NARROW narrowing due to side etching meters 0.0 1e-7
.TE
.sp 0.1i
.pp
The capacitor has a capacitance computed as
.EQ
CAP = CJ times ( LENGTH - NARROW ) times ( WIDTH - NARROW ) + 2 times CJSW times ( LENGTH + WIDTH - 2 * NARROW )
.EN
.sp 0.2i
.sh 2 "Uniform Distributed RC Model"
.sp 0.1i
.pp
The URC model is derived from a model proposed by L. Gertzberrg in
1974.
The model is accomplished by a subcircuit type expansion of the
URC line into a network of lumped RC segments with internally
generated nodes. The RC segments are in a geometric
progression, increasing toward the middle of the URC line, with
K as a proportionality constant. The number of lumped segments
used, if not specified on the URC line card, is determined by the
following formula:
.EQ
N = {log left [ {F sub max} times {R over L} times {C over L} times 2 times pi times {l sup 2} times left ( { { ( K - 1 ) } over K} right ) sup 2 right ]} over { log K }
.EN
.pp
The URC line will be made up strictly of resistor and capacitor
segments unless the ISPERL parameter is given a non-zero value,
in which case the capacitors are replaced with reverse biased
diodes with a zero-bias junction capacitance equivalent to the
capacitance replaced, and with a saturation current of ISPERL
amps per meter of transmission line and an optional series
resistance equivalent to RSPERL ohms per meter.
.TS
center;
l l l l l l l.
name parameter units default example area
.sp 0.2i
1 K Propagation Constant - 2.0 1.2 -
2 FMAX Maximum Frequency of interest Hz 1.0G 6.5MEG -
3 RPERL Resistance per unit length Ohm/m 1000 10 -
4 CPERL Capacitance per unit length F/m 1.0E-15 1PF -
5 ISPERL Saturation Current per unit length Amp/m 0 - -
6 RSPERL Diode Resistance per unit length Ohm/m 0 - -
.TE
.sp 0.2i
.sh 2 "Switch Model"
.sp 0.1i
.pp
The switch model allows an almost ideal switch to be described in SPICE.
The switch is not quite ideal, in that the resistance can not
change from 0 to infinity, but must always have a finite positive value.
By proper selection of the on and off resistances, they can
be effectively zero and infinity in comparison to other circuit elements.
The parameters available are:
.TS
center;
l l l l l.
name parameter units default switch
.sp .2i
VT threshold voltage Volts 0.0 S
IT threshold current Amps 0.0 W
VH hysteresis voltage Volts 0.0 S
IH hysteresis current Amps 0.0 W
RON on resistance \(*W 1.0 both
ROFF off resistance \(*W 1/GMIN* both
.TE
.sp .1i
.pp
*(See the .OPTIONS card for a description of GMIN, its default value
results is a off resistance of 1.0e+12 ohms.)
.sp .2i
.pp
The use of an ideal element that is highly non-linear such as a switch
can cause large discontinuities to occur
in the circuit node voltages.
A rapid change such as that associated
with a switch changing state can cause
numerical roundoff or tolerance problems
leading to erroneous results or timestep
difficulties.
The user of switches can improve the
situation by taking the following
steps:
.pp
First of all it is wise to set ideal
switch impedences only high and low
enough to be negligible with respect to
other circuit elements.
Using switch impedences that are close
to "ideal" in all cases will aggravate
the problem of discontinuities mentioned
above.
Of cource, when modeling real devices
such as MOSFETS, the on resistance
should be adjusted to a realistic level
depending on the size of the device
being modelled.
.pp
If a wide rango of ON to OFF resistance
must be used in the switched (ROFF/RON >1e+12), then the
tolerance on errors allowed during
transient analysis should be decreased
by using the .OPTIONS card and
specifying TRTOL to be less than the
default value of 7.0.
When switches are placed around
capacitors, then the option CHGTOL
should also be reduced.
Suggested values for these two options
are 1.0 and 1e-16 respectively.
These changes inform SPICE3 to be more
careful around the switch points so that
no errors are made due to the rapid
change in the circuit.
.sp 0.2i
.sh 2 "Diode Model"
.sp 0.1i
.pp
The dc characteristics of the diode are determined by the parameters IS
and N. An ohmic resistance, RS, is included. Charge storage effects are
modeled by a transit time, TT, and a nonlinear depletion layer capacitance
which is determined by the parameters CJO, VJ, and M. The temperature
dependence of the saturation current is defined by the parameters EG, the energy
and XTI, the saturation current temperature exponent. Reverse breakdown is
modeled by an exponential increase in the reverse diode current and is
determined by the parameters BV and IBV (both of which are positive numbers).
.sp 0.1i
.TS
center;
l l l l l l l.
name parameter units default example area
.sp 0.2i
1 IS saturation current A 1.0E-14 1.0E-14 *
2 RS ohmic resistance Ohm 0 10 *
3 N emission coefficient - 1 1.0
4 TT transit-time sec 0 0.1Ns
5 CJO zero-bias junction capacitance F 0 2PF *
6 VJ junction potential V 1 0.6
7 M grading coefficient - 0.5 0.5
8 EG activation energy eV 1.11 1.11 Si
0.69 Sbd
0.67 Ge
9 XTI saturation-current temp. exp - 3.0 3.0 jn
2.0 Sbd
10 KF flicker noise coefficient - 0
11 AF flicker noise exponent - 1
12 FC coefficient for forward-bias - 0.5
depletion capacitance formula
13 BV reverse breakdown voltage V infinite 40.0
14 IBV current at breakdown voltage A 1.0E-3
.TE
.sp 0.2i
.sh 2 "BJT Models (both NPN and PNP)"
.sp 0.1i
.pp
The bipolar junction transistor model in SPICE is an adaptation of
the integral charge control model of Gummel and Poon. This modified
Gummel-Poon model extends the original model to include several effects
at high bias levels. The model will automatically simplify to the simpler
Ebers-Moll model when certain parameters are not specified.
The parameter names
used in the modified Gummel-Poon model have been chosen to be more easily
understood by the program user, and to reflect better both physical and
circuit design thinking.
.pp
The dc model is defined by the parameters
IS, BF, NF, ISE, IKF, and NE which determine
the forward current gain characteristics,
IS, BR, NR, ISC, IKR, and NC which determine
the reverse current gain characteristics,
and VAF and VAR which determine the output conductance for forward and reverse
regions. Three ohmic resistances RB, RC, and
RE are included, where RB can be high current dependent.
Base charge storage
is modeled by forward and reverse transit times, TF and TR, the forward transit
time TF being bias dependent if desired, and nonlinear depletion layer
capacitances which are determined by
CJE, VJE, and MJE for the B-E junction ,
CJC, VJC, and MJC for the B-C junction and
CJS, VJS, and MJS for the C-S (Collector-Substrate) junction.
The temperature
dependence of the saturation current, IS, is determined by the energy-gap, EG,
and the saturation current temperature exponent, XTI.
Additionally base current temperature
dependence is modeled by the beta temperature exponent XTB in the new
model.
.pp
The BJT parameters used in the modified Gummel-Poon model
are listed below. The parameter names used in earlier versions of SPICE2
are still accepted.
.sp 0.2i
Modified Gummel-Poon BJT Parameters.
.sp 0.2i
.TS
center;
l l l l l l l.
name parameter units default example area
.sp 0.2i
1 IS transport saturation current A 1.0E-16 1.0E-15 *
2 BF ideal maximum forward beta - 100 100
3 NF forward current emission coefficient - 1.0 1
4 VAF forward Early voltage V infinite 200
5 IKF corner for forward beta
high current roll-off A infinite 0.01 *
6 ISE B-E leakage saturation current A 0 1.0E-13 *
7 NE B-E leakage emission coefficient - 1.5 2
8 BR ideal maximum reverse beta - 1 0.1
9 NR reverse current emission coefficient - 1 1
10 VAR reverse Early voltage V infinite 200
11 IKR corner for reverse beta
high current roll-off A infinite 0.01 *
12 ISC B-C leakage saturation current A 0 1.0E-13 *
13 NC B-C leakage emission coefficient - 2 1.5
14 RB zero bias base resistance Ohms 0 100 *
15 IRB current where base resistance
falls halfway to its min value A infinite 0.1 *
16 RBM minimum base resistance
at high currents Ohms RB 10 *
17 RE emitter resistance Ohms 0 1 *
18 RC collector resistance Ohms 0 10 *
19 CJE B-E zero-bias depletion capacitance F 0 2PF *
