# txlineMicrostrip

Create microstrip transmission line

## Description

Use the txlineMicrostrip object to create a standard, embedded, inverted, or suspended microstrip transmission line. This figure shows the cross sections of the four types of microstrip transmission lines you can create using the txlineMircostrip object. The physical characteristics of the microstrip transmission line include the conductor width (w), the conductor thickness (t), the dielectric thickness (d), the relative permittivity constant (ε), and the height of the conductor above the ground plane (h) .

## Creation

### Description

txline = txlineMicrostrip creates a standard microstrip transmission line object.

example

txline = txlineMicrostrip(Name,Value) sets Properties using one or more name-value pairs. For example, txline = txlineMicrostrip('Width',0.0046) creates a standard microstrip transmission line with a width of 0.0046 meters.

## Properties

expand all

Name of the microstrip transmission line, specified as a string scalar or a character vector.

Example: 'Name','microstrip1'

Example: txline.Name = 'microstrip1'

Data Types: char | string

Type of microstrip transmission line, specified as one of the following:

• 'Standard' Standard microstrip transmission line

• 'Embedded' Embedded microstrip transmission line

• 'Inverted' Inverted microstrip transmission line

• 'Suspended' Suspended microstrip transmission line

Note

When you create a default txlineMicrostrip object or set the Type property to 'Standard', the Type property does not show in MATLAB

Example: 'Type','Embedded'

Example: txline.Type = 'Embedded'

Data Types: char | string

Physical length of the microstrip transmission line, specified as a positive scalar in meters.

Example: 'LineLength',0.0200

Example: txline.LineLength = 0.0200

Data Types: double

Physical width of the microstrip transmission line, specified as a positive scalar in meters.

Example: 'Width',0.0008

Example: txline.Width = 0.0008

Data Types: double

Physical height of the conductor, specified as a positive scalar in meters.

Example: 'Height',0.000835

Example: txline.Height = 0.000835

Data Types: double

Dielectric thickness of the inverted, embedded, or suspended microstrip transmission line, specified as a positive scalar in meters. Default values of dielectric thickness for the embedded, inverted, and suspended microstrip transmission lines are is listed in the table.

Type of MicrostripDefault value of DielctricThickness
'Embedded'Height*2
'Inverted'Height
'Suspended'Height/2

Note

• When you create a standard microstrip transmission line, the DielectricThickness property does not show in MATLAB.

• By default txlineMicrostrip object sets the dielectric thickness of the standard microstrip transmission line to the value of the Height.

Example: 'DielectricThickness',0.0012

Example: txline.DielectricThickness = 0.0012

#### Dependencies

To enable this property, set Type as 'Embedded' or 'Inverted', or 'Suspended'.

Data Types: double

Physical thickness of the microstrip transmission line, specified as a positive scalar in meters. You can now model microstrip with thickness set to 0 mm.

Example: 'Thickness',0.000008

Example: txline Thickness = 0.000008

Data Types: double

Relative permittivity of the dielectric, specified as a positive scalar.

Example: 'EpsilonR',8.8

Example: txline.EpsilonR = 8.8

Data Types: double

Loss angle tangent of the dielectric, specified as a nonegative scalar.

Example: 'LossTangent',1

Example: txline.LossTangent = 1

Data Types: double

Conductivity of the conductor, specified as a nonnegative scalar in Siemens per meter (S/m).

Example: 'SigmaCond',2

Example: txline.SigmaCond = 2

Data Types: double

Stub transmission line termination, specified as 'NotApplicable', 'Open', or 'Short'.

Example: 'Termination','Short'

Example: txline.Termination = 'Short'

Data Types: char

Type of stub, specified as 'NotAStub', 'Series', or 'Shunt'.

Example: 'StubMode','Series'

Example: txline.StubMode = 'Series'

Data Types: char

Number of input and output ports, returned as a positive scalar.

Data Types: double

Terminals of the microstrip transmission line, returned as a cell array of strings.

Data Types: char | string

## Object Functions

 sparameters Calculate S-parameters for RF data, network, circuit, and matching network objects groupdelay Group delay of S-parameter object or RF filter object or RF Toolbox circuit object noisefigure Calculate noise figure of transmission lines, series RLC, and shunt RLC circuits getZ0 Calculate characteristic impedance with and without dispersion for transmission line circuit Circuit object clone Create copy of existing circuit element or circuit object

## Examples

collapse all

Create a microstrip transmission line using these specifications:

• Width: 0.08 mm

• Height: 1.6 mm

• Line length: 12.2777 mm

• Thickness: 10e-6 m

• Conductivity: 5.88e7 S/m

• Relative permittivity of the dielectric: 3.9

microstriptxline = txlineMicrostrip('Width',0.08e-3,'Height',1.6e-3,...
'LineLength',12.2777e-3,'Thickness',10e-6,'EpsilonR',3.9,'SigmaCond',5.88e7);

Calculate the S-parameters of the transmission line at 10 GHz.

sparam = sparameters(microstriptxline,10e9,50);

Calculate the group delay of the transmission line at 10 GHz.

gd = groupdelay(microstriptxline,10e9,'Impedance',50)
gd = 4.2440e-11

This example uses RF PCB Toolbox to calculate electromagnetic (EM) solver S-parameters of the microstrip line.

Create Suspended Microstrip Line

Create a suspended microstrip transmission line with a copper conductor and Teflon substrate.

tx = txlineMicrostrip('Type','Suspended',...
'LineLength',0.04705,'Width',3.5e-3,...
'Height',1.6e-3,"DielectricThickness",0.8e-3,...
"EpsilonR",2.1,"LossTangent",0.2e-3,...
'SigmaCond',596e5,"Thickness",3.556e-5,...
"StubMode","NotAStub","Termination","NotApplicable");

Behavioral Modeling

Calculate and plot the S-parameters with the reference impedance of 50$\Omega$.

freq = (1:40)*100e6;
Srf = sparameters(tx,freq,50);
rfplot(Srf)

Calculate the characteristic impedance.

Zc_rf = getZ0(tx)
Zc_rf = 75.0279

EM Modeling

Input the microstrip transmission line to the microstripLine object from the RF PCB Toolbox for EM modeling.

tx_em = microstripLine(tx)
tx_em =
microstripLine with properties:

Length: 0.0471
Width: 0.0035
Height: 0.0016
GroundPlaneWidth: 0.0175
Substrate: [1x1 dielectric]
Conductor: [1x1 metal]

View the suspended microstrip transmission line.

show(tx_em)

Calculate and plot the S-parameters using EM solver from RF PCB Toolbox.

Sem = sparameters(tx_em,freq,50);
rfplot(Sem)

Zc_em = getZ0(tx_em)
Zc_em = 72.6234 - 0.2018i

Select the dielectric and metal layers for an inverted microstrip transmission line from the dielectric and metal libraries, respectively, of the RF PCB Toolbox.

dFR4 = dielectric('FR4');
dFR4.Thickness = 3.2e-4;
mCopper = metal('Copper');

Create an inverted microstrip transmission line with a copper conductor and an FR4 substrate at 6 GHz with the line length of 0.5$\lambda$ and the reference impedance of 75$\Omega$. The air to substrate thickness ratio is calculated using:

$\frac{\mathrm{Thickness}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{of}\text{\hspace{0.17em}}\mathrm{air}\text{\hspace{0.17em}}\mathrm{layer}}{\mathrm{Thickness}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{of}\text{\hspace{0.17em}}\mathrm{substrate}}=\frac{12.8\mathit{e}-4}{3.2\mathit{e}-4}=4$

prototype_behavioral = txlineMicrostrip('Type','Inverted',...
'DielectricThickness',dFR4.Thickness,"EpsilonR",dFR4.EpsilonR, ...
'Height',12.8e-4,"LossTangent",dFR4.LossTangent, ...
"SigmaCond",mCopper.Conductivity,"Thickness",mCopper.Thickness);

Input the inverted microstrip transmission line to the microstripLine object from the RF PCB Toolbox for EM modeling.

prototype_em = microstripLine(prototype_behavioral);

Use the design (Antenna Toolbox) function to design the microstripLine (RF PCB Toolbox) object at 6 GHz with the line length of 0.5$\lambda$ and reference impedance of 75$\Omega$.

tx = design(prototype_em,6e9,'Z0',75,'LineLength',0.5);

View the microstipLine object.

show(tx)

Plot S-Parameters

Calculate and plot the behavioral and electromagnetic (EM) solver modeled S-parameters of the line with the reference impedance of 50$\Omega$. Use the Behavioral name-value argument of the sparameters (RF PCB Toolbox) function to compute the behavioral S-parameters.

freq = (1:5:66)*100e6;
Srf = sparameters(tx,freq,50,'Behavioral',true);
Sem = sparameters(tx,freq,50);
rfplot(Srf,'-s','db')
hold on
rfplot(Sem,'-x','db')
title('Behavioral vs. EM solver modeled S-parameters');

## Algorithms

• When you set the StubMode property to 'Shunt', the 2-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit.

Zin is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as:

$\begin{array}{c}A=1\\ B=0\\ C=1/{Z}_{in}\\ D=1\end{array}$

When you set the StubMode property to 'Series', the 2-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit.

Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as:

$\begin{array}{c}A=1\\ B={Z}_{in}\\ C=0\\ D=1\end{array}$

## References

[1] Garg, Ramesh, I. J. Bahl, and Maurizio Bozzi. Microstrip Lines and Slotlines . 3rd ed. Artech House Microwave Library. Boston: Artech House, 2013.

[2] Wadell, Brian C. Transmission Line Design Handbook. The Artech House Microwave Library. Boston: Artech House, 1991.

Introduced in R2020b