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Transmission Line (Equivalent Baseband)

Model general transmission line

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  • RF Blockset / Equivalent Baseband / Transmission Lines

  • Equivalent Baseband Transmission Line block

Description

The Transmission Line block models the transmission line described in the block dialog box in terms of its physical parameters. The transmission line, which can be lossy or lossless, is treated as a two-port linear network. The block enables you to model the transmission line as a stub or as a stubless line.

Parameters

expand all

Main

Characteristic impedance of the transmission line, specified as a scalar or complex scalar in ohms.

Propagation velocity of a uniform plane wave on the transmission line, specified as a scalar in meters per seconds.

Reduction in strength of the signal as it travels over the transmission line, specified as a positive scalar in dB/m..

Modeling frequencies, specified as a positive vector in Hz.

Method to interpolate the network parameters, specified as one of the following:

MethodDescription
LinearLinear interpolation
SplineCubic spline interpolation
CubicPiecewise cubic Hermite interpolation

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

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

Stubless Transmission Line

  • Not a stubNot 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.

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

    A=ekd+ekd2B=Z0*(ekdekd)2C=ekdekd2*Z0D=ekd+ekd2

    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 = αa + , where αa is the attenuation coefficient and β is the wave number. The attenuation coefficient αa is related to the specified loss, α, by

    αa=ln(10α/20)

    The wave number β is related to the specified phase velocity, Vp, by

    β=2πfVp

    The phase velocity VP is also known as the wave propagation velocity.

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.

    Shunt transmission line

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

    for a short circuited transmission line

    Zin=jZ0tanγl

    and for the open circuited transmission line

    Zin=jZ0cotγl

    where

    • Z0 is the characteristic impedance and

    • γ is the propagation constant

    The ABCD-parameters for the shunt stub are calculated as

    A=1B=0C=1/ZinD=1

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.

    Series transmission line

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

    A=1B=ZinC=0D=1

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

Frequency data source, specified as User-specified.

Frequency data range, specified as a vector in hertz.

Reference impedance, specified as a nonnegative scalar in ohms.

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.

  • 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.

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

S11S12S21S22
GroupDelayGammaInGammaOutVSWRIn
VSWROutOIP3IIP3NF
NFactorNTempTF1TF2
TF3GtGaGp
GmagGmsgGammaMSGammaML
KDeltaMuMuPrime

Note

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

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

S11S12S21S22
GroupDelayGammaInGammaOutVSWRIn
VSWROutOIP3IIP3NF
NFactorNTempTF1TF2
TF3GtGaGp
GmagGmsgGammaMSGammaML
KDeltaMuMuPrime

Note

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

Plot format, specified as one of the following.

Y parameter1Y 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.
GroupDelayns, 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
NTempKelvin
Gt, Ga, Gp, Gmag, and Gmsg.dB, Magnitude (decibels), and None.

Dependencies

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

Plot format, specified as one of the following.

Y parameter2Y 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.
GroupDelayns, 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
NTempKelvin
Gt, Ga, Gp, Gmag, and Gmsg.dB, Magnitude (decibels), and None.

Dependencies

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

Frequency plot, specified as Freq.

Frequency plot format, specified as one of the following.

AutoHzkHzMHz
GHzTHz  

Y-axis scale, specified as Linear or Log.

Dependencies

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

X-axis scale, specified as Linear or Log.

Dependencies

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

Plot the specified data using the plot button.

References

[1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000.

Version History

Introduced before R2006a