Impedance Mismatch

There are a few classic physics problems that it can really help to have a mental map of. One is, of course, wave propagation. From big-wave surfing, through loudspeaker positioning, to quantum mechanics, having an intuition for the basic dynamics of constructive and destructive interference is key. Total energy of a system, and how it splits and trades between kinetic and potential, is another.

We were talking about using a bike generator to recharge batteries on the Podcast last night, and we stumbled on a classic impedance mismatch situation. A pedaling person can put out 100 W, and a cell phone battery wants around 5 W to charge. You could pedal extremely lightly for nearly three hours, but I’d bet you’d rather hammer the bike for 10 minutes and get on with your life. The phone wants to be charged lightly — it’s high impedance — and you want to put out all your power at once — you’re a low impedance source.

The same phenomenon explains why you have to downshift your internal combustion automobile as you slow down. In high gear, it presents too high an impedance, and the motor can only turn so slowly before stalling. This is also why all vibrating string acoustic instruments have bridges that press down on big flat flexible surfaces, and why horns are horn shaped. Air is easy to vibrate, but to be audible you want to move a lot of it, so you spread out the power. Lifting a heavy rock with human muscle power is another classic impedance mismatch.

If these are fundamentally all the same problem, then they should all have similar solutions. The gear on the bike or the car, the bridge on a cello, the flared horn on the trumpet, and the lever under the boulder all serve to convert a large force over a short distance or time or area into a lower force over more distance, time, or area.

Pop quiz! What are the common impedance converters in the world of volts and amps? The two that come to my mind are the genafsbezre and the obbfg/ohpx pbairegre (rot13!). What am I missing?

66 thoughts on “Impedance Mismatch

  1. I figured the last two references were entertainment BS, but I googled “genafsbezre” anyway and it triggered Chrome’s protective “don’t go there” warning! What?

      1. Here are some English ones I found after iterating through the wordlist on my computer:
        abe nor
        ares nerf
        cheryl purely
        ebola robyn
        green terra
        irk vex
        nag ant
        nun aha
        one bar
        ones barf
        onyx balk
        or be
        ova bin
        pent crag
        rail envy
        reef errs
        roof ebbs
        she fur
        sync flap
        tang gnat
        try gel
        vend iraq

  2. A coworker’s spouse was buying a used road bicycle from us. She had not ridden a bike since coaster-brake days and while checking the bike over, asked “So what are gears on a bicycle *for*, anyway?”

    A naive, but really not dumb question, actually. How would you answer a question like that out of the blue?

    She’s an electrical engineer. I told her the gears were an impedance transformer, adjustable for different load impedances. I could see the light go on. She got it right away.

    1. Trying to explain bicycle gearing using impedance is not likely to be helpful when talking to non-engineers. But most people can relate to levers, so showing how different sizes of sprockets (or gears) fundamentally relate to different lengths of levers is more likely to be productive. Impedance is all about the ratio between force-like parameters and motion-like parameters in a system; the greater the ratio, the greater the impedance. But just for examples, in electronics, voltage is the force-like parameter, while current is the motion-like parameter, so a high-impedance circuit is one where there is more voltage than current, while in mechanical systems, the force-like parameter is, well, force or torque, while the motion like parameter is linear or rotary motion, so a high-impedance configuration for a bicycle is a “higher” gear, where you have to apply more force to the pedals, but don’t have to pedal as fast.

    2. I have to say, I’m astonished that an electrical engineer needed to ask the question. I understand that mechanical engineering is not her specialty; still, the lack of mental dexterity there is surprising. I blame it on educational practices that over-emphasize specialization, discourage generalization, and result in “siloization” of knowledge and thinking.

      1. This seems a bit odd to me as well, as an EE I was required to take statics and dynamics courses in my first year and the stuff about gear ratios was covered back in high school physics.

  3. Common impedance converters: antennas

    Not so commonly known yet widespread: gyrator. Real world implementations of gyrators are used in filters, mainly to create large virtual inductors out of other basic components.

    1. Gyrators are active components. They *simulate* the desired response, but actively use power to do so, so are not a true impedance transformation.

      I would even disqualify antennas: They couple power in the form of electrical voltage&current into a electromagnetic field, analogous to a loudspeaker coupling voltage & current to an acoustic field. Antennas are more like transducers than transformers.

      1. On what basis are you disqualifying active devices? In electronics, MOST impedance transformation is done with active components, mainly because they are usually a smaller, lighter, and cheaper solution than transformers.

        1. An impedance transformation is intended to match a source power input to a load, whether it’s a transformer or a lever. The purpose is to transfer power more efficiently, NOT simply to direct power from a different source, like an amplifier. It’s an important distinction.

          Note I’m not disqualifying active components as a class. A buck converter qualifies, for example: it has an input impedance and an output impedance, but does not *simulate* that output impedance by drawing power from another source.

          A gyrator, opamp, transistor, any amplifier, etc., can present a different impedance to its input and output, but requires external power to do so.

          1. But wait, and first I want to say I get where you are coming from i think, drawing a distinction between the active components that can present the impedance difference but that maybe is not the purpose of them in all situations. But the distinction being drawn at requiring a separate power source kinda fails when looking at a smps, as it relies on those active components to draw that extra power, not to mention any conversion not being 100 percent efficient and therefore requiring additional power to make this transformation in the name of efficiency

          2. But that’s exactly what some transistor circuits DO, and this is their only purpose. In fiberoptic communications, transimpedance amplifiers are used specifically to match the impedance of a photodiode to the 100Ω balanced circuits that follow. Common-collector “emitter followers”, just like their vacuum tube “cathode follower” forefathers, are specifically used not for gain, but to drive lower-impedance loads than gain stages are able to drive.

      2. Antennas are absolutely impedance transformers. You just don’t normally think of the EM environment surrounding a circuit as part of the circuit. But of course, it is.

        Transducers couple different forms of energy. With antennas it’s electromagnetic fields on both sides.

          1. No, specifically the Veritasium interpretation. No RF engineer would ever ignore the steady-state portion of the solution and claim that only the transient carries any power. Veritasium is a physics teacher, and it is quite common for physicists to naively ignore half of the universe in their smug superiority over mere engineers.

        1. “No RF engineer would ever ignore the steady-state portion of the solution and claim that only the transient carries any power.”

          Pretty sure if I’m making a filter/splitter/coupler/etc. that doesn’t go down to DC, it’s okay to ignore the steady state solution… because it doesn’t exist.

          PCB antennas and PCB impedance transformers can look *exactly* the same, with the only difference being that the antenna ends in an open.

      3. “Antennas are more like transducers than transformers” – except for tuned ferrite antennas working in the near field. These are actually transformers, although not in a way that most people would immediately recognize.

        1. That would be a *pair* of “tuned ferrite antennas”: One to convert time-varying electric current (and associated back-emf) to time-varying magnetic field, and a second nearby one to intercept some of that magnetic field and convert it into electrical power.

          It’s two coupled transducers, really.

          And you don’t even need the ferrites. A pair of air-cored coupled loops can be separated by a diameter or more and still achieve more than 50% coupling efficiency. You do need to make fairly high Q resonant coils, match them very well, and pay attention to capacitive coupling & detuning due to nearby meat, but it does work.

      4. Not in theory. Just the implementations are. Some particular cases can be realized with passive components though. There are also electro-mechanical implementations that are passive.

        1. Better said that “power from voltage and current” and “power from electromagnetic field” are the same thing. Obviously current and field aren’t the same thing – you can’t have a current without a field, but you can have a field without a current.

          The energy’s always stored in the field. I don’t understand the weird distinction he’s trying to make regarding a “steady state.” If I have a DC current flowing down a coax wire, I can calculate power via current times voltage…. *or* I can calculate the power via the Poynting vector from the electric field (which is radially outward) and the magnetic field (which is curling around the wire). And I’ll get the exact same result.

          Claiming an antenna is a transducer which transfers energy from current to field makes no sense, because the current’s energy is *already* in the field. Hence the reason I can screw up the gain of an amp with a signal on microstrip easily by bringing metal close to it – because the field isn’t confined to where the current is.

  4. I fried my favorite amp,a Klempt,is has/had the ability to run on
    any mains power in the world and there is a selector switch for
    speakers 5ohms or 20, anyhow it would run no mater what settings were chosen,90 v mains and 20 ohm output,all dimed
    into random speaker cab,did that for.years, then it smoked the
    transformer,not sure if it was impedence missmatch or refreshing beverage spillage.

  5. How about transistors? Bipolar transistors in common-collector configuration couple a high-impedance source to a lower-impedance load, and in common-base configuration couple low-impedance sources to higher-impedance loads. JFETs and MOSFETs are especially good for transforming from high to low impedance.

    1. Along the same “lines”, you can get impedance transformation on a twin conductor balanced transmission line, just by changing spacing along the length. This is also technically a transformer, but less obviously so. You see this in antenna designs that match the antenna to the transmission line by way of a Y-shaped feed.

  6. I was a physics major in college (class of ‘93) and did only a bit of circuits. Obviously had heard of impedance and that a mismatch is bad because power gets reflected. But now I actually understand impedance fifty times better. Must have had a mismatch in my ears because this concept was obviously reflected. Actually I think I just never pursued an adequate explanation. Thanks hackaday.

    1. Actually there is an impedance mismatch in your ears. We’ve got three tiny bones in each ear that act as levers to match impedance between air and the fluid in the cochlea.

  7. Sometimes I have to distinguish for someone the difference between a transformer and an amplifier. I cup my hands to my mouth and say “this is not an amplifier” because it has no power source it’s just an impedance converter.

    The whole of the beginning of sound production and reproduction was wrapped up in such impedance converting as in horns and in pre-electric days an amplifier with an air source for power loud enough to play from the top of the brand new Eiffel tower to all of Paris.

    The earliest Voice of the Theater speakers were enormous horns with 25% efficiency to get something from a single tube stage output.

  8. The bike-to-phone mismatch isn’t the best example – in everything else the power is the same and something else needs matching to maximise power flow, but wanting a short pedal to lead to a long trickle charge is a very different problem

    The solutions to the rest of the examples (engine speed matching to wheels, string motion to air motion, different voltage to current ratios) all have quite small, simple solutions because they’re effectively converting between two types of work instantaneously; slow-charging a phone from a pulse of pedal power would need energy to be stored, storing work is hard, and converting work to something else (like chemistry) is nearly always harder and slower, hence why batteries and engines are heavier than motors and gearboxes

  9. When trying to explain the purpose of end of line termination to customers (in particular DMX512 which is RS485), the example that seems to be understandable to many is the “remember your high school physics class – make a wave on a fixed end rope, get an out of phase reflection, make a wave on a free end rope, get an in phase reflection, so somewhere fixed and free is no reflection, and that’s the characteristic impedance of the line”

    1. There is no way for the circuit to know what voltages it should be without knowing what the load is on a far end of a relatively long transmission line. I see reflection as nature’s way of sending information about the far end back to the transmitter and readjusting its voltage accordingly.

      Initially, it can only see the short section of the transmission line, so its impedance shows up as the load for voltage divider.

      If the far end has a lower impedance, then it send back a -ve pulse to drop the voltage.
      If the far end is exactly the same, then there is no adjustments needed. i.e. no reflection
      If the far end has a higher impedance, then it sends back a +ve pulse to raise the voltage.

      If the pulses are large enough, they might interfere with your circuits.

    1. Not exactly. Impedance is voltage/current, while power is voltage x current. Kind of a big difference. In Elliot’s examples, he is keeping power constant while changing impedance.

  10. My take on this would be a capacitor/supercapacitor bank, which would store the energy from the 100 W over the 10 min of pedaling, and then slowly deliver 5 W to the phone over an hour or two. Not exactly an impedance mismatch solution, but a solution nonetheless.
    A flywheel could work, too, but you’d probably need a fairly big one as well as a clutch to not waste power and achieve maximum velocity.

  11. Sorry, just bc the phone only wants 5W does not make it high impedance, or low impedance, or any particular impedance. Impedance is the ratio of a static quantity and a dynamic quantity, where the product of same yields power. Static quantities have units without time in them: force, torque, voltage. Dynamic ones include time: meters/sec, radians/sec, coulombs/sec.

    A 5W load can be low impedance – imagine it pulls 5A at 1V, that’s 5W at 0.2 ohms. Or it can be high impedance – suppose with 5kV on it, it draws 1mA, again 5W but 5 _million_ ohms.

    Having gobs more power than your load can absorb is not inherently an impedance mismatch. Suppose you have 100W source that can provide 1A at 100V, that’s a 100 ohm ratio. Can a 5W load be 100 ohms? Sure: sqrt(5W ” 100ohm) = 22.36V, sqrt(5W/100ohm) = 0.2236A.

    Not sure why the article makes such bones about impedance, when the problem description is more along the lines of the difference between power and energy. What you’re really getting at here is “my phone wants X amount of energy” vs “I have X amount of energy”, and how to transfer that energy when the phone can only assimilate that energy at a rather slower rate than is desirable. You can have *that* problem at any impedance you like.

    1. You’re getting lost in the details.

      It’s about the general meaning of the word “impede” : to interfere with or slow the progress of. Two mutually commutable things that would naturally occur at different rates or progressions is an impedance mismatch. The particular case is just confusing because the parts also have electrical impedance.

      A phone battery is actually somewhat low in electrical impedance as well and can be charged over some minutes. Some phones have 15 minute rapid charging capabilities. It’s just not very healthy for it.

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