Purposely lossy coax: How to determine resistance?

"Joel Koltner"

The thinness helps to minimise capacitance while still keeping the cable diameter small.

BTW

Doug Ford is an old mate - formerly he designed professional audio and lighting products for local Sydney manufacturers.

..... Phil

Joel, Thanks for the link to a nice article. I'm afraid I can't help you. I hardly do any transmission line things... And I've forgotten all that Dr. Henry Neubauer taught me as a second year EE. But the problem looks like 'ringing' in the lumped LC parts. Can a tranmission line have the equivalent of a Q? Perhaps setting that near one will give the correct lumped resistance?

George H.

Thanks George, I'll keep that idea in mind. I might end up having to do some simple simulations with, e.g., various loads, plotting what distributed resistance seems to work well, plot the results and see if there's any, "aha!" moments.

The LT Spice lossy transmission line model might help, but it doesn't include skin effect.

A passive 10x probe acheives its bandwidth sort of the same way a current-mode opamp does: as the signal frequency goes up, load the hell out of the source.

Do you know about this?

Yeah, I'll buy that. There's some optimal point where you start giving up bandwidth with excessive loading vs. having comb filter-like effects (from the reflections bouncing around) without enough loading.

I believe I've seen it before but I'd forgotten about it; thanks for the link.

Tek introduced a 1GHz passive probe last year. Although it's probably mostly for bragging rights (clearly someone at Tek wanted to push the envelope a bit...), the specs are quite respectable as well.

---Joel

I googled (Transmission line +Q) and found a Ham article with equations.

There was some equation that had R =3D 2*alpha*Zo.. in ohms/foot... but I didn't dig enough to figure out what alpha was... But the 2*Zo part looked promising.

George H.

Ah, this article:

That seems more about modeling transmission lines as lumped circuits, but it definitely looks promising as solid background information. Thanks a lot!

Yup that's it... just a google find so no idea of the quality. (NPI)

For short lengths a transmission line is like a cavity... well sorta...

Yeah, lumped elements is how I'm thinking about the problem. There's some critical resistive loading. It's related to the characteristic impedance.

George H.

do

No! Should I print out all 116 pages? (I'm only at page 10 but it looks great.)

George H.

IMO QEX magazine is often surprisingly good -- it's a great resource that many academics are blinded to, unfortunately!

Heck, I'd even suggest that these days, while IEEE journals certainly do have good articles in them, the SNR is no better or even worse than with QEX. :-)

Are you asking the "distortionless line" question?

/ R + jwL \ Zo =3D sqrt( --------- ) \ G + jwC /

/ 1 + jwL/R R \ =3D sqrt( --------- * --- ) \ 1 + jwC/G G /

Condition of distortionless:

L C

--- =3D --- R G

propConstant =3D attnConstant + j*phaseConstant

propConstant =3D sqrt((R+jwL)*(RC/L+jwC))

attnConstant =3D R*sqrt(C/L) phaseConstant =3D w*sqrt(C*L)

Is the attnConstant the one you're looking for? It seems like R & G would be built in to create the loss.

G =3D RC/L

Funny how you can put the differential quantities in Q form:

/ 1 + jQseries R \ Zo =3D sqrt( -------------- * --- ) \ 1 + jQshunt G /

Since Qseries =3D Qshunt for distortionless, and G =3D RC/L, then the same- old familiar form drops out:

Zo =3D sqrt(L/C)

I might be without knowing it. :-)

...or R = L*G/C = G * Zo^2. That would certainly work, although I get a feeling that passive high-frequency probes (that use this lossy coax) aren't distortionless: With 50ohm coax, from the article posted I know that R is roughly 100ohms/meter, so to satisfy the above equation it'd require ... G = R/Zo^2 = 100/50^2 = 40mS/meter. I'm pretty sure that's orders of magnitude higher than any real coax is?

---Joel

get a

that's

yeah. A distortionless line is a neat idea, but it isn't what they do on further examination.

After making my post I downloaded that Tek paper someone referenced. It explains what they are doing in there.

They basically say G approaches 0, so

/ jwL R \ Zo =3D sqrt( ----- + ----- ) \ jwC jwC /

As w gets big, it is back to same the same old formula. It doesn't matter that Zo is bigger at low frequencies.

It is an very interesting topic for me. I had known that the probe lines were lossy for a long time, but only had a vague feel about how they operated. I knew it was crap without them though, based on experience. lol!

Yet you know, I'm sure, that the highest performance today does not use that technique, and instead amounts to active probes and a 50 Ohm doubly termed setup, which perhaps is not surprising.

Thanks to your question, I now have a new set of interview questions. Then, if I don't like their "tatoos," I can say in the wrap-up "the dude doesn't even know how a simple scope probe works!"

Good point, thanks.

I generally agree, although a passive probe wins on sales price and -- in many cases -- performs well from millivolts to many tens of volts, whereas active probes usually aren't designed (from a noise perspective) to cover that many decades. How many users actually care about these factors is likely a significant function of whether you ask the Tek salesguy vs. the LeCroy or Agilent salesguy...

(Tek's presently the only company offering a 1GHz passive probe; they even include one per channel with their 1GHz scopes. If you want the

I didn't know that the "magic" of passive probes was the use of lossy coax until I was some years out of college, although I *do* remember thinking the first time I saw the simplified schematic of a probe that no way could you just blithely ignore the meter-long coax with the then-already-400MHz passive probes that were available!

---Joel

I join you in having learned stuff from this thread.

Enjoy

?-)))

I'm just wondering (out loud) if the added R gives you a situation where the real as well as the reactive impedance components of the transmission line match.

If you view a transmission line as a bunch of lumped impedances strung together, then you'll want to match the dielectric loss of the cable (parallel component) with a series loss that have same ratio as the imaginary components (L and C).

I believe that gets you back to a distortionless line again, right? -- But in the case of the scope probe coax, AFAIK while the center conductor (R) is significantly lossy, there dielectric is still almost lossless (G approaches 0).

I wonder if anyone has ever mass produced distortionless coax? I'm guessing the answer is "no" in then it'd be difficult to provide the requisite hi-Z termination much above some many MHz... whereas you can provide a pretty good 50ohm termination to at least some GHz... and just making the center conductor lossy is sufficient if your goal is to not have to worry about termination impedances too much.

---Joel

There's no difference between "unavoidable" series resistance (copper cable", and "intentional" resistance (resistance wire). Both contribute to to the resistance per unit length in the same way.

Given the transmission line equation:

Zo = sqrt(R + jX / G - jB) (note the sign of B, by convention, capacitive susceptance is negative)

Then for nonzero R and/or G, Zo *must* be complex, ie. any line with finite losses has complex Zo.

Only in the case of a theoretical lossless line does this reduce to the familiar:

Zo = sqrt(jX/-jB) = sqrt(jwL/jwC) = sqrt(L/C).

RG223 (nominally Zo=50) has Zo = 50.34 -j5.38 at 100KHz, and 174.56

-j167.25 at 1KHz ! Only above about 1MHz does it get to 50 + 0j, to one significant figure. [Based on Belden figures for R and L, with G dielectric losses assumed negligible]

The use of resistive cable in oscilloscope probes damps ringing on fast transients (lower Q), but brings its own problems in high frequency probes, since it degrades rise time, needing receiving end series-parallel LCR compensation to sharpen the response up again. The probes I use (PMK