Why 50 ohm impedances?

[kc5tja]

http://www.signalintegrity.com/Pubs/edn/why50.htm

Some interesting reading material.

[GARTHWILSON]

I'd have to say it's because 50Ω is very close to the impedance of one of the common, simple antenna types. Otherwise there's nothing magical about it. I had to lay out a PC board last year with a 50Ω transmission line to a microwave chip antenna that soldered onto the board.

When I was active in amateur radio, I made a gizmo to measure complex impedances of my RF circuits, but I didn't get it finished and calibrated before I left the company where I was working in RF applications engineering where I had all the good equipment available to me. Since as a radio amateur I operated mobile so much in the low bands, I always had a random-length wire antenna and just tuned it to (50+j0)Ω with a transmatch, so I didn't have to worry about making an antenna of a particular impedance.

As for what they say in the article about the height of the trace above the ground plane, I have to say it's not the issue; because for any height, you can still get the impedance you want by adjusting the width. It's a similar story with skin-effect losses.

I wonder if anyone proofread that article before it got posted though. Some secretary must have typed it up and asked what that funny character was, and someone said "It's the Greek letter omega," so she looked it up and found the lower-case one looked like a "w". Right. Watts. Really good. Not.

[kc5tja]

Actually, it's because your browser isn't properly fetching the "symbols" font. W, in that font, is in fact a capital omega.

The "height" that the article is talking about is not referring to the height of the copper layer on the board, but rather the spacing between the signal trace and the nearest ground.

I would imagine that you don't have total, absolute freedom about trace widths and heights, for the same reason you don't have total freedom for the like in microwave amplifier circuits. If a trace is too tall, capacitive coupling with adjacent traces starts to have an effect, and eventually will dominate the benefits offered by impedance-controlled traces.

As far as the "natural" impedance of antennas, I have to say that only two natural impedances exist: 37.5 ohms, and 76 ohms. No balanced or unbalanced antenna has a "natural" impedance of 50 ohms without doing something funky to its geometric configuration, such as the 45-degree downward sloping ground radials of a quarter-wave ground-plane antenna. A folding dipole, IIRC, has a natural impedance of 280 ohms, which is why 300-ohm twin-lead is so often used with that kind of antenna.

Other antennas with a "natural" impedance of 50 ohms are actually end-fed antennas with tuning stubs on the ends -- I refer you to the J-pole for an example.

[GARTHWILSON]

Quote:

Actually, it's because your browser isn't properly fetching the "symbols" font. W, in that font, is in fact a capital omega.

I'm using Firefox 3.6.13. What do I need to do to get it? Edit: It's showing up properly now.

Quote:

The "height" that the article is talking about is not referring to the height of the copper layer on the board, but rather the spacing between the signal trace and the nearest ground.

Same thing. It's how high the trace is off the ground plane which may be on the other side of the board (in the case of only 2-layer) or it may be on an inside layer. If it's inside, you have to be very specific in the instructions to the PCB manufacturer so the spacing ends up being correct.

Quote:

I would imagine that you don't have total, absolute freedom about trace widths and heights

You won't necessarily have tight control over the height, but you can adjust the width to get the desired impedance for whatever height you're stuck with. My particular CAD does not allow a continually-variable trace width. You have to pick a set of 16 widths for the particular board, which normally way more than enough; but when I did the board with the 2.4GHz chip antenna last year (which specifically called for 50Ω transmission line to feed it), I overlapped traces to get .001" resolution on the width.

The antenna towers at the 50,000W AM transmitter I was in on the job of installing in 1981 in Hawaii were about 56Ω with a reactive component of six or eight ohms. They were a little over .26λ tall IIRC (297' for 870kHz), with a ground plane of copper wires burried in the ground, radiating out.

[kc5tja]

There's a matching network of some kind on that antenna then (capacitance hat? Loading coil? Stub?). A quarter-wave vertical with a flat ground plane around it must have a 37.5 ohm impedance, per physics. This has been tested every which way and back.

Soil conditions affect radiation pattern, of course, but I'm not aware of it affecting feedpoint impedance. I may be wrong on this, though. My ARRL handbook is buried at the bottom of a massive RubberMaid container, and I'm too lazy to dig it out now. Too lazy to Google too. Such as it is, after having gotten back from Aikido, practicing knife disarms and villain apprehension.

And now, it's time for me to impedance match some Zs.

(Seriously, of all the years I've ever taken Aikido classes, this is the first time we've trained in police-style takedowns. Cool stuff! But, exhausting.)

[GARTHWILSON]

Quote:

There's a matching network of some kind on that antenna then (capacitance hat?

That's looking into the tower itself. No coils, stubs, or hats, and the guy wires were synthetic, not conductive. The tuning house at the base (which looks like an out house) tunes that to 50+j0 ohms for the 3" coax that comes from the transmitter building.

Quote:

A quarter-wave vertical with a flat ground plane around it must have a 37.5 ohm impedance, per physics. This has been tested every which way and back.

That's what my ARRL antenna book says too, so I don't know why the measurement came out to what it did, but I understand it was pretty close to the design goal. It would be fun to experiment (not just for impedance, but also gain, radiation patterns, etc.). The high frequencies where the antennas are small and easier to experiment with require more-expensive test equipment. A pure mathematician shouldn't need to experiment much (except where certain factors in real life are nearly impossible to model), but that's not me.

[GARTHWILSON]

More on it, from Dr. Johnson's mailbag:
http://www.sigcon.com/Pubs/edn/why50mail.htm

[BigDumbDinosaur]

GARTHWILSON wrote:

Some secretary must have typed it up and asked what that funny character was, and someone said "It's the Greek letter omega," so she looked it up and found the lower-case one looked like a "w". Right. Watts. Really good. Not.

It must be your browser. I'm seeing an Omega.

[rfpowerdude]

kc5tja wrote:

http://www.signalintegrity.com/Pubs/edn/why50.htm

Some interesting reading material.

That's one of the best explanations I have heard.

GARTHWILSON wrote:

More on it, from Dr. Johnson's mailbag:
http://www.sigcon.com/Pubs/edn/why50mail.htm

The minimum loss reason is as good as any and coincides with the previous explanation.

I have gotten so used to 50ohms that the history becomes lost in the everyday world of RF...

[GARTHWILSON]

The capital omega shows up for me properly now. The OP was almost three years ago.

I worked in VHF/UHF power-transistor applications engineering in the mid-1980's, mostly at 175MHz and transistors up to 150 watts output, with a little work also at 30MHz and 450MHz and even less at 1.2GHz. We didn't touch antennas though. All amplifier outputs in the lab went into dummy loads. All equipment--transmission lines, directional couplers, circulators, attenuators, spectrum and network analyzers, etc.--was 50Ω, with the exception of intentionally high SWR loads (all-phase) for testing. I never really questioned the 50Ω choice, and in amateur radio, I always used a transmatch to match whatever the antenna gave me to (50+j0)Ω.

[zz_indigo]

GARTHWILSON wrote:

The capital omega shows up for me properly now. The OP was almost three years ago.

I worked in VHF/UHF power-transistor applications engineering in the mid-1980's, mostly at 175MHz and transistors up to 150 watts output, with a little work also at 30MHz and 450MHz and even less at 1.2GHz. We didn't touch antennas though. All amplifier outputs in the lab went into dummy loads. All equipment--transmission lines, directional couplers, circulators, attenuators, spectrum and network analyzers, etc.--was 50Ω, with the exception of intentionally high SWR loads (all-phase) for testing. I never really questioned the 50Ω choice, and in amateur radio, I always used a transmatch to match whatever the antenna gave me to (50+j0)Ω.

For transmitting in high power is better low impedance (25,12.5 Ohm) lower supply voltage.
But for recieving is better high impedance (300,75Ohm). lower loss on wires.
50Ohm is compromis. for Transmit and recieve applications. (ham radio, CB)
But audio and video equipment uses 75/300 ohm. (mic input, vga, RGB/composite/.. video) low power requirements on transmiting side, low loss on wires.

p.s. Sorry for my poor english.

[GARTHWILSON]

zz_indigo wrote:

For transmitting in high power is better low impedance (25,12.5 Ohm) lower supply voltage.

The impedances at the transistors were extremely low, and matching networks brought them up or down to 50 ohms. Often the impedance looking into the power transistors' input was a fraction of an ohm, plus a few ohms of reactance (either inductive or capacitive, depending on the type of transistor and the frequency.) Trying to broadband these got interesting.

[zz_indigo]

GARTHWILSON wrote:

zz_indigo wrote:

For transmitting in high power is better low impedance (25,12.5 Ohm) lower supply voltage.

The impedances at the transistors were extremely low, and matching networks brought them up or down to 50 ohms. Often the impedance looking into the power transistors' input was a fraction of an ohm, plus a few ohms of reactance (either inductive or capacitive, depending on the type of transistor and the frequency.) Trying to broadband these got interesting.

inpedance of transistor in circuit is depends of transistor type, used componnents and used circuit. Common emitor/common base/common colector.

[GARTHWILSON]

These were always common-emitter (for bipolar) or common-source (for MOSFET) configurations. The width of the base/gate tab was always greater than that of the collector/drain tab, because of the extremely low input impedances at the high frequencies and power levels. The drive levels could be as much as ten watts or more, to get an output of 150W for example.