Quote of the Day
All right, sweethearts, what are you waiting for? Breakfast in bed? Another glorious day in the Corps! A day in the Marine Corps is like a day on the farm. Every meal's a banquet! Every paycheck a fortune! Every formation a parade! I LOVE the Corps!
— Sergeant Apone in the movie "Aliens". I love this line.
Introduction
I was asked today how long a telephone line in North America can be and still work properly. This is an interesting question and worth writing about here. The US still has about 112 million of these lines in service (2011), however the number of lines is declining each year. I can see the days of the classic copper phone line coming to an end over the next few decades. Like analog video, it will eventually be replaced by digital services. For a fiber optic deployment (i.e. no copper), the old phones lines can re-purposed to carry the power needed by the fiber optic interface if AC power is not available. To carry power, the resistance of the line -- which is determined by the length and cross-sectional area of the line -- becomes very important. When carrying voice signals, phone line resistance was limited to ensure that the central office could detect the phone going off-hook. This post will use the maximum allowed line resistance to determine the maximum possible line length.
The answer to the maximum length question is "it depends" -- which is the answer to all interesting engineering questions. It depends on things like:
- the telephone standards the line was built to (e.g. TR-57 or GR-909)
- the wire used (specifically, the cross-sectional area of the wire and the ohms of resistance per unit length)
- the temperature of the wire (this can vary enormously between a buried deployment and an aerial deployment)
For voice communication from an Optical Network Terminal (ONT), I deal with phone lines shorter than 500 feet (a short line as defined in GR-909). However, quite a few ONTs in remote locations are powered from old phone lines using high-voltage power supplies. Service providers use the old phone lines to provide power to the ONTs because the cost of running a new AC power line to a single remote unit is about $10K per kilometer. Some of these old phone lines run many thousands of feet, are available for free, and are capable of carrying enough power to operate an ONT (~10 W).
The question that I received was in regards to powering a remote ONT over old phone lines using a device similar to this. These units drive old telephone lines with ±190VDC. The question came from an engineer working on a remote powering project who wanted to know what kind of line lengths he can expect to encounter. The analysis presented below provided him with the information he needed.
Background
Limits on Phone Line Length
TR-57 is the standard most North American phone lines are designed to. This standard sets the resistance limit on a phone line at 1500 Ω. I quote requirement R-30 here.
With loop closure applied to the COT line unit, the sum of the RT line unit resistance between its tip and ring conductors plus Rdc (maximum recommended loop resistance of the cable between the RT and the Network Interface) recommended by the manufacturer of the DLC system shall be ≤ 1500 ohms.
This requirement does not set a length limit -- only a resistance limit. For my analysis, I will ignore any resistances within the ONT. They exist, but are small compared to the resistance of a long copper wire.
Copper Wire Resistance
Equation 1 can be used to compute the resistance of a copper wire.
| Eq. 1 |  |
where
- RWire is the resistance of the wire.
- ρ(T) is the resistivity of copper as a function of temperature T.
- L is the length of the wire.
- A is the cross-sectional area of the wire.
For my analysis of length, I need to mention the telephony signal goes out and back over a pair of copper wires (called tip and ring). This means that the signal traverse two lengths of copper wire between the central office and the phone. I will account for the two-way nature of the phone signal in my analysis below.
In the US, wire area is usually specified in an archaic unit called the American Wire Gauge (AWG). Most outdoor phone wires in the US are one of three AWG sizes:
- 22 AWG (circular diameter = 0.644 mm)
- 24 AWG (circular diameter = 0.511 mm)
- 26 AWG (circular diameter = 0.405 mm)
Resistivity
Equation 2 provides a common model for the resistivity of copper, which I will use here. Note that temperature of wires can become fairly high -- think of a wire pair in a bundle of other similar wires somewhere in Arizona during the summer. The wires being in a bundle is important because they will (a) self-heat, and (b) the heat tends to stay trapped in the bundle.
| Eq. 2 | ![\displaystyle \rho \left( T \right)=1.724\cdot {{10}^{-8}}\cdot \left( 1+0.00393\cdot \left( T-20\text{ }{}^\circ C \right) \right)\text{ }\left[ \text{ }\!\!\Omega\!\!\text{ }\cdot \text{m} \right]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Crho+%5Cleft%28+T+%5Cright%29%3D1.724%5Ccdot+%7B%7B10%7D%5E%7B-8%7D%7D%5Ccdot+%5Cleft%28+1%2B0.00393%5Ccdot+%5Cleft%28+T-20%5Ctext%7B+%7D%7B%7D%5E%5Ccirc+C+%5Cright%29+%5Cright%29%5Ctext%7B+%7D%5Cleft%5B+%5Ctext%7B+%7D%5C%21%5C%21%5COmega%5C%21%5C%21%5Ctext%7B+%7D%5Ccdot+%5Ctext%7Bm%7D+%5Cright%5D&bg=ffffff&fg=000&s=0&c=20201002) |
Analysis
Figure 1 shows how I determined the maximum length of a phone line as a function of wire gauge and temperature.
Figure 1: Max Length of a Phone Line as a Function of Temperature and Wire Gauge.
Conclusion
Just a quick answer to a question on how long a telephone line can be. I personally have encountered lines over 18,000 feet long and I am sure longer lines are out there. I probably should mention that not all telephone lines are compatible with the old Bell System rules. I have been told the US government setup its own phone system for the Forest Service nearly a century ago that has its own special rules (e.g. one wire lines with Earth return). I have no idea exactly what those folks did. I know one engineer who had to interface with it and he said it was pretty strange.
Here's an EE problem that has been bugging me. If you go to Radio Shack to buy resistors, they don't sell you just one. They sell you N identical resistors of R ohms, in a pack. My question : how do you write a simple computer program, e.g. in matlab, that will yield every possible value of resistance if you combine all N resistors in every way possible. I don't see how to begin this. The number of values does go up rapidly with N. If you buy three 1 ohm resistors you can have 3 ohms. 1/3 ohm, or 1.5 ohms. Try 4 resistors. By the time you reach 10 the number of values seems mind boggling. How would one code this problem ? A. David Wunsch u mass lowell
Hi David,
You are asking about a classic EE problem. I have seen this discussed a number of times in different forums (recent example). I know of one paper that has published a solution using Mathematica (here). If you have access to Mathematica, that may be the quickest way to a solution. Mathematica is nice for solving this type of problem because it handles set operations so cleanly. I am sure I could code it up in Mathcad as well. The method presented in that paper can be extended to other languages (I have the start of a Python routine -- the solution involves Farey and Fibonacci sequences).
I would finish up the Python routine, but I am in the middle of writing a proposal. I hope my response is helpful.
Mathscinotes
I would like to know about analog telephone line resistance loss, from the telephone system to the end user analog telephone point, the distant is about 5km, I am using the fired rate cable , cable gauge 22AWG, due to the manufacturer cable length maximum 2km, I will required to join the cable using the 110 punch down termination block and required 4 joints. The analog circuit voltage is -48VDC maximum loop resistance is 1500ohm include the telephone set.
What will be the line resistance loss
The 1500Ω maximum loop resistance is the value quoted in requirement R30 from TR-57 (the bible of analog telephony). This is the maximum allowed load on a telephone line that will still be detected as off-hook by the central office.
You then ask what will be the line loss on a line with a reach of 5 km (i.e. 10 km of wire). This is not a maximum loss situation and we can compute that value as follows:
Note that this value will leave ~16V as overhead for the SLIC (Subscriber Line Interface Circuits), which typically need ~4 V of overhead voltage to operate properly.
The answer you get is strongly dependent on the loop current value being used. For my calculations here, I used 28 mA, but you will see values between 23 mA and 35 mA being commonly used.
mark
Thanks Mark.
I am using a PABX system, the line circuit is -48Vdc.
Using a 24AWG cable from the PABX system to the 1st termination block and out going cable is 22AWG Fire Rated Cable.
The user telephone point is approx. 5km away from the system and I required to joint the cable (considered 4 joints from the PABX system to the last joint before t the telephone point (using the 110 punch down block to loop). what is the line resistance loss in this case and what will the estimated loop resistance.
The analysis is similar to my previous answer. Here is a snapshot of the Mathcad work.
Hi.
I have a project that we used a cat5e telephone wires(24awg) that will use to an analog phone. The installed cable is 350m. Will this run in analog phone?
Thank you.
I recommend that people use Cat5e over Cat3 all the time. In fact, I own a condo that I rent out where I run Ethernet and voice on the same cable (limited to 100Mbps data service). My home and garage in northern MN is done with Cat6 (similar to Cat5e). Most of my customers have been running phones on Cat5e for years.
350m is not an issue. Cat5e will run analog phone service over thousands meters, but data is limited to 100m. Both have 24 AWG conductors.
mark
In our project the distance from the PABX & end user is 9 Km approx. and the cable size used are 22 & 24 AWG. Also these cable are spliced in several locations. Is the end user telephone work without any repeaters.