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Electrical Output Impedance (damping factor)... again!

Discussion in 'audio' started by ToTo Man, Jan 9, 2020.

  1. ToTo Man

    ToTo Man the band not the dog

    @Paul Burke's recent posting of this article by Scott Hinson on effects of an amplifier's output impedance on the frequency and time response of a loudspeaker has raised a few questions that I’m interested in discussing:

    1a) In reality, how common is it to find amplifiers whose Zout varies significantly with frequency?

    1b) What is typically the extent of the variation?

    1c) Is it possible to generalise and say at which frequencies an amplifier’s Zout is likely to be higher than its published Zout and at which frequencies it’s likely to be lower?

    1d) Does the amplifier's Zout curve depend on general circuit topology or can it vary between amplifiers that ostensibly share a largely similar design?

    1e) Is there a feasible way for the home listener to measure the Zout curve of their amplifier?


    Next, in this article by Jan Meier and Tyll Hertsens, Meier suggests that too low a Zout can result in overdamping and that a higher Zout may be required to achieve 'critical damping', i.e. optimal impulse response from a given headphone. The article focuses on headphones and headphone amplifiers, which usually have higher load and output impedances than loudspeakers and loudspeaker amplifiers, so I'm not sure how much of this is transferrable, but I'll ask anyway:

    2a) At which frequencies is Zout most significant when it comes to affecting the optimal impulse response from a loudspeaker or headphone?

    2b) Is there a feasible way for the home listener to determine what Zout yields the optimal impulse response from their particular loudspeaker or headphone?


    An exclusively solid-state amplifier user for the last 20 years with damping factors ranging from 30 to 300, I'm unlikely to have experienced the effects of a high Zout on the performance of my loudspeakers, and I’ve never been intrigued enough to experiment by inserting resistors between my amp and speakers to simulate its effect.

    I have however had ample opportunity to experiment with different Zouts on various headphones. This was made especially convenient by auditioning a headphone amp with four Zout taps (0.1Ω, 33Ω, 82Ω and 120Ω). I'll therefore share my subjective experiences of this, for what they're worth (I suspect @Julf and Co. will be “tuning out” at this point :rolleyes:).

    My experience is that Zout can have a significant effect on the tuning and/or dynamics of a headphone, especially if the headphone has a low nominal impedance and an impedance curve that varies with frequency.

    The most common effect is perhaps heard with open-backed headphones that have an impedance peak in the bass. A higher Zout not only causes an elevated frequency response around the impedance peak, but also makes the bass sound undesirably sluggish / slow to respond, especially if Zout equals or exceeds the nominal impedance of the headphone.

    I remember trying the 80Ω Focal Utopia from the amp's 82Ω and 120Ω taps, yielding damping factors of 1 and 0.67 respectively, and it was so slow, boomy and uncontrolled it was unlistenable. The 300Ω Sennheiser HD600 on the other hand sounded fine from all of the Zout taps, even the 120Ω tap (damping factor of 2.5), gaining just a gentle frequency response lift at its Fs without much loss of perceived speed/control. The 600Ω Beyerdynamic DT880 was the least responsive to Zout of all the headphones I tried, its presentation remained very similar whether driven from the 0.1Ω tap (damping factor of 6000) or the 120Ω tap (damping factor of 5).

    I noticed that with several headphones, including the HD600 and Utopia, driving them with a higher Zout resulted in a less dry and sweeter treble response, with high frequencies appearing to shimmer/linger for longer giving the illusion of a wider/larger soundstage. As both of these headphones have virtually flat impedance curves through the midrange and treble frequencies, a higher Zout should have no effect on their amplitude response at these frequencies. Switching to the lowest Zout and applying a bass boost with EQ to mimic the effect of the higher Zout did not affect the treble presentation, so I don’t think the increased distortion (IMD or THD?) from boosted bass is the cause of the change in treble presentation. This surely leaves only the increased time response from the higher Zout as the reason for the "wetter" sounding treble, unless it is purely placebo?!

    Driving a low impedance (32Ω) closed-back headphone with a ruler-flat impedance curve, there was, as expected, no change whatsoever in the headphone's tonal balance regardless of what Zout tap I used. I did however notice that as I increased Zout, the performance of this headphone steadily worsened and became increasingly "lifeless". At the 120Ω setting (damping factor of 0.27), all of the dynamics from this headphone were effectively crushed so the headphone was clearly being starved of power even at modest SPLs, 0.1Ω was clearly the preferred choice here.
    Last edited: Jan 10, 2020
  2. Arkless Electronics

    Arkless Electronics Trade: Amp design and repairs.

    Christ on a bike! Sorry, I ain't writing a book to answer your questions...

    A few of them... briefly, though. And simplified rather (remember how I keep going on about the importance of negative feedback?)

    It is normal for there to be large variation's in Zout for a feedback amplifier. ie the vast majority of amplifiers.
    The negative feedback (NFB) is largely responsible for getting very low Zout. NFB must be gradually rolled back as frequency increases otherwise the amp will become unstable, hence Zout increases (as does THD) with increasing frequency. The point above which things start to get worse can be as low as 1Hz (not a misprint. In some op-amps it can be 0.1Hz!). The greater the amount of NFB, and therefore generally the lower the Zout, the lower will be the frequency above which things start to get worse. Note though that huge amounts of NFB at 1Hz type frequencies can still allow for a useful amount at 20KHz... we're talking of gains of say 1 million without feedback even though with NFB a typical power amp will have a gain of about 30.
    Happily the greatest need for low Zout is at bass frequencies (to control woofers), where Zout will be at its lowest anyway due to plenty of NFB.
    An amp with a DF of say 200 @ 20Hz may well have a DF of only 4 @ 20KHz...

    Topology can make big differences but at the end of the day it's pretty much down to how much NFB is used or can be used... There is a fascinating paper by Prof E Cherry on this where he shows that by and large the "native" Zout of the output stage is so dominated by the NFB as to not really matter.... (topologies with high Zout tend to have higher gain which results in potentially greater feedback being used hence negating the higher Zout).

    Zero feedback amps can have constant Zout right across the audio spectrum but it will be MUCH higher than an amp with NFB. DF's in the range 3 to 20 would be typical here.

    The biggest misunderstanding with DF is that due to the speaker voice coil having typically 8R Z very high DF's are utterly pointless anyway! There's sweet FA difference between a DF of 50 and 500!
    All the real action is between say 1 (or less...) and around 16 ish and by around 30-40 ish there's nothing more to be had. Of course for a 4R speaker you need half the Zout for the same DF.

    It's not really possible for DF (Zout) to be measured at home unless you have a fair bit of test gear... at minimum an oscilloscope, signal generator, AC millivolt meter, a selection of accurate non-inductive high power resistors and, if using the TdP "reverse amplifier" method, a robust power amp to stick current up the arse end of the amp being tested....
    Not knowing precisely what you are doing is likely to release copious amounts of the magic smoke!
  3. Julf

    Julf Facts are our friends

    I definitely agree with the latter part. The first part depends on your definition of "critical damping".

    Why would we?

    Of course. Why wouldn't it?

    That is one of the explanations for "tube sound" - the high output impedance caused by the output transformer.
  4. Shadders

    Shadders pfm Member

    All amplifiers Zout changes with frequency - Hifi News has reports on amplifiers with the output impedance given for 20Hz and 20kHz.

    In general, the lower the frequency, the lower the output impedance -although not always true.

    You can have the same circuit topology, but a reasonable difference in Zout, as it can depend on parameters of the circuit (values of components, number of components such as parallel output transistors)

    ToTo Man likes this.
  5. Julf

    Julf Facts are our friends

    Output impedance curve of Hypex nc400:

  6. Arkless Electronics

    Arkless Electronics Trade: Amp design and repairs.

    Ah.. no... only indirectly. It's caused by the lack of NFB, which is in turn due to the phase shift of the output transformer preventing you from using much NFB due to instability. There are techniques though which allow infinite or even negative Zout with a valve amp, as shown by RCA back in 1959.
  7. Shadders

    Shadders pfm Member

    Arkless Electronics likes this.
  8. Arkless Electronics

    Arkless Electronics Trade: Amp design and repairs.

    Shadders likes this.
  9. ToTo Man

    ToTo Man the band not the dog

    As per the graph in the Meier article, my interpretation of 'critical damping' is where the impulse response neither overshoots or undershoots and returns to equilibrium in the quickest time possible. Does this correspond with your interpretation?

    Because I haven't presented measurements to substantiate my subjective listening impressions, particularly my controversial comments about hearing differences in treble decay times with different Zouts (I was previously shot down by an objectivist over on Head-Fi for suggesting such). :)
  10. Julf

    Julf Facts are our friends

    Sure. Note that they talk about total resistance (amp output + load), not amp output impedance.

    Indeed, I would not necessarily agree with that part. It is more likely that what you hear is frequency response variations.
  11. davidsrsb

    davidsrsb pfm Member

    When you are discussing headphones, remember that amplifiers that attenuate the speaker output with a resistor divider are likely to be about 100 Ohm Zout, actually the spec for driving headphones. This will have large effects on a typical 32 Ohm moving coil driver with a high treble impedance peak compared with a dedicated headphone amplifier
  12. ToTo Man

    ToTo Man the band not the dog

    Good point. Having gone through a random selection of headphone impedance measurements there are quite a few that have a rising impedance over 10kHz, the AKGs seem particularly guilty of this. Perhaps this is responsible for the added 'sweetness' I hear from high Zout. On the other hand, with open-back designs, the extent of the treble impedance rise is typically dwarfed by the size of the bass impedance peak so I'd expect the bass boost at Fs to be by far the dominant measurable and audible tonal colouration when driving the headphone from high Zout. I am ignoring phase angle here, AIUI a load with a varying phase angle is more challenging for the amplifier but I'm not sure how this affects the frequency and/or time response.
  13. ToTo Man

    ToTo Man the band not the dog

    If output impedance really does have such a negligible effect on impulse response and decay times as the Hinson article suggests, then why do so many listeners cite it as the main reason that lightweight, stiff-suspension speakers designed during the era of high output impedance amplification perform most optimally when driven by an amplifier with high output impedance? If it were purely an amplitude frequency response issue then this could surely be compensated for fairly easily with EQ?
  14. davidsrsb

    davidsrsb pfm Member

    It depends what you mean by high output impedance. With speakers 0.3 Ohms is on the edge of obvious audibility. Some valve amplifiers have much higher impedance at the deep bass and high treble thanks to the output transformer and restricted negative feedback. Some SETs can be comparable with the speaker.
    Julf likes this.
  15. John Phillips

    John Phillips pfm Member

    The interaction of amplifier and 'speaker gets quite complex when you dig beyond the obvious linear effects. But it's normal human behaviour to look for simple explanations. One of the simplifications is in the typical but IMHO unrealistic linear model of amplifier output impedance, and a second is in believing that measurements based on that simple model are useful in all circumstances.

    "Explanations exist; they have existed for all time; there is always a well-known solution to every human problem—neat, plausible, and wrong." - H.L. Mencken in 1920.​

    The art is always to find the right simplification for humans to deal with that still leads to useful results in specific circumstances. Generalizations are never true.
    ToTo Man and darrenyeats like this.
  16. tuga

    tuga Legal Alien

    These measurements allow us to compare the response of the amplifier into both a flat and a simulated speaker load (black trace) with 10dB feedback or with no feedback

    Fig.2 Cary CAD-805RS, 845 tube, 10dB feedback, frequency response from 4 ohm tap at 2.83V
    into: simulated loudspeaker load (gray), 8 ohms (blue), 4 ohms (magenta), 2 ohms (red) (1dB/vertical div.).

    Fig.3 Cary CAD-805RS, 845 tube, 0dB feedback, frequency response from 16 ohm tap at 2.83V
    into: simulated loudspeaker load (gray), 8 ohms (blue), 4 ohms (magenta), 2 ohms (red) (1dB/vertical div.).
    Last edited: Jan 16, 2020
  17. davidsrsb

    davidsrsb pfm Member

    It is hard with valve amplifiers to separate the effects of high output impedance from the high distortion at the frequency extremes.
    There is a reason amplifiers were measured at 1 kHz
    Julf likes this.
  18. ToTo Man

    ToTo Man the band not the dog

    The above graphs are illustrating effects in the amplitude domain only, is that correct?

    A characteristic I neglected to mention in my previous post is phase, which I understand is largely correlated with frequency response, such that every time there is an upward or downward shift in frequency response there is also corresponding change in phase. I suppose this could compound the audibility of the amplitude frequency response aberrations?
  19. ToTo Man

    ToTo Man the band not the dog

    So when trying to predict why, e.g. a Tannoy Monitor Gold, sounds different when driven by a Quad 303 or Quad 306, it is too simplistic to attribute it to output impedance? Output impedance may well be a contributing factor, but it is a by-product of topology design, and thus it is impossible to separate it from the other the features of said design. Is that a fair conclusion?
  20. davidsrsb

    davidsrsb pfm Member

    Phase is a very secondary effect.
    The distortion soars at low frequencies and the impedance becomes very non linear with it. The simple valve follower that some people like to use to get "valve sound" completely misses the mark of the complexity going on in a push pull running out of feedback and with a transformer going into low frequency saturation.
    It is an effect, but many like it.

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