My understanding of amplifiers

[PaulyT]

The question of how amplifiers work and how things like impedance and efficiency come into play has come up in a few different contexts lately, so I'm going to start this thread to 1) explain how I currently understand it, and 2) help me solidify my understanding and get corrections if I'm wrong. So while I'm not an electronics professional, I have enough understanding of the physics to grasp the general concepts, be able to apply various equations, etc. Of course I more than welcome input from those who know more than me!

So where to start?

For me the first and most fundamental concept that has crystallized my understanding of this whole thing is the notion of an audio amplifier as a constant voltage gain device:

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:text-link:

That is, the job of an amp - and an amp's ONLY job - is to maintain a voltage across its output terminals that is a constant, linear multiple of the voltage of the input. It is not a constant current device. It is not a constant power (wattage) device. Now this doesn't mean the voltage is constant - of course, in an audio signal, it's fluctuating positive/negative in a complex way, which is what encapsulates the music, which you can think of as the cause of (on the microphone side) and result of (on the speaker side) the pattern of the voltage. But this base principle still applies: in a perfect amp, the voltage of the output is always an exact multiple of the voltage of the input at any given moment in time. Everything else follows from this constant voltage gain idea, so it's important to establish this idea first.

More to come... no time right now to write everything in one post, and I want to separate particular points into individual posts anyway so that you don't have to read a huge long treatise all at once.

Please comment, discussion is welcome!

 

[Flint]

David Hafler claimed the ideal amp was a straight wire with gain.

 

[PaulyT]

Yup, no internal impedance, just voltage gain.

 

[PaulyT]

So, next we have Ohm's law:

:text-link:

which states that V = I x R, where V is voltage, I is current, and R is resistance (which for simplicity we can say is the same thing as impedance; impedance is used in AC circuits (like audio systems), and resistance for DC).

Now, remember I said an amp is a constant voltage device. So, for the same input signal, and the same gain setting on the amp, the voltage does NOT change if you plug in speakers of different impedances. Let me say it again: voltage is NOT dependent on load impedance (assuming the amp is not clipping). So it is incorrect to say things like "higher impedance load means higher voltage."

Aside: I think from what soundhound once said, the "gain" knobs on most amps is not really changing the actual gain of the amplification stage, but rather just attenuating the input, but for our purposes it amounts to the same thing, that the volume control on an amp, if it has one, is changing the gain - making the output voltage higher or lower for a given input voltage. But it is still a constant multiple, that doesn't change, just the multiplier.

Anyway, back to the point: Ohm's law says that if the voltage is constant (taking that as a given based on my earlier posts), then current goes up as impedance goes down. That is, more current will flow through the speakers (or headphones, the principle is the same) if the impedance is low. More current is needed to drive a 4ohm speaker than an 8ohm speaker.

Now in audio transducers, impedance is not constant with frequency. So for instance, if you were playing a "pure tone" sine wave - where there is one and only one frequency in the input signal - the amount of current flowing through the speaker would typically be higher in the low frequency (bass) range compared to the high frequency (treble), because impedance is higher in the treble range. There is a good discussion of this here:

:text-link:

(note that one talks about the amp's own impedance as well, I'll get to that more later...)

Note that nowhere in here is there anything about efficiency. Efficiency does NOT affect the current or voltage of a system, but rather the SPL level for a given voltage level. Efficiency must also vary by frequency, otherwise the SPL response (what we measure when we do RTA) would vary with impedance, and your response curve would not be anywhere near flat. I guess one major trick to good speaker design is to balance impedance changes with efficiency changes to smooth out the response.

More on efficiency later... don't want to get too sidetracked yet.

 

[PaulyT]

Now, power. Seems audiophiles are obsessed with power ratings, but to my mind the power is a derived principle, not a first principle. Let me explain.

We have Joule's law:

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which states that P = I x V. P = power (e.g. watts), I = current, V = voltage. So for a constant voltage (there's that key point again!), the power goes up as the current goes up. That makes some intuitive sense - high current requires more power, bigger power supply, bigger transformers to handle high current, etc.

You can then combine this with Ohm's law (V=IxR), and algebraically one way to express these two equations together is P = V^2 / R. So, yet again taking voltage as a constant, this means that if resistance (impedance) goes up, power goes down, and vise-versa. This is why an ideal amp will, for example, provide twice the power into a 4ohm speaker than it will to an 8ohm speaker. The voltage is NOT changing, only the current and hence the power! In reality, at some point the amp will clip, and it won't be able to produce the ideal current/power, hence the tables you see for amp specs that list power-vs-impedance that are not exact linear multiples (e.g. 200W into 8ohm, 300W into 4ohm, etc.)

This is one reason why a higher-powered amp is needed for low impedance speakers.

 

[heeman]

[youtube]http://www.youtube.com/watch?v=Y_22XOakyxM[/youtube]

Just a little bit on Current from Parasound.

 

[PaulyT]

Thanks, that makes sense. High current is needed to maintain that all-important constant voltage, especially as the impedance of the load goes lower.

 

[PaulyT]

... and jives pretty well with another interesting page I was just reading.

:text-link:

Interesting comments in there as well about speaker cables. Also some good discussion of damping factor (the ratio of speaker impedance to amp output impedance).

 

[Yesfan70]

I haven't had a chance to check all those links (intend to), but one thing I don't understand is why so many owners of higher efficiency speakers, like Klipsch, will buy a high powered amp.

If you have a speaker with a sensitivity of 98dB/w/m, why would you need a 200/ch Watt amp? I could understand if you were using a speaker like Dynaudios that usually are 4 ohm rated and have an efficiency of 88dB/w/m and wanted to get a little more juice to them.

In my mind, I'm thinking an 8 Ohm speaker with a sensitivity in the high 90s should get by with a basic 100W receiver and not run out of steam anytime soon.

 

[heeman]

http://www.axiomaudio.com/dynamicheadroom.html

An interesting article on Dynamic Range/Headroom.

 

[heeman]

I haven't had a chance to check all those links (intend to), but one thing I don't understand is why so many owners of higher efficiency speakers, like Klipsch, will buy a high powered amp.

If you have a speaker with a sensitivity of 98dB/w/m, why would you need a 200/ch Watt amp? I could understand if you were using a speaker like Dynaudios that usually are 4 ohm rated and have an efficiency of 88dB/w/m and wanted to get a little more juice to them.

In my mind, I'm thinking an 8 Ohm speaker with a sensitivity in the high 90s should get by with a basic 100W receiver and not run out of steam anytime soon.

Onlly if the amplifier has the current capablilities to handle the peaks. The wattage ratings are more or less unimportant, it is the available current of the amplifier.

This is the reason I use discreet power amplifiers in my system and NOT the onboard amps in my receiver.

 

[PaulyT]

Now, efficiency. This isn't directly related to amplifiers, but it's come up a few times as well, so I'm going to put down my thoughts on it here anyway.

Actually as I understand it, the term we we mostly use it around here should really be "sensitivity" - which means what SPL a speaker produces at a given distance for a given power, and usually at a single given frequency. E.g. 90dB for 1W @ 1M @ 1kHz. "Efficiency" is more often used to describe how much energy is converted to sound, compared to how much energy is fed to the speaker - which is generally a very small number, like 1%. But efficiency in that sense is not really directly relevant.

:text-link:

Sensitivity when specified in power (watts) can be a little misleading because of varying speaker impedance; 1W for a low impedance speaker is actually a lower voltage than 1W for a high impedance speaker. The link above mentions that sometimes sensitivity is specified in volts rather than watts (e.g. 2.83V, which is equivalent to 1W @ 8ohm). That makes more sense to me. But speaker marketing isn't about making sense.

Why does sensitivity matter? Because it is what determines how loud a speaker (or headphone) will be for a given input signal level and amplifier gain. That is, say you have a headphone amp and two sets of headphones. You play the same music with the same volume setting on the amp. The headphones that have the higher sensitivity (in Volts! not in Watts) will sound louder. Period. The loudness (SPL) has nothing to do with the impedance. As long as the amp is capable of producing adequate current to maintain its constant voltage, it doesn't matter whether the headphones are high or low impedance; the sensitivity alone will determine how loud they are.

But again, here we have a problem with sensitivity specified in Watts, especially on headphones where impedance can vary widely (25-600ohm). I think this is where the confusion arises between sensitivity and impedance in the headphone world. Two headphones could have exactly the same sensitivity-in-Watts, but to get that same power level with a low impedance headphone means decreasing the voltage! Remember P = V^2 / R; so for constant power, lower resistance/impedance means lower voltage. To get lower voltage, what do you do? You turn down the amp. When you plug in your high impedance phones, you need to increase the voltage - turn up the amp - to get the same power output. In other words, if two headphones have the same sensitivity rating in watts, a high impedance headphone will seem "harder to drive" because you have to turn up the amp to get to that power. This is counter-intuitive, which is why I have a problem with sensitivity being measured in watts. It's not really useful for headphones.

So I think I understand now my difference of opinion with Rope/Dane's statement of "high impedance headphones are harder to drive." It's not the impedance only, but rather the sensitivity coupled with impedance. My thought was the opposite - "low impedance headphones are harder to drive" because they require more current, which not all amps, especially tube amps, will be able to produce. Of course, what this really means is that "hard to drive" is an ambiguous phrase at best.

 

[PaulyT]

Yesfan, I agree. In fact I remember Altec(SH)@S&V posting a graph that showed the distortion on an amp was lowest when the amp was driven to some fairly high fraction of its capacity. So in other words a moderately powered amp being pushed a bit may actually sound better than a really high power amp that's barely using any of its available power. This is just from my memory, though, I don't have anything to back this up right now.

 

[Rope]

The vast majority of SS amplifiers used in home theater/ two channel listening applications are designed for speakers with nominal impedance of 4 to 8-Ohms. Design considerations, or goals for these amplifiers is, reasonably low distortion, high input impedance, low out put impedance (stable to 2-Ohms), flat frequency response, and low noise floor.

Enter high impedance headphones. Have amplifier design considerations/goals changed? I would think so, since now amp manufacturers are dealing with out put impedance that range from 16 to 600-Ohms. What was once thought to be an ideal (low out put impedance), is now, or could possibly be a hindrance, depending on the owners headphone selection. Other considerations when selecting a headphone, or amplifier, could be HP sensitivity. I have to be cautious when I connect my 25-Ohm HPs to my variable out put stage amp as not to fry drivers.

IMHO, the AKG K701 have received a bum rap because most owners do not power them sufficiently.

Rope

 

[PaulyT]

Output impedance in SS amps is, from what I can tell, almost a non-issue. The output impedance of these is like 0.01ohms, which is so much lower than the impedance of any headphone - or speaker - that it's pretty irrelevant. Does come into play with tube amps where output impedance can be in the ~3ohm range, but still headphone impedance is almost always a lot higher than speakers, so that's not a direct problem. As I understand it, it's more that tube amps don't have the ability to push as much current as SS amps, but that is not a function of impedance (of either the amp output or the load).

Good discussion of this here, one of the links I posted earlier:

:text-link:


And I don't know what you mean by "output impedance stable to 2ohm"... that doesn't make sense. You mean power (current) output stable to 2ohm?

And again, impedance is not the same thing as sensitivity. A low impedance headphone is not necessarily more sensitive. As I discussed in my previous post, there's a reason why low impedance headphones sound louder if the sensitivity is specified in Watts, which is (unfortunately) the norm.

 

[Flint]

Output impedance of an amp affects the Damping Factor which is influenced by the ratio of the output impedance of the amp to the input impedance of the speaker.

If the output impedance of an amp is high enough to be impactful, then the passive crossover in the speaker will be out of tolerance since all values for speaker crossover filters are determined with the assumption the output impedance of the amp is approaching zero.

 

[Rope]

I do not recall stating impedance is in any way related to sensitivity. Usually the confusion comes when mentioning sensitivity and efficiency, which are two different items.

An amplifiers ability to remain stable with as little as a 2- Ohm load becomes essential when driving any 4-Ohm speaker. At certain frequencies the load may dip to 2-Ohms, depending on the speakers impedance curve. A standard receiver will have difficulty powering a 4-Ohm speaker, again dependent on the speakers impedance curve.

A SS headphone amplifier with limited voltage (juice) will have problems handling a high Ohm headphone. OTL and some tube amplifiers are not as prone to having difficulties with higher Ohm HPs.

Rope

 

[PaulyT]

Output impedance of an amp affects the Damping Factor which is influenced by the ratio of the output impedance of the amp to the input impedance of the speaker.

Not only influenced by, in fact defined as amp output impedance over speaker impedance:

:text-link:

 

[PaulyT]

An amplifiers ability to remain stable with as little as a 2- Ohm load becomes essential when driving any 4-Ohm speaker. At certain frequencies the load may dip to 2-Ohms, depending on the speakers impedance curve. A standard receiver will have difficulty powering a 4-Ohm speaker, again dependent on the speakers impedance curve.

Sure, but it's not the amp output impedance that's stable to 2ohm (which is what you said earlier) - it's the amp's ability to provide adequate current to maintain voltage when the load impedance drops.

A SS headphone amplifier with limited voltage (juice) will have problems handling a high Ohm headphone. OTL and some tube amplifiers are not as prone to having difficulties with higher Ohm HPs.

Perhaps, but why would this be generally true? That's what I'm trying to understand. By Ohm's law, headphones (or speakers) of lower impedance require the amp to produce MORE current to maintain a given voltage. And this voltage is determined by input level and amp gain, nothing else - not the headphones' impedance.

My own experience is consistent with this. My OTL tube amp has no trouble driving Senn 580's (300ohm), AKG K701 (62ohm), Denon D5000 (25ohm), but when it came to the HiFiMan HE-5 (also 25ohm I believe), it was clearly underpowered, presumably because of the relatively low sensitivity of the HE-5 (87dB @ 1mW compared to 106dB of the Denons).

Anyway, my point is that it's not the impedance of a headphone alone that makes the amplifier work hard, and to say simply that "high impedance requires more current" is directly opposite of what Ohm's law states. And why would headphones work differently from speakers in that sense? That doesn't compute.

 

[Flint]

My father, a EE from the 1950s who designed and built tube amplifers (mostly RF amps) for the military for decades, would always tell me that it isn't an amp's ability to drive high voltage into 100hz (low frequencies) that mattered. He was always asking how well and amp could drive high voltage into 20,000Hz, because that was ultimately a much harder job for the power supply. Why? Because if you calculate the area of a sine wave and compare 1 sec of 100hz to 1 sec of 20,000Hz, the 20,000Hz sine wave is significantly more area - thus more power for given amount of time.