More mud

October 6, 2021
 by Paul McGowan

A few days ago I wrote a blog post about impedance. It seems to have stirred more mud than cleared the waters.

Might as well go for broke.

This post will focus on 4Ω vs. 8Ω speakers and varying impedances with frequency of those speakers.

First a bit of a refresher. It is a misnomer to think that 4Ω speakers take more power than 8Ω speakers. They do not.

Loudspeakers are rated according to their sensitivity: how loudly they play with a 1-watt input. A 4Ω speaker with a sensitivity rating of 90dB takes the exact same amount of power as an 8Ω speaker rated at 90dB/watt/meter to generate 90dB of sound in a room.

Second bit of refresher. Most loudspeaker impedance ratings are nominal (existing in name only). This means that your typical 8Ω speaker is mostly 8Ω but not always.

Scrounging around the internet I found the following graph from Stereophile.

 

Take a look at the solid line and ignore the dotted line. The vertical row of numbers is the impedance. The horizontal row of numbers is the frequency. Though the graph shows the speaker’s impedance varying between 12Ω and 4Ω, we would say the nominal (average) impedance is 6Ω.

Now. let’s imagine we have a power amplifier that is capable of producing its rated wattage at 6Ω and above. That would mean that from 6Ω up to anything higher (to the limits of its output voltage), the amplifier could output its full rated power. Call it 10 watts maximum.

Third bit of refresher: amps x volts=watts. This means the wattage is a combination of voltage and amperage. The less current (amps) needed (by a rising impedance) the more voltage is required to keep the watts the same and vice versa (just look at the formula to see that).

Upon close examination of the amp’s spec sheet, we see that at 3Ω our amp still only outputs 10 watts. It doesn’t double in power as we would hope. This means the amp is running out of current (amps) and its output voltage is dropping with lowered impedance of the speaker.

So what?

Here’s what. In order to maintain a constant loudness, we must maintain the amplifier’s output voltage into the speaker. Since amps x volts = watts, then we have to conclude that as the impedance of the speaker decreases beyond the amplifier’s ability to produce more watts, the voltage must be going down and hence the loudness at the output of the speaker.

See? More mud.

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29 comments on “More mud”

  1. The two main properties of an a/c signal are voltage and current. Power factor is the ratio between useful true power to the total apparent power consumed by an electrical component or a complete electrical system installation.

    Power factor is also the measure of cosine of angle between voltage supplied and the current delivered. Depending on the load connected (inductive, capacitive or resistive) the current drawn can change its angle.

    A poor power factor is usually the result of a significant phase or time difference between the voltage and current. The ideal power factor is unity or one. The goal here is to deliver efficient in-phase power. Consequently, in this application, ideal low impedance is the result of proper time relationship between voltage and current.

    Further, if you place an amplifier and loudspeaker together they do not play music. Therefore, you have to view the speaker cable as a fundamental system component. Once you connect the amp to the speaker via a cable you’ve constructed an active circuit.

    Speakers can be rated with a nominal impedance and amplifiers have rated power into various loads, 8, 4, or 2 ohms. For the sake of this writing we’ll consider the application a solid state amplifier.

    Now, as previously discussed impedance in this application between amplifier, cable and speaker is a dynamic state that includes voltage, current, resistance and reactance. How do you measure these individual properties within the circuit? It’s an active dynamic state, though you can engineer these components individually to be as linear as possible.

    As most are aware speaker cables possess the following measurable properties; resistance, inductance and capacitance. But what about impedance and how do you measure that? Well one would have to go out to the megahertz region and look at impedance phase angles. The impedance phase angle for any component is the phase shift between the voltage across that component and current through that component.

    An ideal cable has a proper balance of these electrical properties and is engineered to deliver in-phase power verifiable through measurement and listening.

    What i find fascinating is how few high-end manufacturers engineer and design home music system solutions that incorporate a complete amplifier -> speaker cable -> speaker system design other than active loudspeakers. It’s usually a consortium of various manufacturers amplifier A, cable B and speaker C.

    In closing, i have never claimed to be an engineer though my father graduated from Harvard with a degree in engineering and i certainly didn’t invest 40 years of my life in the high-end audio industry (1/3 rd of those years working for manufacturers) with an end goal of ignorance. These are just over simplified concepts you pick up along the path in an attempt to understand the designers and engineers intent you had the privilege of standing shoulder to shoulder with.

    1. dr g,
      The problem with audio manufacturers (high-end or otherwise) designing a complete amplifier -> loudspeaker cable -> loudspeaker chain is that the purchasing customer more than likely would prefer to chose their own loudspeaker cable, depending on their subjective listening preference.

      “An ideal cable has a proper balance of these electrical properties & is engineered to deliver in-phase power, verifiable through measurement & listening”

      Ultimately it is the “listening” by the end consumer that will determine how “ideal” said cable is, within said customer’s chosen home audio system.

      I don’t see any ‘PS Audio’ interconnects, loudspeaker wires or power cables for sale here anymore; only ‘AudioQuest’ brand ones now.

  2. Paul’s been scrounging again.

    “…as the impedance of the (loud)speaker decreases
    beyond the amplifier’s ability to produce more watts,..”
    I’d start worrying about clipping.

  3. Indeed. The mud thickens.

    Last week I learned that those coloured lines on resistors weren’t just decoration, so that can be considered progress.

  4. So your 10 watt amp is power supply limited? Not surprising since power supply can get very expensive and doesn’t show up on standard advertising specs. I look for doubling power into 4 ohms and love if it doubles into 2 ohms which is super rare. But of course besides adding to power supply cost it adds to output cost since now the output has to be robust enough to handle all that potential current.

    1. hahax, Be careful with this doubling business if you are looking at high power amps ( 500 W RMS per channel and above ). Amps that are Class A and Class AB ( still the most common amps ) are not 100% efficient ( no amp is ). Typically the range from 50% to 70% efficient. So now at 500W per channel into 8 Ohms we have 1000 W total at 70% efficiency the amp is going to draw about 1500 W from the wall socket. If you are running only the amp on a 15 A house circuit ( 1800 W in the US ) you will find the amp is tripping the circuit breaker for the house circuit. A good manufacture will tell you in advance that the amp must have a dedicated 20 A house circuit. Now you go and get 4 Ohm speakers. You expect your well made amp to deliver 1000W RMS per channel. That’s a total of 2000 W and a 70% efficiency it need 2900 W. That is more than a 20 A house circuit can supply ( 2400 W in the US ). Thus you cannot expect these kinds of amps to double the power they deliver as the load impedance drops. Also for those who want KW power the only choice is mono block amps with a dedicated 20 A line for each amp!

      1. The maximum power is drawn for instants only. It is not easy to trip the house set up. With Class D amps, in particular, you can get these huge watts at low impedances with no tripping. It still makes sense to have a 20 Amp circuit anyway.

    1. Jb4….I think it’s time to start listening to your music more and digesting whatever you can by trying to understand Pau’s explanations and not reading too deeply in the technical comments. Many of them and making my head spin and I have a decent amount of engineering knowledge. I just don’t have time to get involved so deeply any more. I think that Paul’s initial post several days ago should have satisfied most of us but now it seems to have stirred up a Hornet’s nest which is synonymous with confusion. It’s really not your lack of understanding in question. An electronics engineer or an ardent student of electronics and audio eats this kind of information for breakfast. Some of these community comments posts are getting more intense and that may make them frightening for some of us especially with so many posts coming from different perspectives. Perhaps that’s why you feel the way you do. The bottom line is it’s all about enjoying the music.

      1. stimpy2,
        Thanks for the advice and I like your humor…or are you serious and do you really think that what I wrote today was ment seriously ?.
        Fortunately PaulMcGowan knows better so I don’t have to take the first flight to Boulder for my job interview.
        Or maybe you think that I feel/felt miserable for 1 second (“Perhaps that’s why you feel the way you do”) ?
        Don’t worry, I feel fine, have never been depressed in my entire life and don’t plan to start now.
        I like reading all these posts and comments, even if some of them are “a bit” beyond my pay grade.
        And I agree, the bottom line is it’s all about enjoying the music.

        1. I’m a serious guy even with my storage sense of humor so I did take your comment seriously. I even have difficulty seeing the sarcasm in so many of the other posts. I take too much to heart. If you get a job with PSA, I’m going to send in my application because I want to get the hell out of Florida and I’ve been in Boulder before, definitely a place I would love because of the nature of the area of and it’s a lot closer to both my sons who live in San Diego.

  5. The varying impedance of a speaker shows how important amplifier damping factor is. With a high damping factor (low amplifier output impedance) the power an amp delivers across the frequency range is effectively constant. With a low damping factor the speakers impedance variation with frequency affects the sound level generated, and hence the tonal balance.

  6. Interesting thread. For those of us just dipping not immersing in theoretical analysis of impedance try https://geoffthegreygeek.com
    Same theory but maybe easier to digest?
    Eventually mud settles leaving clear water on top so we can all see what’s going on.
    Great post and great comments!

  7. I may be (likely, in fact) wrong, but I don’t notice tube amps claiming output doubling when driving lower (8 ohm to 4 ohm) speakers. What gives?

    1. Good morning Secretguy!
      I will put it to you, this way.
      I have a very excellent understanding about how tube amps work.
      Letts start with the power supply all the way to the outputs of the amp.
      For starters, a typical tube amp, has 450 or more volts hitting the plates of the tubes.
      And that voltage, is then transfered to the output transformers that are driving the speakers.
      Just as it was when the stereo boom took place in the early to mid 1950’s, most of them are still designed and built this way today.
      A tube amp, will have moldable impedance taps on the secondary wounding’s of the output transformer.
      It doesn’t matter which speaker you use, rather it’s an 8ohm, or 4ohm speaker.
      If you have an amp that’s rated at 75 watts, rather it’s 4ohms or 8ohms, the amp will still deliver 75 watts to the speaker.
      Where this principle brakes the rules, is with OTL tube amps.
      They pretty much operate on the same principle, as transistor amps do.

  8. Paul, If I have two sets of speakers, one a 4 ohm and one an 8 ohm. Both speakers have 90 db efficiency. Both speakers capable of 120 db of maximum sound pressure. The 8 ohm speakers are driven by an amplifier rated 100 wpc into 8 ohms, the 4 ohm speakers are driven by the same amplifier rated at 200 wpc into 4 ohms. Will the 4 ohm speaker play louder since there are 200 watts available from the amplifier before it starts to clip and only 100 watts available for the 8 ohm speakers before clipping begins?

    1. Good morning Joe!
      Perhaps I’m a day late, but cense Paul didn’t answer this question for you, then I will.
      The 4ohm and 8ohm speakers, are gonna put a 6ohm load on the amp.
      That is, providing that you hooked the speakers up to the amp in parallel.
      At best, the amp won’t deliver anymore power then 150 watts to the speakers.
      The loads that both speakers may be presenting to the amp are different, each speaker will be receiving 75 watts each.
      But it all depends on how high you have the volume turned up.
      If you have it just about maxed out, it’s then, and only then, you’ll have to start worrying about your amp clipping.

    2. I don’t think so. I think the same output voltage from the amplifier will then cause each of the two speakers to play at the same level of that same signal. It takes twice as much current to maintain the same output voltage into 4Ω as it does 8Ω but it’s the output voltage that makes for how loud something plays.

      One thing I screwed up in the post and had forgotten (and was thankfully corrected by good friend Keith Howard) is that when speakers are rated for efficiency it isn’t using 1 watt it is using the voltage equivalent of 1 watt into 8Ω, or 2.83V. That output amplifier voltage applied to your 8Ω speaker will produce 90dB of sound. That same output voltage of 2.83V applied to your 4Ω speaker will also produce 90dB. Now, from the amplifier’s viewpoint, it required 1 watt to produce that output voltage into the 8Ω speaker and it required 2 watts to produce that same output voltage into the 4Ω speaker.

      But, given the same input voltage both will play at the same loudness.

  9. Oh crap…since I’ve been drinking I don’t remember what we’ve been talking about…but,Great Britain Paul,the ceo of Pearl Acoustics(?). Did a video on what one watt will do…and apparently a couple watts can play plenty loud. I know head room etc..

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