# Modem signal over coaxial cable

#### mmuj

Joined Dec 15, 2009
11
Hi All

I need to use low speed phone line modem chip (cmx868) to communicate over dedicated 8 miles long coaxial cable. cmx868 uses 1.2/2.4kHz signal for tx/rx. as it is low frequency signal do i need worry about coaxial cable characteristics impedance which is 50 ohm?

2.4kHz signal wave length is over 80 miles (roughly speaking) so signal quater wave length is over 20 miles, more than twice the cable length so in transmission line terminology my coaxial cable length is "short". Apart from copper resisitive losses due i need to worry about capacitance of the cable?

mmuj

#### SgtWookie

Joined Jul 17, 2007
22,230
Have a look here:
http://en.wikipedia.org/wiki/Coaxial_cable
Scroll down to the "physical parameters" section. There are lots of formulas for you to use to develop models with.

An 8-mile-long chunk of coax is going to look like a very large LC network.
There are many different types of 50 Ohm cable; RG-58/U and RG-8/U are just two of them, and are quite different physically and electrically - even though the impedance is quite close.

Take a look at figure 4a in the datasheet. The output impedance of the modem is 600 Ohms. You would need to match that impedance to the coax at both ends, or you will have big problems.

My guess is that you will need to have repeaters at periodic intervals along the coax; how many would depend on what coax you are using.

#### mmuj

Joined Dec 15, 2009
11

Parameters of coaxial cable in use has got R = 15 mohm /m, L = 250nH/m & C = 100pF/m so for a lumbed circuit of 10 miles roughly values are R < 50ohm, L < 5mH & C < 20nF. By adding 50 ohm to source impedance of 600 ohm and simulating resulting circuit reveales frequency response of rlc circuit at 2.4kHz that attanuation is less even 1 dB.

so my understanding is that for such a low frequency coaxial cable should act like a rc circuit or even just series resistance.

your opinion will help me clarify my understanding.

Cheers,

mmuj

#### rogs

Joined Aug 28, 2009
279
At the low frequencies you are talking about, I suspect the 'characteristic' impedance of the coax cable will hardly enter into things.

There is some quite useful data here http://home.mira.net/~marcop/ciocahalf.htm - especially the graphs near the end.

I have only had practical experience of running coax cable lengths up to about a mile - using DTMF in my case. Only the cable resistance seemed to figure in any attenuation at those frequencies. (Using a 600 Ohm driver and receiver)

My 'instinct' is that you'll have no problems at all --but I have to bow to the experience of those with a more theoretical background.
There is the the danger of confusing the characteristics of coax at high and low frequencies though......

#### crutschow

Joined Mar 14, 2008
34,406
Parameters of coaxial cable in use has got R = 15 mohm /m, L = 250nH/m & C = 100pF/m so for a lumbed circuit of 10 miles roughly values are R < 50ohm, L < 5mH & C < 20nF. By adding 50 ohm to source impedance of 600 ohm and simulating resulting circuit reveales frequency response of rlc circuit at 2.4kHz that attanuation is less even 1 dB.

so my understanding is that for such a low frequency coaxial cable should act like a rc circuit or even just series resistance.
I calculated a total cable resistance of 244Ω and a total capacitance of 1.6μF for 10 miles of cable. You inductance value appears correct. How did you arrive at your values?

#### mmuj

Joined Dec 15, 2009
11
Thanks everyone

To answer crutschow question, actually i did verable calculation but to get exact values i take an example of the cable in use. its parameter are (roughly speaking 10 miles = 52 kfeet)
R = 3 ohm / kfeet
C = 50pF/ kfeet
L = not provided so i took from RG-58 76uH/kfeet , it is not important becuase of low frequency

for 10 miles (52k feet)
R = 3 ohm * 52 = 156 ohm
C = 50pF * 52 = 2.6nF
L = 76mH * 52 = 3.95mH

another question, do i need to worry about any of 600:600 ohm standard modem transrformer or one like MIdcom 82111 is ok ?

Cheers,

mmuj

#### ifixit

Joined Nov 20, 2008
652
Hi mmuj,

From post #3 if RG-58 capacitance per meter is 100 pF / meter,
and 10 miles = 16Km or 16,000 meters,
then capacitance of 10 miles of RG-58 is 16000 x 28.8e-12 = 1.6uF.
Cable series R is 0.015Ω x 16000 = 240Ω.
This calculation compares well with Carl's more accurate numbers.

From rfcafe.com if RG-58 capacitance per meter is ~ 28.8 pF / meter,
and 10 miles = 16Km or 16,000 meters,
then capacitance of 10 miles og RG-58 is 16000 x 28.8e-12 = 0.46uF.

Xc for 0.46uF is ~144Ω at 2400Hz, & 288Ω at 1200Hz.

Cable delay at 5nS per meter is 16000 x 5e-9 = 80uS, roughly 20% of the highest carrier frequency.

I'm not sure how to model this situation accurately, but my gut tells me it will likely work. However, the recieved signal will have some phase distortion and level attenuation, but should still be usable so long as the baud rate is not too high.

The characteristic impedance of the cable can be ignored. You would be better off to use a lower impedance driver such as 50-100Ω instead of 600Ω which will reduce signal loss at the receiver

What baud rate were you thinking of using?
Half duplex, or full duplex?

Regards,
Ifixit