Cable model aims to represent passive losses & propagation due to a coaxial cable transmission. The frequency response of insertion losses are modeled after the following expressions [1]:
Where f is for the frequency in Hz; K1, K2 are frequency-dependency proportionality constants for squared-root of frequency (resistive loss) and frequency (dielectric loss) respectively, in dB/100 feet; L is for cable length in feet/100; c0 is the lightspeed in vacuum in m/s; εr is the relative dielectic constant.
Hrolloff(f) is a N-th order pole lowpass frequency response, convenient to model cutoff frequency of the cables (which are due either by mode propagation led by geometry, or by frequency limitations of connectors used in the cable):
Where f is for the frequency in Hz; fcutoff is for the cable cutoff frequency in Hz; N is for the low-pass pole order.
In this model, cable characteristic impedance is considered to be perfectly matched to project-defined Z0.
The model includes the following properties:
| Property | Description | Units* |
|---|---|---|
| L | Cable length | m |
| K1 | Resistive loss proportinality constant for f1/2 | dB / 100 feet / MHz1/2 |
| K2 | Dielectric loss proportinality constant for f | dB / 100 feet / MHz |
| E_r | Relative dielectric constant | - |
| f_cutoff | Cutoff frequency | GHz |
| cutoff_order | Order of the cutoff pole | - |
*Units note: Please mind that units in block properties are selected for the best user convenience, and they might not match the units in the above model formulas. All the needed conversions are done as needed.
Some cable presets are included as built-in in Radio System Toolbox:
The following parametric sweeps show the model behavior as the different properties are changed:
Parametric sweep over L (1 to 40 meters)
Parametric sweep over f_cutoff (3 to 9 GHz)
Parametric sweep over cutoff_order (2 to 8 meters)
Parametric sweep over K1 (0.2 to 1.0 dB / 100 feet / MHz1/2)
