Noise figure measurements--tire kicking requested

On a sunny day (Tue, 13 Dec 2011 17:15:18 -0500) it happened Phil Hobbs wrote in :

Dunno, but it so happens I am working now with germanium transistors the idea it to connect one to my cryocooler and that can easily do 70 K. To get the noise down and see if I can detect some radiation with it. I guess if you could cool further down then you can do better measurements? Condensation is my biggest problem.

Sure, cooling it further relaxes the accuracy requirements on the low noise end. On the other hand, it's not obviously an improvement in usability to require 1 degree accuracy at 25K vs 0.1 degrees at 240K.

Cheers

Phil Hobbs

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Dr Philip C D Hobbs
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ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

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I never did noise sources that way but oscillators. One thing to keep in mind when it comes to temperature accuracy is the fact that your coax cable is a heat sink. It introduces an error because it'll lead to the outside world directly or through a (thermally conductive) coax jack.

Hoping that you do not need frequent and fast temperature ramps you could consider heating/cooling a larger styrofoam cavity and curl up some coax in there. Sort of a "heat inductor" :-)

--
Regards, Joerg

http://www.analogconsultants.com/

Thanks. Really skinny coax as used in cell phones (0.8 mm) leaks only about 6 mW/K for a 10 cm length.

I hope that two measurements will be enough, but for a sanity check I probably want a few more.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

How about using a resistor at some fixed temperature and switching on/off some excess noise, rather than moving the temperature. That's the way classic NF meters work. I recall one HP unit switching the noise on and off at some hundreds of Hz, and using something like a phase-sensitive detector to drive a meter movement. Not very complex.

You can buy the on/off noise sources. Noisecom maybe.

From first principles, use the shot noise of a photodiode as the excess noise source. You'd still have to keep the resistor at some low, constant temperature.

Lakeshore will sell you calibrated cryo-diodes and thermistors.

John

Thanks.

I thought about the photodiode approach, which I've used before. The problem is the accuracy. It doesn't take much capacitance to make a 1% error in 50 ohms at 300 MHz--1 pF is enough.

The NoiseCom et al. noise sources run quite a bit too hot for this measurement--they're like 40-60 dB noise figures. (They also cost $2k if you want a calibrated one, iirc.) I've been talking with Shane from Radiovation, who makes USB-powered noise sources for $275. They're fine for making fake signals, but they aren't calibrated--at that price, it would be amazing if they were--and they're also too hot for LNA measurements.

I'm really hoping to avoid cryogenics. The easy way to do this measurement is with a dewar of LN2--do the measurement once, dunk the cable in the LN2, do it again, simple math gives the answer. These days I don't have an LN2 tap 20 yards down the hall the way I used to.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

[...]

Hey, there's an idea.

How about two small buckets of oil? One chilled to -30C and the other heated to +60C. Nicely insulated, lid on top, small hole in lid, through which the coax with the resistor gets poked. That way the coax is exposed to the temperature as well. I used to have a home made oil-filled dummy load and the oil had no effect on the RF. Until the bucket leaked, but it has lasted me 30 years.

Ok, don't use the black soupy stuff that had been in the old Chrysler for nobody remembers how many thousand miles :-)

--
Regards, Joerg

http://www.analogconsultants.com/

No relevant experience, just some thoughts. I see no insurmountable problems -- I've considered doing the same thing, only with a glass of ice water (or dry ice in acetone) and a beaker of boiling water. Using a TE device makes it more of an instrument and less of an ongoing high- school physics experiment.

Note that if you get ambitious you can stack TE devices to get almost arbitrary amounts of cooling, if you don't mind using lots of power at the "hot" end. At some point the cost of the TE stack and its drive electronics will rival a split Sterling cooler.

Itty bitty flexible coax is lossy, particularly at higher frequency. Pay attention to the loss of the line, and take into account the fact that the cold lossy portions aren't going to generate as much noise as the hot lossy portions. Maybe you want to use itty bitty hardline?

If a coax relay has repeatability problems of 0.3dB (3%), what makes you think that a coax connection to an amplifier won't have the same issues? Or are you assuming that you'll make it and it'll stay the same?

How is the impedance of the line going to change with temperature, oh Mr. "1%"?

"R" as "measurement ratio" and "R" as "resistance" together in the same discussion is confusing -- bad you.

Your resistance will change with temperature, thus changing the loading on the amplifier in ways that will have to be corrected for -- unless you can find a resistor that does not significantly change resistance.

--
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Why am I not happy that they have found common ground?

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Well, if you drop your 0603/microcoax into boiling LN2 (or whatever, but LN2 is easy) the temperature should be pretty well defined and conduction leak should be fully absorbed... Alternately some oil in a test tube all placed in boiling water should give you good high temperature accuracy. Now if you want to automate the temperature shift, well...

For the relay 0.3dB funnies, it's probably uncertainties at relay end of life and way much better for a new one. I once had repeatability issues in my 4195A front attenuators of about the 0.2/0.3dB order. Changed the relays which saw heavy use (prod line) and all is back to the 0.01/0.02dB level... Oh, and HP didn't use coax relays in this 500MHz fine instrument... OK those are calibrated out, but still impact return loss...

--
Thanks,
Fred.

Phil Hobbs wrote: : I need a gizmo for making accurate measurements of low noise : temperatures from near DC to a few hundred megahertz. I'd like to be in : +- 0.1 dB territory for noise temperatures from about 25 K to 300 K. : Something pretty well based on first principles that doesn't itself need : calibration would be the ticket.

: I've been looking at switching between hot and cold resistors using a : coax relay, but they all seem to have return loss funnies down at the : 0.3 dB level.

: I'm leaning towards just putting an 0603 resistor on the end of a few : inches of 0.81 mm coax and silver-epoxying the shield to a small : Peltier. The heat leak won't be much (only about 0.6 mW/K for 10 cm : length. With appropriately placed Styrofoam, I can run that from : probably -30 C to +60 C, which will give me about 1.4 dB change in the : thermal noise. The measurement would basically be to run a few : temperature cycles, measuring the output noise as it goes.

: The output noise will be proportional to the sum of the noise : temperatures of the amplifier and the resistor. As long as the gain of : the amp stays constant, I can calculate its noise temperature as follows

: R = (measured total power at Th)/(measured total power at Tc)

: (Th - R*Tc) : Tn = ----------- : R-1

: Assuming the amp and power meter are linear, all the level calibrations : cancel out, so I ought to be sensitive only to errors in Th, Tc, and R. : Getting a 2% measurement down at 25K from this setup will require : something like 0.2 K temperature accuracy, which isn't that easy to do, : but I can probably do nearly that well with a diode-connected : transistor. Down at the 25K end, 5% wouldn't be that awful as long as : it sits still, and I can do that well with a YSI glass bead thermistor.

: Any relevant experiences/suggestions/criticisms welcomed.

I don't have much experience on ultra-stable gain contraptions, so I'd rather suggest ways to reduce the acuracy requirement.

If you can get hold of liquid nitrogen, through a colleaque in a local physics lab for instance, matters would become rather easy. LN can be carried around in a stainless steel thermobottle which you can get from a local camping store. The cold resitor can just be hanging from a twisted pair or a small-diameter coax. I have wired a full LHe dipstick by using prefabricated U.FL-U.FL cables (like DigiKey H11554-ND), which saved me the trouble of soldering the connectors to the cable. The SMD resistors specified at 25 ppm/C, or even at 50 ppm/C (I like Susumu RR0816Q series) hold their values quite well down to LHe, but of course this is something you may want to calibrate out, depending on your accuracy requirements.

The role of the hot resistor in the cold/hot resistor noise figure measurement is just to calibrate the gain of your amplifier chain. As John L. pointed out, it is much easier just to use a cold *attenuator*, and "warm it up" by feeding additional noise into it. At frequencies I'm typically interested in I can do it with an ARB generator. At microwaves, where you usually must calibrate everything, the hot resistor *is* nice, as a sure-fire self-calibrated flatband noise source. With the attenuator, pseudorandom noise is just one convenient way to do the gain and frequency response calibration (when doing noise measurements you have a spectrum analyzer hooked at the amp output anyway), but a chirp or a sine sweep would work equally well.

If you are not operating at very high frequencies, it is possible to just measure separately the voltage noise of the amplifier by using a room-temperature source resistance significantly lower than the noise match, and current noise by using a source significantly higher than the noise match. Make the load resistors into the attenuator shape so that you can measure the gain on-the-fly. You then calculate Tn = un in / 2 kB . If the source is ac coupled it does not affect the amplifier biasing as it otherwise would. Parasitics are likely to cause a frequency rolloff when the source is away from the designed match, but you can recognize that (and to an extent cancel out) from the measured gain response. But a few hundred MHz may be difficult this way.

One more possibility is to make an actively cooled resistor out of an amplifier, following Percival's ideas, but to make it unconditionally stable and figure out *its* characteristics may be more work than your attempt for ultra-stable gains. I think I have seen this suggested somewhere ... ahh, here it is: Frater and Williams, IEEE Tran. MTT, vol 20 no 4 p 344,

1981.

Regards, Mikko

Good stuff, thanks.

I thought of boiling water, but keeping the coax dry would be an issue. Water getting in will change the loss a lot.

Unfortunately it's very difficult to get more than about 110 C worth of cooling with stacked Peltiers, because only the last stage is running unloaded--they're so inefficient that the earlier stages run at a fairly small delta-T. You also have to use much bigger ones as you go down the stack--the optimum is roughly tripling the area at each stage, and eventually the lateral temperature drops make it impossible. If you don't use nice beefy copper heat spreaders between stages, a stacked Peltier is liable to melt if you turn it on suddenly. If you do use spreaders, you have to worry about the CTE mismatch, which is no joke.

The best competing alternative is probably dry ice and acetone--I can get a bit of dry ice from a $12 hardware store fire extinguisher, probably enough to do the measurement if I use a glass thermos bottle.

I'll check. They use it in cell phones, so my hope is that it isn't too bad up to 300 MHz or so.

As long as it doesn't vary between the hot and cold measurements, it doesn't affect the answer much--it more or less cancels out, like the amplifier gain and frequency response.

Snippy, very snippy. ;) The dielectric will have something like 100 ppm/K CTE, and the jacket should keep the shield snug around it. The usual catalogue formula for Z0 is

Z0 = 138/sqrt(epsilon) log10(D/d).

So if Z0 is nominally 52 with epsilon=2.25, D/d is 3.67. Taking 100 ppm as the tempco of D/d, which will be reasonably close, and bounding the tempco of epsilon by +- 200 ppm (i.e. +-2% over 100 C range) the tempco of Z0 will be

dZ0/dT ~ Z0*(0.5*TCeps/epsilon-100ppm/((D/d) log(D/d))).

we can bound the TC of Z0 between +- 2.3 milliohms/K. Thus in a 100 C range, we might be off by 1 quarter of an ohm.

And of course that represents a considerably smaller error in the incident noise power since the heated section isn't very long, and it doesn't get heated uniformly. So I think we're probably okay there, but thanks for bringing it up--it's something to watch. It might be worth putting some heat shrink over the coax to make sure the shield doesn't lose contact with the dielectric.

I didn't use R for resistance in my original post.

There are 0603 resistors that are good to 0.02% and 5 ppm/K. For instance I could use two of these:

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

Thanks, Mikko. The actively-cooled resistor is just an N**2 times larger R with negative feedback with a gain of -N**2 applied to the cold end, leading to effectively the same resistance but with N times lower noise voltage, right? (I use that trick all the time, but never called it by that name.)

The LN2 approach is what I used to use when I had an LN2 tap down the hall, but it's a fairly major pain at this point--I'd have to get a few hundred bucks' worth delivered, and it evaporates in a week even in a good dewar.

Part of what I'm trying to build is a setup where I can forget about measurement noise for most purposes, and put it in as a simple correction when I do have to worry about it. It'll eventually rely on the feedback trick, but I need some first-principles thing to measure it against, or I won't know when I've got there.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

I simply used an SMA terminator at the end of a piece of UT47 semi-rigid stuck in a dewar with LN2. The terminator resistance changed by less than 0.25 Ohm, about 25ppm/K. Good enough for me. Losses in the coax and connectors would tend to make the cold source look hotter than it really is, so you want the shortest practical length of good quality coax and flawless connectors.

Ah yes, the Y-method of noise measurement. The traditional symbol would be Y instead of R. Haus and Adler published about this in the late fifties.

Jeroen Belleman

Hi, Jeroen,

Yes, I'm aware it's a relatively old technique--I'm just trying to build one of my own without taking all week at it, and wondered about other folks's experience.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

n

Sounds fun, Some random thoughts.

The several hundred MHz moves it out of my =91comfort=92 zone.

You might look up Shot noise thermometry. I=92ve talked several times with Lafe Spi#$%** , who last I heard was at NIST in Boulder. They use tunnel junctions to get a fundamentally calibrated noise source. (Shot noise and Johnson noise from the same device) You might be able to get a sample? I monkeyed around with doing the same trick with a resistor and photodiode, but getting the BW to stay constant is tricky. If you went with a simple doubling of the noise signal the PD trick can work... (then there=92s the 100=92s of MHz.)

I=92ve done the diode connected transistor temp sensor down to 77K. I=92d be happy to send you a transistor and calibration curve. Bad news is the transistor is a TO-220, TIP32. It might be too big. (To calibrate it you need to measure the forward voltage drop at 10uA and measure the temperature. The single point calibration seems to be good to ~0.2 mV, but it=92s hard to check... and I only wanted it good to a degree.

Sticking things in bubbling liquid sounds easy, but I found the bubbles can add some extra noise. So a probe with a tail sticking into the liquid works nicely, whereas immersing the probe in the liquid led to more noise. I assume this had something to do with the leads moving around... variable C. So perhaps a =91stiffer=92 layout might work.

George H.

**Hmm, just thought I shouldn=92t broadcast his name, you can find it on a paper he coauthored while at Yale, or contact me via email.

But did the RF have any effect on the oil?

;-)

Before I got a ready source of transformer oil in small (gallon) quantities, I have been known to use ATF without ill effects.

--
"For a successful technology, reality must take precedence 
over public relations, for nature cannot be fooled."
                                       (Richard Feynman)

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Good Dewars are better than that. I've heard tales of 3-4 months. And even the old one I purchased from my neighbor's junk/treasure pile holds for 6 weeks (60 liter's)

George H.

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Yes, it is a widely used technique. If you are interested about the history of the approach, I put the original paper for you to download

. I'll remove it tomorrow. I think I encountered the principle for the first time on Kittel's book on thermodynamics, it was about damping of the pointer of an ammeter with the aid of a laser goniometer.

An interesting experiment would be to actually physically cool some object with a transistor, along the lines of Nyquist's gedanken experiment. It is just hard to achieve in practice, the numbers are not reasonable at ordinary temperatures. Some colleaques cooled recently a gravitational antenna weighting more than a ton to the temperature of

0.17 mK, using back-action of a SQUID! Well, actually they cooled only one mechanical mode of it ...

Regards, Mikko

I used 40 2K/2W carbon resistors in parallel between two sheets of FR4 in a fan tunnel as a test load for my 2-Meter rig (50 years ago :-) ...Jim Thompson

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