Talk:Characteristic impedance

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This article contains material from the Federal Standard 1037C, which, as a work of the United States Government, is in the public domain.

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Help with this template Comments: edit – history – watch – refresh I don't see a reason why this page cannot be unified with the page dealing with "wave impedance"

1 Does the definition of characteristic impedance in terms of permittivity and permeability belong here?
- 1.1 Example
2 Four comments
3 Electrical and electromagnetic impedances
4 Meaning of high or low characteristic impedance

[edit] Does the definition of characteristic impedance in terms of permittivity and permeability belong here?

Pozar defines the characteristic impedance of a transmission line in terms of the RLGC parameters of the transmission line, and uses the term intrinsic impedance to refer specifically to the relation between the magnitudes of the electric and magnetic fields of a plane wave traveling in an optical medium.

Should this article use the RLGC parameters consistently throughout, perhaps with a statement that the characteristic impedance of a transmission line is analogous to the intrinsic impedance of an optical medium?

Pozar, David (February 2004). Microwave Engineering, 3rd edition.

IJW 01:59, 14 September 2006 (UTC)

Sounds reasonable. And if you believe this should be here, then be bold and edit the article!

Atlant 13:08, 14 September 2006 (UTC)

I have edited the article to define the characteristic impedance in terms of RLGC parameters and linked to Medium (optics) instead of defining characteristic impedance in terms of permittivity and permeability. I also removed the section on frequency dependence because it is misleading; R and G are not constant and the frequency dependence of $Z 0$ is not as simple as the previous version of the article stated. At AC and higher frequencies $R \sim \sqrt{\omega}$ and $G ˜ω$ . Only at very low frequencies (where the thickness of the conductors is comparable to the skin depth) is R relatively constant, but the frequency dependence of G remains. I will revisit this section to include these facts and give a more complete treatment.

IJW 14:41, 14 September 2006 (UTC)

Following is the section on frequency dependence that I deleted:

=== variation with frequency === The impedance of a real lossy transmission line is not constant, but varies with frequency. At low frequencies, when

$\omega L \ll R$ and $\omega C \ll G$ ,

the characteristic impedance of a transmission line is

$Z_0 = \sqrt{R/G}$ .

At high frequencies where

$\omega L \gg R$ and $\omega C \gg G$ ,

then the characterstic impedance is

$Z_0 = \sqrt{L/C}$ .

So there are two distinct characteristic impedances for every line. Usually G is very small so the low-frequency impedance is high, whereas the high-frequency impedance is low. The break points in the impedance frequency graph are at $ω 1 = G / C$ and $ω 2 = R / L$ (where $ω = 2π f$ ). If $R/G \gg L/C$ , it is obvious that $\omega_2 \gg \omega_1$ . Between these two break frequencies the cable impedance decreases smoothly.
[edit] Example

Take the case of a 50Ω coaxial cable with polyethylene dielectric. R is about 100 mΩ/m and G < 20 pS/m (based on measurements of leakage resistance in a 1 m length). Using $L = C Z 2$ , L can be calculated at about 250 nH/m. So,

ω₂ = R/L = 200 krad/s (f₂ = 30 kHz)

and

ω₁ = G/C = 0.2 rad/s (f₁ = 30 millihertz)

At 100 Hz the 50 ohm coaxial cable will have an impedance of about 900 ohms, only reaching 50 ohms at about 30 or 40 kHz. The phase angle of the impedance between the two break frequencies is leading (the cable looks capacitive).

IJW 17:11, 14 September 2006 (UTC)

[edit] Four comments

A definition should give the method to measure the item defined. If you define the characteristic impedance as the ratio of voltage to current in the line, you simply cannot measure it. The only place where the measure can be done is at the end of a semi-infinite line. Then, instead of talk about waves, why not define the characteristic impedance as the impedance measured at the end of a semi-infinite line?
Of course, in the two definitions, there is always the problem of reflections if the line is finite. You can replace the "last infinite length" of the line with an impedance equal to the characteristic impedance. The proposed definition allows this.
You can also use a finite length of line and make the measure before the arrival of reflections (a pulse generator and an oscilloscope are enough).
In a transmission line, you cannot have a voltage wave without current or a current wave without voltage. Any wave is voltage plus current. You can write two equations, one for voltage and one for current but they form the same wave. There is not "a pair of waves".
You can hardly talk of "transmission line" or "characteristic impedance" when the length of the line is negligible compared to the wavelength in the line. You have just a conductor with negligible inductance and stray capacitance. This is the case of IJW example of the coaxial cable at 30 kHz. It just begins to be a transmission line at a length of a few hundreds of meters and then it behaves more as a resistance than as a transmission line. The characteristic impedance depends on frequency. However, when this is the case, in low frequency, the transmission line is no more interesting. This is not the most interesting aspect of transmission lines. LPFR 12:17, 15 September 2006 (UTC)
The vacuum characteristic impedance should be mentioned here,related to the rf domain where the carcateristical impedance is very important. —The preceding unsigned comment was added by 194.138.39.55 (talk • contribs) .

Impedance of a transmission line or impedance of an electrical circuit is the ratio of a voltage divided by a current, both of them measurable quantities. Impedance of vacuum or impedance o a substance is something ( $\scriptstyle{\sqrt{\mu\over \varepsilon}}$ ) related to the properties of the substance in an electromagnetic field. It just happened that the units of this value are ohms and people could not avoid calling it "impedance". Impedance of a line and impedance of vacuum are very different things. The difference is still greater if you think of transmission lines built with discrete inductors and capacitors used (in the past) as delay lines. LPFR 12:05, 1 October 2006 (UTC)

[edit] Electrical and electromagnetic impedances

As Mebden himself wrote in the page "intrinsic impedance", electrical impedance and electromagnetic impedance should not be confused. The impedance of a transmission line is an electrical impedance and the impedance of a medium is an electromagnetic impedance. LPFR 08:51, 23 October 2006 (UTC)
Impedance of a transmission line or impedance of an electrical circuit is the ratio of a voltage divided by a current, both of them measurable quantities. Impedance of vacuum or impedance o a substance is something ( $\scriptstyle{\sqrt{\mu\over \varepsilon}}$ ) related to the properties of the substance in an electromagnetic field. It just happened that the units of this value are ohms and people could not avoid calling it "impedance". Impedance of a line and impedance of vacuum are very different things. The difference is still greater if you think of transmission lines built with discrete inductors and capacitors used (in the past) as delay lines. LPFR 12:05, 1 October 2006 (UTC)

[edit] Meaning of high or low characteristic impedance

Would it be accurate to add this (e.g. to the introduction): "A high-quality (high conductance) transmission line tends to have a low characteristic impedance, and vice versa." (Or is it the other way around?) --Coppertwig 13:18, 11 January 2007 (UTC)

Electrical conductance is pretty orthogonal to impedance; you can design a transmission line in a wide variety of impedances (to suite the need) although some impedances are a lot "easier" (natural for the materials employed?) than others. So I guess I disagree with your proposed addition.

Atlant 13:41, 11 January 2007 (UTC)

My goal here is to have this page and related pages improved to the point that a person similar to myself can quickly and correctly understand the concepts being presented. So if something seems unclear or contradictory, that means it needs to be edited.

For now, I'm thinking in terms of transmission lines with zero conductance and zero inductance. The equation given for characteristic impedance in that situation seems to me to reduce to being equal to the resistance of a unit length of the transmission line.

I really like the mention of the infinitely long transmission line in the opening paragraph: it appeals to the intuition in a simple, relatively easily understandable way. However, by itself it isn't enough; I'd like at least one more sentence with similar simplicity and appeal but providing complementary information.

Problem: The first paragraph seems to be claiming that the characteristic impedance is equal to the impedance (resistance, in the case I'm considering) of an infinitely long piece of transmission line, while the equation seems to reduce (in the case I mentioned) to the resistance of a unit length of transmission line. Those can't both be true, can they? It seems to me that there's something wrong. (If they can both be true, this needs to be explained in the article.)

Also, if you're talking about a transmission line with two conductors, (such as often plug into electrical appliances), then with the infinite one you're attaching to both of the conductors, whereas when measuring the impedance of a unit length, it would seem to make sense to measure only one of the conductors at a time. This clouds the issue.

Question I'd like to see answered in the first or second paragraph of the article: which has a larger characteristic impedance as a transmission line: a pair of thick copper wires, or a pair of thin copper wires (straight, separated by an insulator)? Again, I'm thinking in terms of the resistive part of the impedance. (After I understand that, I might tackle the imaginary part.) Doubling the cross-section of the copper wire cuts its resistance in half, I believe. Or do they both have the same characteristic impedance? (I don't think they do.) The answer to this question is basically the same thing as the sentence I proposed at the beginning of this discussion.

Could somebody just give a few examples? Would a coaxial cable tend to act as a capacitor at high frequencies, for example? What happens to the characteristic impedance when you double the thickness of the conductor of a coaxial cable?

I mean: if there's anybody out there who understands what characteristic impedance is, could you please explain it more fully and illustrate it with examples? Thanks. --Coppertwig 04:44, 12 January 2007 (UTC)