information on awg length vs impedance?

[macwanj]

Hi all,

Does anybody know where I can find information on wire length and impedance? I know that the gauge of the wire does little to affect the impedance.

 

[JohnRoberts]

http://en.wikipedia.org/wiki/Electrical_resistance

http://en.wikipedia.org/wiki/American_wire_gauge

 

[macwanj]

Ha! Didn't occur to me to wiki it...thanks anyways John.

 

[PRR]

> information on wire length and impedance?

JR gave you a simple resistance chart.

PentodePress has resistance, inductance, and reactance:
http://pentodepress.com/calculator/wire-inductance.html
Watch your decimal-points. (I would argue that "milliOhm" is meaningless in most causal audio, bump the dot over three.) (And micro-Ohms? Angels dancing on pins!)

> I know that the gauge of the wire does little to affect the impedance.

How so?

Line Impedance has almost nothing to do with wire, for short wires such as "we" usually use.

333 feet of #22 cable is 5.4 ohms one wire, 10.8 ohms round-trip. Put 600.0R on the far end, the DC/LF impedance is 611 ohms, which "is" 600 for any practical purpose. At 20KHz the inductance is about 64 more ohms... that may start to matter. If the source is zero-impedance, the "600.0" load gets 600/(600+11)= 0.98 at LF, 0.90 at 20KHz, -0.7dB roll-off. Going to #10 is better, but not near the change of cost. And 333 feet of typical "cable" shows ~~10,000pFd capacitance, so our source has to be under 50 ohms or we will get another 1dB droop.

As we go past hundreds of feet, we get fairly constrained in "good" impedance. That's why very-long audio systems favor 150 ohms: cable-pairs always zone-in around 90-140R. (500/600R comes from pre-Cable wide-pairs on glass insulators, which was obsolete before electronics became common; 600R still worked fine on cable past 1,000'.) Coax runs half that: hence all the 50 and 75 ohm RF coax. Wide-space pair may reach double: 300-ohm TV twinlead.

But few of us need to run Long Lines, and if we do we should have a box to tweak the top octave, cuz that's a lot cheaper than over-kill cables.

30 foot runs around the studio, terminated in "10K", ARE 10K, whether the wire-loss is 5 ohm or 0.2 ohms. The actual loss is under 0.1dB. The few-ohm parasitics are as dust upon the rock.

Small-stuff wiring is mostly about mechanical strength. #22 can be broken by hand, we like fatter stuff in rough studio/stage work, and the added copper-cost is offset by fewer breakdowns.

Speaker runs, it matters. 30 feet of #22 into 8 ohms loses 10% of costly power, and may show 1dB mis-damping since speakers are never perfect 8 ohms. Even 30' #10 won't be ruler-flat to 20KHz in an 8 ohm resistor (though speakers being wonky resistors, and never as flat as a half-good line, it works fine).

 

[macwanj]

Hey PRR thanks for that very informative reply; the link that you put up was exactly what I was looking for. I was thinking inductance when I wrote impedance in my earlier post. I was thinking that due to the skin effect at higher frequencies, wire gauges from say 22 to 10 don't have significant changes in surface area and hence VHF see the same impedances within these wire gauges. A flat piece of copper or a ground plane will offer more surface area and alleviate problems due to the skin effect. Is this correct reasoning? I recently bought Ralph Morrison's book on grounding and shielding and I'm slowly digesting the material...

 

[CJ]

Then you have capacitance problems, so somewhere in the middle...

 

[JohnRoberts]

Skin effect is generally not of consequence at audio frequencies.

Transmission line effects are generally not of consequence for modest distances.

Look first at simple RCL unless you are operating at very high frequencies.

JR

 

[PRR]

> wire gauges from say 22 to 10 don't have significant changes in surface area

True. Hold that thought.

> and hence VHF see the same impedances within these wire gauges. A flat piece of copper or a ground plane will offer more surface area

Yes, but.... who cares about "VHF"? There shouldn't be any of that crap inside good-audio boxes. Leave that to the VHF engineers.

> Ralph Morrison's book on grounding and shielding and I'm slowly digesting the material...

Digest in layers. Don't obsess too much on one technique.

> wire gauges from say 22 to 10 don't have significant changes ...ground plane will offer more surface area

"More", but if #22 isn't the answer then a ground plane may not be enough better to "eliminate" the problem.

What you mostly see done wrong in grounding is like the case of a combination dance-hall and surgery-ward. Dancing feet shake the surgeon's scalpel and bad things happen. Yes, you can go under and double-up all the joists, get less shake; even joist the floor solid and get an obvious change. But a better, and often cheaper, plan is to move the surgery to another building where dancing is banned. Doctors are smart enough to object to working in Sally's Square-Dance Saloon, but electronics are not. You have to be aware what parts are sensitive and what parts stomp, and keep them apart. Physically, but also from the point of view of electric flows.

And any place you could have a Ground Plane, the inductance of wire is "zero" for all audio frequencies. It takes dozens or hundreds of feet of wire to build-up enough inductance to bother most audio circuits. You are not going to run a foot-wide copper strap 300 feet down the street; there's always a better way to go far.

Yes, it can matter at 100MHz. The length of an emitter lead affects UHF circuits. This is starting to matter now that ICs routinely reach 100MHz bandwidth, and we may have to build stuff as small short islands in a sea of copper-foil "ground plane". And the makers of such chips usually offer a suggested PCB patern to get you started.

The combination of L and C in a Loooong audio line is interesting. The modern attack is to drive with ~~100 ohms and load in >10K. The 100r will swamp a lot of capacitance. The >10K will not mind quite high series inductance. Most of us do not have such large venues that the L and C reactances start to converge, and we have to abandon the lumped-parameter simplification. At some greater distance, we get echoes... actually we always do, but a foot of wire is one nano-Second so with "any" wire-loss the echo is "totally gone" long before we can perceive it. And for most cable driven 22r-470r, the echo-loss is quite high. (For ~~100r source AND load, echo is nearly zero; but broadband loss is unnecessarily high and double-termination hasn't been routine in audio for decades.) Telcos have to care, we don't. (Video engineers have to double-terminate all lines except the shortest casual stubs... 100 feet cable-echo will stutter-up fine video detail.)

 

[macwanj]

Thanks for all the responses gentlemen; yesterday I read one of Bill Whitlock's papers on interfacing and it seems tat transmission line effects don't come into play until you reach longer lengths. I realize that as far as audio devices are concerned, VHF isn't really a concern. However, I'm trying to learn as much as I can about the topic. While designing recording gear is a hobby, sound reenforcement is really my day job which is why I need to learn everything I can about the effects of transmission lines and such. On some of our shows, we run really looong audio lines; some that are almost 2000ft; theres a lot of interfacing  going on between house sound, production sound and broadcast trucks. In most of these cases the company uses fibre lines. I'm still new to the idea of transmission lines; can anybody suggest some good reading material on the subject?

Ralph Morrison's book is fairly dense but I admire the fact that he starts from basic principles in physics. I never really had a conceptual understanding of voltage as a force field or how you can simplify certain caes with a lumped LCR parameter and how in other cases this is not possible. There is so much lore behing grounding and interfacing that it makes life difficult for noobies like me. John mentioned in some other posts that text books are your friend and I think hes right. Perhaps we need to start a thread about must read books wheter it be on electronics, transmission lines or pcb design... just my 2 cents...

 

[PRR]

> On some of our shows, we run really looong audio lines; some that are almost 2000ft

Bah. One of my first paying jobs included a nasty line which we *thought* was maybe 3,000 feet. It turned out to be over 7 miles.

Even then, it wasn't really a "transmission line" in the classic sense.

> transmission line effects don't come into play until you reach longer lengths.

The usual idea is "a significant fraction of a wave will fit in the line". In another view, when the two ends of the line are not the "same" voltage. If you 'scope both ends of a 30 foot run, the audio is the same at both ends. If you bring 30 miles of wire back to the start, and freq-sweep, you'll see real phase shift.

I don't dig speed of light. I do recall that one foot is one nanoSecond. What is audio? Say up-to 20KHz. So one audio cycle takes more than 1/20th of a milliSecond. Or 50 microSecnds. Or 50,000 nanoSeconds.

So a "long line" in audio is approaching 10 miles. (My 7-mile line didn't need to pass 5KHz, so it was just at the edge of "long", less than 1/4 wave at 5KHz.)

You can get into other troubles long before you must face Transmission Line Theory. My 7 miles of bad wire passed every wheezy power transformer in three towns. It probably had dozens of splices, some made before I was born. It is very possible it had loading-coils, which peak-up 2KHz while clobbering everything over 3KHz. And this was pre-CarterFone-- I hadda use the Telco-supplied interface and at the low tariff we paid, we got the cheapest type. (IIRC, it was a 2uFd cap.... nah?)

Digital techniques make sub-Volt ground differences unimportant. Optic lines don't reference distant grounds. While you can "always" tame a Long Copper Line, sometimes it takes hours or years. Many many studio to transmitter links, "working" on miles of telco pair, got bypassed with small microwave links, because the quality was better, less prone to telco accidents, and long-term the high price could be les than monthly telco tariffs.

 

[Andy Peters]

You can get into other troubles long before you must face Transmission Line Theory.

Of course you know this, but cable capacitance over that very long line will do wonderful things to your HF response.

-a

 

[macwanj]

Bah. One of my first paying jobs included a nasty line which we *thought* was maybe 3,000 feet. It turned out to be over 7 miles.

Wow! 7 miles of audio lines?? Hopefully you didn't end up with a tangled up mountain of wire ; )

 

[PRR]

> tangled up mountain of wire

You call the Phone Company, say you need one pair from the Admin building to the Dorm, they give you two ends and signal gets through.

And the tariff is by shortest-path, so we assumed the wire was.

No, the Admin bldg was in one exchange and the Dorm was in another exchange. In another town. And they had spare lines everywhere -except- from Admin to Dorm. So the "easy way" was to put a jumper in each exchange, zig-zag-zig.

Sometimes you order such line on-purpose. My dad was on a telemetry project, customers might have miles of wire between sensor and recorder. They needed a worst-case test-line, to uncover problems in the lab before stuff went out to customers. But who wants to shuttle back and forth from one end to the other? Well, this was LA in the 1950s, and it happened the plant was on the edge between the City telco and the Rural telco. And there was a phone-pole 10 miles up the road which also sat on the border.

So they called each company and had each one connect plant to pole. Each using their own particular codes and practices and running all over some ugly (high EMI) neighborhoods. When the lines were ready, somebody cross-connected the pole-ends, and brought the two plant-ends to a terminal strip. 20 miles of bad wire, the worst of two telcos, as easy to use as jumper-cables. If they could recover sensor signal through that, they could probably do it in Akron or Pittsburgh.

Long lines are fun.