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Bipolar transistor graphs

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=VTNFlog(Ic/IS)+IcRE

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-afar)/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=VTNln(Ic/ISS), vbc = vbe - Vce

 

atf=1+XTF(Ic/(Ic+ITF))2e(vbc/(1.44•VTF))

 

tf =TF(atf+2(atf-1)ITF/(Ic+ITF)+VTN(atf-1)/(1.44VTF))

 

fa =(1-vbc/VAF)(1-vbc/VAF)

 

Ft =1/(2PI(tf/fa+VTN(cje+cjc(1+IcRC/(VTN)))/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 = RSId - 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 = IdLAMBDA

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)< FCPB}

 

Crss=CGS/(1-FC)1.5(1-FC1.5+.5(Vds-Vgs)/PB)

 

 

{(Vds-Vgs)>=FCPB}

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< FCPB

 

Crss=Ciss+CDS/(1-FC)1.5(1-FC1.5+.5Vgs/PB){Vgs>=FCPB}

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 + IdRS + sqrt(Id/BETA)

 

gm = 2.0BETA (vgs - VTO)

 

En = sqrt((8kTgm)/3 + (KFIDAF) / 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 = KPW/L

 

t1 = (2Idsbeta)1/2

 

Gfs = t1 / (1+RSt1)

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 = KPW/L

 

vgst = Vgs - VTO - IdRS

 

vds = vgst - (vgst2-2Id/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 Vgs<VTO

 

Ids=(KPW/L)(Vgs-VTO-.5Vds)Vds(1+LAMBDAVds)

 

Vgs-Vth>Vds

 

Ids=(.5KPW/L)(Vgs-VTO)2(1+LAMBDAVds)

 

Vgs-Vth<Vds

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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