VALUE attribute
<value> may be a simple number or an expression involving time-domain variables. The expression is evaluated in the time domain only. Consider the expression:
100+I(L2)*2
I(L2) refers to the value of the L2 current, during a transient analysis, a DC operating point calculation prior to an AC analysis, or during a DC analysis. It does not mean the AC small signal L2 current. If the operating point value for L2 current was 2, the inductance would be evaluated as 100+2*2=104. The constant value, 104, is used in AC analysis.
FREQ attribute
If <fexpr> is used, it replaces the value determined during the operating point. <fexpr> may be a simple number or an expression involving frequency domain variables. The expression is evaluated during AC analysis as the frequency changes. For example, suppose the <fexpr> attribute is this:
10mh+I(L1)*(1+1E-9*f)/5m
In this expression, F refers to the AC analysis frequency variable and I(L1) refers to the AC small signal current through inductor L1. Note that there is no time-domain equivalent to <fexpr>. Even if <fexpr> is present, <value> will be used in transient analysis.
Initial conditions
The initial condition assigns an initial current through the inductor in transient analysis if no operating point is done (or if the UIC flag is set).
Stepping effects
Both the VALUE attribute and all of the model parameters may be stepped. If VALUE is stepped, it replaces <value>, even if it is an expression. The stepped value may be further modified by the quadratic and temperature effects.
Quadratic effects
If [model name] is used, <value> is multiplied by a factor, QF, which is a quadratic function of the time-domain current, I, through the inductor.
QF = 1+ IL1•I + IL2•I2
This is intended to provide a subset of the old SPICE 2G POLY keyword, which is no longer supported.
Temperature effects
The temperature factor is computed as follows:
If [model name] is used, <value> is multiplied by a temperature factor, TF.
TF = 1+TC1•(T-Tnom)+TC2•(T-Tnom)2
TC1 is the linear temperature coefficient and is sometimes given in data sheets as parts per million per degree C. To convert ppm specs to TC1 divide by 1E6. For example, a spec of 200 ppm/degree C would produce a TC1 value of 2E-4.
T is the device operating temperature and Tnom is the temperature at which the nominal inductance was measured. T is set to the analysis temperature from the Analysis Limits dialog box. TNOM is determined by the Global Settings TNOM value, which can be overridden with a .OPTIONS statement. T and Tnom may be changed for each model by specifying values for T_MEASURED, T_ABS, T_REL_GLOBAL, and T_REL_LOCAL. See the .MODEL section of Chapter 20, "Command Statements", for more information on how device operating temperatures and Tnom temperatures are calculated.
Monte Carlo effects
LOT and DEV Monte Carlo tolerances, available only when [model name] is used, are obtained from the model statement. They are expressed as either a percentage or as an absolute value and are available for all of the model parameters except the T_parameters. Both forms are converted to an equivalent tolerance percentage and produce their effect by increasing or decreasing the Monte Carlo factor, MF, which ultimately multiplies the final value.
MF = 1 ± tolerance percentage /100
If tolerance percentage is zero or Monte Carlo is not in use, then the MF factor is set to 1.0 and has no effect on the final value.
The final inductance, lvalue, is calculated as follows:
lvalue = <value> * L * QF * TF * MF
408 Chapter 22: Analog Devices
Model statement form
.MODEL <model name> IND ([model parameters])
Examples
.MODEL LMOD IND (L=2.0 LOT=10% IL1=2E-3 IL2=.0015)
.MODEL L_W IND (L=1.0 LOT=5% DEV=.5% T_ABS=37)
Model parameters |
|
|
|
Name |
Parameter |
Units |
Default |
L |
Inductance multiplier |
|
1 |
IL1 |
Linear current coefficient |
A-1 |
0 |
IL2 |
Quadratic current coefficient |
A-2 |
0 |
TC1 |
Linear temperature coefficient |
°C-1 |
0 |
TC2 |
Quadratic temperature coefficient |
°C-2 |
0 |
T_MEASURED |
Measured temperature |
°C |
|
T_ABS |
Absolute temperature |
°C |
|
T_REL_GLOBAL |
Relative to current temperature |
°C |
|
T_REL_LOCAL |
Relative to AKO temperature |
°C |
|
Noise effects
There are no noise effects included in the inductor model.
Isource
Schematic format
PART attribute <name>
Examples
I1
CURRENT_SOURCE
VALUE attribute <value>
Examples 1U
10
The Isource produces a constant DC current. It is implemented internally as a SPICE independent current source.
410 Chapter 22: Analog Devices
JFET
SPICE format
Syntax
J<name> <drain> <gate> <source> <model name> + [area] [OFF] [IC=<vds>[,vgs]]
Example
J1 5 7 9 2N3531 1 OFF IC=1.0,2.5
Schematic format
PART attribute <name>
Example
J1
VALUE attribute
[area] [OFF] [IC=<vds>[,vgs]]
Example
1.5 OFF IC=0.05,1.00
MODEL attribute <model name>
Example
JFET_MOD
The value of [area], whose default value is 1, multiplies or divides parameters as shown in the table. The [OFF] keyword turns the JFET off for the first operating point iteration. The initial condition, [IC= <vds>[,vgs]], assigns initial drain-source and gate-source voltages. Negative VTO implies a depletion mode device and positive VTO implies an enhancement mode device. This conforms to the SPICE 2G.6 model. Additional information on the model can be found in reference (2).
Model statement forms
.MODEL <model name> NJF ([model parameters])
.MODEL <model name> PJF ([model parameters])
411
Examples
.MODEL J1 NJF (VTO=-2 BETA=1E-4 LAMBDA=1E-3)
.MODEL J2 PJF (VTO= 2 BETA=.005 LAMBDA=.015)
Model Parameters |
|
|
|
Name |
Parameter |
Units |
Def. Area |
VTO |
Threshold voltage |
V |
-2.00 |
|
BETA |
Transconductance parameter |
A/V2 |
1E-4 |
* |
LAMBDA |
Channel-lengthmodulation |
V-1 |
0.00 |
|
RD |
Drain ohmic resistance |
Ω |
0.00 |
/ |
RS |
Source ohmic resistance |
Ω |
0.00 |
/ |
CGS |
Zero-bias gate-source junction cap. |
F |
0.00 |
* |
CGD |
Zero-bias gate-drain junction cap. |
F |
0.00 |
* |
M |
Gate junction grading coefficient |
|
0.50 |
|
PB |
Gate-junctionpotential |
V |
1.00 |
|
IS |
Gate-junction saturation current |
A |
1E-14 |
* |
FC |
Forward-bias depletion coefficient |
|
0.50 |
|
VTOTC |
VTO temperature coefficient |
V/°C |
0.00 |
|
BETATCE |
BETA exp. temperature coefficient |
%/°C |
0.00 |
|
XTI |
IS temperature coefficient |
|
3.00 |
|
KF |
Flicker-noise coefficient |
|
0.00 |
|
AF |
Flicker-noise exponent |
|
1.00 |
|
T_MEASURED |
Measured temperature |
°C |
|
|
T_ABS |
Absolute temperature |
°C |
|
|
T_REL_GLOBAL Relative to current temperature |
°C |
|
|
T_REL_LOCAL |
Relative to AKO temperature |
°C |
|
|
Model equations
Figure 22-11 JFET model
412 Chapter 22: Analog Devices
Notes and Definitions
Parameters BETA, CGS, CGD, and IS are multiplied by [area] and parameters RD and RS are divided by [area] prior to their use in the equations below.
Vgs = Internal gate to source voltage
Vds = Internal drain to source voltage
Id = Drain current
Temperature Dependence
T is the device operating temperature and Tnom is the temperature at which the model parameters are measured. Both are expressed in degrees Kelvin. T is set to the analysis temperature from the Analysis Limits dialog box. TNOM is determined by the Global Settings TNOM value, which can be overridden with a .OPTIONS statement. Both T and Tnom may be customized for each model by specifying the parameters T_MEASURED, T_ABS, T_REL_GLOBAL, and T_REL_LOCAL. See the .MODEL section of Chapter 20, "Command Statements", for more information on how device operating temperatures and Tnom temperatures are calculated.
VTO(T) = VTO + VTOTC•(T-Tnom)
BETA(T) = BETA•1.01BETACE•(T-Tnom)
IS(T) = IS•e1.11•(T/Tnom-1)/VT•(T/Tnom)XTI
EG(T) = 1.16 - .000702•T2/(T+1108)
PB(T) = PB•( T/Tnom)- 3•VT•ln((T/Tnom))-EG(Tnom)•(T/Tnom)+EG(T)
CGS(T) = CGS•(1+M•(.0004•(T-Tnom) + (1 - PB(T)/PB)))
CDS(T) = CDS•(1+M•(.0004•(T-Tnom) + (1 - PB(T)/PB)))
Current equations
Cutoff Region : Vgs ≤ VTO(T)
Id = 0
Saturation Region : Vds > Vgs - VTO(T)
Id=BETA(T)•(Vgs - VTO(T))2•(1+LAMBDA•Vds)
Linear Region : Vds < Vgs - VTO(T)
Id=BETA(T)•Vds•(2•(Vgs - VTO(T))- Vds)•(1+LAMBDA•Vds)
Capacitance equations
If Vgs ≤ FC • PB(T) then
Cgs = CGS(T)/(1 - Vgs/PB(T))M Else
Cgs = CGS(T)•(1 - FC•(1+M)+M•(Vgs/PB(T)))/ (1 - FC) (1-M)
If Vgd ≤ FC • PB(T) then
Cgd = CGD(T)/(1 - Vgd/PB(T))M Else
Cgd = CGD(T)•(1 - FC•(1+M)+M•(Vgd/PB(T)))/ (1 - FC) (1-M)
Noise
The resistors RS and RD generate thermal noise currents.
Ird2 = 4•k•T / RD
Irs2 = 4•k•T / RS
The drain current generates a noise current.
I2 = 4•k•T•gm•2/3 + KF•IdAF / Frequency where gm = ∂ Id / ∂ Vgs (at operating point)
414 Chapter 22: Analog Devices
K (Mutual inductance / Nonlinear magnetics model)
SPICE formats
K<name> L<inductor name> <L<inductor name>>* + <coupling value>
K<name> L<inductor name>* <coupling value> + <model name>
Examples
K1 L1 L2 .98
K1 L1 L2 L3 L4 L5 L6 .98
Schematic format
PART attribute <name>
Example
K1
INDUCTORS attribute
<inductor name> <inductor name>*
Example
L10 L20 L30
COUPLING attribute <coupling value>
Example 0.95
MODEL attribute [model name]
Example
K_3C8
If <model name> is used, there can be a single inductor name in the INDUCTORS attribute. If model name is not used, there must be at least two inductor names in the INDUCTORS attribute.
The K device specifies the linear mutual inductance between two or more inductors. You can optionally specify a nonlinear magnetic core.
Coupled linear inductors
In this mode, the K device provides a means to specify the magnetic coupling between multiple inductors. The equations that define the coupling are:
dIi |
|
dIj |
|
dIk |
|
Vi = Li dt |
+ Mij |
|
+ Mik |
|
+ ... |
dt |
dt |
where Ii is the current flowing into the plus lead of the i'th inductor. For linear inductors, <model name> is not used.
Nonlinear magnetic core(s)
If a <model name> is supplied, the following things change:
1.The linear K device becomes a nonlinear magnetic core. The model for the core is a variation of the Jiles-Atherton model.
2.Inductors are interpreted as windings and each inductor <value> is interpreted as the number of turns for the winding. In this case, <value> must be a constant whole number. It may not be an expression.
3.The list of coupled inductors may contain just one inductor. Use this method to create a single magnetic core device, not coupled to another inductor.
4.A model statement is required to define the model parameters or <model name> must be in the model library referenced by .LIB statements.
The nonlinear magnetics model is based on the Jiles-Atherton model. This model is based upon contemporary theories of domain wall bending and translation. The anhysteretic magnetization curve is described using a mean field approach. All magnetic domains are coupled to the bulk magnetization and magnetic fields. The anhysteretic curve is regarded as the magnetization curve that would prevail if there were no domain wall pinning. Of course, such pinning does occur, mainly at defect sites. The hysteresis effect that results from this pinning is modeled as a simple frictional force, characterized by a single constant, K. The resulting state equation produces a realistic ferromagnetic model.
The Core is modeled as a state-variable nonlinear inductor. MC7 solves a differential equation for the B and H fields and derives the terminal current and voltage
416 Chapter 22: Analog Devices
