF)+VT•N•(atf-1)/(1.44•VTF)) fa =(1-vbc/VAF)•(1-vbc/VAF) Ft =1/(2•PI•(tf/fa+VT•N•(cje+cjc•(1+Ic•RC/(VT•N)))/Ic)) Guidelines Use data from the Ft vs. Ic graphs. If unavailable, use typical values from the tables. If the typical value is unavailable, use an average of the min and max values.

258 Chapter 17: The MODEL Program JFET graphs

 Title Id vs. Vgs Purpose This screen estimates the value of BETA, VTO, and RS. Input Values for Vgs and Id. Output Model values for BETA, VTO, and RS. Equations Vgs = RS•Id - VTO - sqrt(Id/BETA)
 Title Gos vs. Id Purpose This screen estimates the value of LAMBDA. Input Enter values for Gos and Id. Output Model value for LAMBDA. Equations Gos = Id•LAMBDA
 Title Crss vs. Vgs Purpose This screen estimates the value of CGD, PB, and FC. Input Enter values for Crss and Vgs. Conditions The value of Vds at which the capacitance was measured. Output Model values for CGD, PB, FC. Equations Crss=CGS/(1-(Vds-Vgs)/PB).5 {(Vds-Vgs)< FC•PB} Crss=CGS/(1-FC)1.5•(1-FC•1.5+.5•(Vds-Vgs)/PB) {(Vds-Vgs)>=FC•PB}
 Title Ciss vs. Vgs Purpose This screen estimates the value of CGS. Input Enter values for Ciss and Vgs. Conditions The value of Vds at which the capacitance was measured. Output Model value for CGS. Equations Crss=Ciss+CDS/(1-Vgs/PB).5 {Vgs< FC•PB Crss=Ciss+CDS/(1-FC)1.5•(1-FC•1.5+.5•Vgs/PB){Vgs>=FC•PB}
 Title Noise Purpose This screen estimates the value of KF and AF. Input Enter the values of En and frequency. Conditions The value of Ids at which the measurement is made. Output Model values for KF and AF. Equations vgs = VTO + Id•RS + sqrt(Id/BETA) gm = 2.0•BETA •(vgs - VTO) En = sqrt((8•k•T•gm)/3 + (KF•IDAF) / freq)/gm

259 MOSFET graphs

All voltage and current values are entered as positive quantities for N-channel devices and negative quantities for P-channel devices.

 Title Transconductance vs. Ids graph Purpose This screen estimates KP, W, L, VTO, and RS. Input One or more pairs of Gfs and Ids values. Output Model values KP, RS, W, VT, L. Equations beta = KP•W/L t1 = (2•Ids•beta)1/2 Gfs = t1 / (1+RS•t1) Guidelines Use data from the Gfs vs. Id curves. If unavailable, use typical values from the specification tables. Use data points from the highest current values to get the most accurate value of RS.
 Title Static drain-source on resistance vs. Drain current Purpose This screen estimates RD from the Ron vs. Id curves. Input One or more pairs of Ron and Id values. Conditions The value of Vgs. Output Model value for RD. Equations beta = KP•W/L vgst = Vgs - VTO - Id•RS vds = vgst - (vgst2-2•Id/beta)1/2 RON = RD + RS + 1/(beta•(vgst - vds)) Guidelines Use data from the Ron vs. Id curves. If unavailable, use typical values from the tables. Use low current values for the best results.
 Title Output Characteristic Curves Purpose This screen estimates all of the principal model values except the capacitance values. It uses the already estimated values of W, VTO, RD, RS, LAMBDA, KP, and L as an estimate and optimizes the fit of the characteristic Id vs Vds curves to the user data points. Input Triplets of Ids, Vds, and Vgs values. Output Model values for W, VTO, RD, RS, LAMBDA, KP, and L. KP and L are not optimized but are used in the calculation. Equations Ids=0.0 VgsVds Ids=(.5•KP•W/L)•(Vgs-VTO)2•(1+LAMBDA•Vds) Vgs-Vth

260 Chapter 17: The MODEL Program

 Guidelines If the previous screens have been used, do not initialize before optimizing. Otherwise, use the initialize option prior to optimizing. If the Output Characteristic Curves are not available, skip this screen and use the model values from the prior screens. Title Idss vs Vds Purpose This screen estimates RDS, the fixed resistor connected from drain to source. It models the drain-source leakage. Input One pair of Idss and Vds values. Output Model value for RDS. Equations RDS=Vds/Idss Guidelines Use data from the specification tables or from the graphs. Title Cds vs Vds Purpose This screen estimates the values of CBD, PB, and MJ. Input The values of Ciss, Coss, and Crss. Output Model values for CBD, PB, FC, and MJ. Equations Cds= CBD / (1-Vds/PB)MJ Guidelines Use data from the specification tables or from the graphs. Title Vgs vs Qg Purpose This screen estimates the values of CGSO and CGDO. Input Enter Q1 and Q2. Q1 is the gate charge at the first breakpoint in the graph. Q2 is the gate charge at the second breakpoint. Conditions The values of VDS(or VDD) and ID for the measurement. Output Model values for CGSO and CGDO. Equations The program runs a circuit simulation and measures Vgs and Qgs. Guidelines Use data from the specification tables or from the graphs. Title Gate Resistance Purpose This screen estimates the value of RG, the gate resistance. Input Enter the value of Tf, the 90% to 10% fall time. Conditions The values of VDD and ID at which the measurement is made. Output Model value for RG. Equations The program runs a circuit simulation, measures the fall time and adjusts RG to fit the specified value of Tf. Guidelines Use data from the specification tables or from the graphs.

261 Opamp graphs

 Title Screen 1 Purpose This screen provides for direct entry of the model parameters from the data sheets. The parameters are: LEVEL :Model level (1,2,3). Always use level 3. TYPE :1=NPN, 2=PNP, 3=NJFET input C :Compensation capacitor A :DC open-loop voltage gain ROUTAC :AC output resistance ROUTDC :DC output resistance VOFF :Offsetvoltage Input Values for LEVEL, TYPE, C, A, ROUTAC, ROUTDC, and VOFF. Output Values for LEVEL, TYPE, C, A, ROUTAC, ROUTDC, and VOFF.
 Title Screen 2 Purpose This screen provides for direct entry of the model parameters from the data sheets. The parameters are: IOFF :Input offset current SRP :Positive slew rate (V/Sec) SRN :Negative slew rate (V/Sec) IBIAS :Input bias current VEE :Negative power supply VCC :Positive power supply VPS :Positivevoltageswing Input Values for IOFF, SRP, SRN, IBIAS, VEE, VCC, and VPS. Output Values for IOFF, SRP, SRN, IBIAS, VEE, VCC, and VPS.
 Title Screen 3 Purpose This screen provides for direct entry of the model parameters from the data sheets. The parameters are: VNS :Negative voltage swing CMRR :Common mode rejection ratio GBW :Gainbandwidth PM :Phase margin PD :Powerdissipation IOSC :Output short-circuit current Input Values for VNS, CMRR, GBW, PM, PD, and IOSC. Output Values for VNS, CMRR, GBW, PM, PD, and IOSC.

262 Chapter 17: The MODEL Program Core graph

 Title Core B-H Purpose This screen estimates the nonlinear magnetic core model values MS, ALPHA, A, C, and K. Model values for Area, Path, and Gap are entered directly from the data sheet table. Input Triplets of H, B, and Region values. Output Model values for MS, ALPHA, A, C, and K. Equations Jiles-Atherton state equations. Guidelines Enter the data from the B-H graph. H is entered in Oersteds, B in Gauss, and the Region value is 1, 2, or 3. Region Value Otherwise known as: H = 0 to Hmax 1.0 Initial permeability curve H = Hmax to - Hmax 2.0 Top B-H curve H = - Hmax to Hmax 3.0 Bottom B-H curve

If the Initial permeability curve is unavailable, skip it and enter values for regions 2 and 3. For the best results, enter an equal number of data points for each region. Sometimes only the top part of the B-H curve is given. In this case, select an equal number of data points from each of the given parts of the three regions.

Enter the data for each core material first. Once a particular material is modeled, copy the part and use the copy as a template to model parts that use the same material, but have different values of Area, Path, or Gap. This avoids duplication of the same B-H curve.

263

264 Chapter 17: The MODEL Program Chapter 18 Convergence

What's in this chapter

This chapter describes convergence, or the lack thereof. It explains the source of many non-convergence error messages and some of the remedies available.

265 Convergence defined

To do its work, Micro-Cap 7 must solve nonlinear equations. Neither people nor computers are able to solve these equations analytically, so they must be solved numerically. There are many techniques for numerically solving equations, but they all rely upon a rule that tells the algorithm when to stop. Usually it is embodied in a piece of code like this:

while (error > RELTOL*V + VNTOL and iterations < MAXITERATIONS)

{

error=Solve(); iterations = iterations +1;

}

This code says to continue iterating the solution while the error is greater than some tolerance and we have not yet exceeded the specified maximum number of iterations. The error itself is defined as the difference in successive estimates of the final answer. Thus, if we get the same answer from one iteration to the next, or at least the difference between two successive answers is less than some acceptable tolerance then we say the solution converged, and the answer at this one data point is accepted as correct.

This criteria is checked for every nonlinear variable in the circuit. If any of these variables fails to converge, then the infamous message,

"Internal time step too small",

or one of its many cousins, is issued.

Convergence checks are applied during each nonlinear analysis operation, including the transient and AC analysis operating point calculations, all transient analysis data points, and all DC transfer analysis data points. The linear part of AC analysis is the only part when convergence checking is not necessary.

Convergence is the agreement of successive approximations to an answer.

266 Chapter 18: Convergence

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