Thursday, October 19, 2017

Voyager - Looked at From My Home Turf

We talked about Voyager in August, as the farthest objects mankind has ever launched, and the first manmade objects to leave the solar system.

Likewise, I know I've said I retired from a career as an RF (Radio Frequency) engineer, so communications links, like the two Voyagers' links back to Earth are what I spent most of my life doing.  It's my home turf.  We still have contact with the two probes yet their signals are astonishingly, mind-blowingly weak.  Microwaves and RF magazine editor Lou Frenzel reminded me of some of these things in a piece this Tuesday.

Lou starts out by saying the speed of light is too slow.  We used to ask technician job applicants what the speed of light is, and some didn't know, so let me put it here:   299,792,458 meters/second or 186,383 miles/second.  At 186,383 miles per second, Voyager 1's signals take 19-1/2 hours to get to Earth.  Voyager 1 is 13,082,682,600 miles away, give or take a few million in approximation errors. 13 billion miles away.

One of the fundamental problems in communications links is that the signal strength falls off as an inverse squared relationship (1/Distance(squared)).  We use the term path loss to describe how much signal is weakened by this effect.  How much loss is there for Voyager 1's signals?  The number is astonishing:
The free space path loss is computed with the expression:

dB = 37 dB + 20log(f) + 20log(d)

Here, f is the frequency in MHz and d is the distance in miles. The Voyager 1 used two frequencies, 2.3 GHz in the S band and 8.4 GHz in the X band. Using the lower frequency and the previously estimated 13 billion miles distance, the path loss is:

dB = 37 + 20log(2,300) + 20log(13,000,000,000)

dB = 37 + 67.3 + 202.3 = 306.6 dB
That's a phenomenally large amount of path loss; you can say the power is reduced by 10^30.66.  Ignoring the .66, that's 1 / 1,000,000,000,000,000,000,000,000,000,000  of the signal getting here.

The next thing we need to do is determine how much signal gets here in power units.  The transmitter on Voyager 1 delivered 23 watts to its antenna at some point.  Whether it does now or not, I can't answer.  It's common for receiver designers to refer to powers as dBm, that is, powers with reference to a milliwatt, 1/1000 of a watt, in 50 ohms.  If that transmitter is still delivering 23 Watts, the power would be expressed as 43.6 dBm.  To be my pedantic, some-would-say AR self, a dBm is a power; a dB is a ratio of powers.

Here is where you find out why we always work in dBs: it turns multiplication and division into addition and subtraction.  We find the power at earth by subtracting the path loss from the power output. 43.6 -306.6 = -263 dBm.  Again, an astonishingly small signal.  For VHF or HF radios that most hams or hobbyists have, they're concerned with signals around a microvolt; millionth of a volt.  Perhaps 0.5 microvolt.  That's -113 dBm, 150 dB stronger than Voyager 1's signal; 1,000,000,000,000,000 times stronger.

The other fundamental problem in communications links is that there's an inherent limit to the strength of a signal we can receive, and that is set by the inherent thermal noise of our components.  If you were to put a 50 ohm resistor on a bench and measure the power it produces from just being at room temperature, you would find it produces -174 dBm.  Much lower than the -113 dBm above, but still far, far stronger than the -263 dBm from Voyager.  Perhaps you've heard of radio telescopes being cooled by liquid helium to almost absolute zero?  This is why.  

How can we possibly handle signals that much weaker than the thermal noise?  We get apparent amplification out of antennas, also called antenna gain, on both ends of the link.  Voyager's antenna itself gives 57 dB gain.  (Antenna gain is worthy of another article itself).
At the receiving end of the link is one or more big dishes. There are several large antennas at NASA’s Deep Space Network stations, such as Goldstone in the U.S., Canberra in Australia, or near Madrid in Spain. There are six antennas—one 26 meters (85 ft), four 34 meters (112 ft), and one 70 meters (230 ft)—each having super cooled front-ends for low noise. Using the 70 meter Goldstone dish gives the signal an 82 dB boost. The antennas can also be arrayed to produce more gain and improved reception.
Adding 82 dB gain from the Deep Space Network to the 57 dB gain from Voyager and we can add 139 dB to the signal from Voyager.  That brings up the level to -124 dBm.

One last concept to introduce; that the noise we get depends on the bandwidth we measure in.
P = kTB 
where k is Boltzmann's constant, T is temperature in degrees Kelvin and B is the bandwidth in Hz  

To really fill in those numbers, I need to know things I don't know, in particular, the modulation scheme used by Voyager and the temperature of their "super-cooled front-ends", but it passes a rough sanity check.  Lou Frenzel says Voyager is transmitting 1000 bits/second or so.  I'll swag a bandwidth of 1500 Hz and say I'd need a signal of -136 to decode Voyager, if the data modulation is similar to others I worked with in the early '80s.  So it looks like we can receive Voyager with some margin to spare.

Hope y'all enjoyed a little trip around the old block for me.


  1. Thanks for the math, from someone who wanted to be an EE but fell on my face. I'm sure you could tell stories from work that would cheer us up from the news. One time I asked my friend if he could design me a 1 ghz amplifier. He said no problem. I said how about a 100 Ghz amp? He said thats a different problem. Recapitulating an old joke, I told him we have already determined you are a prostitute, I am just trying to find your 3db point.

  2. That's an absolutely stunning amount of path loss if you know anything about RF.

    On a similar tale, we were interviewing an alleged RF Engineer at Boeing. She wowed us with her exploits, the things she'd worked on, and a killer resume. Then somebody noticed she'd previously been in the business end of things rather than the technical side. Hmmmm....could she do a 6GHZ, terrestrial link budget if we gave her all the parameters?

    "No", she said. She replied that she was a real Engineer now, and left the financials to other people.

    "Thank you, ma'am. We'll let you know" was the official end of the interview.....

  3. SiGB,thanks for the review of some basic engineering. I have been doing management type work for the past 15 years as a systems engineer figuring out requirements, modeling the concepts of operation and similar stuff. There was no real "ciphering" (thanks Jethro). Drjim, I know of what you write.

    With my impending retirement, I will be getting back into some real "engineering" (Please don't tell the Texas Board of Professional Engineers, they will arrest me ;-) ) for my Amateur Radio avocation.

    73 de WD5HHH

    1. BillB, I have to say you have what may be an even worse call for CW than I had as a Novice back in '76. People would just send a string of dits and let me interpret it. That was in the days when we were transitioning to keyers from bugs and it wasn't that uncommon to get way too many dits anyway.

      On a more serious note, hope the transition to retirement works out well for you and the fun ramps up exponentially.

  4. The technologies used on Voyager have made their way into Amateur Radio. Joe Taylor K1JT has released several of the communications protocols into the public domain and people are making reliable contacts (including EME or moon-bounce) with five watts and under. - check out the Map tab in this link. Active display of all operating beacons.

  5. Thanks for the interesting in depth article. It is a great example of technology and is, quite literally, the most 'way out' thing man has yet done.

  6. "super-cooled" is often liquid nitrogen ... 77K (-321 F). Don't know if that's true for Voyager, but it is for other things.

    Since a "typical" ambient temperature is often between 315K - 335K and junction temperatures perhaps 25K higher, 77K represents a substantial lowering. If appropriate for Voyager.

    1977. How did that get to be so long ago?


    1. I've never been to Goldstone (the Deep Space Network) but I have been to Green Bank NRAO (National Radio Astronomy Observatory) and they used liquid Helium.

      I'm equally sure that they choose the coolant for the mission, and wouldn't use He if N2 would work.

      Voyager itself is heated by its power dissipation, otherwise it would be at the temperature of deep space.

  7. Great stuff from '70s tech.

    Now 'splain why, with Moore's Law and a few hundred other things, no one's working on sending out a 4K camera to see the same things Voyager did, at a wee few orders better resolution.

    We've proved it's doable, as Voyager flies out of the solar system.

    Or sending similar packages to each planet, the moons of Jupiter and Saturn, etc.

    Instead of, I dunno, not spending one second of NASA budget on asstardian pseudoscience things like anthropo-fraudulent globull warming, or outreach to sixth century goat-humping superstitions.

    Let alone abdicating completely more manned space travel.

    I can get over no jet packs and flying cars, but going to the moon a few times, and then just...quitting?

    When Matt friggin' Damon has a better grasp of what NASA's mission should be than NASA does, it's probably time to burn it down, and start over from scratch. (Or move the entire military side to Vandenburg, and lease Canaveral and Houston back to Space-X etc. The only thing NASA should be doing is running the museum and memorabilia concession sales.)

    I grew up a short bicycle ride from Rocketdyne, and on Saturdays listened to them testing engines in the hills outside LA. Which you could hear from 30 miles away. Now half their facility is a strip mall. Two generations have been gypped out of their heritage.

    Space is our wading pool. As Neil McDonough said in a Cadillac commercial "Were we nuts when we pointed to the moon? That's right, we went up there...and you know what we got? Bored. So we left. Got a car up there, left the keys in it. D'ya know why? 'Cause we're the only ones going back up there, that's why."

    Boom. Mic drop.

    Just saying.

    1. Fun fact: Mars is the only known planet inhabited entirely by robots. I have a fun story on that subject coming soon, too.

      At some point NASA transitioned from simply being an arthritic bureaucracy to something worse. James Hansen, the actual "man" in "man-made global warming" because he's the guy that fudged the data, was accusing management of trying to silence him while they were building him a platform to speak from.

      NASA now stands for No Americans in Space Anymore. It may be that with private space companies doing so well that the right place for NASA is hiring taxi rides to orbit to do whatever they do. More likely, what they should be doing is developing leading edge (that is, risky but big payoff) technologies with the likes of SpaceX, Blue Origin, ATK, etc., and let them go to Mars or wherever.

      If I were king of the forest, I'd be putting a Juno or Cassini orbiter around all four of the gas giants and more robots on the surface of everything else. Voyager was only possible because of the orbital lineup that gave them the "grand tour", slingshotting from one planet to the next, and completing the tour. OK, then commit to more powerful upper stages, ion engines, nuclear engines or some other way to get to the outer planets in much less time.

      Don't accelerate and coast, accelerate half the way there and decelerate the second half.

      My wife worked on the Cape for a decade, although that was years ago. Even then a lot of people thought the most incredible thing about NASA was they got things done around the bureaucracy.

    2. More Junos and Cassinis? From your lips to god's ear.

      I get the Grand Tour thing, but we should have progressed in launch vehicles to the point that we don't care about that lovely one-time window anymore. Send craft to all of them, regularly, instead of doing the Solar System In One Tour. For the time, it was genius economy, but now it's time to dig in for the long haul, not just hit-and-run tour bus tourism.

      It took one president about 5 minutes to give both the pointy heads and the ignoratii in government a vision that propelled them forward for a decade.

      All I'm asking for is that, from time to time, someone else come along and get them another push. Momentum and serendipity will take care of the rest. I'm sending this on a flatscreen bigger than my parents' color TV was in 1969, from a PC with more computing power than the sum total of the entire world's space programs in 1969. Because we went to the moon.

      We don't starve now in the first World because we have entire supermarkets full of packaged and canned goods, because back 200+ years ago, Napoleon needed a better way to feed his armies on the march.

      Discovery drives technology, and technology changes the world.

      It's long past time to give the fat kid on the swing another push.