SPICE User's Guide

Table of Contents

INTRODUCTION CIRCUIT ELEMENTS AND MODELS INTERACTIVE INTERPRETER APPENDIX A
CIRCUIT DESCRIPTION ANALYSES AND OUTPUT CONTROL BIBLIOGRAPHY APPENDIX B

INTRODUCTION

 1.  INTRODUCTION
      SPICE is a general-purpose circuit  simulation  program
 for  nonlinear  dc,  nonlinear transient, and linear ac ana-
 lyses.  Circuits may contain resistors,  capacitors,  induc-
 tors,  mutual  inductors,  independent  voltage  and current
 sources, four types of dependent sources, lossless and lossy
 transmission lines (two separate implementations), switches,
 uniform distributed RC lines, and the five most common  sem-
 iconductor  devices:  diodes, BJTs, JFETs, MESFETs, and MOS-
 FETs.
      The SPICE3 version is based  directly  on  SPICE  2G.6.
 While  SPICE3 is being developed to include new features, it
 continues to support those  capabilities  and  models  which
 remain in extensive use in the SPICE2 program.
      SPICE has built-in models for  the  semiconductor  dev-
 ices,  and  the  user  need specify only the pertinent model
 parameter values.  The model for the BJT  is  based  on  the
 integral-charge  model  of Gummel and Poon;  however, if the
 Gummel- Poon parameters are not specified, the model reduces
 to  the  simpler  Ebers-Moll model.  In either case, charge-
 storage effects, ohmic resistances, and a  current-dependent
 output  conductance may be included.  The diode model can be
 used for either junction diodes or Schottky barrier  diodes.
 The  JFET  model  is  based on the FET model of Shichman and
 Hodges.   Six  MOSFET  models  are  implemented:   MOS1   is
 described by a square-law I-V characteristic, MOS2 [1] is an
 analytical model, while MOS3 [1] is a semi-empirical  model;
 MOS6  [2]  is a simple analytic model accurate in the short-
 channel region; MOS4 [3,  4]  and  MOS5  [5]  are  the  BSIM
 (Berkeley Short-channel IGFET Model) and BSIM2.  MOS2, MOS3,
 and MOS4 include second-order effects such as channel-length
 modulation,   subthreshold   conduction,  scattering-limited
 velocity  saturation,  small-size   effects,   and   charge-
 controlled capacitances.
TYPES OF ANALYSIS ANALYSIS AT DIFFERENT TEMPERATURES CONVERGENCE  

TYPES OF ANALYSIS

 1.1.  TYPES OF ANALYSIS
DC Analysis Transient Analysis SmallSignal Distortion Analysis Noise Analysis
AC SmallSignal Analysis PoleZero Analysis Sensitivity Analysis  

DC Analysis

 1.1.1.  DC Analysis
      The dc analysis portion  of  SPICE  determines  the  dc
 operating  point  of  the circuit with inductors shorted and
 capacitors opened.  The dc analysis options are specified on
 the  .DC,  .TF,  and  .OP  control  lines.  A dc analysis is
 automatically performed prior to  a  transient  analysis  to
 determine  the transient initial conditions, and prior to an
 ac  small-signal  analysis  to  determine  the   linearized,
 small-signal  models  for  nonlinear devices.  If requested,
 the dc small-signal value of a transfer function  (ratio  of
 output variable to input source), input resistance, and out-
 put resistance is also computed as a part of  the  dc  solu-
 tion.   The  dc  analysis  can  also  be used to generate dc
 transfer curves:  a specified independent voltage or current
 source  is  stepped  over  a user-specified range and the dc
 output variables  are  stored  for  each  sequential  source
 value.

AC Small-Signal Analysis

 1.1.2.  AC Small-Signal Analysis
      The ac small-signal portion of SPICE  computes  the  ac
 output  variables  as  a function of frequency.  The program
 first computes the dc operating point  of  the  circuit  and
 determines  linearized,  small-signal  models for all of the
 nonlinear devices in the circuit.  The resultant linear cir-
 cuit  is  then  analyzed over a user-specified range of fre-
 quencies.   The  desired  output  of  an  ac  small-  signal
 analysis is usually a transfer function (voltage gain, tran-
 simpedance, etc).  If the circuit has only one ac input,  it
 is  convenient to set that input to unity and zero phase, so
 that output variables have the same value  as  the  transfer
 function of the output variable with respect to the input.

Transient Analysis

 1.1.3.  Transient Analysis
      The transient analysis portion of  SPICE  computes  the
 transient  output  variables  as  a  function of time over a
 user-specified time interval.  The  initial  conditions  are
 automatically  determined  by  a  dc  analysis.  All sources
 which are not time dependent (for example,  power  supplies)
 are  set  to their dc value.  The transient time interval is
 specified on a .TRAN control line.

Pole-Zero Analysis

 1.1.4.  Pole-Zero Analysis
      The pole-zero analysis portion of  SPICE  computes  the
 poles and/or zeros in the small-signal ac transfer function.
 The program first computes the dc operating point  and  then
 determines  the  linearized, small-signal models for all the
 nonlinear devices in the circuit.  This circuit is then used
 to find the poles and zeros of the transfer function.
      Two types of transfer functions are allowed  :  one  of
 the  form  (output voltage)/(input voltage) and the other of
 the form (output voltage)/(input current).  These two  types
 of  transfer  functions cover all the cases and one can find
 the poles/zeros of functions like input/output impedance and
 voltage  gain.   The input and output ports are specified as
 two pairs of nodes.
      The pole-zero analysis works  with  resistors,  capaci-
 tors,   inductors,  linear-controlled  sources,  independent
 sources, BJTs,  MOSFETs,  JFETs  and  diodes.   Transmission
 lines are not supported.
      The method used in the analysis is a sub-optimal numer-
 ical  search.  For large circuits it may take a considerable
 time or fail to find all poles and  zeros.   For  some  cir-
 cuits,  the  method  becomes  "lost"  and finds an excessive
 number of poles or zeros.

Small-Signal Distortion Analysis

 1.1.5.  Small-Signal Distortion Analysis
      The  distortion  analysis  portion  of  SPICE  computes
 steady-state harmonic and intermodulation products for small
 input signal magnitudes.  If signals of a  single  frequency
 are  specified  as  the  input  to  the circuit, the complex
 values of the second and third harmonics are  determined  at
 every  point  in  the  circuit.  If there are signals of two
 frequencies input to the circuit, the analysis finds out the
 complex  values  of  the  circuit  variables  at the sum and
 difference of the input frequencies, and at  the  difference
 of  the  smaller  frequency  from the second harmonic of the
 larger frequency.
      Distortion analysis is supported for the following non-
 linear  devices: diodes (DIO), BJT, JFET, MOSFETs (levels 1,
 2, 3, 4/BSIM1, 5/BSIM2, and 6) and MESFETS.  All linear dev-
 ices are automatically supported by distortion analysis.  If
 there are switches present in the circuit, the analysis con-
 tinues  to  be  accurate provided the switches do not change
 state under the small excitations used for distortion calcu-
 lations.

Sensitivity Analysis

 1.1.6.  Sensitivity Analysis
      Spice3 will calculate  either  the  DC  operating-point
 sensitivity  or the AC small-signal sensitivity of an output
 variable with respect to all  circuit  variables,  including
 model  parameters.   Spice  calculates  the difference in an
 output variable (either a node voltage or a branch  current)
 by  perturbing  each parameter of each device independently.
 Since the method is a numerical approximation,  the  results
 may  demonstrate  second  order  affects in highly sensitive
 parameters, or may fail to show very low but non-zero sensi-
 tivity.   Further, since each variable is perturb by a small
 fraction of its value, zero-valued parameters are not analy-
 ized  (this  has  the  benefit of reducing what is usually a
 very large amount of data).

Noise Analysis

 1.1.7.  Noise Analysis
      The noise  analysis  portion  of  SPICE  does  analysis
 device-generated noise for the given circuit.  When provided
 with an input source and an output port, the analysis calcu-
 lates the noise contributions of each device (and each noise
 generator within the device) to the output port voltage.  It
 also  calculates  the input noise to the circuit, equivalent
 to the output noise referred to the specified input  source.
 This  is done for every frequency point in a specified range
 - the calculated value of the noise corresponds to the spec-
 tral  density of the circuit variable viewed as a stationary
 gaussian stochastic process.
      After  calculating  the   spectral   densities,   noise
 analysis  integrates  these  values  over the specified fre-
 quency range to arrive at the  total  noise  voltage/current
 (over   this   frequency   range).   This  calculated  value
 corresponds to the variance of the circuit  variable  viewed
 as a stationary gaussian process.

ANALYSIS AT DIFFERENT TEMPERATURES

 1.2.  ANALYSIS AT DIFFERENT TEMPERATURES
      All input data for SPICE is assumed to have been  meas-
                                     o
 ured  at a nominal temperature of 27 C, which can be changed
 by use of the TNOM parameter on the  .OPTION  control  line.
 This  value  can  further be overridden for any device which
 models temperature effects by specifying the TNOM  parameter
 on the model itself.  The circuit simulation is performed at
                    o
 a temperature of 27 C, unless overridden by a TEMP parameter
 on  the  .OPTION  control  line.   Individual  instances may
 further override the circuit temperature through the specif-
 ication of a TEMP parameter on the instance.
      Temperature dependent support is  provided  for  resis-
 tors,  diodes,  JFETs,  BJTs, and level 1, 2, and 3 MOSFETs.
 BSIM (levels 4 and 5) MOSFETs have an alternate  temperature
 dependency  scheme which adjusts all of the model parameters
 before input to SPICE.  For details of the BSIM  temperature
 adjustment, see [6] and [7].
      Temperature appears explicitly in the exponential terms
 of  the BJT and diode model equations.  In addition, satura-
 tion currents have a built-in temperature  dependence.   The
 temperature  dependence of the saturation current in the BJT
 models is determined by:
                              XTI
                          |T |        | E q(T  T )|
                            1            g   1  0
          I (T ) = I (T ) |--|     exp|-----------|
           S  1     S  0
                          |T |        |k (T  - T )|
                            0              1    0
 where k is Boltzmann's constant,  q  is  the  electronic
 charge, E  is the energy gap which is a model parameter,
          G
 and XTI is the saturation current  temperature  exponent
 (also a model parameter, and usually equal to 3).
      The temperature dependence of forward and reverse  beta
 is according to the formula:
                                      XTB
                                  |T |
                                    1
                    B(T ) = B(T ) |--|
                       1       0
                                  |T |
                                    0
 where T  and T  are in degrees  Kelvin,  and  XTB  is  a
        1      0
 user-supplied  model  parameter.  Temperature effects on
 beta are carried out by appropriate  adjustment  to  the
 values  of  B , I  , B , and I   (spice model parameters
              F   SE   R       SC
 BF, ISE, BR, and ISC, respectively).
      Temperature dependence of the saturation current in the
 junction diode model is determined by:
                             XTI
                             ---
                              N
                         |T |        |  E q(T  T ) |
                           1             g   1  0
         I (T ) = I (T ) |--|     exp|-------------|
          S  1     S  0
                         |T |        |N k (T  - T )|
                           0                1    0
 where N is the emission coefficient, which  is  a  model
 parameter,  and  the other symbols have the same meaning
 as above.  Note that for Schottky  barrier  diodes,  the
 value  of  the  saturation current temperature exponent,
 XTI, is usually 2.
      Temperature appears explicitly in the value of junction
 potential, U (in spice PHI), for all the device models.  The
 temperature dependence is determined by:
                                   | N N   |
                                      a d
                          kT       |------ |
                   U(T) = --  log        2
                           q     e |N (T)  |
                                     i
 where k is Boltzmann's constant,  q  is  the  electronic
 charge,  N   is the acceptor impurity density, N  is the
           a                                     d
 donor impurity density, N  is the intrinsic carrier con-
                          i
 centration, and E  is the energy gap.
                  g
      Temperature appears explicitly in the value of  surface
 mobility, M  (or UO), for the MOSFET model.  The temperature
            0
 dependence is determined by:
                                M (T )
                                 0  0
                       M (T) = -------
                        0          1.5
                               | T|
                               |--|
                               |T |
                                 0
      The effects of temperature on resistors is  modeled  by
 the formula:
                                                    2
       R(T) = R(T ) [1 + TC  (T - T ) + TC  (T - T ) ]
                 0         1       0      2       0
 where T is the circuit temperature, T   is  the  nominal
                                      0
 temperature,  and TC  and TC  are the first- and second-
                     1       2
 order temperature coefficients.

CONVERGENCE

 1.3.  CONVERGENCE
      Both dc and transient  solutions  are  obtained  by  an
 iterative  process which is terminated when both of the fol-
 lowing conditions hold:
 1)   The nonlinear branch  currents  converge  to  within  a
      tolerance of 0.1% or 1 picoamp (1.0e-12 Amp), whichever
      is larger.
 2)   The node voltages converge to  within  a  tolerance  of
      0.1% or 1 microvolt (1.0e-6 Volt), whichever is larger.
      Although the algorithm used in SPICE has been found  to
 be  very  reliable,  in some cases it fails to converge to a
 solution.  When this failure occurs, the program  terminates
 the job.
      Failure to converge in dc analysis is usually due to an
 error  in specifying circuit connections, element values, or
 model parameter values.  Regenerative switching circuits  or
 circuits  with  positive feedback probably will not converge
 in the dc analysis unless the OFF option is used for some of
 the  devices  in  the feedback path, or the .NODESET control
 line is used to force the circuit to converge to the desired
 state.

CIRCUIT DESCRIPTION

 2.  CIRCUIT DESCRIPTION
GENERAL STRUCTURE AND CONVENTIONS DEVICE MODELS COMBINING FILES  
TITLE LINE COMMENT LINES AND .END LINE SUBCIRCUITS    

GENERAL STRUCTURE AND CONVENTIONS

 2.1.  GENERAL STRUCTURE AND CONVENTIONS
      The circuit to be analyzed is described to SPICE  by  a
 set  of element lines, which define the circuit topology and
 element values, and a set of control lines, which define the
 model  parameters  and  the run controls.  The first line in
 the input file must be the title, and the last line must  be
 ".END".   The  order  of  the  remaining  lines is arbitrary
 (except, of course, that continuation lines must immediately
 follow the line being continued).
      Each element in the circuit is specified by an  element
 line  that  contains  the element name, the circuit nodes to
 which the element is connected, and the values of the param-
 eters  that  determine the electrical characteristics of the
 element.  The first letter of the element name specifies the
 element  type.   The  format  for the SPICE element types is
 given in what follows.  The strings  XXXXXXX,  YYYYYYY,  and
 ZZZZZZZ denote arbitrary alphanumeric strings.  For example,
 a resistor name must begin with the letter R and can contain
 one  or  more  characters.   Hence,  R,  R1,  RSE, ROUT, and
 R3AC2ZY are valid resistor names.  Details of each  type  of
 device are supplied in a following section.
      Fields on a line are separated by one or more blanks, a
 comma,  an equal ('=') sign, or a left or right parenthesis;
 extra spaces are ignored.  A line may be continued by enter-
 ing  a  '+'  (plus) in column 1 of the following line; SPICE
 continues reading beginning with column 2.
      A name field must begin with a letter (A through Z) and
 cannot contain any delimiters.
      A number field may be an integer  field  (12,  -44),  a
 floating  point field (3.14159), either an integer or float-
 ing point number followed by  an  integer  exponent  (1e-14,
 2.65e3),  or  either  an  integer or a floating point number
 followed by one of the following scale factors:
       12         9                    6         3               -6
 T = 10     G = 10             Meg = 10    K = 10      mil = 25.4
       -3                 -6         -9          -12         -15
 m = 10     u (or  M) = 10     n = 10      p = 10      f = 10
 Letters immediately following a number that  are  not  scale
 factors  are  ignored,  and  letters immediately following a
 scale factor are ignored.  Hence, 10, 10V, 10Volts, and 10Hz
 all  represent  the  same number, and M, MA, MSec, and MMhos
 all represent  the  same  scale  factor.   Note  that  1000,
 1000.0,  1000Hz,  1e3, 1.0e3, 1KHz, and 1K all represent the
 same number.
      Nodes names may be arbitrary  character  strings.   The
 datum  (ground) node must be named '0'.  Note the difference
 in SPICE3 where the nodes are treated as  character  strings
 and not evaluated as numbers, thus '0' and '00' are distinct
 nodes in SPICE3 but not in SPICE2.  The circuit cannot  con-
 tain  a  loop of voltage sources and/or inductors and cannot
 contain a cut-set  of  current  sources  and/or  capacitors.
 Each  node  in  the  circuit  must have a dc path to ground.
 Every node must have at least  two  connections  except  for
 transmission line nodes (to permit unterminated transmission
 lines) and MOSFET substrate nodes (which have  two  internal
 connections anyway).

TITLE LINE, COMMENT LINES AND .END LINE

 2.2.  TITLE LINE, COMMENT LINES AND .END LINE
Title Line .END Line Comments  

Title Line

 2.2.1.  Title Line
 Examples:
     POWER AMPLIFIER CIRCUIT
     TEST OF CAM CELL
      The title line must be the first  in  the  input  file.
 Its  contents  are  printed verbatim as the heading for each
 section of output.

.END Line

 2.2.2.  .END Line
 Examples:
     .END
      The "End" line must always be the last in the input
 file.   Note  that the period is an integral part of the
 name.

Comments

 2.2.3.  Comments
 General Form:
     * <any comment>
 Examples:
     * RF=1K      Gain should be 100
     * Check open-loop gain and phase margin
      The asterisk in the  first  column  indicates  that
 this  line  is  a  comment  line.   Comment lines may be
 placed anywhere in the circuit description.   Note  that
 SPICE3  also considers any line with leading white space
 to be a comment.

DEVICE MODELS

 2.3.  DEVICE MODELS
 General form:
     .MODEL MNAME TYPE(PNAME1=PVAL1 PNAME2=PVAL2 ... )
 Examples:
     .MODEL MOD1 NPN (BF=50 IS=1E-13 VBF=50)
      Most simple circuit elements typically require  only  a
 few  parameter values.  However, some devices (semiconductor
 devices in particular) that are included  in  SPICE  require
 many parameter values.  Often, many devices in a circuit are
 defined by the same set of  device  model  parameters.   For
 these  reasons,  a set of device model parameters is defined
 on a separate .MODEL line and assigned a unique model  name.
 The  device  element  lines in SPICE then refer to the model
 name.
      For these more complex device types, each  device  ele-
 ment  line  contains the device name, the nodes to which the
 device is connected, and the device model  name.   In  addi-
 tion,  other  optional  parameters may be specified for some
 devices:  geometric factors and an  initial  condition  (see
 the following section on Transistors and Diodes for more de-
 tails).
      MNAME in the above is the model name, and type  is  one
 of the following fifteen types:
             R      Semiconductor resistor model
             C      Semiconductor capacitor model
             SW     Voltage controlled switch
             CSW    Current controlled switch
             URC    Uniform distributed RC model
             LTRA   Lossy transmission line model
             D      Diode model
             NPN    NPN BJT model
             PNP    PNP BJT model
             NJF    N-channel JFET model
             PJF    P-channel JFET model
             NMOS   N-channel MOSFET model
             PMOS   P-channel MOSFET model
             NMF    N-channel MESFET model
             PMF    P-channel MESFET model
      Parameter values are defined by appending the parameter
 name  followed  by  an  equal  sign and the parameter value.
 Model parameters that are not given a value are assigned the
 default  values  given  below  for each model type.  Models,
 model parameters, and default values are listed in the  next
 section along with the description of device element lines.

SUBCIRCUITS

 2.4.  SUBCIRCUITS
      A subcircuit that consists of  SPICE  elements  can  be
 defined  and  referenced  in  a  fashion  similar  to device
 models.  The subcircuit is defined in the input  file  by  a
 grouping  of  element lines;  the program then automatically
 inserts the group of elements  wherever  the  subcircuit  is
 referenced.   There is no limit on the size or complexity of
 subcircuits, and subcircuits may contain other  subcircuits.
 An example of subcircuit usage is given in Appendix A.
.SUBCKT Line .ENDS Line Subcircuit Calls  

.SUBCKT Line

 2.4.1.  .SUBCKT Line
 General form:
     .SUBCKT subnam N1 <N2 N3 ...>
 Examples:
     .SUBCKT OPAMP 1 2 3 4
      A circuit definition is  begun  with  a  .SUBCKT  line.
 SUBNAM  is  the  subcircuit  name,  and  N1, N2, ... are the
 external nodes, which cannot be zero.  The group of  element
 lines  which  immediately follow the .SUBCKT line define the
 subcircuit.  The last line in a subcircuit definition is the
 .ENDS line (see below).  Control lines may not appear within
 a subcircuit definition;   however,  subcircuit  definitions
 may contain anything else, including other subcircuit defin-
 itions, device models, and  subcircuit  calls  (see  below).
 Note  that  any  device  models  or  subcircuit  definitions
 included as part of a  subcircuit  definition  are  strictly
 local  (i.e., such models and definitions are not known out-
 side the subcircuit definition).  Also,  any  element  nodes
 not  included  on  the .SUBCKT line are strictly local, with
 the exception of 0 (ground) which is always global.

.ENDS Line

 2.4.2.  .ENDS Line
 General form:
     .ENDS <SUBNAM>
 Examples:
     .ENDS OPAMP
      The "Ends" line must be the last one for  any  sub-
 circuit  definition.   The subcircuit name, if included,
 indicates which subcircuit definition is being terminat-
 ed;   if omitted, all subcircuits being defined are ter-
 minated.  The name is needed only when nested subcircuit
 definitions are being made.

Subcircuit Calls

 2.4.3.  Subcircuit Calls
 General form:
     XYYYYYYY N1 <N2 N3 ...> SUBNAM
 Examples:
     X1 2 4 17 3 1 MULTI
      Subcircuits  are  used  in  SPICE   by   specifying
 pseudo-elements beginning with the letter X, followed by
 the circuit nodes to be used in  expanding  the  subcir-
 cuit.

COMBINING FILES: .INCLUDE LINES

 2.5.  COMBINING FILES: .INCLUDE LINES
 General form:
     .INCLUDE filename
 Examples:
     .INCLUDE /users/spice/common/wattmeter.cir
      Frequently, portions of circuit  descriptions  will  be
 reused  in  several  input  files,  particularly with common
 models and  subcircuits.   In  any  spice  input  file,  the
 ".include"  line  may  be used to copy some other file as if
 that second file appeared in place of the ".include" line in
 the original file.  There is no restriction on the file name
 imposed by spice beyond those imposed by the local operating
 system.

CIRCUIT ELEMENTS AND MODELS

 3.  CIRCUIT ELEMENTS AND MODELS
      Data  fields  that  are  enclosed  in   less-than   and
 greater-than  signs  ('<  >')  are  optional.  All indicated
 punctuation (parentheses, equal signs, etc.) is optional but
 indicate  the  presence  of  any delimiter.  Further, future
 implementations may require the punctuation  as  stated.   A
 consistent  style  adhering  to  the  punctuation shown here
 makes the input  easier  to  understand.   With  respect  to
 branch voltages and currents, SPICE uniformly uses the asso-
 ciated reference convention (current flows in the  direction
 of voltage drop).
ELEMENTARY DEVICES VOLTAGE AND CURRENT SOURCES TRANSMISSION LINES TRANSISTORS AND DIODES

ELEMENTARY DEVICES

 3.1.  ELEMENTARY DEVICES
Resistors Capacitors Inductors Switch Model
Semiconductor Resistors Semiconductor Capacitors Coupled Inductors  
Semiconductor Resistor Model Semiconductor Capacitor Model Switches  

Resistors

 3.1.1.  Resistors
 General form:
     RXXXXXXX N1 N2 VALUE
 Examples:
     R1 1 2 100
     RC1 12 17 1K
      N1 and N2 are the two  element  nodes.   VALUE  is  the
 resistance (in ohms) and may be positive or negative but not
 zero.

Semiconductor Resistors

 3.1.2.  Semiconductor Resistors
 General form:
     RXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <TEMP=T>
 Examples:
     RLOAD 2 10 10K
     RMOD 3 7 RMODEL L=10u W=1u
      This is the more general form of the resistor presented
 in  section  6.1,  and  allows  the  modeling of temperature
 effects and for the calculation  of  the  actual  resistance
 value from strictly geometric information and the specifica-
 tions of the process.  If VALUE is specified,  it  overrides
 the  geometric  information  and defines the resistance.  If
 MNAME is specified, then the resistance  may  be  calculated
 from  the  process  information  in  the model MNAME and the
 given LENGTH and WIDTH.  If VALUE  is  not  specified,  then
 MNAME  and LENGTH must be specified.  If WIDTH is not speci-
 fied, then it is taken from the default width given  in  the
 model.   The  (optional)  TEMP  value  is the temperature at
 which this device is to operate, and overrides the  tempera-
 ture specification on the .OPTION control line.

Semiconductor Resistor Model (R)

 3.1.3.  Semiconductor Resistor Model (R)
      The resistor model consists of  process-related  device
 data  that  allow  the  resistance  to  be  calculated  from
 geometric information and to be corrected  for  temperature.
 The parameters available are:
 name     parameter                           units    default   example
                                                o
 TC1      first order temperature coeff.      Z/ C     0.0       -
                                                o 2
 TC2      second order temperature coeff.     Z/ C     0.0       -
 RSH      sheet resistance                    Z/[]     -         50
 DEFW     default width                       meters   1e-6      2e-6
 NARROW   narrowing due to side etching       meters   0.0       1e-7
                                              o
 TNOM     parameter measurement temperature    C       27        50
      The sheet resistance is used with the narrowing parame-
 ter  and  L  and W from the resistor device to determine the
 nominal resistance by the formula
                              L - NARROW
                      R = RSH ----------
                              W - NARROW
 DEFW is used to supply a default value for W if one  is  not
 specified  for the device.  If either RSH or L is not speci-
 fied, then the standard default resistance value of 1k Z  is
 used.  TNOM is used to override the circuit-wide value given
 on the .OPTIONS control line where the  parameters  of  this
 model  have been measured at a different temperature.  After
 the nominal resistance is calculated,  it  is  adjusted  for
 temperature by the formula:
                                                   2
        R(T) = R(T ) [1 + TC1 (T - T ) + TC2 (T-T ) ]
                  0                 0            0

Capacitors

 3.1.4.  Capacitors
 General form:
     CXXXXXXX N+ N- VALUE <IC=INCOND>
 Examples:
     CBYP 13 0 1UF
     COSC 17 23 10U IC=3V
      N+ and N- are the  positive  and  negative  element
 nodes,   respectively.   VALUE  is  the  capacitance  in
 Farads.
      The (optional) initial condition is the initial  (time-
 zero)  value of capacitor voltage (in Volts).  Note that the
 initial conditions (if any) apply 'only' if the  UIC  option
 is specified on the .TRAN control line.

Semiconductor Capacitors

 3.1.5.  Semiconductor Capacitors
 General form:
     CXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <IC=VAL>
 Examples:
     CLOAD 2 10 10P
     CMOD 3 7 CMODEL L=10u W=1u
      This  is  the  more  general  form  of  the   Capacitor
 presented  in section 6.2, and allows for the calculation of
 the actual capacitance value from strictly geometric  infor-
 mation  and  the specifications of the process.  If VALUE is
 specified, it defines the capacitance.  If MNAME  is  speci-
 fied,  then  the  capacitance is calculated from the process
 information in the model MNAME  and  the  given  LENGTH  and
 WIDTH.   If  VALUE  is  not specified, then MNAME and LENGTH
 must be specified.  If WIDTH is not specified,  then  it  is
 taken  from  the  default  width given in the model.  Either
 VALUE or MNAME, LENGTH, and WIDTH may be specified, but  not
 both sets.

Semiconductor Capacitor Model (C)

 3.1.6.  Semiconductor Capacitor Model (C)
      The capacitor model contains process  information  that
 may  be  used  to  compute  the  capacitance  from  strictly
 geometric information.
 name     parameter                       units       default   example
                                                  2
 CJ       junction bottom capacitance     F/meters    -         5e-5
 CJSW     junction sidewall capacitance   F/meters    -         2e-11
 DEFW     default device width            meters      1e-6      2e-6
 NARROW   narrowing due to side etching   meters      0.0       1e-7
      The capacitor has a capacitance computed as
 CAP = CJ (LENGTH - NARROW) (WIDTH - NARROW) + 2 CJSW (LENGTH + WIDTH - 2 NARROW)

Inductors

 3.1.7.  Inductors
 General form:
     LYYYYYYY N+ N- VALUE <IC=INCOND>
 Examples:
     LLINK 42 69 1UH
     LSHUNT 23 51 10U IC=15.7MA
      N+ and N- are the  positive  and  negative  element
 nodes,  respectively.   VALUE  is the inductance in Hen-
 ries.
      The (optional) initial condition is the initial  (time-
 zero)  value  of  inductor current (in Amps) that flows from
 N+, through the inductor, to N-.  Note that the initial con-
 ditions  (if  any) apply only if the UIC option is specified
 on the .TRAN analysis line.

Coupled (Mutual) Inductors

 3.1.8.  Coupled (Mutual) Inductors
 General form:
     KXXXXXXX LYYYYYYY LZZZZZZZ VALUE
 Examples:
     K43 LAA LBB 0.999
     KXFRMR L1 L2 0.87
      LYYYYYYY and LZZZZZZZ are the names of the two cou-
 pled  inductors,  and  VALUE  is the coefficient of cou-
 pling, K, which must be greater than 0 and less than  or
 equal  to  1.  Using the 'dot' convention, place a 'dot'
 on the first node of each inductor.

Switches

 3.1.9.  Switches
 General form:
     SXXXXXXX N+ N- NC+ NC- MODEL <ON><OFF>
     WYYYYYYY N+ N- VNAM MODEL <ON><OFF>
 Examples:
     s1 1 2 3 4 switch1 ON
     s2 5 6 3 0 sm2 off
     Switch1 1 2 10 0 smodel1
     w1 1 2 vclock switchmod1
     W2 3 0 vramp sm1 ON
     wreset 5 6 vclck lossyswitch OFF
      Nodes 1 and 2  are  the  nodes  between  which  the
 switch  terminals are connected.  The model name is man-
 datory while the initial conditions are  optional.   For
 the voltage controlled switch, nodes 3 and 4 are the po-
 sitive and negative controlling nodes respectively.  For
 the  current  controlled switch, the controlling current
 is that  through  the  specified  voltage  source.   The
 direction  of  positive controlling current flow is from
 the positive node, through the source, to  the  negative
 node.

Switch Model (SW/CSW)

 3.1.10.  Switch Model (SW/CSW)
      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:
     name   parameter            units   default   switch
     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        Z       1.0       both
     ROFF   off resistance       Z       1/GMIN*   both
      *(See the .OPTIONS control line for  a  description  of
 GMIN,  its  default  value  results  in an off-resistance of
 1.0e+12 ohms.)
      The use of an ideal element that  is  highly  nonlinear
 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:
      First, it is wise to set ideal switch  impedances  just
 high  or  low  enough to be negligible with respect to other
 circuit elements.  Using switch impedances that are close to
 "ideal"  in all cases aggravates the problem of discontinui-
 ties mentioned above.  Of course, 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
 modeled.
      If a wide range of ON to OFF resistance must be used in
 the switches (ROFF/RON >1e+12), then the tolerance on errors
 allowed during transient analysis  should  be  decreased  by
 using  the  .OPTIONS control line 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.

VOLTAGE AND CURRENT SOURCES

 3.2.  VOLTAGE AND CURRENT SOURCES
Independent Sources Linear Dependent Sources Nonlinear Dependent Sources  

Independent Sources

 3.2.1.  Independent Sources
 General form:
     VXXXXXXX N+ N- <<DC> DC/TRAN VALUE> <AC <ACMAG <ACPHASE>>>
     +       <DISTOF1 <F1MAG <F1PHASE>>> <DISTOF2 <F2MAG <F2PHASE>>>
     IYYYYYYY N+ N- <<DC> DC/TRAN VALUE> <AC <ACMAG <ACPHASE>>>
     +       <DISTOF1 <F1MAG <F1PHASE>>> <DISTOF2 <F2MAG <F2PHASE>>>
 Examples:
     VCC 10 0 DC 6
     VIN 13 2 0.001 AC 1 SIN(0 1 1MEG)
     ISRC 23 21 AC 0.333 45.0 SFFM(0 1 10K 5 1K)
     VMEAS 12 9
     VCARRIER 1 0 DISTOF1 0.1 -90.0
     VMODULATOR 2 0 DISTOF2 0.01
     IIN1 1 5 AC 1 DISTOF1 DISTOF2 0.001
      N+ and N- are the positive and negative nodes,  respec-
 tively.   Note  that  voltage  sources need not be grounded.
 Positive current is assumed to flow from the positive  node,
 through  the source, to the negative node.  A current source
 of positive value forces current to flow out of the N+ node,
 through  the source, and into the N- node.  Voltage sources,
 in addition to being used for circuit  excitation,  are  the
 'ammeters'  for  SPICE, that is, zero valued voltage sources
 may be inserted into the circuit for the purpose of  measur-
 ing  current.   They  of  course  have  no effect on circuit
 operation since they represent short-circuits.
      DC/TRAN is the dc and transient analysis value  of  the
 source.   If  the source value is zero both for dc and tran-
 sient analyses, this value may be omitted.   If  the  source
 value  is  time-invariant  (e.g.,  a power supply), then the
 value may optionally be preceded by the letters DC.
      ACMAG is the ac magnitude and ACPHASE is the ac  phase.
 The  source  is  set  to  this value in the ac analysis.  If
 ACMAG is omitted following the keyword AC, a value of  unity
 is  assumed.   If  ACPHASE  is  omitted,  a value of zero is
 assumed.  If the source is not an ac small-signal input, the
 keyword AC and the ac values are omitted.
      DISTOF1 and DISTOF2 are the keywords that specify  that
 the independent source has distortion inputs at the frequen-
 cies F1 and F2 respectively  (see  the  description  of  the
 .DISTO  control  line).   The keywords may be followed by an
 optional magnitude and phase.  The  default  values  of  the
 magnitude and phase are 1.0 and 0.0 respectively.
      Any independent source can be assigned a time-dependent
 value  for  transient  analysis.   If a source is assigned a
 time-dependent value, the time-zero value  is  used  for  dc
 analysis.   There  are  five  independent  source functions:
 pulse,  exponential,  sinusoidal,  piece-wise  linear,   and
 single-frequency FM.  If parameters other than source values
 are omitted or set to zero, the  default  values  shown  are
 assumed.   (TSTEP is the printing increment and TSTOP is the
 final time (see the .TRAN control line for explanation)).
Pulse Exponential SingleFrequency FM  
Sinusoidal PieceWise Linear    

Pulse

 3.2.1.1.  Pulse
 General form:
     PULSE(V1 V2 TD TR TF PW PER)
 Examples:
     VIN 3 0 PULSE(-1 1 2NS 2NS 2NS 50NS 100NS)
      parameter               default value         units
      -----------------------------------------------------
      V1 (initial value)                      Volts or Amps
      V2 (pulsed value)                       Volts or Amps
      TD (delay time)         0.0             seconds
      TR (rise time)          TSTEP           seconds
      TF (fall time)          TSTEP           seconds
      PW (pulse width)        TSTOP           seconds
      PER(period)             TSTOP           seconds
      A single pulse so specified is described by the follow-
 ing table:
      time          value
      -------------------
      0             V1
      TD            V1
      TD+TR         V2
      TD+TR+PW      V2
      TD+TR+PW+TF   V1
      TSTOP         V1
      Intermediate points are determined by linear interpola-
 tion.

Sinusoidal

 3.2.1.2.  Sinusoidal
 General form:
     SIN(VO VA FREQ TD THETA)
 Examples:
     VIN 3 0 SIN(0 1 100MEG 1NS 1E10)
      parameters                default value   units
      -------------------------------------------------------
      VO     (offset)                           Volts or Amps
      VA     (amplitude)                        Volts or Amps
      FREQ   (frequency)        1/TSTOP         Hz
      TD     (delay)            0.0             seconds
      THETA  (damping factor)   0.0             1/seconds
      The shape of the waveform is described by the following
 table:
      time          value
      ------------------------------------------------------------
      0 to TD       VO
                             -(t - TD)THETA
      TD to TSTOP   VO + VA e               sin(2 J FREQ (t + TD))

Exponential

 3.2.1.3.  Exponential
 General Form:
     EXP(V1 V2 TD1 TAU1 TD2 TAU2)
 Examples:
     VIN 3 0 EXP(-4 -1 2NS 30NS 60NS 40NS)
      parameter                   default value   units
      ---------------------------------------------------------
      V1   (initial value)                        Volts or Amps
      V2   (pulsed value)                         Volts or Amps
      TD1  (rise delay time)      0.0             seconds
      TAU1 (rise time constant)   TSTEP           seconds
      TD2  (fall delay time)      TD1+TSTEP       seconds
      TAU2 (fall time constant)   TSTEP           seconds
      The shape of the waveform is described by the following
 table:
      time           value
      ----------------------------------------------------------------------------
       0 to TD1      V1
                                    |     ------------|
                                              TAU1
                                    |    -(t - TD1)   |                -(t - TD2)
      TD1 to TD2     V1 + (V2 - V1)  1 - e
                                    |    ----------|             |     ----------|
                                    |       TAU1   |             |        TAU2   |
      TD2 to TSTOP   V1 + (V2 - V1)   - e            + (V1 - V2)  1 - e

Piece-Wise Linear

 3.2.1.4.  Piece-Wise Linear
 General Form:
     PWL(T1 V1 <T2 V2 T3 V3 T4 V4 ...>)
 Examples:
     VCLOCK 7 5 PWL(0 -7 10NS -7 11NS -3 17NS -3 18NS -7 50NS -7)
      Each pair of values (Ti, Vi) specifies that  the  value
 of  the  source  is  Vi  (in Volts or Amps) at time=Ti.  The
 value of the source at intermediate values of time is deter-
 mined by using linear interpolation on the input values.

Single-Frequency FM

 3.2.1.5.  Single-Frequency FM
 General Form:
     SFFM(VO VA FC MDI FS)
 Examples:
     V1 12 0 SFFM(0 1M 20K 5 1K)
      parameter                 default value   units
      -------------------------------------------------------
      VO  (offset)                              Volts or Amps
      VA  (amplitude)                           Volts or Amps
      FC  (carrier frequency)   1/TSTOP         Hz
      MDI (modulation index)
      FS  (signal frequency)    1/TSTOP         Hz
 The shape of the waveform  is  described  by  the  following
 equation:
                        |                            |
        V(t)=V  + V  sin 2 J FC t + MDI sin(2 J FS t)
              O    A    |                            |

Linear Dependent Sources

 3.2.2.  Linear Dependent Sources
      SPICE  allows  circuits  to  contain  linear  dependent
 sources characterized by any of the four equations
         i = g v          v = e v          i = f i          v
 = h i
 where g, e, f, and h are constants representing transconduc-
 tance,  voltage  gain,  current  gain,  and transresistance,
 respectively.
Linear VoltageControlled Current Sources Linear VoltageControlled Voltage Sources Linear CurrentControlled Current Sources Linear CurrentControlled Voltage Sources

Linear Voltage-Controlled Current Sources

 3.2.2.1.  Linear Voltage-Controlled Current Sources
 General form:
     GXXXXXXX N+ N- NC+ NC- VALUE
 Examples:
     G1 2 0 5 0 0.1MMHO
      N+ and N- are  the  positive  and  negative  nodes,
 respectively.   Current  flow is from the positive node,
 through the source, to the negative node.  NC+  and  NC-
 are the positive and negative controlling nodes, respec-
 tively.  VALUE is the transconductance (in mhos).

Linear Voltage-Controlled Voltage Sources

 3.2.2.2.  Linear Voltage-Controlled Voltage Sources
 General form:
     EXXXXXXX N+ N- NC+ NC- VALUE
 Examples:
     E1 2 3 14 1 2.0
      N+ is the positive node, and  N-  is  the  negative
 node.   NC+  and  NC- are the positive and negative con-
 trolling nodes,  respectively.   VALUE  is  the  voltage
 gain.

Linear Current-Controlled Current Sources

 3.2.2.3.  Linear Current-Controlled Current Sources
 General form:
     FXXXXXXX N+ N- VNAM VALUE
 Examples:
     F1 13 5 VSENS 5
      N+ and N- are  the  positive  and  negative  nodes,
 respectively.   Current  flow is from the positive node,
 through the source, to the negative node.  VNAM  is  the
 name  of  a voltage source through which the controlling
 current flows.  The direction  of  positive  controlling
 current  flow  is  from  the  positive node, through the
 source, to the negative node  of  VNAM.   VALUE  is  the
 current gain.

Linear Current-Controlled Voltage Sources

 3.2.2.4.  Linear Current-Controlled Voltage Sources
 General form:
     HXXXXXXX N+ N- VNAM VALUE
 Examples:
     HX 5 17 VZ 0.5K
      N+ and N- are  the  positive  and  negative  nodes,
 respectively.   VNAM  is  the  name  of a voltage source
 through which the controlling current flows.  The direc-
 tion  of  positive  controlling current flow is from the
 positive node, through the source, to the negative  node
 of VNAM.  VALUE is the transresistance (in ohms).

Non-linear Dependent Sources

 3.2.3.  Non-linear Dependent Sources
 General form:
     BXXXXXXX N+ N- <I=EXPR> <V=EXPR>
 Examples:
     B1 0 1 I=cos(v(1))+sin(v(2))
     B1 0 1 V=ln(cos(log(v(1,2)^2)))-v(3)^4+v(2)^v(1)
     B1 3 4 I=17
     B1 3 4 V=exp(pi^i(vdd))
      N+ is the positive node, and N- is the  negative  node.
 The  values of the V and I parameters determine the voltages
 and currents across and through  the  device,  respectively.
 If  I is given then the device is a current source, and if V
 is given the device is a voltage source.  One and  only  one
 of these parameters must be given.
      The small-signal AC behavior of the nonlinear source is
 a  linear dependent source (or sources) with a proportional-
 ity constant equal to the derivative (or derivatives) of the
 source at the DC operating point.
      The expressions given for V and I may be  any  function
 of voltages and currents through voltage sources in the sys-
 tem.  The following functions of real variables are defined:
                 abs     asinh   cosh   sin
                 acos    atan    exp    sinh
                 acosh   atanh   ln     sqrt
                 asin    cos     log    tan
      The function "u" is the  unit  step  function,  with  a
 value  of  one for arguments greater than one and a value of
 zero for arguments less than zero.  The function "uramp"  is
 the  integral of the unit step: for an input x, the value is
 zero if x is less than zero, or if x is  greater  than  zero
 the value is x.  These two functions are useful in sythesiz-
 ing piece-wise non-linear functions, though convergence  may
 be adversely affected.
      The following standard operators are defined:
      +       -       *       /       ^       unary -
      If the argument of log, ln, or sqrt becomes  less  than
 zero,  the  absolute  value  of  the argument is used.  If a
 divisor becomes zero or the argument of log  or  ln  becomes
 zero,  an  error will result.  Other problems may occur when
 the argument for a function in a partial derivative enters a
 region where that function is undefined.
      To get time into the expression you can  integrate  the
 current  from a constant current source with a capacitor and
 use the resulting voltage (don't forget to set  the  initial
 voltage  across the capacitor).  Non-linear resistors, capa-
 citors, and inductors may be synthesized with the  nonlinear
 dependent  source.   Non-linear resistors are obvious.  Non-
 linear capacitors and inductors are implemented  with  their
 linear  counterparts  by  a  change of variables implemented
 with the nonlinear dependent source.  The following  subcir-
 cuit will implement a nonlinear capacitor:
     .Subckt nlcap   pos neg
     * Bx: calculate f(input voltage)
     Bx   1    0    v = f(v(pos,neg))
     * Cx: linear capacitance
     Cx   2    0    1
     * Vx: Ammeter to measure current into the capacitor
     Vx   2    1    DC 0Volts
     * Drive the current through Cx back into the circuit
     Fx   pos  neg  Vx 1
     .ends
 Non-linear inductors are similar.

TRANSMISSION LINES

 3.3.  TRANSMISSION LINES
Lossless Transmission Lines Lossy Transmission Line Model Uniform Distributed RC Model  
Lossy Transmission Lines Uniform Distributed RC Lines    

Lossless Transmission Lines

 3.3.1.  Lossless Transmission Lines
 General form:
     TXXXXXXX N1 N2 N3 N4 Z0=VALUE <TD=VALUE> <F=FREQ <NL=NRMLEN>>
     +                    <IC=V1, I1, V2, I2>
 Examples:
     T1 1 0 2 0 Z0=50 TD=10NS
      N1 and N2 are the nodes at port 1;  N3 and N4  are  the
 nodes  at  port 2.  Z0 is the characteristic impedance.  The
 length of the line may be expressed in either of two  forms.
 The  transmission  delay,  TD, may be specified directly (as
 TD=10ns, for example).  Alternatively, a frequency F may  be
 given, together with NL, the normalized electrical length of
 the transmission line with respect to the wavelength in  the
 line at the frequency F.  If a frequency is specified but NL
 is omitted, 0.25 is  assumed  (that  is,  the  frequency  is
 assumed  to  be  the  quarter-wave  frequency).   Note  that
 although both forms for expressing the line length are indi-
 cated as optional, one of the two must be specified.
      Note that this  element  models  only  one  propagating
 mode.  If all four nodes are distinct in the actual circuit,
 then two modes may be excited.  To simulate  such  a  situa-
 tion, two transmission-line elements are required.  (see the
 example in Appendix A for further clarification.)
      The (optional) initial condition specification consists
 of  the voltage and current at each of the transmission line
 ports.  Note that the  initial  conditions  (if  any)  apply
 'only'  if  the UIC option is specified on the .TRAN control
 line.
      Note that a lossy transmission line  (see  below)  with
 zero  loss  may  be  more  accurate  than  than the lossless
 transmission line due to implementation details.

Lossy Transmission Lines

 3.3.2.  Lossy Transmission Lines
 General form:
     OXXXXXXX N1 N2 N3 N4 MNAME
 Examples:
     O23 1 0 2 0 LOSSYMOD
     OCONNECT 10 5 20 5 INTERCONNECT
      This  is  a  two-port  convolution  model  for  single-
 conductor lossy transmission lines.  N1 and N2 are the nodes
 at port 1;  N3 and N4 are the nodes at port 2.  Note that  a
 lossy  transmission line with zero loss may be more accurate
 than than the lossless transmission line due to  implementa-
 tion details.

Lossy Transmission Line Model (LTRA)

 3.3.3.  Lossy Transmission Line Model (LTRA)
      The uniform RLC/RC/LC/RG transmission line  model  (re-
 ferred  to  as  the  LTRA model henceforth) models a uniform
 constant-parameter distributed transmission  line.   The  RC
 and  LC  cases  may  also  be  modeled using the URC and TRA
 models; however, the newer LTRA model is usually faster  and
 more  accurate  than  the others.  The operation of the LTRA
 model is based on the convolution of the transmission line's
 impulse responses with its inputs (see [8]).
      The LTRA model takes a number of  parameters,  some  of
 which must be given and some of which are optional.
 name           parameter                               units/type       default      example
 R              resistance/length                       Z/unit           0.0          0.2
 L              inductance/length                       henrys/unit      0.0          9.13e-9
 G              conductance/length                      mhos/unit        0.0          0.0
 C              capacitance/length                      farads/unit      0.0          3.65e-12
 LEN            length of line                                           no default   1.0
 REL            breakpoint control                      arbitrary unit   1            0.5
 ABS            breakpoint control                                       1            5
 NOSTEPLIMIT    don't limit  timestep  to  less  than   flag             not set      set
                line delay
 NOCONTROL      don't do complex timestep control       flag             not set      set
 LININTERP      use linear interpolation                flag             not set      set
 MIXEDINTERP    use linear when quadratic seems bad                      not set      set
 COMPACTREL     special reltol for history compaction   flag             RELTOL       1.0e-3
 COMPACTABS     special abstol for history compaction                    ABSTOL       1.0e-9
 TRUNCNR        use   Newton-Raphson    method    for   flag             not set      set
                timestep control
 TRUNCDONTCUT   don't   limit   timestep   to    keep   flag             not set      set
                impulse-response errors low
      The following types of lines have been  implemented  so
 far:  RLC (uniform transmission line with series loss only),
 RC (uniform RC line), LC (lossless transmission  line),  and
 RG  (distributed  series resistance and parallel conductance
 only).  Any other combination will yield  erroneous  results
 and should not be tried.  The length LEN of the line must be
 specified.
      NOSTEPLIMIT is a flag that will remove the default res-
 triction  of limiting time-steps to less than the line delay
 in the RLC case.  NOCONTROL is  a  flag  that  prevents  the
 default limiting of the time-step based on convolution error
 criteria in the RLC and RC cases.  This speeds up simulation
 but  may  in  some  cases  reduce  the  accuracy of results.
 LININTERP is a flag that, when specified,  will  use  linear
 interpolation instead of the default quadratic interpolation
 for calculating delayed  signals.   MIXEDINTERP  is  a  flag
 that, when specified, uses a metric for judging whether qua-
 dratic interpolation is not applicable and if so uses linear
 interpolation;  otherwise  it  uses  the  default  quadratic
 interpolation.  TRUNCDONTCUT is  a  flag  that  removes  the
 default  cutting  of  the  time-step  to limit errors in the
 actual calculation of impulse-response  related  quantities.
 COMPACTREL  and  COMPACTABS  are quantities that control the
 compaction of the past history of values stored for convolu-
 tion.   Larger  values  of  these lower accuracy but usually
 increase simulation speed.  These are to be  used  with  the
 TRYTOCOMPACT  option,  described  in  the  .OPTIONS section.
 TRUNCNR is a flag that turns on the  use  of  Newton-Raphson
 iterations  to  determine  an  appropriate  timestep  in the
 timestep control routines. The default is a trial and  error
 procedure by cutting the previous timestep in half.  REL and
 ABS are quantities that control the setting of breakpoints.
      The option most worth experimenting with for increasing
 the  speed  of simulation is REL.  The default value of 1 is
 usually safe from the point of view of  accuracy  but  occa-
 sionally increases computation time.  A value greater than 2
 eliminates all breakpoints and may be worth trying depending
 on  the  nature  of the rest of the circuit, keeping in mind
 that it might not be safe from the  viewpoint  of  accuracy.
 Breakpoints  may  usually  be  entirely  eliminated if it is
 expected the circuit will not display sharp discontinuities.
 Values  between  0 and 1 are usually not required but may be
 used for setting many breakpoints.
      COMPACTREL may  also  be  experimented  with  when  the
 option  TRYTOCOMPACT  is  specified in a .OPTIONS card.  The
 legal range is between  0  and  1.   Larger  values  usually
 decrease  the  accuracy  of the simulation but in some cases
 improve speed.   If  TRYTOCOMPACT  is  not  specified  on  a
 .OPTIONS card, history compaction is not attempted and accu-
 racy is high.  NOCONTROL, TRUNCDONTCUT and NOSTEPLIMIT  also
 tend to increase speed at the expense of accuracy.

Uniform Distributed RC Lines (Lossy)

 3.3.4.  Uniform Distributed RC Lines (Lossy)
 General form:
     UXXXXXXX N1 N2 N3 MNAME L=LEN <N=LUMPS>
 Examples:
     U1 1 2 0 URCMOD L=50U
     URC2 1 12 2 UMODL l=1MIL N=6
      N1 and N2 are the two element nodes the  RC  line  con-
 nects,  while  N3  is the node to which the capacitances are
 connected.  MNAME is the model name, LEN is  the  length  of
 the  RC  line in meters.  LUMPS, if specified, is the number
 of lumped segments to use in modeling the RC line  (see  the
 model  description for the action taken if this parameter is
 omitted).

Uniform Distributed RC Model (URC)

 3.3.5.  Uniform Distributed RC Model (URC)
      The URC model is derived from a model  proposed  by  L.
 Gertzberrg  in 1974.  The model is accomplished by a subcir-
 cuit type expansion of the URC line into a network of lumped
 RC  segments  with  internally generated nodes.  The RC seg-
 ments are in a geometric progression, increasing toward  the
 middle  of  the  URC  line, with K as a proportionality con-
 stant.  The number of lumped segments used, if not specified
 for the URC line device, is determined by the following for-
 mula:
                                             2
                     |     R C        |(K-1)|  |
                           _ _      2
                  log|F        2 J L  |-----|  |
                       max
                     |     L L        |  K  |  |
             N =  ------------------------------
                              log K
      The URC line is made up strictly of resistor and  capa-
 citor  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  satura-
 tion  current  of ISPERL amps per meter of transmission line
 and an optional series resistance equivalent to RSPERL  ohms
 per meter.
      name     parameter                            units   default   example   area
  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           Z/m     1000      10        -
  4   CPERL    Capacitance per unit length          F/m     1.0e-15   1pF       -
  5   ISPERL   Saturation Current per unit length   A/m     0         -         -
  6   RSPERL   Diode Resistance per unit length     Z/m     0         -         -

TRANSISTORS AND DIODES

 3.4.  TRANSISTORS AND DIODES
      The area factor used on the diode, BJT, JFET, and  MES-
 FET  devices  determines  the  number of equivalent parallel
 devices of a specified model.  The affected  parameters  are
 marked  with  an  asterisk  under  the heading 'area' in the
 model descriptions below.  Several geometric factors associ-
 ated  with  the  channel and the drain and source diffusions
 can be specified on the MOSFET device line.
      Two different forms of initial conditions may be speci-
 fied  for  some  devices.   The  first  form  is included to
 improve the dc convergence for circuits  that  contain  more
 than one stable state.  If a device is specified OFF, the dc
 operating point is determined with the terminal voltages for
 that device set to zero.  After convergence is obtained, the
 program continues to iterate to obtain the exact  value  for
 the  terminal  voltages.   If a circuit has more than one dc
 stable state, the OFF option can be used to force the  solu-
 tion  to  correspond  to  a  desired  state.  If a device is
 specified OFF when in reality the device is conducting,  the
 program  still  obtains  the  correct solution (assuming the
 solutions converge) but more iterations are  required  since
 the  program  must  independently  converge  to two separate
 solutions.  The .NODESET control line serves a similar  pur-
 pose  as  the  OFF option.  The .NODESET option is easier to
 apply and is the preferred means to aid convergence.
      The second form of initial conditions are specified for
 use  with  the  transient analysis.  These are true 'initial
 conditions' as opposed to the convergence aids  above.   See
 the  description  of the .IC control line and the .TRAN con-
 trol line for a detailed explanation of initial conditions.
Junction Diodes BJT Models MOSFETs MESFET Models
Diode Model Junction FieldEffect Transistors MOSFET Models  
Bipolar Junction Transistors JFET Models MESFETs  

Junction Diodes

 3.4.1.  Junction Diodes
 General form:
     DXXXXXXX N+ N- MNAME <AREA> <OFF> <IC=VD> <TEMP=T>
 Examples:
     DBRIDGE 2 10 DIODE1
     DCLMP 3 7 DMOD 3.0 IC=0.2
      N+ and N- are the positive and negative nodes,  respec-
 tively.   MNAME  is the model name, AREA is the area factor,
 and OFF indicates an (optional) starting  condition  on  the
 device  for  dc  analysis.  If the area factor is omitted, a
 value of 1.0 is assumed.  The (optional)  initial  condition
 specification  using  IC=VD is intended for use with the UIC
 option on the .TRAN control line, when a transient  analysis
 is  desired starting from other than the quiescent operating
 point.  The (optional) TEMP  value  is  the  temperature  at
 which  this device is to operate, and overrides the tempera-
 ture specification on the .OPTION control line.

Diode Model (D)

 3.4.2.  Diode Model (D)
      The dc characteristics of the diode are  determined  by
 the  parameters  IS  and N.  An ohmic resistance, RS, is in-
 cluded.  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  tem-
 perature  dependence of the saturation current is defined by
 the parameters  EG,  the  energy  and  XTI,  the  saturation
 current  temperature  exponent.   The nominal temperature at
 which these parameters were measured is TNOM, which defaults
 to  the circuit-wide value specified on the .OPTIONS control
 line.  Reverse breakdown is modeled by  an  exponential  in-
 crease in the reverse diode current and is determined by the
 parameters BV and IBV (both of which are positive numbers).
      name   parameter                           units   default    example    area
  1   IS     saturation current                  A       1.0e-14    1.0e-14    *
  2   RS     ohmic resistance                    Z       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
                                                 o
 15   TNOM   parameter measurement temperature    C      27         50

Bipolar Junction Transistors (BJTs)

 3.4.3.  Bipolar Junction Transistors (BJTs)
 General form:
     QXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE, VCE> <TEMP=T>
 Examples:
     Q23 10 24 13 QMOD IC=0.6, 5.0
     Q50A 11 26 4 20 MOD1
      NC, NB, and NE are the  collector,  base,  and  emitter
 nodes,  respectively.   NS is the (optional) substrate node.
 If unspecified, ground is used.  MNAME is  the  model  name,
 AREA  is  the  area  factor, and OFF indicates an (optional)
 initial condition on the device for the dc analysis.  If the
 area  factor  is  omitted,  a  value of 1.0 is assumed.  The
 (optional) initial condition specification using IC=VBE, VCE
 is intended for use with the UIC option on the .TRAN control
 line, when a transient analysis  is  desired  starting  from
 other  than the quiescent operating point.  See the .IC con-
 trol line description for a better way to set transient ini-
 tial  conditions.  The (optional) TEMP value is the tempera-
 ture at which this device is to operate, and  overrides  the
 temperature specification on the .OPTION control line.

BJT Models (NPN/PNP)

 3.4.4.  BJT Models (NPN/PNP)
      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  ori-
 ginal  model to include several effects at high bias levels.
 The model automatically simplifies to the simpler Ebers-Moll
 model when certain parameters are not specified.  The param-
 eter 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.
      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  deter-
 mine  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 capaci-
 tances 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 tem-
 perature dependence  is  modeled  by  the  beta  temperature
 exponent  XTB  in  the  new model.  The values specified are
 assumed to have been measured at the temperature TNOM, which
 can  be specified on the .OPTIONS control line or overridden
 by a specification on the .MODEL line.
      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.
         Modified Gummel-Poon BJT Parameters.
      name   parameter                               units   default    example   area
 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               Z       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                        Z       RB         10        *
 17   RE     emitter resistance                      Z       0          1         *
 18   RC     collector resistance                    Z       0          10        *
 19   CJE    B-E zero-bias depletion capacitance     F       0          2pF       *
 20   VJE    B-E built-in potential                  V       0.75       0.6
 21   MJE    B-E junction exponential factor         -       0.33       0.33
 22   TF     ideal forward transit time              sec     0          0.1ns
 23   XTF    coefficient for bias dependence of TF   -       0
 24   VTF    voltage describing VBC
             dependence of TF                        V       infinite
 25   ITF    high-current parameter
             for effect on TF                        A       0                    *
 26   PTF    excess phase at freq=1.0/(TF*2PI) Hz    deg     0
 27   CJC    B-C zero-bias depletion capacitance     F       0          2pF       *
 28   VJC    B-C built-in potential                  V       0.75       0.5
 29   MJC    B-C junction exponential factor         -       0.33       0.5
 30   XCJC   fraction of B-C depletion capacitance   -       1
             connected to internal base node
 31   TR     ideal reverse transit time              sec     0          10ns
 32   CJS    zero-bias collector-substrate
             capacitance                             F       0          2pF       *
 33   VJS    substrate junction built-in potential   V       0.75
 34   MJS    substrate junction exponential factor   -       0          0.5
 35   XTB    forward and reverse beta
             temperature exponent                    -       0
 36   EG     energy gap for temperature
             effect on IS                            eV      1.11
 37   XTI    temperature exponent for effect on IS   -       3
 38   KF     flicker-noise coefficient               -       0
 39   AF     flicker-noise exponent                  -       1
 40   FC     coefficient for forward-bias
             depletion capacitance formula           -       0.5
                                                     o
 41   TNOM   Parameter measurement temperature        C      27         50

Junction Field-Effect Transistors (JFETs)

 3.4.5.  Junction Field-Effect Transistors (JFETs)
 General form:
     JXXXXXXX ND NG NS MNAME <AREA> <OFF> <IC=VDS, VGS> <TEMP=T>
 Examples:
     J1 7 2 3 JM1 OFF
      ND, NG, and NS are the drain, gate, and  source  nodes,
 respectively.   MNAME  is  the  model name, AREA is the area
 factor, and OFF indicates an (optional) initial condition on
 the  device for dc analysis.  If the area factor is omitted,
 a value of 1.0 is assumed.  The (optional) initial condition
 specification,  using  IC=VDS,  VGS is intended for use with
 the UIC option on the .TRAN control line, when  a  transient
 analysis  is  desired starting from other than the quiescent
 operating point.  See the .IC control line for a better  way
 to set initial conditions.  The (optional) TEMP value is the
 temperature at which this device is to  operate,  and  over-
 rides  the  temperature specification on the .OPTION control
 line.

JFET Models (NJF/PJF)

 3.4.6.  JFET Models (NJF/PJF)
      The JFET model is derived from the FET model of  Shich-
 man  and  Hodges.  The dc characteristics are defined by the
 parameters VTO and BETA, which determine  the  variation  of
 drain  current  with  gate voltage, LAMBDA, which determines
 the output conductance, and IS, the  saturation  current  of
 the  two  gate junctions.  Two ohmic resistances, RD and RS,
 are included.  Charge storage is modeled by nonlinear deple-
 tion  layer  capacitances for both gate junctions which vary
 as the -1/2 power of junction voltage and are defined by the
 parameters CGS, CGD, and PB.
      Note that in Spice3f and later, a fitting  parameter  B
 has been added.  For details, see [9].
      name     parameter                                  units   default   example   area
  1   VTO      threshold voltage (V                       V       -2.0      -2.0
                                   TO                        2
  2   BETA     transconductance parameter (B)             A/V     1.0e-4    1.0e-3    *
  3   LAMBDA   channel-length modulation
               parameter (L)                              1/V     0         1.0e-4
  4   RD       drain ohmic resistance                     Z       0         100       *
  5   RS       source ohmic resistance                    Z       0         100       *
  6   CGS      zero-bias G-S junction capacitance (C  )   F       0         5pF       *
                                                    gs
  7   CGD      zero-bias G-D junction capacitance (C  )   F       0         1pF       *
                                                    gs
  8   PB       gate junction potential                    V       1         0.6
  9   IS       gate junction saturation current (I )      A       1.0e-14   1.0e-14   *
                                                  S
 10   B        doping tail parameter                      -       1         1.1
 11   KF       flicker noise coefficient                  -       0
 12   AF       flicker noise exponent                     -       1
 13   FC       coefficient for forward-bias               -       0.5
               depletion capacitance formula
                                                          o
 14   TNOM     parameter measurement temperature           C      27        50

MOSFETs

 3.4.7.  MOSFETs
 General form:
     MXXXXXXX ND NG NS NB MNAME <L=VAL> <W=VAL> <AD=VAL> <AS=VAL>
     + <PD=VAL> <PS=VAL> <NRD=VAL> <NRS=VAL> <OFF>
     + <IC=VDS, VGS, VBS> <TEMP=T>
 Examples:
     M1 24 2 0 20 TYPE1
     M31 2 17 6 10 MODM L=5U W=2U
     M1 2 9 3 0 MOD1 L=10U W=5U AD=100P AS=100P PD=40U PS=40U
 ND, NG, NS, and NB are the drain,  gate,  source,  and  bulk
 (substrate)  nodes,  respectively.  MNAME is the model name.
 L and W are the channel length and width, in meters.  AD and
 AS  are  the  areas  of  the drain and source diffusions, in
       2
 meters .  Note that the suffix U specifies microns (1e-6  m)
                            2
 and  P  sq-microns (1e-12 m ). If any of L, W, AD, or AS are
 not specified, default values are used.  The use of defaults
 simplifies  input  file  preparation, as well as the editing
 required if device geometries are to be changed.  PD and  PS
 are  the  perimeters  of  the drain and source junctions, in
 meters.  NRD and NRS  designate  the  equivalent  number  of
 squares  of  the  drain  and source diffusions; these values
 multiply the sheet resistance RSH specified  on  the  .MODEL
 control line for an accurate representation of the parasitic
 series drain and source resistance of each  transistor.   PD
 and  PS  default to 0.0 while NRD and NRS to 1.0.  OFF indi-
 cates an (optional) initial condition on the device  for  dc
 analysis.   The  (optional)  initial condition specification
 using IC=VDS, VGS, VBS is intended  for  use  with  the  UIC
 option  on the .TRAN control line, when a transient analysis
 is desired starting from other than the quiescent  operating
 point.   See the .IC control line for a better and more con-
 venient way to specify transient  initial  conditions.   The
 (optional)  TEMP value is the temperature at which this dev-
 ice is to operate, and overrides the temperature  specifica-
 tion  on the .OPTION control line.  The temperature specifi-
 cation is ONLY valid for level 1, 2, 3, and 6  MOSFETs,  not
 for level 4 or 5 (BSIM) devices.

MOSFET Models (NMOS/PMOS)

 3.4.8.  MOSFET Models (NMOS/PMOS)
      SPICE provides four MOSFET device models, which  differ
 in  the formulation of the I-V characteristic.  The variable
 LEVEL specifies the model to be used:
     LEVEL=1 ->    Shichman-Hodges
     LEVEL=2 ->    MOS2 (as described in [1])
     LEVEL=3 ->    MOS3, a semi-empirical model(see [1])
     LEVEL=4 ->    BSIM (as described in [3])
     LEVEL=5 ->    new BSIM (BSIM2; as described in [5])
     LEVEL=6 ->    MOS6 (as described in [2])
 The dc characteristics of the level 1 through level  3  MOS-
 FETs  are  defined by the device parameters VTO, KP, LAMBDA,
 PHI and GAMMA.  These parameters are computed  by  SPICE  if
 process  parameters  (NSUB,  TOX,  ...) are given, but user-
 specified values always override.  VTO  is  positive  (nega-
 tive)  for  enhancement  mode  and  negative  (positive) for
 depletion  mode  N-channel  (P-channel)   devices.    Charge
 storage is modeled by three constant capacitors, CGSO, CGDO,
 and CGBO which represent overlap capacitances, by  the  non-
 linear thin-oxide capacitance which is distributed among the
 gate, source, drain, and bulk regions, and by the  nonlinear
 depletion-layer  capacitances  for  both substrate junctions
 divided into bottom and periphery, which vary as the MJ  and
 MJSW  power of junction voltage respectively, and are deter-
 mined by the parameters CBD, CBS, CJ, CJSW, MJ, MJSW and PB.
 Charge  storage  effects are modeled by the piecewise linear
 voltages-dependent capacitance model proposed by Meyer.  The
 thin-oxide  charge-storage effects are treated slightly dif-
 ferent for the LEVEL=1 model.  These voltage-dependent capa-
 citances  are included only if TOX is specified in the input
 description and they are represented using Meyer's  formula-
 tion.
      There is some overlap among the  parameters  describing
 the  junctions, e.g. the reverse current can be input either
                              2
 as IS (in A) or as JS (in A/m ). Whereas  the  first  is  an
 absolute value the second is multiplied by AD and AS to give
 the reverse  current  of  the  drain  and  source  junctions
 respectively.   This methodology has been chosen since there
 is no sense in relating always junction characteristics with
 AD  and  AS  entered  on  the  device line; the areas can be
 defaulted.  The same idea  applies  also  to  the  zero-bias
 junction capacitances CBD and CBS (in F) on one hand, and CJ
        2
 (in F/m ) on the other.   The  parasitic  drain  and  source
 series  resistance  can be expressed as either RD and RS (in
 ohms) or RSH (in ohms/sq.), the latter being  multiplied  by
 the number of squares NRD and NRS input on the device line.
      A discontinuity in the MOS level 3 model  with  respect
 to  the  KAPPA  parameter has been detected (see [10]).  The
 supplied fix has been implemented  in  Spice3f2  and  later.
 Since  this  fix  may  affect  parameter fitting, the option
 "BADMOS3" may be set to use the old implementation (see  the
 section  on  simulation  variables and the ".OPTIONS" line).
 SPICE level 1, 2,  3 and 6 parameters:
      name     parameter                               units   default           example
 1    LEVEL    model index                             -       1
 2    VTO      zero-bias threshold voltage (V  )       V       0.0               1.0
                                             TO           2
 3    KP       transconductance parameter              A/V     2.0e-5            3.1e-5
                                                        1/2
 4    GAMMA    bulk threshold parameter (\)            V       0.0               0.37
 5    PHI      surface potential (U)                   V       0.6               0.65
 6    LAMBDA   channel-length modulation
               (MOS1 and MOS2 only) (L)                1/V     0.0               0.02
 7    RD       drain ohmic resistance                  Z       0.0               1.0
 8    RS       source ohmic resistance                 Z       0.0               1.0
 9    CBD      zero-bias B-D junction capacitance      F       0.0               20fF
 10   CBS      zero-bias B-S junction capacitance      F       0.0               20fF
 11   IS       bulk junction saturation current (I )   A       1.0e-14           1.0e-15
                                                  S
 12   PB       bulk junction potential                 V       0.8               0.87
 13   CGSO     gate-source overlap capacitance
               per meter channel width                 F/m     0.0               4.0e-11
 14   CGDO     gate-drain overlap capacitance
               per meter channel width                 F/m     0.0               4.0e-11
 15   CGBO     gate-bulk overlap capacitance
               per meter channel length                F/m     0.0               2.0e-10
 16   RSH      drain and source diffusion
               sheet resistance                        Z/[]    0.0               10.0
 17   CJ       zero-bias bulk junction bottom cap.
                                                          2
               per sq-meter of junction area           F/m     0.0               2.0e-4
 18   MJ       bulk junction bottom grading coeff.     -       0.5               0.5
 19   CJSW     zero-bias bulk junction sidewall cap.
               per meter of junction perimeter         F/m     0.0               1.0e-9
 20   MJSW     bulk junction sidewall grading coeff.   -       0.50(level1)
                                                               0.33(level2, 3)
 21   JS       bulk junction saturation current
                                                          2
               per sq-meter of junction area           A/m                       1.0e-8
 22   TOX      oxide thickness                         meter   1.0e-7            1.0e-7
                                                           3
 23   NSUB     substrate doping                        1/cm    0.0               4.0e15
                                                           2
 24   NSS      surface state density                   1/cm    0.0               1.0e10
                                                           2
 25   NFS      fast surface state density              1/cm    0.0               1.0e10
                          continued
      name    parameter                              units    default   example
 26   TPG     type of gate material:                 -        1.0
                  +1 opp. to substrate
                  -1 same as substrate
                   0  Al gate
 27   XJ      metallurgical junction depth           meter    0.0       1M
 28   LD      lateral diffusion                      meter    0.0       0.8M
                                                       2
 29   UO      surface mobility                       cm /Vs   600       700
 30   UCRIT   critical field for mobility
              degradation (MOS2 only)                V/cm     1.0e4     1.0e4
 31   UEXP    critical field exponent in
              mobility degradation (MOS2 only)       -        0.0       0.1
 32   UTRA    transverse field coeff. (mobility)
              (deleted for MOS2)                     -        0.0       0.3
 33   VMAX    maximum drift velocity of carriers     m/s      0.0       5.0e4
 34   NEFF    total channel-charge (fixed and
              mobile) coefficient (MOS2 only)        -        1.0       5.0
 35   KF      flicker noise coefficient              -        0.0       1.0e-26
 36   AF      flicker noise exponent                 -        1.0       1.2
 37   FC      coefficient for forward-bias
              depletion capacitance formula          -        0.5
 38   DELTA   width effect on threshold voltage
              (MOS2 and MOS3)                        -        0.0       1.0
 39   THETA   mobility modulation (MOS3 only)        1/V      0.0       0.1
 40   ETA     static feedback (MOS3 only)            -        0.0       1.0
 41   KAPPA   saturation field factor (MOS3 only)    -        0.2       0.5
                                                     o
 42   TNOM    parameter measurement temperature       C       27        50
      The level 4 and level 5 (BSIM1  and  BSIM2)  parameters
 are  all  values obtained from process characterization, and
 can be generated automatically.  J. Pierret [4] describes  a
 means  of  generating  a  'process'  file,  and  the program
 Proc2Mod provided with SPICE3 converts this file into a  se-
 quence  of  BSIM1 ".MODEL" lines suitable for inclusion in a
 SPICE input file.  Parameters marked below with an * in  the
 l/w  column also have corresponding parameters with a length
 and width dependency.  For example, VFB is the basic parame-
 ter  with  units  of Volts, and LVFB and WVFB also exist and
 have units of Volt-Mmeter The formula
                            P            P
                             L            W
               P = P  + ---------- + ----------
                    0
                        L            W
                         effective    effective
 is used to evaluate the  parameter  for  the  actual  device
 specified with
                   L          = L      - DL
                    effective    input
 and
                   W          = W      - DW
                    effective    input
      Note that unlike the other models in  SPICE,  the  BSIM
 model  is  designed  for use with a process characterization
 system that provides all the parameters, thus there  are  no
 defaults  for  the  parameters,  and leaving one out is con-
 sidered an error.  For an example set of parameters and  the
 format  of  a  process  file,  see the SPICE2 implementation
 notes[3].
      For more information on BSIM2, see reference [5].
 SPICE BSIM (level 4) parameters.
 name    parameter                                                                 units      l/w
 VFB     flat-band voltage                                                         V          *
 PHI     surface inversion potential                                               V          *
                                                                                    1/2
 K1      body effect coefficient                                                   V          *
 K2      drain/source depletion charge-sharing coefficient                         -          *
 ETA     zero-bias drain-induced barrier-lowering coefficient                      -          *
                                                                                     2
 MUZ     zero-bias mobility                                                        cm /V-s
 DL      shortening of channel                                                     Mm
 DW      narrowing of channel                                                      Mm
                                                                                    -1
 U0      zero-bias transverse-field mobility degradation coefficient               V          *
 U1      zero-bias velocity saturation coefficient                                 Mm/V       *
                                                                                     2  2
 X2MZ    sens. of mobility to substrate bias at v  =0                              cm /V -s   *
                                                 ds                                 -1
 X2E     sens. of drain-induced barrier lowering effect to substrate bias          V          *
                                                                                    -1
 X3E     sens. of drain-induced barrier lowering effect to drain bias at V  =V     V          *
                                                                          ds  dd    -2
 X2U0    sens. of transverse field mobility degradation effect to substrate bias   V          *
                                                                                      -2
 X2U1    sens. of velocity saturation effect to substrate bias                     MmV        *
                                                                                     2  2
 MUS     mobility at zero substrate bias and at V  =V                              cm /V -s
                                                 ds  dd                              2  2
 X2MS    sens. of mobility to substrate bias at V  =V                              cm /V -s   *
                                                 ds  dd                              2  2
 X3MS    sens. of mobility to drain bias at V  =V                                  cm /V -s   *
                                             ds  dd                                   -2
 X3U1    sens. of velocity saturation effect on drain bias at V  =V                MmV        *
                                                               ds  dd
 TOX     gate oxide thickness                                                      Mm
                                                                                   o
 TEMP    temperature at which parameters were measured                              C
 VDD     measurement bias range                                                    V
 CGDO    gate-drain overlap capacitance per meter channel width                    F/m
 CGSO    gate-source overlap capacitance per meter channel width                   F/m
 CGBO    gate-bulk overlap capacitance per meter channel length                    F/m
 XPART   gate-oxide capacitance-charge model flag                                  -
 N0      zero-bias subthreshold slope coefficient                                  -          *
 NB      sens. of subthreshold slope to substrate bias                             -          *
 ND      sens. of subthreshold slope to drain bias                                 -          *
 RSH     drain and source diffusion sheet resistance                               Z/[]
                                                                                      2
 JS      source drain junction current density                                     A/m
 PB      built in potential of source drain junction                               V
 MJ      Grading coefficient of source drain junction                              -
 PBSW    built in potential of source, drain junction sidewall                     V
 MJSW    grading coefficient of source drain junction sidewall                     -
                                                                                      2
 CJ      Source drain junction capacitance per unit area                           F/m
 CJSW    source drain junction sidewall capacitance per unit length                F/m
 WDF     source drain junction default width                                       m
 DELL    Source drain junction length reduction                                    m
      XPART = 0 selects a 40/60 drain/source charge partition
 in  saturation,  while  XPART=1 selects a 0/100 drain/source
 charge partition.
      ND, NG, and NS are the drain, gate, and  source  nodes,
 respectively.   MNAME  is  the  model name, AREA is the area
 factor, and OFF indicates an (optional) initial condition on
 the  device for dc analysis.  If the area factor is omitted,
 a value of 1.0 is assumed.  The (optional) initial condition
 specification,  using  IC=VDS,  VGS is intended for use with
 the UIC option on the .TRAN control line, when  a  transient
 analysis  is  desired starting from other than the quiescent
 operating point.  See the .IC control line for a better  way
 to set initial conditions.

MESFETs

 3.4.9.  MESFETs
 General form:
     ZXXXXXXX ND NG NS MNAME <AREA> <OFF> <IC=VDS, VGS>
 Examples:
     Z1 7 2 3 ZM1 OFF

MESFET Models (NMF/PMF)

 3.4.10.  MESFET Models (NMF/PMF)
      The MESFET model is derived from the GaAs FET model  of
 Statz  et al.  as described in [11].  The dc characteristics
 are defined by the parameters VTO, B, and BETA, which deter-
 mine  the  variation of drain current with gate voltage, AL-
 PHA, which determines saturation voltage, and LAMBDA,  which
 determines  the  output  conductance.  The formula are given
 by:
                                   3
                  2
        B (V  -V )    |    |   V  |  |                             3
            gs  T               ds                                 _
 I  = --------------- |1 - |1-A---|  |(1 + L V  )   for  0 < V   <
  d                                           ds              ds
      1 + b(V   - V ) |    |    3 |  |                             A
             gs    T
                          2
                B (V  -V )                                     3
                    gs  T                                      _
         I  = ---------------(1 + L V  )            for  V   >
          d                          ds                   ds
              1 + b(V   - V )                                  A
                     gs    T
      Two ohmic resistances, RD and RS, are included.  Charge
 storage  is  modeled  by  total gate charge as a function of
 gate-drain and gate-source voltages and is  defined  by  the
 parameters CGS, CGD, and PB.
      name     parameter                            units   default   example   area
  1   VTO      pinch-off voltage                    V       -2.0      -2.0
                                                       2
  2   BETA     transconductance parameter           A/V     1.0e-4    1.0e-3    *
  3   B        doping tail extending parameter      1/V     0.3       0.3       *
  4   ALPHA    saturation voltage parameter         1/V     2         2         *
  5   LAMBDA   channel-length modulation
               parameter                            1/V     0         1.0e-4
  6   RD       drain ohmic resistance               Z       0         100       *
  7   RS       source ohmic resistance              Z       0         100       *
  8   CGS      zero-bias G-S junction capacitance   F       0         5pF       *
  9   CGD      zero-bias G-D junction capacitance   F       0         1pF       *
 10   PB       gate junction potential              V       1         0.6
 11   KF       flicker noise coefficient            -       0
 12   AF       flicker noise exponent               -       1
 13   FC       coefficient for forward-bias         -       0.5
               depletion capacitance formula

ANALYSES AND OUTPUT CONTROL

 4.  ANALYSES AND OUTPUT CONTROL
      The following command lines are for specifying analyses
 or plots within the circuit description file.  Parallel com-
 mands exist in the interactive command interpreter (detailed
 in  the  following  section).  Specifying analyses and plots
 (or tables) in the input file  is  useful  for  batch  runs.
 Batch  mode is entered when either the -b option is given or
 when the default input source is redirected from a file.  In
 batch  mode,  the analyses specified by the control lines in
 the input file (e.g. ".ac", ".tran", etc.)  are  immediately
 executed (unless ".control" lines exists; see the section on
 the interactive command interpretor).   If  the  -r  rawfile
 option  is  given  then  all  data generated is written to a
 Spice3 rawfile.  The rawfile  may  be  read  by  either  the
 interactive  mode  of  Spice3 or by nutmeg; see the previous
 section for details.  In this  case,  the  .SAVE  line  (see
 below)  may  be  used to record the value of internal device
 variables (see Appendix B).
      If a rawfile is not specified, then  output  plots  (in
 "line-printer"  form) and tables can be printed according to
 the .PRINT, .PLOT, and .FOUR control lines, described  next.
 .PLOT,  .PRINT,  and .FOUR lines are meant for compatibility
 with Spice2.
SIMULATOR VARIABLES INITIAL CONDITIONS ANALYSES BATCH OUTPUT

SIMULATOR VARIABLES (.OPTIONS)

 4.1.  SIMULATOR VARIABLES (.OPTIONS)
      Various parameters  of  the  simulations  available  in
 Spice3  can  be  altered  to control the accuracy, speed, or
 default values for some devices.  These  parameters  may  be
 changed  via  the "set" command (described later in the sec-
 tion on the interactive front-end)  or  via  the  ".OPTIONS"
 line:
 General form:
     .OPTIONS OPT1 OPT2 ... (or OPT=OPTVAL ...)
 Examples:
     .OPTIONS RELTOL=.005 TRTOL=8
      The options line allows the user to reset program  con-
 trol  and  user  options  for  specific simulation purposes.
 Additional options for Nutmeg may be specified as  well  and
 take  effect  when  Nutmeg  reads  the  input file.  Options
 specified to Nutmeg via the 'set' command are also passed on
 to  SPICE3 as if specified on a .OPTIONS line.  See the fol-
 lowing section on the interactive  command  interpreter  for
 the parameters which may be set with a .OPTIONS line and the
 format of the 'set' command.  Any combination of the follow-
 ing  options  may  be  included,  in any order.  'x' (below)
 represents some positive number.
 option         effect
 ABSTOL=x       resets the absolute current error tolerance of the
                program.
                The default value is 1 picoamp.
 BADMOS3        Use the older version of the MOS3 model with the "kappa"
                discontinuity.
 CHGTOL=x       resets the charge tolerance of the program.  The default
                value is 1.0e-14.
 DEFAD=x        resets the value for MOS drain diffusion area; the
                default is 0.0.
 DEFAS=x        resets the value for MOS source diffusion area; the
                default is 0.0.
 DEFL=x         resets the value for MOS channel length; the default
                is 100.0 micrometer.
 DEFW=x         resets the value for MOS channel width; the default
                is 100.0 micrometer.
 GMIN=x         resets the value of GMIN, the minimum conductance
                allowed by the program.
                The default value is 1.0e-12.
 ITL1=x         resets the dc iteration limit.  The default is 100.
 ITL2=x         resets the dc transfer curve iteration limit.  The
                default is 50.
 ITL3=x         resets the lower transient analysis iteration limit.
                the default value is 4.  (Note: not implemented in Spice3).
 ITL4=x         resets the transient analysis timepoint iteration limit.
                the default is 10.
 ITL5=x         resets the transient analysis total iteration limit.
                the default is 5000.  Set ITL5=0 to omit this test.
                (Note: not implemented in Spice3).
 KEEPOPINFO     Retain the operating point information when either an
                AC, Distortion, or Pole-Zero analysis is run.
                This is particularly useful if the circuit is large
                and you do not want to run a (redundant) ".OP" analysis.
 METHOD=name    sets the numerical integration method used by SPICE.
                Possible names are "Gear" or "trapezoidal" (or just "trap").
                The default is trapezoidal.
 PIVREL=x       resets the relative ratio between the largest column entry
                and an acceptable pivot value. The default value is 1.0e-3.
                In the numerical pivoting algorithm the allowed minimum
                pivot value is determined by
                EPSREL=AMAX1(PIVREL*MAXVAL, PIVTOL)
                where MAXVAL is the maximum element in the column where
                a pivot is sought (partial pivoting).
 PIVTOL=x       resets the absolute minimum value for a matrix entry
                to be accepted as a pivot.  The default value is 1.0e-13.
 RELTOL=x       resets the relative error tolerance of the program.
                The
                default value is 0.001 (0.1%).
 TEMP=x         Resets the operating temperature of the circuit.  The
                default value is 27 deg C (300 deg K).  TEMP can be overridden
                by a temperature specification on any temperature dependent
                instance.
 TNOM=x         resets the nominal temperature at which device parameters
                are measured.  The default value is 27 deg C (300 deg K).
                TNOM can be overridden by a specification on any temperature
                dependent device model.
 TRTOL=x        resets the transient error tolerance.  The default value
                is 7.0.  This parameter is an estimate of the factor by
                which SPICE overestimates the actual truncation error.
 TRYTOCOMPACT   Applicable only to the LTRA model.
                When specified, the simulator tries to condense LTRA transmission
                lines' past history of input voltages and currents.
 VNTOL=x        resets the absolute voltage error tolerance of the
                program.  The default value is 1 microvolt.
      In addition, the  following  options  have  the  listed
 effect when operating in spice2 emulation mode:
 option   effect
 option   effect
 ACCT     causes accounting and run time statistics to be printed
 LIST     causes the summary listing of the input data to be printed
 NOMOD    suppresses the printout of the model parameters
 NOPAGE   suppresses page ejects
 NODE     causes the printing of the node table.
 OPTS     causes the option values to be printed.

INITIAL CONDITIONS

 4.2.  INITIAL CONDITIONS
.NODESET .IC    

.NODESET: Specify Initial Node Voltage Guesses

 4.2.1.  .NODESET:  Specify Initial Node Voltage Guesses
 General form:
     .NODESET V(NODNUM)=VAL V(NODNUM)=VAL ...
 Examples:
     .NODESET V(12)=4.5 V(4)=2.23
      The Nodeset line helps the program find the dc or  ini-
 tial  transient  solution  by making a preliminary pass with
 the specified nodes held to the given  voltages.   The  res-
 triction is then released and the iteration continues to the
 true solution.  The .NODESET line may be necessary for  con-
 vergence on bistable or a-stable circuits.  In general, this
 line should not be necessary.

.IC: Set Initial Conditions

 4.2.2.  .IC:  Set Initial Conditions
 General form:
     .IC V(NODNUM)=VAL V(NODNUM)=VAL ...
 Examples:
     .IC V(11)=5 V(4)=-5 V(2)=2.2
      The IC line is for  setting  transient  initial  condi-
 tions.   It  has two different interpretations, depending on
 whether the UIC parameter is specified on the .TRAN  control
 line.   Also,  one  should  not  confuse  this line with the
 .NODESET line.  The .NODESET line is only to help dc conver-
 gence,  and  does not affect final bias solution (except for
 multi-stable circuits).  The  two  interpretations  of  this
 line are as follows:
  1.  When the UIC parameter is specified on the .TRAN  line,
 then the node voltages specified on the .IC control line are
 used to compute the capacitor, diode, BJT, JFET, and  MOSFET
 initial  conditions.   This  is equivalent to specifying the
 IC=... parameter on each device line, but is much more  con-
 venient.   The  IC=...  parameter can still be specified and
 takes precedence over the .IC  values.   Since  no  dc  bias
 (initial  transient)  solution  is computed before the tran-
 sient analysis, one should  take  care  to  specify  all  dc
 source  voltages  on  the .IC control line if they are to be
 used to compute device initial conditions.
  2.  When the UIC parameter is not specified  on  the  .TRAN
 control  line,  the  dc bias (initial transient) solution is
 computed before the transient analysis.  In this  case,  the
 node voltages specified on the .IC control line is forced to
 the desired initial values during the bias solution.  During
 transient analysis, the constraint on these node voltages is
 removed.  This is the preferred method since it allows SPICE
 to compute a consistent dc solution.

ANALYSES

 4.3.  ANALYSES
.AC .NOISE .SENS  
.DC .OP .TF  
.DISTO .PZ .TRAN  

.AC: Small-Signal AC Analysis

 4.3.1.  .AC:  Small-Signal AC Analysis
 General form:
     .AC DEC ND FSTART FSTOP
     .AC OCT NO FSTART FSTOP
     .AC LIN NP FSTART FSTOP
 Examples:
     .AC DEC 10 1 10K
     .AC DEC 10 1K 100MEG
     .AC LIN 100 1 100HZ
      DEC stands for decade variation, and ND is  the  number
 of  points per decade.  OCT stands for octave variation, and
 NO is the number of  points  per  octave.   LIN  stands  for
 linear variation, and NP is the number of points.  FSTART is
 the starting frequency, and FSTOP is  the  final  frequency.
 If  this  line is included in the input file, SPICE performs
 an AC analysis of the circuit over the  specified  frequency
 range.   Note that in order for this analysis to be meaning-
 ful, at least one independent source must have  been  speci-
 fied with an ac value.

.DC: DC Transfer Function

 4.3.2.  .DC:  DC Transfer Function
 General form:
     .DC SRCNAM VSTART VSTOP VINCR [SRC2 START2 STOP2 INCR2]
 Examples:
     .DC VIN 0.25 5.0 0.25
     .DC VDS 0 10 .5 VGS 0 5 1
     .DC VCE 0 10 .25 IB 0 10U 1U
      The DC line defines the dc transfer  curve  source  and
 sweep  limits  (again  with  capacitors  open  and inductors
 shorted).  SRCNAM is the name of an independent  voltage  or
 current  source.  VSTART, VSTOP, and VINCR are the starting,
 final, and  incrementing  values  respectively.   The  first
 example  causes  the  value  of the voltage source VIN to be
 swept from 0.25 Volts to 5.0 Volts  in  increments  of  0.25
 Volts.   A  second source (SRC2) may optionally be specified
 with associated sweep parameters.  In this case,  the  first
 source  is swept over its range for each value of the second
 source.  This option can be useful for obtaining semiconduc-
 tor  device  output characteristics.  See the second example
 circuit description in Appendix A.

.DISTO: Distortion Analysis

 4.3.3.  .DISTO:  Distortion Analysis
 General form:
     .DISTO DEC ND FSTART FSTOP <F2OVERF1>
     .DISTO OCT NO FSTART FSTOP <F2OVERF1>
     .DISTO LIN NP FSTART FSTOP <F2OVERF1>
 Examples:
     .DISTO DEC 10 1kHz 100Mhz
     .DISTO DEC 10 1kHz 100Mhz 0.9
      The Disto line does a small-signal distortion  analysis
 of   the   circuit.   A  multi-dimensional  Volterra  series
 analysis is done using multi-dimensional  Taylor  series  to
 represent  the nonlinearities at the operating point.  Terms
 of up to third order are used in the series expansions.
      If the optional parameter F2OVERF1  is  not  specified,
 .DISTO  does a harmonic analysis - i.e., it analyses distor-
 tion in the circuit using only a single input frequency  F1,
 which  is swept as specified by arguments of the .DISTO com-
 mand exactly as in the .AC command.   Inputs  at  this  fre-
 quency  may  be  present  at more than one input source, and
 their magnitudes and phases are specified by  the  arguments
 of the DISTOF1 keyword in the input file lines for the input
 sources (see the description for independent sources).  (The
 arguments  of  the  DISTOF2 keyword are not relevant in this
 case).  The analysis produces  information  about  the  A.C.
 values  of all node voltages and branch currents at the har-
 monic frequencies 2F1 and 3F1, vs. the input frequency F1 as
 it is swept.  (A value of 1 (as a complex distortion output)
 signifies cos(2J(2F1)t) at 2F1  and  cos(2J(3F1)t)  at  3F1,
 using  the  convention  that 1 at the input fundamental fre-
 quency is equivalent to  cos(2JF1t).)  The  distortion  com-
 ponent  desired  (2F1 or 3F1) can be selected using commands
 in nutmeg, and then printed or plotted.  (Normally,  one  is
 interested  primarily  in the magnitude of the harmonic com-
 ponents, so the magnitude of  the  AC  distortion  value  is
 looked  at).   It  should  be  noted that these are the A.C.
 values of the actual harmonic components, and are not  equal
 to  HD2  and HD3.  To obtain HD2 and HD3, one must divide by
 the corresponding A.C. values at F1, obtained  from  an  .AC
 line.  This division can be done using nutmeg commands.
      If the optional F2OVERF1  parameter  is  specified,  it
 should  be  a real number between (and not equal to) 0.0 and
 1.0; in this case, .DISTO does a spectral analysis.  It con-
 siders  the  circuit with sinusoidal inputs at two different
 frequencies F1 and F2.  F1 is swept according to the  .DISTO
 control line options exactly as in the .AC control line.  F2
 is kept fixed at a single frequency as F1 sweeps - the value
 at which it is kept fixed is equal to F2OVERF1 times FSTART.
 Each independent source in the circuit may potentially  have
 two  (superimposed) sinusoidal inputs for distortion, at the
 frequencies F1 and F2.  The magnitude and phase  of  the  F1
 component are specified by the arguments of the DISTOF1 key-
 word in the source's input  line  (see  the  description  of
 independent sources); the magnitude and phase of the F2 com-
 ponent are specified by the arguments of  the  DISTOF2  key-
 word.    The   analysis   produces   plots   of   all   node
 voltages/branch currents at the intermodulation product fre-
 quencies  F1  +  F2,  F1 - F2, and (2 F1) - F2, vs the swept
 frequency F1.  The IM product of interest  may  be  selected
 using  the setplot command, and displayed with the print and
 plot commands.  It  is  to  be  noted  as  in  the  harmonic
 analysis  case,  the  results are the actual AC voltages and
 currents at the intermodulation frequencies, and need to  be
 normalized  with  respect  to  .AC  values  to obtain the IM
 parameters.
      If the DISTOF1 or DISTOF2 keywords are missing from the
 description  of  an  independent source, then that source is
 assumed to have no input  at  the  corresponding  frequency.
 The  default  values  of the magnitude and phase are 1.0 and
 0.0 respectively.  The phase should be specified in degrees.
      It should be carefully noted that the  number  F2OVERF1
 should  ideally be an irrational number, and that since this
 is not possible in practice, efforts should be made to  keep
 the denominator in its fractional representation as large as
 possible, certainly above 3, for accurate results (i.e.,  if
 F2OVERF1 is represented as a fraction A/B, where A and B are
 integers with no common factors, B should  be  as  large  as
 possible; note that A < B because F2OVERF1 is constrained to
 be < 1).   To  illustrate  why,  consider  the  cases  where
 F2OVERF1  is  49/100  and  1/2.  In a spectral analysis, the
 outputs produced are at F1 + F2, F1 - F2 and 2 F1 - F2.   In
 the  latter  case,  F1 - F2 = F2, so the result at the F1-F2
 component is erroneous because there is the strong fundamen-
 tal  F2  component at the same frequency.  Also, F1 + F2 = 2
 F1 - F2 in the latter case, and  each  result  is  erroneous
 individually.   This  problem is not there in the case where
 F2OVERF1 = 49/100, because F1-F2 = 51/100 F1 < > 49/100 F1 =
 F2.   In  this  case, there are two very closely spaced fre-
 quency components at F2 and F1 - F2.  One of the  advantages
 of the Volterra series technique is that it computes distor-
 tions at mix frequencies expressed symbolically (i.e. n F1 +
 m F2), therefore one is able to obtain the strengths of dis-
 tortion components accurately even if the separation between
 them  is  very  small,  as opposed to transient analysis for
 example.  The disadvantage is of course that if two  of  the
 mix   frequencies  coincide,  the  results  are  not  merged
 together and presented (though this could presumably be done
 as  a  postprocessing step).  Currently, the interested user
 should keep track of the mix frequencies himself or  herself
 and  add  the  distortions  at  coinciding  mix  frequencies
 together should it be necessary.

.NOISE: Noise Analysis

 4.3.4.  .NOISE:  Noise Analysis
 General form:
     .NOISE V(OUTPUT <,REF>) SRC ( DEC | LIN | OCT ) PTS FSTART FSTOP
     + <PTS_PER_SUMMARY>
 Examples:
     .NOISE V(5) VIN DEC 10 1kHZ 100Mhz
     .NOISE V(5,3) V1 OCT 8 1.0 1.0e6 1
      The Noise line does a noise analysis  of  the  circuit.
 OUTPUT  is  the  node  at  which  t