3.6 Channel Model

A simple in-house coaxial cable wiring configuration is established by assuming three TV connections involving two splitters and four sections of coaxial cables. The configuration is shown in Figure 3.8. As is common for most home networking with in-house coaxial cable wiring, the transmission path between any TV connection points covers an output port-to-output port connection of a splitter. Because the coaxial cable distance is relatively short and the frequency is not very high for the available gap between the reverse channel and TV channel 2, the output port-to-output port connection produces most signal-level attenuation.

Figure 3.8. A Simple In-House Coaxial Wiring Model

The channel model from TV A to TV C of this simple configuration can be established by first cascading ABCD parameter matrices of a 100-ft coaxial cable section, an output-to-output path of a splitter, a 25-ft coaxial cable section, an input-to-output path of a splitter, and another 35-ft coaxial cable section. The resultant ABCD parameter matrix is then converted to the insertion loss and impulse response of this model in-house coaxial cable wiring configuration. The insertion loss of this model configuration is shown in Figure 3.9. Estimated RLGC primary parameters of the RG-6 coaxial cable are used in this channel model calculation. The corresponding impulse response is shown in Figure 3.10.

Figure 3.9. Transfer Function from TV A to TV C

Figure 3.10. Impulse Response from TV A to TV C

Compared with a straight coaxial cable, the insertion loss of this channel model is much higher and is not even along the frequency scale. The high and uneven signal loss is mainly related to the output port-to-output port path of a splitter. When only attenuation is considered for the normal purpose of a splitter between output ports, the unevenness of the attenuation does not matter. Depending on the signal bandwidth, proper signal-processing techniques might be necessary when a signal is sent through the output port-to-output port path of a splitter. Otherwise, the time domain reflection, as indicated in Figure 3.10, could limit the signaling baud rate.

This coaxial cable channel model is established based upon limited laboratory measurements. Improvements to this model can be achieved by further confirming coaxial cable and splitter models. Transmission characteristics of splitters vary much depending on manufacturers. The effect of the variation can be experimented with by changing the coupling coefficients of the first coil and the second coil of the splitter.