Australian Phone Line Impedance Math

Quote of the Day

The time to reef the sails is before the storm is upon you.

— Old sailing aphorism

Introduction

I am doing some work with international phone circuits and I noticed that the Australian government has test procedures that model the characteristic impedance of the phone line using a resistor/capacitor circuit (see Figure 1). In the US, we model the nominal cable characteristic impedance using a 600 Ω resistor (thick outside plant wiring) or 900 Ω resistor (thinner central office wiring). I thought I would take a quick look at how the Australian load circuit compares to the standard formula-based model used for the characteristic impedance of a wire pair. For testing, we like to use lumped component models of phone wire rather than using long runs of wire pairs -- it is a matter of cost and convenience.

Background

I have discussed modeling the characteristic impedance of a phone line in this post and that presentation is also true for Australia.

Analysis

Circuit

I obtained the Australian phone impedance information from this document. Figure 1 shows the equivalent circuit I will be analyzing.

Figure 1: Equivalent Load Circuit For Australian Phone.

Modeling

Figure 2 shows my circuit analysis results. The characteristic equation is discussed thoroughly in his Wikipedia entry. Appendices A and B discuss my sources for cable information and cable dimensioning.

Figure 2: Characteristic Impedance and Lumped Impedance Circuit Analysis.

Graph

Figure 3 shows my graph of the characteristic impedance formula and the lumped circuit input impedance over a frequency range of from 1 kHz to 4 kHz (normal voice range).

Figure 3: Impedance Versus Frequency (1 kHz to 4 kHz).

Conclusion

I can see that the Australian phone line impedance model is a reasonable approximation for 26 AWG wire over a ~1.7 kHz to 4 kHz frequency range. The US approach is to use a single 600 Ω resistor or 900 Ω resistor to model a phone line. This is a reasonable approach from an impedance magnitude standpoint, but it does not model the phase.

Appendix A: Australian Cable Characteristics

I used this blog post as my source of information on Australian telecom cabling. This quote was important to my analysis.

The reality is that little of Australia’s copper on the distribution side (what matters for FTTN) of the network is over the 0.64mm diameter cable (aka: 22 AWG) that VDSL2 requires, much of it is in the 0.40mm & below class, with some newer areas having 0.50mm deployed. The only places I’ve come across with 0.64mm & above cable are rural areas. Most of the 0.64mm & 0.90mm in the bush is long line PSTN with loading coils. Essentially the higher gauge was used to extend a phone line out to a farmstead or the like.

The cable specifications that I have seen look like American 26 AWG and 28 AWG cable. This is pretty fine wire -- in the US I normally find 24 AWG, some 22 AWG, and even some 19 AWG.

Appendix B: Defintion of Cable Terms

Here is a link to a good reference on transmission line parameters. Figure 4 shows the definitions of the cable parameters r and a.

Figure 4: Cable Dimensions.