The Physics Lesson I Keep Re-Learning

One of the most broadly applicable ideas I’ve ever encountered is the concept of impedance matching. If you’re into radio frequency electronics, you’re probably thinking that I mean getting all your circuit elements working to a common characteristic resistance for maximum power transfer. (If you’re not, you’re probably wondering what that jumble of words even means. Fear not!)

But I mean impedance matching in the larger sense. Think about driving a stick-shift automobile. In low gear, the engine has a lot of torque on the wheels, but it can’t spin them all that fast. In high, the wheels turn fastest, but there’s not enough torque to get you started from a standstill. Sometimes you need more force and less motion, other times more motion and less force. The gearbox lets you match the motor’s power to the resistance – the impedance – it’s trying to overcome.

Or think about a cello. The strings are tight, and vibrate with quite a bit of force, but they don’t move all that much. Air, which is destined to carry the sound to your ear, doesn’t take much force to move, and the cello would play louder if it moved more of it. So the bridge conveys the small, but strong, vibrations of the strings and pushes against the top of the resonant box that makes up the body of the instrument. This in turn pushes a lot of air, but not very hard. This is also why speakers have cones, and also why your ear has that crazy stirrup mechanism. Indeed, counting the number of impedance matches between Yo Yo Ma and your brain, I come up with four or five, including electrical matches in the pre-amp.

I mention this because I recently ran into a mismatch. Fans blow air either hard or in large volume. If you pick a fan that’s designed for volume, and put it in a pressure application, it’s like trying to start driving in fifth gear. It stalled, and almost no air got pushed up through the beans in my new “improved” coffee roaster, meaning I had to rebuild it with the old fan, and quick before the next cup was due.

I ran into this mismatch even though I knew there was a possible impedance issue there. I simply don’t have a good intuitive feel how much pressure I needed to push the beans around – the impedance in question – and I bought the wrong fan. But still, knowing that there is a trade-off is a good start. I hope this helps you avoid walking in my footsteps!

69 thoughts on “The Physics Lesson I Keep Re-Learning

      1. Air flow doesn’t have to make noise, it depends on the obstacles, the bearings, how well it is acoustically isolated etc.
        More optimized fans (radiators etc) can be quieter for the same cooling effect.

      2. Your comment literally misses the point of the article.
        Static pressure and volume are not the same requirement.

        It is possible to have a low noise fan optimized for static pressure.
        In fact, one of the most popular Noctua fans, the NF-F12, is optimized for pressure.

        Low noise usually comes down to finishing quality with PC fans.
        High quality injection molding and a process to remove all the mold artifacts keeps the air doing what it is expected to do.

  1. The example I always use is throwing a baseball vs a whiffle ball. The whiffle ball, being light, is hard to throw because it doesn’t provide enough resistance to fully utilize your muscles. Even though the baseball is heavier it matches the mechanics of your body better, but go too far and you have the reverse problem. It’s hard to throw something heavy like a bowling ball.

      1. no, you wouldn’t.

        you can input a lot more energy into a baseball than a wiffle ball via throwing. there are hard limits on how fast you can move your hand. right around 100mph for trained professionals. a 100mph baseball has a lot more energy than a 100mph wiffle ball.

        1. “…And the answer is…”— Momentum; p .
          p ≡ m*v (mass x velocity).
          One of the basic metrics of physics….and what’s behind one of Physics’ basic laws: The Conservation of Momentum.
          [‘The Conservation of Momentum’: not just a good idea; it’s the law]

  2. “If you pick a fan that’s designed for volume, and put it in a pressure application, it’s like trying to start driving in fifth gear. It stalled, and almost no air got pushed up through the beans in my new “improved” coffee roaster, meaning I had to rebuild it with the old fan, and quick before the next cup was due.”

    New sport, speed roasting.

    1. Endurance roasting, cost efficient roasting, sustainable roasting, augmented flavor roasting, caffeine concentrated roasting, retro roasting, Tour le Ros, 24 hueres de amaretto, Formula C roasting…

    1. You didn’t use the right air compressor. Try a 250CFM diesel unit. 1/2NPS pipe for the nozzle with a 3NPS collar around it for induction and entrainment. (used to work a job with a lot of awkward, high gutters and a steep steel roof. This setup worked from the ground)

      1. I could see that working nicely. My compressor was used primarily for blowing oil and debris off of metal parts, and to run a pneumatic nailer for installing interior trim. One of its requirements was that I be able to carry it up and down the basement stairs on my own.

        The setup I implemented involved some zip ties and eye screws to mount the air nozzle on the end of an eight foot long 1”x2”, and some string run through eye screws to actuate the lever on the nozzle.

        Luckily, my next-door neighbor saw me struggling and loaned his leaf blower and gutter cleaning attachments, which really worked well.

    2. Actually, air compressor blow nozzles do have one thing that helps match things up. The high pressure air spreads out and entrains ambient air as it gets further from the nozzle, so depending on the specific pressure versus flowrate you need, you can move the nozzle further or closer. It’s not necessarily efficient to compress air to high pressures and then throttle it thru a restriction, but still.

  3. Regarding the speakers mentioned, the interface between the amp and the driver isn’t the only place where impedance matching is a consideration. Most speakers have a pronounced mismatch at the interface between the radiating surface and the air. One reason horn-loaded drivers are more efficient is that they basically provide a better impedance match between the driver itself and the air it’s radiating into. Of course, horns also add delay and frequency filtering – they’re reactive elements analogous to RC networks.

    1. Horns are essentially acoustic transformers. Their reactive characteristics are due to the limits forced by physics, which are not well modeled by RLC circuits.

      Speaker math is messy.

    2. I _was_ actually thinking of the air/magnet interface, where the cone is the impedance transformer. Funny enough, I forgot about the amp which also does a small-current inside, large-current outside match, with beefy transistors or even transformers in the olden days.

      Impedance matching is everywhere!

  4. Basic physics never stops. I love it. It’s also right at the level I can comprehend, unless my programs are on.

    Nature bats last. <– Stolen from Paul Taney, Perl guru, sadly now deceased.

      1. You mean Paul Taney the architect? Paul Taney the surveryor? Paul Taney the bebop bassist? Paul Taney the GIS specialist?

        Your point is valid. I don’t know, I don’t care.

        If something isn’t stolen, just give it time, it will be. That is original with me. Or is it?

      1. FWIW Also type of fan effects ability to generate force (static pressure). Axial fans generally can produce less velocity at a given static and power than centrifugal or “squirrel cage” blowers. Few flat blades trying to push air faster thsn it can leak backwards vs many curved blades flinging air.

  5. I was selling a 12-speed bicycle to an electrical engineer a few years ago. She hadn’t ridden a bike since coaster-brake days, and asked “Why are there gears? What do they do?” Knowing she was not at all an ignorant person, I told her they were an impedance transformer, to match your leg impedance to the work load. The light went on. She instantly got it.

        1. Cool story bro.

          Bullshit, but still…

          Perhaps ‘engineer’ means something different in France. It is the most abused of the professional titles.

          In the civilized world all Engineers have to pass calc and classical physics before they even start their specialization. I do get that the Frogs are different. Maybe their EEs do music theory first.

          Every engineer I know, of any specialization, was a pre-teen bicycle mechanic first. Even the rich kids.
          I’d even call it predictive. If you didn’t make 1 bike out of 2 as a kid, you won’t like being an engineer.

  6. for my hydronic system, i had to pick a pump. i knew the length of pipe, number of elbows, and had datasheets for the radiators, and desired flow rate in gallons per minute (GPM). there’s some simple way to estimate the resistance (in PSI drop, i guess) of the whole network given all of that. and then the pump manufacturer has a graph of GPM vs PSI for each of their pumps. and their smallest pump satisfied my requirements, but following the graph, my PSI was too low for the graph (my house is small, so even the smallest pump was overkill). i was sure it would work out but i was upset at coming up with an estimate that the GPM would be “off-scale high”. you don’t want a too-high GPM, and anyways i was upset that the estimate clearly made no sense. i spent a while scratching my head wondering what the limiting factor would be that would present the water from racing through the pipes at a hundred miles an hour.

    but then i remembered GPM was an input into the original formula! as the GPM increases, the resistance through each of the fittings also increases — dramatically. so if i was to repeat the calculation with a higher assumed GPM, i’d get a higher resistance, and maybe i’d have to iterate for it to settle down but it’d wind up at a number that is well within the graph and i’d have an accurate figure. and that resulting GPM was well within my tolerable range so victory..

    anyways that’s just a story about why impedance games tend to wind up with differential equations

    1. There are diferential equations but you dont need them for residential hydronics. There is a process (with a lot of steps) one follows in the correct order to calculate the required data then using charts to select items within given limits then selecting a pump based on a manufacturers performance curves.

      Look online for articles or used books on basics from John Siegenthaler, PE ( not the journalist), or for first principles maybe the IBR installation guide (from mid 80’s is good- i have the no. 200 ver 1986).

      As in the article above, I agree the concept of impedance is nearly universal but the terms are specific to the application and you have to learn them to use the tools. In flow applications static pressure, head (in a closed system in hydronics) coefficient of friction, gpm, max/min velocity, and type/size of piping are the normal variables beside the heat calculations.

  7. “Why do I need to put termination at the end of a DMX512 (RS485) Data line?”

    The example I use to explain line termination for data lines is looking back at high school physics class where you ran a wave down a rope with a fixed end, all the energy reflect back out of phase, and when it has a free end it reflects in phase and somewhere in between fixed and free there is no reflection…and that is the characteristic impedance and that is the maximum energy transferred and no reflection is minimal signal distortion.

  8. Although completely off topic from impedance matching…
    “I had to rebuild it with the old fan, and quick before the next cup was due.”
    I’ve also been home roasting for a bunch of years. On a coretto, a stripped down old bread maker for agitation and bean containment, with a knob controlled heat gun from the top. Very hard to go back to store bought when travelling. Had a K thermocouple for a while, but I melted that. Power controlled by sound, color, smell as you say.
    IMHO, you also should wait a while, anything from 3 days to a week, after roasting, before grinding, for the coffee to taste best. This takes some planning – have to roast before empty. Then after 3 weeks the roast beans taste state, but they never last that long so thats just a theoretical issue.
    Of course, if you run out, grinding immediately after roast is better than no coffee. Just tastes a bit thin.

    1. Depends on how dark or light you’ve roasted. I played around at roasting with a frying pan and found that it’s possible to get quite a bit of CO2 if you go light enough, and it can take weeks to go away and taste better. And on the other hand, some darker stuff doesn’t really taste much different after a long period of storage even at room temp.

      1. sounds reasonable. I’m not into really light or dark, a few days or a week helps for the midrange roasts I’m interested in.

        And I’m pretty sure even waiting a _really_ long time wont improve burnt/extra dark roast coffee.

        I tried roasting in a frying pan once, but the coffee tasted of sausages. A clean billy worked better, but hot air through the beans worked better for my level of roasting skill.

  9. I do not get the cello story. There may be quite some tension in the string, but the lateral force when plucking a string is quite small, and so is the overall vibration. There is also very little energy in the vibration, the whole thing has to be extremely optimized to get any sound out of it at all.

    1. It’s a poor example. In string instruments, there’s a tradeoff between how long a tone lasts after it stops being driven by a bow or a pluck, and how loud a sound it makes. If the string is coupled strongly to the air, the sound is louder but dies more quickly.

      1. There’s also a constructive/destructive interference component due to the resonant chamber (eq. to LC tank circuit?). This moves the energy from some frequencies we don’t care about into the ones we do, making the former quieter and the latter louder.

  10. A lot of folks don’t seem to realize that when the source impedance equals the load impedance (the “maximum power transfer” criterion), half the total power gets delivered to the load and the entire other half gets dissipated in the source.

    1. That applies in very limited circumstances. For instance, it does not apply to a switching power supply for a computer, which might supply 12 volts at 50 Amps with an incremental output impedance of 2 milli-ohms, at an efficiency exceeding 90%.

      1. 12V / 50A = 240m Ohm load impedance (Or 238m Ohm for the load if you factor in the source impedance too), which surely does not match the 2m Ohm source impedance you suggest. Matched impedance would be 12 / (0.002 + 0.002) = 3000A and 90% would probably be dissipated in the cables which feel horribly neglected and may burst into flames out of sheer anger and protest.

        (And that is m from milli, not M from Mega for those who can’t keep their capitals apart from the suburbs).

    2. True for the special case of real-only transmission, but you’re ignoring the more general case of complex impedances: Crucial for understanding transmission lines, RF matching, etc. You can match impedances and get 100% power transfer and zero dissipated in the source or transmission line (assuming an ideal line).

  11. Or you could pair up fans in series (example: Dell 79WM9 from the Poweredge R430) but there are many others), one high volume followed by a ‘pressure’ one, tweaking the ‘cavity’ beween them then becomes an interesting tuning exercise.

  12. In the impedance matching article you took quite a few paragraphs to discuss your view of “impedance matching,” which is not the general acceptance of the term as in use. Oh well, each to their own world. However, it could have been improved if you really discussed the issue of matching the source to the supply, whatever medium.

  13. interesting framework for thinking about an ongoing design for an aircraft PSRU,(propeller speed reduction unit),where optimum engine speed for power/weight density is always higher than the needed subsonic propeller tip speed
    figuring out the gear ratios is trivial,other factors
    that effect how the sytem functions might be seen
    a bit better through the lens of impedence matching,where the real challenge is in designing a PSRU system that does not self destruct due too TV(torsional vibration)
    this is much more complex than most of the other examples,as engine power varies with altitude(air density),and propeller efficiency varies with air speed and propeller rpm and air density,which can be further complicated by a standard aviation impedence matching device called a “constant speed propellor”
    so dealing with average and instantanious power
    mechanicaly,in a 100%dutty cycle application

  14. As a long-time E&M worker-person, I have to put in my two cents for one of the most-neglected physical constants of all time: the characteristic impedance of free space–Z˳,–which is, approximately, 377Ω (≃ 120*pi) (no one needs to know the (exact) nine decimal places, except theoretical physicists).

    Z˳ is defined as √(μ˳/ε˳), where
    μ˳ is the magnetic constant, also known as the permeability of free space; and
    ε˳ is the electric constant, also known as the permittivity of free space.

    No; I don’t bring this up at parties.

Leave a Reply

Please be kind and respectful to help make the comments section excellent. (Comment Policy)

This site uses Akismet to reduce spam. Learn how your comment data is processed.