Transmission Line
Model transmission line
Libraries:
RF Blockset /
Circuit Envelope /
Elements
Description
Use the Transmission Line block to model delaybased, lumped, and distributed transmission lines. Mask dialog box options change automatically to accommodate model type selection.
Examples
Transmission Lines, DelayBased and Lumped Models
Simulate delaybased and lumpedelement transmission lines.
Parameters
Main
Model type — Transmission line model
Delaybased and lossless
(default)  Delaybased and lossy
 Lumped parameter Lsection
 Lumped parameter Pisection
 Coaxial
 Coplanar waveguide
 Microstrip
 Stripline
 Twowire
 Parallelplate
 Equationbased
 RLCG
 ...
Type of transmission line model, specified as one of these.
Transmission Line Types  Description 

 Model transmission line with delay but no loss. 
 Model transmission line with delay and loss.

 Model transmission line with RLGC Lsections.

 Model transmission line with RLGC pisections.

 Model transmission line as a coaxial transmission line. The cross section of a coaxial transmission line is shown in the following figure. Its physical characteristics include the radius of the inner conductor a, and the radius of the outer conductor b.

 Model transmission line as a coplanar waveguide. The cross section of a coplanar waveguide transmission line is shown in the following figure. Its physical characteristics include conductor width w, conductor thickness t, slot width s, substrate height d, and relative permittivity constant ε. 
 Model transmission line as a standard, embedded, inverted, or suspended microstrip transmission line. The crosssections of standard, embedded, inverted, and suspended microstrip transmission lines are shown here. The physical characteristics of such a transmission line include microstrip width w, microstrip thickness t, dielectric thickness d, and relative permittivity constant ε.

 Model transmission line as stripline transmission line. The crosssection of a stripline transmission line is shown in this figure. Its physical characteristics include strip width w, strip thickness t, dielectric thickness h, and relative permittivity constant ε.

 Model transmission line as twowire transmission line. The crosssection of a twowire transmission line is shown in the following figure. Its physical characteristics include the radius of wires a, separation or physical distance between the wire centers S, and relative permittivity and permeability of the wires.

 Model transmission line as a parallelplate transmission line. The crosssection of a parallelplate transmission line is shown in the following figure. Its physical characteristics include plate width w, and plate separation d.

 Model transmission line as an equationbased transmission line. The transmission line, which can be lossy or lossless, is treated as a twoport linear network. 
 Model transmission line as an RLCG transmission line. This line is defined in terms of its frequencydependent resistance, inductance, capacitance, and conductance. The transmission line, which can be lossy or lossless, is treated as a twoport linear network.

Transmission delay — Delay in transmission line
4.7e9 s
(default)  real scalar  s
 ms
 us
 ns
Delay in the transmission line, specified as a real scalar in
s
, ms
,
us
, or ns
.
Dependencies
To enable this parameter, choose one of the following:
Delaybased and lossless
in Model type.Delaybased and lossy
in Model type.
Characteristic impedance — Impedance of transmission line
50 ohm
(default)  real scalar  Ohm
 kOhm
 MOhm
 GOhm
Impedance of the transmission line, specified as a real scalar in
Ohm
, kOhm
,
MOhm
, or
GOhm
.
Dependencies
To enable this parameter, choose one of the following:
Delaybased and lossless
,Delaybased and lossy
, orEquationbased
in Model type.Lumped parameter Lsection
orLumped parameter Pisection
in Model type andBy characterisitc impedance and capacitance
in Parameterization.
Resistance per unit length — Resistance per unit length of transmission line
0.3 Ohm/m
(default)  positive scalar  Ohm/m
 kOhm/m
 MOhm/m
 GOhm/m
Resistance per unit length of the transmission line, specified as a
positive scalar in Ohm/m
,
kOhm/m
,
MOhm/m
, or
GOhm/m
.
Dependencies
To enable this parameter, choose one of the following:
Delaybased and lossy
orRLCG
in Model type.Lumped parameter Lsection
orLumped parameter Pisection
in Model type andBy characterisitc impedance and capacitance
in Parameterization.
Number of segments — Number of segments in transmission line
10
(default)  positive scalar
Number of segments in the transmission line, specified as a positive scalar.
Dependencies
To enable this parameter, choose one of the following:
Delaybased and lossy
in Model type.Lumped parameter Lsection
orLumped parameter Pisection
in Model type andBy characterisitc impedance and capacitance
orBy inductance and capacitance
in Parameterization.
Parameterization — Type of parameters to model segments in transmission line
By characterisitc impedance and
capacitance
(default)  By inductance and capacitance
Type of parameters to model segments in transmission line, specified
as By characterisitc impedance and capacitance
or
By inductance and capacitance
.
Dependencies
To enable this parameter, select Lumped parameter
Lsection
or Lumped parameter
Pisection
in Model
type.
Capacitance per unit length — Capacitance per unit length of transmission line
94e12 F/m
(default)  positive scalar
Capacitance per unit length of the transmission line, specified as a
positive scalar in F/m
,
mF/m
, uF/m
,
nF/m
, or
pF/m
.
Dependencies
To enable this parameter, choose Lumped parameter
Lsection
, Lumped parameter
Pisection
, or RLCG
in
Model type.
Conductance per unit length — Conductance per unit length of transmission line
5e6 S/m
(default)  positive scalar  S/m
 mS/m
 uS/m
 nS/m
Conductance per unit length of the transmission line, specified as a
positive scalar in S/m
,
mS/m
, uS/m
, or
nS/m
.
Dependencies
To enable this parameter, choose Lumped parameter
Lsection
, Lumped parameter
Pisection
, or RLCG
in
Model type.
Inductance per unit length — Inductance per unit length of transmission line
235e9 H/m
(default)  positive scalar  H/m
 mH/m
 uH/m
 nH/m
Inductance per unit length of the transmission line, specified as a
positive scalar in H/m
,
mH/m
, uH/m
, or
nH/m
.
Dependencies
To enable this parameter, choose one of the following:
Lumped parameter Lsection
, orLumped parameter Pisection
in Model type andBy inductance and capacitance
in Parameterization.RLCG
in Model type
Outer radius — Outer radius of coaxial transmission line
2.57 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Outer radius of coaxial transmission line, specified as a positive
scalar in m
, cm
,
mm
, um
,
in
, or
ft
.
Dependencies
To enable this parameter, choose
Coaxial
in Model
type.
Inner radius — Inner radius of coaxial transmission line
2.57 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Inner radius of coaxial transmission line, specified as a positive
scalar in m
, cm
,
mm
, um
,
in
, or
ft
.
Dependencies
To enable this parameter, choose
Coaxial
in Model
type.
Conductor width — Physical width of conductor
0.6 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Physical width of the conductor, specified as a positive scalar in
m
, cm
,
mm
, um
,
in
, or
ft
.
Dependencies
To enable this parameter, choose Coplanar
waveguide
in Model
type.
Slot width — Physical width of slot
0.2 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Physical width of the slot, specified as a positive scalar in
m
, cm
,
mm
, um
,
in
, or
ft
.
Dependencies
To enable this parameter, choose Coplanar
waveguide
in Model
type.
Conductor backed — Infinite bottom conductor
off
(default)  on
Select this parameter to add an infinitebottom conductor to your coplanar waveguide transmission line.
Dependencies
To enable this parameter, set Model type to
Coplanar waveguide
.
Structure — Type of microstrip transmission line
Standard
(default)  Embedded
 Inverted
 Suspended
Type of microstrip transmission line, specified as Standard, Embedded, Inverted, or Suspended.
Dependencies
To enable this parameter, set Model type to
Microstrip
.
Strip Width — Width of microstrip transmission line
0.6 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Width of the microstrip transmission line, specified as a positive
scalar in m
, cm
,
mm
, um
,
in
, or
ft
.
Dependencies
To enable this parameter, set Model type
toMicrostrip
.
Strip thickness — Physical thickness of conductor
5 um
(default)  nonnegative scalar  m
 cm
 mm
 um
 in
 ft
Physical thickness of the conductor, specified as a nonnegative scalar
in m
, cm
,
mm
, um
,
in
, or
ft
.
Dependencies
To enable this parameter, choose Coplanar
waveguide
or Microstrip
in Model type.
Strip Height — Strip height of microstrip transmission line
0.635 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Strip height of the inverted, suspended, or embedded microstrip
transmission line, specified as a positive scalar in
m
, cm
,
mm
, um
,
in
, or
ft
.
Dependencies
To enable this parameter, choose
Microstrip
in Model
type and choose Inverted
,
Suspended
, or
Embedded
in
Structure.
Wire radius — Radius of conducting wires of twowire transmission line
0.67 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Radius of the conducting wires of the twowire transmission line,
specified as a positive scalar in m
,
cm
, mm
,
um
, in
, or
ft
.
Dependencies
To enable this parameter, choose
Twowire
in Model
type.
Wire separation — Physical distance between conducting wires of twowire transmission line
1.62 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Physical distance between the conducting wires of the twowire
transmission line, specified as a positive scalar in
m
, cm
,
mm
, um
,
in
, or
ft
.
Dependencies
To enable this parameter, choose
Twowire
in Model
type.
Plate width — Width of parallelplate transmission line
5 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Width of the parallelplate transmission line, specified as a positive
scalar in m
, cm
,
mm
, um
,
in
, or
ft
.
Dependencies
To enable this parameter, choose
Parallelplate
in Model
type.
Plate separation — Thickness of dielectric separating plates
1 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Thickness of the dielectric separating the plates, specified as a
positive scalar in m
,
cm
, mm
,
um
, in
, or
ft
.
Dependencies
To enable this parameter, choose
Parallelplate
in Model
type.
Phase velocity (m/s) — Propagation velocity of a uniform plane wave on transmission line
299792458
(default)  positive scalar
Propagation velocity of a uniform plane wave on the transmission line, specified as a positive scalar in meters per second.
Dependencies
To enable this parameter, choose
Equationbased
in Model
type.
Loss (dB/m) — Reduction in strength of signal as it travels over transmission line
0
(default)  positive scalar
Reduction in strength of the signal as it travels over the transmission line, specified as a positive scalar in meters per second.
Dependencies
To enable this parameter, choose
Equationbased
in Model
type.
Frequency — Modeling frequencies
1e9 Hz
(default)  positive scalar  Hz
 kHz
 MHz
 GHz
Modeling frequencies, specified as a positive scalar or vector in
Hz
, kHz
,
MHz
, or
GHz
.
Dependencies
To enable this parameter, choose
Equationbased
or
RLCG
in Model
type.
Interpolation method — Interpolation method used to calculate values at the modeling frequencies
Linear
(default)  Spline
 Cubic
Interpolation method used to calculate the values at the modeling
frequencies, specified as Linear
,
Spline
, or
Cubic
.
Dependencies
To enable this parameter, choose
Equationbased
or
RLCG
in Model
type.
Conductivity of conductor — Conductivity of conductor
inf
(default)  scalar  S/m
 mS/m
 uS/m
 nS/m
Conductivity of conductor, specified as a scalar in
S/m
, mS/m
,
uS/m
, or
nS/m
.
Dependencies
To enable this parameter, choose
Coaxial
, Coplanar
waveguide
, Microstrip
,
Twowire
or
Parallelplate
in Model
type.
Dielectric Thickness — Thickness of dielectric on which conductor resides
0.635 mm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Thickness of the dielectric on which the conductor resides, specified
as a positive scalar in m
,
cm
, mm
,
um
, in
, or
ft
.
Default values of the dielectric thickness of coplanar waveguide, standard, embedded, inverted, and suspended microstrip transmission lines are listed in this table.
Model Type  Structure  Default Dielectric Thickness in mm 

Coplanar waveguide  N.A.  0.635 
Microstrip  Standard and
Inverted  0.635 
'Suspended'  0.3175  
'Embedded'  1.37 
Dependencies
To enable this parameter, set Model type to
Microstrip
or Coplanar
waveguide
.
Relative permeability of dielectric — Relative permeability of dielectric
1
(default)  scalar
Relative permeability of the dielectric, specified as a scalar.
Dependencies
To enable this parameter, set Model type to
Coaxial
,
Twowire
, or
Parallelplate
.
Relative permittivity of dielectric — Relative permittivity of dielectric
2.2
(default)  scalar
Relative permittivity of the dielectric, specified as a scalar.
Dependencies
To enable this parameter, set Model type to
Coaxial
, Coplanar
waveguide
, Microstrip
,
Twowire
, or
Parallelplate
.
Loss tangent of dielectric — Loss tangent of dielectric
0
(default)  scalar
Loss tangent of the dielectric, specified as a scalar.
Dependencies
To enable this parameter, set Model type to
Coaxial
, Coplanar
waveguide
, Microstrip
,
Twowire
, or
Parallelplate
.
Line length — Physical length of transmission line
1 cm
(default)  positive scalar  m
 cm
 mm
 um
 in
 ft
Physical length of the transmission line or l,
specified as a positive scalar in m
,
cm
, mm
,
um
, in
, or
ft
.
Dependencies
To enable this parameter, choose one of the following:
Delaybased and lossy
,Coaxial
,Coplanar waveguide
,Microstrip
, orTwowire
,Parallelplate
,Equationbased
, orRLCG
in Model type.Lumped parameter Lsection
orLumped parameter Pisection
in Model type andBy characterisitc impedance and capacitance
orBy inductance and capacitance
in Parameterization.
Stub mode — Type of stub
Not a stub
(default)  Shunt
 Series
Type of stub, specified as Not a stub
,
Shunt
, or
Series
. See Parameter Calculations for Transmission Line with Stub.
Dependencies
To enable this parameter, choose
Coaxial
, Coplanar
waveguide
, Microstrip
Twowire
,
Parallelplate
,
Equationbased
, or
RLCG
in Model
type.
Termination of stub — Type of termination for stub
Open
(default)  Short
Type of termination for stub, specified as
Open
or
Short
.
Dependencies
To enable this parameter, choose Series
or Shunt
in Stub
mode.
Ground and hide negative terminals — Ground RF circuit terminals
on
(default)  off
Select this parameter to internally ground and hide the negative terminals. To expose the negative terminals, clear this parameter. By exposing these terminals, you can connect them to other parts of your model.
By default, this option is selected.
Modeling
Modeling Options — Options to model Sparameters
Frequency domain
(default)  Time domain
Options to model Sparameters, specified as:
Frequency domain
– Computes the baseband impulse response for each carrier frequency independently. This technique is based on convolution. There is an option to specify the duration of the impulse response. For more information, see Compare Time and Frequency Domain Simulation Options for Sparameters.Time domain
– Computes the analytical rational model that approximates the whole range of the data.
For the Amplifier, Antenna, and SParameters blocks, the default
value is Time domain
. For the Transmission
Line block, the default value is Frequency
domain
.
Automatically estimate impulse response duration — Calculate impulse response duration automatically
off
(default)  on
Select Automatically estimate impulse response duration to calculate impulse response duration automatically. Clear the selection to specify impulse response duration.
Dependencies
To enable this parameter, choose Frequency domain
in
Modeling options.
Impulse response duration — Manually specify impulse response duration
0 s
(default)  positive scalar  s
 ms
 us
 ns
Manually specify impulse response duration, specified as a positive scalar in
s
, ms
,
us
, or ns
.
Dependencies
To enable this parameter, clear Automatically estimate impulse response duration.
Fitting options — Fitting options for rationalfit
Share all poles
(default)  Share poles by columns
 Fit individually
Fitting options for rationalfit, specified as Share all
poles
, Share poles by columns
, or
Fit individually
.
For the Amplifier block, the default value is Fit
individually
. For the Sparameters block and
Transmission Line block, the default value is Share all
poles
.
Dependencies
To enable this parameter, choose Time domain
in
Modeling options.
Relative error desired (dB) — Relative error acceptable in rational fit output
40
(default)  real scalar
Relative error acceptable in rational fit output, specified as a real scalar in decibels.
Dependencies
To enable this parameter, choose Time domain
in
Modeling options.
Rational fitting results — Values of rationalfit calculations
readonly (default)
Shows values of Number of independent fits, Number of required poles, and Relative error achieved (dB).
When modeling using Time domain
, the Plot in
Visualization
tab plots the data defined in Data
Source
and the values in the rationalfit
function.
Dependencies
To enable this parameter, choose Time domain
in
Modeling options.
Note
Modeling tab is enabled for all transmission line types except
Delaybased and lossless
,
Delaybased and lossy
, Lumped
parameter Lsection
, and Lumped parameter
pisection
.
More About
Equations for ABCD Parameter Calculations
The following auxiliary equations are used for ABCDparameter calculations.
$$\begin{array}{c}{Z}_{0}=\sqrt{\frac{R+j\omega L}{G+j\omega C}}\\ k={k}_{r}+j{k}_{i}=\sqrt{(R+j\omega L)(G+j\omega C)}\end{array}$$
where
$$\begin{array}{l}R=\frac{1}{2\pi {\sigma}_{cond}{\delta}_{cond}}\left(\frac{1}{a}+\frac{1}{b}\right)\\ L=\frac{\mu}{2\pi}\mathrm{ln}\left(\frac{b}{a}\right)\\ G=\frac{2\pi \omega {\epsilon}^{\u2033}}{\mathrm{ln}\left(\frac{b}{a}\right)}\\ C=\frac{2\pi {\epsilon}^{\prime}}{\mathrm{ln}\left(\frac{b}{a}\right)}\end{array}$$
In these equations:
a is the radius of the inner conductor.
b is the radius of the outer conductor.
σ_{cond} is the conductivity in the conductor.
μ is the permeability of the dielectric.
ε is the permittivity of the dielectric.
ε″ is the imaginary part of ε, ε″ = ε_{0}ε_{r}tan δ, where:
ε_{0} is the permittivity of free space.
ε_{r} is the Relative permittivity constant parameter value.
tan δ is the Loss tangent of dielectric parameter value.
δ_{cond} is the skin depth of the conductor, which the block calculates as $$1/\sqrt{\pi f\mu {\sigma}_{cond}}$$.
f is a vector of internal modeling frequencies.
Z_{0} is the specified characteristic impedance.
k is a vector whose elements correspond to the elements of the input vector,
freq
. The block calculates k from the specified parameters as k = α_{a} + iβ, where α_{a} is the attenuation coefficient and β is the wave number. The attenuation coefficient α_{a} is related to the specified loss, α, by$${\alpha}_{a}=\mathrm{ln}\left({10}^{\alpha /20}\right)$$
The wave number β is related to the specified phase velocity, V_{p}, by
$$\beta =\frac{2\pi f}{{V}_{p}}$$
The phase velocity V_{P} is also known as the wave propagation velocity.
Parameter Calculations for Distributed Transmission Line
When modeling distributed transmission lines, the block first calculates ABCDparameters at a set of internal frequencies. The ABCDparameters are converted Sparameters for simulation.
The block calculates the ABCDparameters from the physical length of the transmission line, d, and the complex propagation constant, k, using the following set of equations:
$$\begin{array}{l}A=\frac{{e}^{kd}+{e}^{kd}}{2}\\ B=\frac{{Z}_{0}*\left({e}^{kd}{e}^{kd}\right)}{2}\\ C=\frac{{e}^{kd}{e}^{kd}}{2*{Z}_{0}}\\ D=\frac{{e}^{kd}+{e}^{kd}}{2}\end{array}$$
Parameter Calculations for Transmission Line with Stub
When you set the Stub mode parameter in the mask dialog box
to Shunt
, the twoport network consists of a transmission line in
series with a stub. You can terminate the stub with a short circuit or an open
circuit as shown in the following figure.
Z_{in} is the input impedance of the shunt circuit. The ABCDparameters 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 Stub mode parameter in the mask dialog box
to Series
, the twoport network comprises a series transmission
line. You can terminate this line with either a short circuit or an open circuit as
shown here.
Z_{in} is the input impedance of the series circuit. The ABCDparameters for the series stub are:
$$\begin{array}{c}A=1\\ B={Z}_{in}\\ C=0\\ D=1\end{array}$$
Tips
In general, blocks that model delay effects rely on signal history. You can minimize numerical error that occur due to a lack of signal history at the start of a simulation. To do so, in the Configuration Parameters dialog box Solver pane you can specify an Initial step size. For models with delaybased Transmission Line blocks, use an initial step size that is less than the value of the Delay parameter.
References
[1] SussmanFort, S. E., and J. C. Hantgan. “SPICE Implementation of Lossy Transmission Line and Schottky Diode Models.” IEEE Transactions on Microwave Theory and Techniques.Vol. 36, No.1, January 1988.
[2] Pozar, David M. Microwave Engineering. Hoboken, NJ: John Wiley & Sons, Inc., 2005.
[3] Gupta, K. C., Ramesh Garg, Inder Bahl, and Prakash Bhartia. Microstrip Lines and Slotlines, 2nd Edition, Norwood, MA: Artech House, Inc., 1996.
[4] Ludwig, Reinhold and Pavel Bretchko. RF Circuit Design: Theory and Applications. Englewood Cliffs: NJ: PrenticeHall, 2000.
[5] True, Kenneth M. “Data Transmission Lines and Their Characteristics.” National Semiconductor Application Note 806, April 1992.
Version History
Introduced in R2012aR2024b: Time domain (rationalfit)
parameter renamed
The Time domain (rationalfit)
parameter value in the
Modeling options parameter has been renamed to
Time domain
in the Transmission Line
block.
When you open a model created before R2024b containing an Transmission
Line block, the parameter name displays as Time
domain
.
R2022a: Three block parameters renamed
The Substrate height, Relative permittivity constant, and Relative permeability constant parameters in the Transmission Line block have been renamed to Dielectric thickness, Relative permittivity of dielectric, and Relative permeability of dielectric, respectively.
When you open a model created before R2022a containing the Transmission Line block, the software replaces the old parameters names with the new ones.
R2022a: Model transmission lines
Use the Transmission Line block to model:
Embedded, inverted, and suspended microstrip transmission lines
Conductorbacked coplanar waveguide transmission lines
Stripline transmission lines
See Also
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