# Inductor (Table lookup)

In this topic:

## Netlist Entry

Uxxxx n1 n2 model_name [IC=initial_condition] [USEIC=use_ic]
 n1 node 1 n2 node 2 initial_condition Initial condition in Amps. Only active if USEIC is non-zero use_ic If non-zero, enable initial condition. This will set the current in the inductor to the value of initial_condition during the DC operating point analysis

## Model syntax

.MODEL model_name TABLE_INDUCTOR parameters
 Name Description Units Default L Inductance 1m H LTABLE Saturation table n/a ITABLE Current table A n/a TABLE_SIZE Number of elements in tables 2 RSERIES Series resistance $\Omega$ 0.0 RSHUNT Shunt resistance $\Omega$ 0.0 (sets to INF) LMIN Minimum inductance H 0.0 SMOOTH Smoothing option (0-3) 0

### Model Example

.MODEL TABLE_IND table_inductor L=1 USEIC=0 IC=0
+ RSERIES=0 RSHUNT=0 SMOOTH=2 TABLE_SIZE=7
+ ITABLE=[0,  8.3333, 16.666, 25, 33.3333, 41.666, 50]
+ LTABLE=[3.36e-07, 3.36e-07, 3.34e-07, 3.27e-07, 3.09e-07, 1.86e-07, 4.21e-08]

The above example has an inductance of 3.36e-07H at 0A falling to 4.21e-08 at 50A.

## Boundary Inductance

The inductance for this device is defined by a lookup table over a specific range. However, the behaviour at currents beyond that defined in the table must also be defined. We refer to the inductance as the 'boundary inductance'. This follows a characteristic of the form:

$A/(C+i^{2})+LMIN/L$

Where $A$ and $C$ are chosen so that the absolute inductance and $\frac{dL}{di}$ matches the table function at the final point.

## Smoothing Function

The SMOOTH parameter can be set to an integer between 1 and 4 to select a smoothing function. The following table describes the alternative strategies available:
 SMOOTH value Function 0 No smoothing function is selected. Inductor follows a PWL (piece-wise-linear) characteristic 1 Local cubic. Fits a cubic polynomial between each pair of points such that the gradient at each point is the average of the slope on either side of the point. This is continuous in the first derivative but is not continuous in the second derivative 2 Cubic spline with boundary conditions: lower: $\frac{dL}{di}=0$ upper: $\frac{d^{2}L}{di^{2}} = 0$ 3 Cubic spline with boundary conditions: lower: $\frac{dL}{di}=0$ upper: $\frac{dL}{di}= \text{slope_of_final_segment}$

SMOOTH=2 and SMOOTH=3 select a cubic spline function. A cubic spline fits a series of cubic polynomials through all points such that the function is continuous in the first and second derivatives. Cubic splines generally require boundary conditions to be set; that is some condition to define the first and last points. This is the only difference between SMOOTH=2 and SMOOTH=3. SMOOTH=2 usually gives the best results but can, in some situations, result in a positive slope at the join with the boundary inductance function. This cannot be matched to the boundary inductance and in these circumstances the device will fail with the error message:

***ERROR*** instance <ref>: Cannot fit spline to table using SMOOTH=2 strategy.
Try using SMOOTH=1 or SMOOTH=3

In this case SMOOTH=1 or SMOOTH=3 can be selected.