Josephson Junction Model

**Type Name:** `jj`

The Josephson junction model is an extended version of the RSJ model as used by Jewett[11].

The parameters marked with an asterisk in the **area** column
scale with the `area` parameter given in the device line.

JJ Model Parametersnameareaparameterunitsdefaultexamplepijjpi junction - 0 1 icrit* Junction critical current A1.0e-3 1.5e-3 cap* Junction capacitance F1.0e-12 5.0e-13 rnorrnorm* Normal state resistance 1.7 2.0 r0orrsub* Subgap resistance 30 50 vgorvgapGap voltage V3.0e-3 2.8e-3 delvGap voltage spread V1.0e-4 8.0e-5 rtypeQuasiparticle branch model - 1 2 cctCritical current model - 1 3 iconCritical current first zero A1.0e-2 2.5e-2 icfactRatio of critical to gap currents - /4 0.7 vshuntVoltage to specify fixed shunt resistance - 0 200uV

If `pijj` is set to a nonzero integer value, instances will be
``pi'' junctions by default, though this can be overridden per
instance by giving `pijj=0` on the device line.

The `rtype` parameter determines the type of quasiparticle branch
modeling employed. Legal values are as follows:

0The junction is completely unshunted (effectively sets rnandr0to infinity).1Standard piecewise-linear model. 2Analytic exponentially-derived approximation. 3Fifth order polynomial expansion model. 4``Temperature'' variation, allow modulation of the gap parameter.

The default is `rtype=1`. Setting `rtype=0` will disable
modeling of the quasiparticle current, effectively setting the RSJ
shunt resistance to infinity. Conditions with `rtype=1` and `2` are as described by Jewett, however it is not assumed that the
normal resistance projects through the origin. The `icfact`
parameter can be set to a value lower than the default BCS theoretical
value to reflect the behavior of most real junctions. The
quasiparticle resistance is approximated with a fifth order polynomial
if `rtype=3`, which seems to give good results for the modeling of
some NbN junctions (which tend to have gently sloping quasiparticle
curves).

`Rtype=4` uses a piecewise-linear quasiparticle characteristic
identical to `rtype=1`, however the gap voltage and critical
current are now proportional to the absolute value of the control
current set with a `control=`*src_name* entry in the device
line. This is to facilitate modeling of temperature changes or
nonequilibrium effects. For control current of 1 (Amp) or greater,
the full gap and critical current are used, otherwise they decrease
linearly to zero. If no device control source is specified, the
algorithm reverts to `rtype=1`. It is expected that a nonlinear
transfer function will be implemented with a controlled source, which
will in turn provide the controlling current to the junction in this
mode. For example, the controlling current can be translated from a
circuit voltage representing temperature with an external nonlinear
source. The functional dependence is in general a complicated
function, but a reasonable approximation is
1 - (*T*/*T*_{c})^{4}
. See the
examples for an example input file (`ex8.cir`) which illustrates
`rtype=4`.

It is currently not possible to use other than the piecewise linear
model with temperature variation. If `rtype=4`, then legal values
for the critical current parameter are `cct=0` (no critical
current) and `cct=1` (fixed critical current). If another value
is specified for `cct`, `cct` reverts to 0. Thus, magnetic
coupling and quasiparticle injection are not simultaneously available.

In general, the `cct` variable can take on the following values:

0No critical current. 1Fixed critical current. 2Sin(x)/x modulated supercurrent. 3Symmetric linear reduction modulation. 4Asymmetric linear reduction modulation.

The `control` parameter should be used with devices using `cct` 2,3, or 4. With `cct=2`, the first zero is equal to the
value of the model parameter `icon`. For `cct=3`, the maximum
critical current is at control current zero, and it reduces linearly
to zero at control current = *icon*
. Junctions with `cct=4`
have maximum critical current at control current = -
`icon`, and
linear reduction to zero at control current = +
`icon`. If `cct` is specified as 2, 3, or 4, the area parameter, if given, is set
to unity. Otherwise, the model parameters are scaled appropriately by
the area before use.

If the `vshunt` parameter is given, every device instance will be
shunted by a linear resistor. This is in addition to the resistance
of the quasiparticle branch. The value of this resistance is

whereR_{s}hunt=Vshunt/Ic