Transmission Line

Model transmission line

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Libraries:
RF Blockset / Circuit Envelope / Elements

Description

Use the Transmission Line block to model delay-based, lumped, and distributed transmission lines. Mask dialog box options change automatically to accommodate model type selection.

Examples

Transmission Lines, Delay-Based and Lumped Models

Simulate delay-based and lumped-element transmission lines.

• Open Script

Parameters

Main

Model type — Transmission line model

Delay-based and lossless (default) | Delay-based and lossy | Lumped parameter L-section | Lumped parameter Pi-section | Coaxial | Coplanar waveguide | Microstrip | Stripline | Two-wire | Parallel-plate | Equation-based | RLCG | ...

Type of transmission line model, specified as one of these.

Transmission Line Types	Description
Delay-based and lossless	Model transmission line with delay but no loss.
Delay-based and lossy –	Model transmission line with delay and loss.
Lumped parameter L-section	Model transmission line with RLGC L-sections.
Lumped parameter Pi-section	Model transmission line with RLGC pi-sections.
Coaxial	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.
Coplanar waveguide	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.
Microstrip	Model transmission line as a standard, embedded, inverted, or suspended microstrip transmission line. The cross-sections 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.
Stripline	Model transmission line as stripline transmission line. The cross-section 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.
Two-wire	Model transmission line as two-wire transmission line. The cross-section of a two-wire 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.
Parallel plate	Model transmission line as a parallel-plate transmission line. The cross-section of a parallel-plate transmission line is shown in the following figure. Its physical characteristics include plate width w, and plate separation d.
Equation based	Model transmission line as an equation-based transmission line. The transmission line, which can be lossy or lossless, is treated as a two-port linear network.
RLCG	Model transmission line as an RLCG transmission line. This line is defined in terms of its frequency-dependent resistance, inductance, capacitance, and conductance. The transmission line, which can be lossy or lossless, is treated as a two-port linear network.

Transmission delay — Delay in transmission line

4.7e-9 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:

• Delay-based and lossless in Model type.

• Delay-based 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:

• Delay-based and lossless, Delay-based and lossy, or Equation-based in Model type.

• Lumped parameter L-section or Lumped parameter Pi-section in Model type and By 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:

• Delay-based and lossy or RLCG in Model type.

• Lumped parameter L-section or Lumped parameter Pi-section in Model type and By 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:

• Delay-based and lossy in Model type.

• Lumped parameter L-section or Lumped parameter Pi-section in Model type and By characterisitc impedance and capacitance or By 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 L-section or Lumped parameter Pi-section in Model type.

Capacitance per unit length — Capacitance per unit length of transmission line

94e-12 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 L-section, Lumped parameter Pi-section, or RLCG in Model type.

Conductance per unit length — Conductance per unit length of transmission line

5e-6 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 L-section, Lumped parameter Pi-section, or RLCG in Model type.

Inductance per unit length — Inductance per unit length of transmission line

235e-9 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 L-section, or Lumped parameter Pi-section in Model type and By 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 infinite-bottom 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 two-wire transmission line

0.67 mm (default) | positive scalar | m | cm | mm | um | in | ft

Radius of the conducting wires of the two-wire transmission line, specified as a positive scalar in m, cm, mm, um, in, or ft.

Dependencies

To enable this parameter, choose Two-wire in Model type.

Wire separation — Physical distance between conducting wires of two-wire transmission line

1.62 mm (default) | positive scalar | m | cm | mm | um | in | ft

Physical distance between the conducting wires of the two-wire transmission line, specified as a positive scalar in m, cm, mm, um, in, or ft.

Dependencies

To enable this parameter, choose Two-wire in Model type.

Plate width — Width of parallel-plate transmission line

5 mm (default) | positive scalar | m | cm | mm | um | in | ft

Width of the parallel-plate transmission line, specified as a positive scalar in m, cm, mm, um, in, or ft.

Dependencies

To enable this parameter, choose Parallel-plate 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 Parallel-plate 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 Equation-based 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 Equation-based 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 Equation-based 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 Equation-based 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, Two-wire or Parallel-plate 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, Two-wire, or Parallel-plate.

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, Two-wire, or Parallel-plate.

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, Two-wire, or Parallel-plate.

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:

• Delay-based and lossy, Coaxial, Coplanar waveguide, Microstrip, or Two-wire, Parallel-plate, Equation-based, or RLCG in Model type.

• Lumped parameter L-section or Lumped parameter Pi-section in Model type and By characterisitc impedance and capacitance or By 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 Two-wire, Parallel-plate, Equation-based, 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 S-parameters

Frequency domain (default) | Time domain

Options to model S-parameters, 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 S-parameters.

• Time domain – Computes the analytical rational model that approximates the whole range of the data.

For the Amplifier, Antenna, and S-Parameters 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 S-parameters 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

read-only (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 Delay-based and lossless, Delay-based and lossy, Lumped parameter L-section, and Lumped parameter pi-section.

More About

Equations for ABCD Parameter Calculations

The following auxiliary equations are used for ABCD-parameter 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

$$\begin{array}{l}R=\frac{1}{2\pi {\sigma }_{cond}{\delta }_{cond}}\left(\frac{1}{a}+\frac{1}{b}\right)\\ L=\frac{\mu }{2\pi }\ln \left(\frac{b}{a}\right)\\ G=\frac{2\pi \omega {\epsilon }^{″}}{\ln \left(\frac{b}{a}\right)}\\ C=\frac{2\pi {\epsilon }^{\prime }}{\ln \left(\frac{b}{a}\right)}\end{array}$$

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″  = ε₀ε_rtan δ, where:

  • ε₀ 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.

• Z₀ 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

  $${\alpha }_a=-\ln \left({10}^{\alpha /20}\right)$$

  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 ABCD-parameters at a set of internal frequencies. The ABCD-parameters are converted S-parameters for simulation.

The block calculates the ABCD-parameters 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 two-port 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 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 Stub mode parameter in the mask dialog box to Series, the two-port 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 ABCD-parameters 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 delay-based Transmission Line blocks, use an initial step size that is less than the value of the Delay parameter.

References

[1] Sussman-Fort, 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: Prentice-Hall, 2000.

[5] True, Kenneth M. “Data Transmission Lines and Their Characteristics.” National Semiconductor Application Note 806, April 1992.

Version History

Introduced in R2012a

R2024b: 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

• Conductor-backed coplanar waveguide transmission lines

• Stripline transmission lines