Coaxial Transmission Line

Model coaxial transmission line

• 

Libraries:
RF Blockset / Equivalent Baseband / Transmission Lines

Description

The Coaxial Transmission Line block uses S-parameters to model its frequency behavior. A cross-section of the 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.

Parameters

Main

Outer radius (m) — Radius of outer conductor

2.57e-3 (default) | scalar

Radius of the outer conductor of the coaxial transmission line, specified as a scalar in meters.

Inner radius(m) — Radius of Inner conductor

0.725e-3 (default) | scalar

Radius of the inner conductor of the coaxial transmission line, specified as a scalar in meters.

Relative permeability constant — Relative permeability of dielectric

1 (default) | real scalar

Relative permeability of the dielectric, expressed as the ratio of the permeability of the dielectric to permeability in free space μ₀, specified as a real scalar.

Relative permittivity constant — Relative permittivity of dielectric

2.3 (default) | real scalar

Relative permittivity of the dielectric, expressed as the ratio of the permittivity of the dielectric to permittivity in free space ε₀, specified as a real scalar.

Loss tangent of dielectric — Dielectric loss tangent

0 (default) | nonnegative scalar

Loss tangent of the dielectric, specified as a nonnegative scalar.

Conductivity of the conductor (S/m) — Conductivity of conductor

inf (default) | positive scalar

Conductivity of the conductor, specified as a positive scalar in Siemens/meters.

Transmission line length (m) — Physical length of transmission line

0.01 (default) | positive scalar

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

Stub mode — Type of stub

Not a stub (default) | Shunt | Series

The block enables you to model the transmission line as a stub or as a stubless line.

Stubless Transmission Line

• Not a stub—Not a stub

  If you model a coaxial transmission line as stubless line, the Coaxial Transmission Line block first calculates the ABCD-parameters at each frequency contained in the modeling frequencies vector. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters. For more information, see Stub Mode - Not a Stub.

Shunt Transmission Line

• Shunt—This parameter provides a two-port network that consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown in these diagrams.

  

  Z_in is the input impedance of the shunt circuit and it is calculated as follows:

  for a short circuited transmission line

  $${\text{Z}}_{\text{in}}=j{Z}_0\tan \gamma l$$

  and for the open circuited transmission line

  $${\text{Z}}_{\text{in}}=-j{Z}_0\cot \gamma l$$

  where

  • Z₀ is the characteristic impedance and

  • $$\gamma$$ is the propagation constant

  The ABCD-parameters for the shunt stub are calculated as

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

Series Transmission Line

• Series—This mode parameter provides a two-port network that consists of a series transmission line that you can terminate with either a short circuit or an open circuit as show in these diagrams.

  

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

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

Termination of stub — Stub termination

Open (default) | Short

Stub termination for stub modes Shunt and Series. Choices are Open or Short

Dependencies

To enable this parameter, select Shunt or Series in Stub mode

Visualization

Source of frequency data — Frequency data source

User-specified (default)

Frequency data source, specified as User-specified.

Frequency data (Hz) — Frequency data range

[1e9:1e6:3e9] (default) | vector

Frequency data range, specified as a vector in hertz.

Reference impedance (ohms) — Reference impedance

50 (default) | nonnegative scalar

Reference impedance, specified as a nonnegative scalar in ohms.

Plot type — Type of data plot

X-Y plane (default) | Composite data | Polar plane | Z Smith chart | Y Smith chart | ZY Smith chart

Type of data plot to visualize using the given data, specified as one of the following:

• X-Y plane — Generate a Cartesian plot of the data versus frequency. To create linear, semilog, or log-log plots, set the Y-axis scale and X-axis scale accordingly.

• Composite data — Plot the composite data. For more information, see Create Plots Using Equivalent Baseband Library Blocks.

• Polar plane — Generate a polar plot of the data. The block plots only the range of data corresponding to the specified frequencies.

• Z smith chart, Y smith chart, and ZY smith chart — Generate a Smith^® chart. The block plots only the range of data corresponding to the specified frequencies.

Y parameter1 — Type of parameters to plot

S11 (default) | S12 | S21 | S22 | GroupDelay | OIP3 | IIP3 | NF | ...

Type of parameters to plot, specified as one of the following.

S11	S12	S21	S22
GroupDelay	GammaIn	GammaOut	VSWRIn
VSWROut	OIP3	IIP3	NF
NFactor	NTemp	TF1	TF2
TF3	Gt	Ga	Gp
Gmag	Gmsg	GammaMS	GammaML
K	Delta	Mu	MuPrime

Note

Y parameter1 is disabled when you select Plot type to Composite data.

Y parameter2 — Type of parameters to plot

S11 (default) | S12 | S21 | S22 | GroupDelay | OIP3 | IIP3 | NF | ...

Type of parameters to plot, specified as one of the following.

S11	S12	S21	S22
GroupDelay	GammaIn	GammaOut	VSWRIn
VSWROut	OIP3	IIP3	NF
NFactor	NTemp	TF1	TF2
TF3	Gt	Ga	Gp
Gmag	Gmsg	GammaMS	GammaML
K	Delta	Mu	MuPrime

Note

Y parameter2 is disabled when you select Plot type to Composite data.

Y format1 — Plot format

Magnitude (decibels) (default) | Mag | Magnitude (linear) | Angle | Real | Imaginary | ...

Plot format, specified as one of the following.

Y parameter1	Y format1
S11, S12, S21, S22, GammaIn, GammaOut, TF1, TF2, TF3, GammaMS, GammaML, and Delta.	dB, Magnitude (decibels), Abs, Mag, Magnitude (linear), Angle, Angle(degrees), Angle(radians), Real, Imag, and Imaginary.
GroupDelay	ns, us, ms, s, and ps.
VSWRIn and VSWROut.	Magnitude (decibels) and None.
OIP3 and IIP3.	dBm, W, and mW.
NF	dB and Magnitude (decibels).
NFactor, K, Mu, and MuPrime.	None
NTemp	Kelvin
Gt, Ga, Gp, Gmag, and Gmsg.	dB, Magnitude (decibels), and None.

Dependencies

To enable Y format1, set Plot type to X-Y plane.

Y format2 — Plot format

Magnitude (decibels) (default) | Mag | Magnitude (linear) | Angle | Real | Imaginary | ...

Plot format, specified as one of the following.

Y parameter2	Y format2
S11, S12, S21, S22, GammaIn, GammaOut, TF1, TF2, TF3, GammaMS, GammaML, and Delta.	dB, Magnitude (decibels), Abs, Mag, Magnitude (linear), Angle, Angle(degrees), Angle(radians), Real, Imag, and Imaginary.
GroupDelay	ns, us, ms, s, and ps.
VSWRIn and VSWROut.	Magnitude (decibels) and None.
OIP3 and IIP3.	dBm, W, and mW.
NF	dB and Magnitude (decibels).
NFactor, K, Mu, and MuPrime.	None
NTemp	Kelvin
Gt, Ga, Gp, Gmag, and Gmsg.	dB, Magnitude (decibels), and None.

Dependencies

To enable Y format2, set Plot type to X-Y plane.

X parameter — Frequency plot

Freq (default)

Frequency plot, specified as Freq.

X format — Frequency plot format

Hz (default) | Auto | kHz | MHz | GHz | THz

Frequency plot format, specified as one of the following.

Auto	Hz	kHz	MHz
GHz	THz

Y scale — Y-axis scale

Linear (default) | Log

Y-axis scale, specified as Linear or Log.

Dependencies

To enable this parameter, set Plot type to X-Y plane.

X scale — X-axis scale

Linear (default) | Log

X-axis scale, specified as Linear or Log.

Dependencies

To enable this parameter, set Plot type to X-Y plane.

Plot — Plot specified data

button

Plot the specified data using the plot button.

More About

Stub Mode - Not a Stub

This block calculates the ABCD-parameters using the physical length of the transmission line, d, and the complex propagation constant k using the equations:

$$\begin{array}{l}A=\frac{e^{kd}+e^{-kd}}{2}\\ B=\frac{Z_0*\left(e^{kd}-e^{-kd}\right)}{2}\\ C=\frac{e^{kd}-e^{-kd}}{2*Z_0}\\ D=\frac{e^{kd}+e^{-kd}}{2}\end{array}$$

Z₀ and k are vectors whose elements correspond to the elements of f, a vector of modeling frequencies, determined by the Output Port block. Both can be expressed in terms of the resistance (R), inductance (L), conductance (G), and capacitance (C) per unit length (meters)

$$\begin{array}{c}{Z}_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}}\\ k=k_r+j{k}_i=\sqrt{(R+j\omega L)(G+j\omega C)}\end{array}$$

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 of the conductor.

• μ is the permeability of the dielectric. μ  = μ₀ μ_r, where:

  • μ₀ is the permeability in free space.

  • μ_r is the Relative permeability constant

• The is a complex dielectric constant given by ε   =  ε′ − јε″= ε′ (1 − јtanδ)

• ε′ is the real part of complex dielectric constant ε, ε′  = ε₀ε_r.

• ε″ is the imaginary part of complex dielectric constant 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 $$1/\sqrt{\pi f\mu {\sigma }_{cond}}$$.

References

[1] Pozar, David M. Microwave Engineering. Hobken, NJ, John Wiley & Sons, Inc., 2005.

Version History

Introduced in R2009a