Attenuation of AC signal through a cable

[morasu]

Hi guys,

I am trying to see how much attenuation I am going to get with a signal with a center frequency of 416.7 kHz going through about 100 meters of a cable. I was calculating the impedance by taking the square route of the cable resistance squared plus the capacitive reactance squared. I was getting about -4 dBV, which seems about right but after including the inductive reactance in the calculation, I am getting a gain of 5 dBV. I do not know why I am getting a positive gain when the signal should be attenuated. Should I ignore the inductance? Underneath is a copy of my .m. Any information on the subject would be greatly appreciated.

close all; clear all; clc;

v1 = 24; % max voltage input of hydrophone
I = 200*10^-3; % max current of hydrophone

l = 0.59058*10^-6*100; % inductance of cable for 100m 

c = 108.273*10^-12*100; %capacitance of cable for 100m
f = linspace(374000.7,458000.7); %frequency range of hydrophone
xc = (2*pi*f*c).^-1; %capacitive reactance
xl = (2*pi*f*l); % inductive reactance

x = xc; % reactance
z = sqrt(67^2 + x.^2); % total impedance sqrt(R^2 + X^2)

v2 = I.*z; % output voltage

g = v2./v1; % Gain
G = 20*log10(g);

plot(f,G)
xlabel('Frequency (Hz)')
ylabel('Gain (dB)')
title('Gain vs Frequency for 100 m of Cable')

figure(2)
plot(f,z)
xlabel('Frequency (Hz)')
ylabel('Impedance (Ohms)')
title('Impedance vs Frequency for 100 m of Cable')

 

[THINKER_KAM_MAN]

what? 100 Mtr cable? is it coaxial, is it on a reel 416Khz that's RF.
you need to use transmission line principals for that,
if its on a reel and its electrical cable you need to consider the inductance and the self
resonance frequency, equivalent circuit equal resistance,in series:
with tuned cct. and you need to work out the Z. of the arrangement.
if its played out then you need to calculate the loss of the transmission line when terminated.
100Mtr = approx 1/8 wave lengt at 416K

 

[albbg]

You can estimate the losses using the following equations:

Lcopper=11.39/Z*√f*(1/d+1/D)
Ldielectric=90.96*f*√ε*tan(δ)

Lcable=Lcopper+Ldielectric in dB/m

where:
Z is the characteristic impedance of the cable in ohm (typically 50 ohm)
f the frequency in GHz
d the diameter of the central conductor in mm
D the inner diameter of the outer conductor, in mm
ε the dielectric constant (typically 2 for PTFE)
δ the dielectric loss tangent (typically 0.0003 for PTFE)

However since the frequency is low you can expect losses <1 dB/100m even with cheap cables

To Saad880
the sentence "Rg8 cable is best to catch the signals" makes no sense; the choice of a cable depends from many factors.

 

[THINKER_KAM_MAN]

If you are using coaxial cable then
why not refer to the manufactures specifications
for cable loss.

 

[morasu]

If you are using coaxial cable then
why not refer to the manufactures specifications
for cable loss.

They don't have the losses on the spec sheet... after talking to a representative, apparently Belden only does it for some of their cables... whichever ones they feel like?

 

[morasu]

I will try that, and sorry what is PTFE?

- - - Updated - - -

Yeah they werent on the spec sheet and after talking to a Belden representative, apparently they don't make the calculations for all their cables?

 

[morasu]

So I was hopeful with this equation, but I guess there is no dielectric on the cable because it is a microphone cable. Is there another formula that leaves out the dielectric constant?

 

[FvM]

So I was hopeful with this equation, but I guess there is no dielectric on the cable because it is a microphone cable.

I hope there will be a dielectric (insulating matter) in your cable, otherwise it shorts the signal. Microphone cables are mostly using PVC (like power cables) or possibly PE. PVC has higher dielectric losses than PE or PTFE, but still so low that dielectric losses can be ignored for low impedance signals and frequency below 1 MHz. At the end of the day, only copper losses will matter for this application.

Lcopper=11.39/Z*√f*(1/d+1/D)
Ldielectric=90.96*f*√ε*tan(δ)

The calculation assumes, that the cable is terminated with it's characteristic impedance, otherwise the loss changes.