Characteristic Impedance of a Transmission Lineby KasraMohammad Tags: characteristic, impedance, line, transmission 

#1
Apr812, 05:34 PM

P: 20

So we are told in our class that the characteristic impedance of a coaxial cable is impractical to be at a value like 500Ohms. Why is that?
The assumption is that the transmission line is lossless and that the dielectic constant (E_{r}) is 1 



#2
Apr812, 06:34 PM

P: 3,843

You cannot have characteristic impedance larger than the free air impedance of 377Ω. That is even if you have a wire in free space great distance from ground, earth or anything, the impedance is only 377Ω. Anything that has ground or shield or anything closer by is going to be lower. Any coax line impedance is
[tex]Z_0=\sqrt{ \frac{R+jωL}{G+jωC}}[/tex] And is going to be a lot lower than than free air. 



#3
Apr812, 07:00 PM

P: 1,784

There are a few transmission lines over 500 ohms but appears they are used as delay lines.
http://ieeexplore.ieee.org/xpl/login...mber%3D1697084 http://www7.taosnet.com/ebear/coaxlist.html 



#4
Apr812, 07:20 PM

P: 20

Characteristic Impedance of a Transmission Line
Ok I can sit well with that explanation. So a transmission line cannot have an impedance larger than the impedance of free air, which is at 377. So how come resistors are able to bypass this law yet transmission lines cannot? Does it have to do with material limitation in the construction of a transmission line??




#5
Apr812, 07:20 PM

P: 3,843

Why delay lines can have higher than 377Ω. I can't login to IEEE. delay line is just tx line!!!




#6
Apr812, 07:23 PM

P: 3,843





#7
Apr812, 09:15 PM

P: 20





#8
Apr812, 09:36 PM

P: 3,843

This is getting into transmission line theory where we treat the voltage and current at every point as time dependent signal and we use phasor representation. When you work with transmission lines, you work in propagation environment where signal at each point of the tx line is different and is time dependent. Think of it this way, EM wave takes time to travel from one end of the tx line to the other, the consequence voltage and current at every point along the line is different as it take time for the signal at one point of the line to move to the second point. After you study EM and get into RF tx lines, you will understand this. 



#9
Apr812, 10:10 PM

P: 20

I see what your saying. The higher the impedance in the resistor of the load, the more of a jump the voltages gets because the signal is reversed back towards the source, causing either a constructive or destructive wave interference. I'm sure i'll get a more intuitive understanding of this and why the tx line impedance cannot exceed the free air impedance after I finish my current course (Upper Division Undergraduate Electromagnetism)




#10
Apr812, 10:12 PM

P: 1,784

The abstract of the IEEE reference says:
Abstract A cable with an impedance of the order of 1000 ohms is described. It resembles the usual flexible concentric cable with a 3/8inch outside diameter, but its inner conductor is a singlelayer coil continuously wound on a flexible core of 0.110inch diameter. The cable is suitable for video connections from chassis to chassis and to remote indicators. The second reference shows all known cables and their impedances such as: Cable Imped Max Oper O.D. Type (Ohms) Volts Inches Remarks  RG65A/U 950 1,000 .405 High impedance delay line, video cable RG185/U 2000  .282 Delay cable RG186/U 1000  .405 Delay cable RG266/U 1530 4,000 .400 Delay cable 



#11
Apr812, 11:05 PM

P: 3,843

I saw the abstract and the table on impedance in the second link, but what is the theory behind it?
Only thing I know so far that some point in the tx line is high impedance only through standing wave due to mismatch at the termination particular in open or shorted termination where at some length the impedance goes to infinity. eg. at λ/4 of a shorted tx line. 



#12
Apr912, 06:23 AM

Sci Advisor
PF Gold
P: 2,243

but your second sentence suggests not ? RF ladderline is readily available as 300 Ohm or 450 Ohm impedance cheers Dave 



#13
Apr912, 07:56 AM

P: 330





#14
Apr912, 08:19 AM

P: 1,784





#15
Apr912, 11:12 AM

P: 4,664

If you calculate the attenuation due to copper skineffect losses as a function of characteristic impedance, the minimum impedance will be below 100 ohms. The minimum impedance is also slightly dependent on the dielectric.
Thw characteristic impedance of a coaxial line is (see Eq(10) in http://kom.aau.dk/~okj/te7/coaxnote.pdf) [tex] Z_o=\frac{1}{\surd\varepsilon}\frac{377}{2\pi}Ln \frac{D}{d} [/tex]where ε is the relative permittivity of the dielectric, and d and D are the inner and outer conductor diameters. There is no fundamental upper limit to Z_{o}, but impedances over 377 ohms are very impractical, except for high impedance delay lines. I have used special coaxial delay lines (HH1600, 1600 ohms, 1 microsec per foot) which have a helical center conductor to add inductance, but they are very dispersive and lossy. 



#16
Apr912, 11:25 AM

P: 3,843





#17
Apr912, 11:43 AM

P: 3,843

Looks like I am wrong about the upper limit of the impedance. Sorry.




#18
Apr912, 03:31 PM

P: 20




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