coupledStripLine

Create coupled transmission line in stripline form

Since R2024a

Description

Use the coupledStripLine object to create an edge-coupled differential pair transmission line in a stripline form. Coupled striplines are used to connect RF components, such as directional couplers, within the inner layers of a PCB board.

For the electromagnetic (EM) interactions between the ground planes, the feeds are located on the centers of the strips' edges at the board boundary and are simultaneously excited against both ground planes.

Types and applications of coupled stripline transmission lines:

• Symmetric or Plain — Transmission lines embedded in the internal layers of a PCB equally (symmetrically) spaced between two ground planes.

  Symmetric Coupled Stripline Transmission Line

• Asymmetric — Transmission lines embedded in the internal layers of a PCB unequally (asymmetrically) spaced between two ground planes.

  Asymmetric Coupled Stripline Transmission Line

• Suspended — PCB stripline suspended between two parallel ground planes with air gaps between the stripline and the ground planes. This configuration provides higher Q and lower losses than solid dielectric layers.

  Suspended Coupled Stripline Transmission Line

Creation

Syntax

sline = coupledStripLine

sline = coupledStripLine(name=value)

Description

sline = coupledStripLine creates a default coupled transmission line in the stripline form. The default properties are for a resonant frequency of 2.5 GHz along the X-Y plane.

sline = coupledStripLine(name=value) sets properties using one or more name value pair arguments. For example, sline = coupledStripLine('Length',0.0300) creates a coupled stripline of length 0.0300 meters. Properties not specified retain their default values.

Properties

Length — Length of coupled stripline

0.0202 (default) | positive scalar

Length of the coupled stripline in meters, specified as a positive scalar.

Example: strip = coupledStripLine('Length',0.0300)

Data Types: double

Width — Width of coupled stripline

0.0026 (default) | positive scalar

Width of the coupled stripline in meters, specified as a positive scalar.

Example: strip = coupledStripLine('Width',0.0037)

Data Types: double

Spacing — Spacing between coupled lines

9.7000e-4 (default) | positive scalar

Spacing between the coupled lines in meters, specified as a positive scalar.

Example: strip = coupledStripLine('Spacing',0.00037)

Data Types: double

Height — Height from ground plane to coupled stripline

0.0016 (default) | positive scalar

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

Example: strip = coupledStripLine('Height',9.000e-04)

Data Types: double

GroundPlaneWidth — Width of ground plane

0.0156 (default) | positive scalar

Width of the ground plane in meters, specified as a positive scalar.

Example: strip = coupledStripLine('GroundPlaneWidth',0.0350)

Data Types: double

Substrate — Type of dielectric material

'Teflon' (default) | dielectric object

Type of dielectric material used as a substrate, specified as a dielectric object. For more information see dielectric. The default dielectric material Teflon has an EpsilonR of 2.2, loss tangent of 0.03, and a thickness of 0.0032.

Example: d = dielectric('FR4'); strip = coupledStripLine('Substrate',d)

Data Types: string | char

Conductor — Type of metal used for conducting layers

'PEC' (default) | metal object

Type of metal used for the conducting layers, specified as a metal object. For more information see metal.

Example: m = metal('PEC'); strip = coupledStripLine('Conductor',m)

Data Types: string | char

Object Functions

charge	Calculate and plot charge distribution
current	Calculate and plot current distribution
design	Design symmetric coupled stripline transmission line around given frequency
feedCurrent	Calculate current at feed port
getZ0	Calculate characteristic impedance of transmission line
mesh	Change and view mesh properties of metal or dielectric in PCB component
show	Display PCB component structure or PCB shape
sparameters	Calculate S-parameters for RF PCB objects

Examples

Default Coupled Strip Line

Create and view a default coupled strip line.

strip = coupledStripLine

strip = 
  coupledStripLine with properties:

              Length: 0.0202
               Width: 0.0026
             Spacing: 9.7000e-04
              Height: 0.0016
    GroundPlaneWidth: 0.0156
           Substrate: [1×1 dielectric]
           Conductor: [1×1 metal]

show(strip)

Multi-Layer Coupled Strip Line

Create and view a coupled strip line at the interface of a multi-layered dielectric.

sub = dielectric('FR4','Teflon');
sub.Thickness = [0.003 0.001];
coupledstripline = coupledStripLine('Height',0.003,'Substrate',sub);
show(coupledstripline);

Plot the charge and current distribution on this transmission line.

current(coupledstripline,2.5e9)

figure;
charge(coupledstripline,2.5e9)

Symmetric Coupled Stripline Transmission Line

Create and show a symmetric coupled transmission line

freq = linspace(1e9, 5e9, 41);
s1 = coupledStripLine;
s1

s1 = 
  coupledStripLine with properties:

              Length: 0.0207
               Width: 0.0051
             Spacing: 0.0019
              Height: 0.0030
    GroundPlaneWidth: 0.0241
           Substrate: [1x1 dielectric]
           Conductor: [1x1 metal]

figure; show(s1);
title('Symmetric coupled stripline');

sp1 = sparameters(s1, freq);
figure; rfplot(sp1, 1:4, 1);
title('Symmetric coupled stripline');

Asymmetric Coupled Stripline Transmission Line

Create, and show an asymmetric coupled stripline transmission line

freq = linspace(1e9, 5e9, 41);
s2 = coupledStripLine;
s2

s2 = 
  coupledStripLine with properties:

              Length: 0.0207
               Width: 0.0051
             Spacing: 0.0019
              Height: 0.0030
    GroundPlaneWidth: 0.0241
           Substrate: [1x1 dielectric]
           Conductor: [1x1 metal]

s2.Substrate.Name        = {'Teflon', 'Teflon'};
s2.Substrate.EpsilonR    = [2.1        2.1];
s2.Substrate.LossTangent = [2e-4       2e-4];
s2.Substrate.Thickness   = [s2.Height  s2.Height/2];
figure; show(s2);
title('Asymmetric coupled stripline');

sp2 = sparameters(s2, freq);
figure; rfplot(sp2, 1:4, 1)
title('Asymmetric coupled stripline');

Suspended Coupled Stripline Transmission Line

Create and show a suspended coupled stripline transmission line

freq = linspace(1e9, 5e9, 41);
s3 = coupledStripLine;
suspendedSubThickness = 0.001;
t1 = s3.Height - suspendedSubThickness; % Thickness of air gap below suspended dielectric
t2 = suspendedSubThickness;             % Thickness of suspended dielectric
t3 = t1 + t2;                           % Thickness of air gap above suspended dielectric
s3.Substrate.Name        = {'Air', 'Teflon', 'Air'};
s3.Substrate.EpsilonR    = [1      2.1       1];
s3.Substrate.LossTangent = [0      2e-4      0];
s3.Substrate.Thickness   = [t1     t2        t3];
s3

s3 = 
  coupledStripLine with properties:

              Length: 0.0207
               Width: 0.0051
             Spacing: 0.0019
              Height: 0.0030
    GroundPlaneWidth: 0.0241
           Substrate: [1x1 dielectric]
           Conductor: [1x1 metal]

figure; show(s3)
title('Suspended coupled stripline');

sp3 = sparameters(s3, freq);
figure; rfplot(sp3, 1:4, 1);
title('Suspended coupled stripline')

More About

Parametric Analysis Guidelines

• The characteristic impedance of the line is the geometric mean of the even mode (Z_oe) and the odd mode impedances (Z_oo). For example, to design a line of 50 ohms for the given even mode impedance, select the odd mode impedance accordingly.

• Decreasing the spacing between the coupled lines will Increase in the difference between the odd and even mode impedances.

• Increase in Z_oe will increase the coupled power.

• Increase in the Width and the Spacing properties decreases the characteristic impedance.

• If Spacing tends to infinity, both odd and even mode impedances reduce to the characteristic impedance of an isolated strip between ground planes.

• Increase the operating frequency of the coupled strip line by decreasing the dimensions of the line.

Design Function

The figure shows transverse field distributions for two fundamental transverse electro-magnetic (TEM) modes. These modes exists on a pair of parallel conducting strips between parallel ground planes.

• Even coupled strip mode — In the first figure, strips are at the same potential and carry equal currents in the same direction. This mode is called the even coupled strip mode because of the even symmetry of the electric field about the vertical axis.

• Odd coupled strip mode — In the second figure, strips are at equal but opposite potentials and carry equal currents in the opposite direction. This mode is called odd coupled strip mode because of the odd symmetry of the electric field.

The figures also show that the capacitance per strip to ground is less for the even case and more for the odd case. The characteristic impedances of the two modes are unequal, being greater for the even mode than for the odd mode.

References

[1] Pozar, Microwave Engineering / David M. Pozar, University of Massachusetts at Amherst.

[2] Cohn, S.B. “Shielded Coupled-Strip Transmission Line.” IEEE Transactions on Microwave Theory and Techniques 3, no. 5 (October 1955): 29–38. https://doi.org/10.1109/TMTT.1955.1124973.

Version History

Introduced in R2024a