spiralInductor

Create spiral inductor in four different shapes

Since R2021b

Description

Use the spiralInductor object to create a spiral inductor in one of four different shapes: square, circle, hexagon, or octagon. The spiral inductor is a two-port planar inductor with a single or multiple dielectric layers. A turn in a spiral inductor is the length of a complete 360-degree revolution. Spiral inductor filaments have uniform spacing and width throughout the structure. Spiral inductors are an integral part of many radio-frequency and microwave circuits, acting as resonant elements or chokes. The inductor feed can be configured in one of the following two ways:

Note

This PCB object supports behavioral modeling. For more information, see Behavioral Models. To analyze the behavioral model for a spiral inductor, set the Behavioral property in the sparameters function to true or 1

• The input and output ports are punched through at the same layer.

• The input port is routed out from the layer below the inductor by a via hole. The output port is extended to the end of the dielectric in the same layer.

Creation

Syntax

inductor = spiralInductor

inductor = spiralInductor(Name=Value)

Description

inductor = spiralInductor creates a square spiral planar inductor with default properties for a resonant frequency of 600 MHz.

inductor = spiralInductor(Name=Value) sets Properties using one or more name-value arguments. For example, spiralInductor(SpiralShape="Octagon") creates an octagonal spiral inductor. Properties not specified retain their default values.

Properties

SpiralShape — Shape of spiral inductor

"Square" (default) | "Circle" | "Hexagon" | "Octagon"

Shape of the spiral inductor, specified as either "Square", "Circle", "Hexagon", or "Octagon".

Example: inductor = spiralInductor(SpiralShape="Circle")

Data Types: string | char

InnerDiameter — Inner diameter of polygon along edge

5.0000e-04 (default) | positive scalar

Inner diameter of the polygon along the edge in meters, specified as a positive scalar.

Example: inductor = spiralInductor(InnerDiameter=8.0000e-04)

Data Types: double

Width — Strip width

2.5000e-04 (default) | positive scalar

Strip width in meters, specified as a positive scalar.

Example: inductor = spiralInductor(Width=3.8000e-04)

Data Types: double

Spacing — Distance between strips

2.5000e-04 (default) | positive scalar

Distance between the strips in meters, specified as a positive scalar.

Example: inductor = spiralInductor(Spacing=3.8000e-04)

Data Types: double

NumTurns — Number of turns in spiral inductor

4 (default) | positive scalar

Number of turns in the spiral inductor, specified as a positive scalar. You can specify a minimum of 1 turn and a maximum of 12 turns. One turn length is the length of a complete 360-degree revolution.

Example: inductor = spiralInductor(NumTurns=6)

Data Types: double

Height — Height from ground plane to inductor

0.0010 (default) | positive scalar

Height from the ground plane to the inductor in meters, specified as a positive scalar.

Example: inductor = spiralInductor(Height=0.0056)

Data Types: double

GroundPlaneLength — Length of ground plane

0.0056 (default) | positive scalar

Length of the ground plane in meters, specified as a positive scalar. This object does not support infinite ground plane length.

Example: inductor = spiralInductor(GroundPlaneLength=0.046)

Example: double

GroundPlaneWidth — Width of ground plane

0.0056 (default) | positive scalar

Width of the ground plane in meters, specified as a positive scalar. This object does not support infinite ground plane width.

Example: inductor = spiralInductor(GroundPlaneWidth=0.046)

Example: double

Substrate — Type of dielectric material

dielectric object

Type of dielectric material used as a substrate, specified as a dielectric object. The dielectric material in a spiralInductor object with default properties have the following properties:

• Name—{'RTDuroid','RTDuroid','RTDuroid'}

• EpsilonR—[3.66,3.66,3.66]

• LossTangent—[0.0013,0.0013,0.0013]

• Thickness—[0.508e-3,0.508e-3,0.508e-3]

Example: d = dielectric("FR4"); inductor = spiralInductor(Substrate=d)

Data Types: string | char

Conductor — Type of metal used in conducting layers

metal object

Type of metal used in the conducting layers, specified as a metal object. The type of metal in a spiralInductor object with default properties is Copper

Example: m = metal("PEC"); inductor = spiralInductor(Conductor=m)

Data Types: string | char

Object Functions

charge	Calculate and plot charge distribution
current	Calculate and plot current distribution
feedCurrent	Calculate current at feed port
getZ0	Calculate characteristic impedance of transmission line
inductance	Calculate inductance
layout	Plot all metal layers and board shape
mesh	Change and view mesh properties of metal or dielectric in PCB component
shapes	Extract all metal layer shapes of PCB component
show	Display PCB component structure or PCB shape
sparameters	Calculate S-parameters for RF PCB objects

Examples

Create Default Spiral Inductor

Create and view a default spiral inductor.

inductor = spiralInductor

inductor = 
  spiralInductor with properties:

          SpiralShape: 'Square'
        InnerDiameter: 5.0000e-04
                Width: 2.5000e-04
              Spacing: 2.5000e-04
             NumTurns: 4
               Height: 0.0010
    GroundPlaneLength: 0.0056
     GroundPlaneWidth: 0.0056
            Substrate: [1x1 dielectric]
            Conductor: [1x1 metal]

show(inductor)

Octagonal Spiral Inductor

Create and view a two-turn octagonal spiral inductor.

inductor = spiralInductor(SpiralShape="Octagon",NumTurns=2);
show(inductor)

Measure the inductance of the inductor.

figure
inductance(inductor,600e6)

ind = inductance(inductor,600e6)

ind = 1.0744e-08

Analyze Spiral Inductor Using Behavioral S-parameters

Create a spiral inductor using gold as the conductor.

inductor = spiralInductor;
inductor.Conductor = metal("Gold");
show(inductor)

Compute and plot the behavioral S-parameters of the inductor at 600 MHz.

spar = sparameters(inductor,600e6,Behavioral=true);
rfplot(spar)

More About

Parametric Analysis Guidelines

• The inductance of a spiral inductor is directly proportional to the physical parameters such as NumTurns, Spacing, and Width.

• The decrease in the width reduces the capacitance between the turns of the inductor.

Inductor Length and Area

Inductor length equation:

$$inductorlength=NumTurns*Davg*N*\tan \left(\frac{\pi }{N}\right)$$

where,

• N = Number of sides of the polygon

• $$D_{avg}=\frac{(d_{out}-d_{in})}{(d_{out}+d_{in})}$$

  where when obj = spiralInductor,

  $$\begin{array}{l}{d}_{in}=obj.InnerDiameter\\ d_{out}=obj.InnerDiameter+2((obj.NumTurns\ast obj.Width)+(obj.NumTurns-1)\ast obj.Spacing)\end{array}$$

References

[1] Beeresha, R.S., A.M. Khan, and H.V. Manjunatha Reddy. “The Design and EM-Simulation of Square Spiral Inductor Using Simple Equations.” Materials Today: Proceedings 5, no. 4 (2018): 10875–82. https://doi.org/10.1016/j.matpr.2018.05.074.

[2] Mohan, S.S., M. del Mar Hershenson, S.P. Boyd, and T.H. Lee. “Simple Accurate Expressions for Planar Spiral Inductances.” IEEE Journal of Solid-State Circuits 34, no. 10 (October 1999): 1419–24. https://doi.org/10.1109/4.792620.

Version History

Introduced in R2021b