Micro-Cap v7.1.6 / RM
.PDF
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=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 Vgs<VTO |
|
Ids=(KP•W/L)•(Vgs-VTO-.5•Vds)•Vds•(1+LAMBDA•Vds) |
|
Vgs-Vth>Vds |
|
Ids=(.5•KP•W/L)•(Vgs-VTO)2•(1+LAMBDA•Vds) |
|
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