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Why Amplifiers Don't Always Sound Right : Output Impedence and All That
TAS 71 - May/June 1991 Robert E. Greene
What a perfect amplifier would sound like is not easy to say. But what it would do is easy to describe: It would generate an exact, enlarged replica of its input voltage at its output terminals, no matter what was connected across its output. As such, this is impossible, because voltages cannot be maintained across a short circuit; therefore a shorted amplifier won't be able to replicate its input voltage. So we have to restrict our attention to reasonable loads, not too close to short circuits. But even in this case, there are reasons why real amplifiers aren't quite perfect. Some of the reasons are complicated. Some of them are arguably not yet understood. But there is one reason for imperfection that is comprehensible and also important in practice: this is the matter of what is called output impedance. Exactly what this is and how it affects amplifier sound is what this article is about.
As an amplifier is played and voltages are generated at the output terminals, current runs via the speaker cables through the speakers. Without current, there would be no power, hence no sound. The current for one channel runs from one amplifier output terminal to the other, which way varying as the signal changes. If output current is running from terminal A through cable and speaker and then another cable to terminal B, then current must run inside the amplifier from terminal B to terminal A. This has to happen because current cannot accumulate anywhere. But there is resistance to current flow: The cables and the speakers have resistance; so does the amplifier. The current flow from one terminal to another inside the amplifier encounters resistance, too. This internal resistance is called the output impedance of the amplifier. In transistor amplifiers it is usually low, on the order of 0.05 ohms. In tube amps, it is usually much higher, more like 0.5 to 1.0 ohms, or even more.
In effect, each channel of the amplifier is driving two loads in series; the external cable plus speaker load and the output impedance load. Some of its total voltage is used up on the internal, output impedance load. There is a formula for this. If V TOTAL is the total voltage, RE is the external load, and Ro the output impedance, then the voltage applied to the external load is:
But the details of the formula don't matter here. All you need to know is the general idea.
If output impedance is small compared to the external load, almost all of the total voltage goes to the driving of the external cable-plus speaker load. But if the external load has resistance (impedance) that is small enough to be anything like the same size as the amplifier's output impedance, then quite a lot of the total voltage goes to driving the internal load and so the external load gets correspondingly less of the total voltage.
Suppose the total voltage signal is an almost perfectly amplified replica of the input. (This is what happens in real amplifiers-the total is right, not necessarily the external part of the totaL) Suppose also that the fraction of the total lost in the internal resistance of the amp is always the same, say five percent of the total. Then the cable-speaker combination always gets 95 percent of the total. But 95 percent of a perfectly amplified signal is still a perfectly amplified signal; it's just at a lower volume. So there is no problem with the internal voltage drop in the amp as long as it is a constant fraction of the total.
The internal voltage drop will be a constant fraction of the total as long as the ratio of speaker-plus-cable resistance to output impedance is constant. But here is a difficulty: Real speakers almost always have a resistance (impedance) that depends on frequency and so varies according to frequency. At some frequencies, the impedance may be low; at other frequencies it will go up to much larger values. There is no way an amplifier designer can anticipate these changes in a detailed way, because they are different for different speakers. Speaker designers try to be careful not to let the impedance of their speakers go too low: Ultra-low impedance demands too much current from the amplifier. But they seldom manage to make their speakers' impedance constant.
As a result of the unpredictably fluctuating speaker impedance, the actual frequency response of an amplifier into a real speaker, not an idealized constant resistance, is usually not flat. The way this problem is supposed to be handled is for the amplifier to have really low output impedance; then the internal voltage loss in the amp is small. Even though it changes with frequency, it always stays a small percentage of the signal, so the externally applied voltage always almost equals the voltage total-and it is the total that is the almost perfect replica of input in real amplifiers. So everything is fine as long as output impedance is really low.
Watch out, though. Some amplifiers, including almost all tube amps, don't pull this trick off. An output impedance of 0.5 ohms is pretty low for a tube amp, actually. But it is not really low enough to make the amp nearly flat into speaker loads. Suppose your speaker's impedance fluctuates from, say, 4 ohms to 20 ohms as frequency varies. That kind of variation is very common, almost a general rule for multidriver box speakers on account of crossovers, resonances, etc. But even this will make frequency response vary greatly using that 0.5 ohm tube amp. The response is about 0.8 dB higher at the 20 ohm frequencies than at the 4 ohm frequencies. That kind of variation is definitely audible. A 1 ohm output impedance will give a 1.5 dB shift in this situation.1 And you wondered why trying a tube amp in your system changed the sound so much?
This already bad situation becomes even worse when one confronts an amplifier having substantial output impedance with one of those speakers with an impedance dropping abruptly to 2 ohms or even 1 ohm in certain frequency ranges, but with a higher impedance in other frequency ranges. Low speaker impedance demands lots of current from an amplifier, but that is just a matter of having a big enough (and stable enough) amp to play loudly without driving the amp into current limiting. All a speaker with, say, a 2 ohm impedance at all frequencies needs is a big stable amp, and then, no problem. The problem arises from variation in impedance and most especially deep dips in impedance at some frequencies.These graphs show some examples:
It is worth noting that upward jumps in impedance from, for example, a reasonable level of 4 ohms up to 8 ohms, have less impact on frequency response than the dips in impedance to really low levels. With an amp of 1 ohm output impedance again, a 4 ohm speaker impedance has the speaker seeing 0.8 of the total voltage; the 8 ohm speaker impedance gives 0.889 of the total voltage. The dB difference is 0.9 dB-audible but not nearly so bad as the 4 dB difference we found in going from 4 ohms down to 1 ohm of speaker impedance.
The following table shows how far down in decibels the voltage at the speaker terminals willi be from the total voltage generated by the amplifier, as determined by speaker impedance and amplifier- output impedance together with cable impedance. Across the top are four possibilities for output-plus-cable total impedance. Vertically, seven possible speaker impedances are listed. The table entries are the decibel drops. To find variations of voltage as speaker impedance varies, you take differences. For example, with 0.5 ohm output impedance (plus cable imped. ance), the voltage difference from a frequency where speaker impedance is 2 ohms to one where speaker impedance is 15 ohms is 1.94 - 0.28 = 1.66 dB. The lower speaker impedance, I 2 ohms in this case, always has the lower voltage; so the 2 ohm frequency is down 1.66 dB I relative to the 15 ohm frequency.
Even extremely large peaks in speaker impedance aren't that bad, comparatively, in their effect on frequency response. The speaker cannot see more than the total voltage, no matter how high its impedance. So in our example of a 4 ohm speaker with 1 ohm output-impedance amp, a huge peak in speaker impedance would just take us from 80 percent to 100 percent of the total, about a 2 dB change. That's still not as bad as the 4 dB in dropping from 4 ohms to 1 ohm. However, enormous speaker impedance peaks at certain frequencies are symptomatic of resonances,2 either electrical or mechanical, and these are sometimes undesirable even though they may not be observable in frequency response terms. But that is another story.
Even with speakers that have reasonable impedance behavior themselves, there are additional things to worry about. Some amps change output impedance with frequency, compounding the speaker impedance variation difficulty. Moreover, any cable impedance (resistance or inductance or capacitance) actually counts as part of the output impedance of the amplifier as far as what voltage signal the speaker terminals "see." And it is the speaker terminal voltage that determines what you hear!
Speaker Cables
Few speaker cables have any substantial amount of resistance in the ordinary Ohm's Law sense. But you should certainly be very cautious about using ones that do. (Roughly speaking: forget such cables-they can't work right.) What many cables do have is enough inductance or capacitance to be a problem. When you look at the "specs" of inductance or capacitance for cables, the numbers don't sound like much. But the effect varies with frequency. A little bit of inductance that won't have much effect at midrange or low frequencies turns into a much larger obstruction to the high frequencies. For example, one microhenry is, in a sense, equivalent to 6 milliohms at 1 kHz-not much, really. But at 20 kHz, it is equivalent to 120 milliohms or 0.12 ohms, an amount comparable to the output impedance of the amp itself. Similarly, capacitance in amounts which won't do much in the midrange and highs would cause a substantial roll-off of the deep bass if it were in the series, like the bass-blocking capacitors on the input to the electrostatic speakers. But cable capacitance is in parallel, not in series, so it too rolls off the highs. But it turns out that for speaker cables, inductance is far more significant than capacitance. ( For iterconnects, it is the other away around.)
The whole business of the interaction between the resistance, inductance, and capacitance of cables and the frequency balance the speaker sees is a little bit complicated. (Ordinary resistance combined with inductance does not just add up the resistance and the ohmequivalent of the inductance, for instance.) I am going to save this stuff for a later article. When it comes to that, I oversimplified a bit in talking about the output impedance of amplifiers, too, by lumping resistance, inductance, and capacitance together as total impedance. But the essential points remain valid and we avoided any complex math.3
Leaving further technical details for later, we still have the basic picture: The only hope for flat response into a real-world speaker is low output impedance for the amplifier and low impedance for the cables-low resistance, low inductance, and low capacitance. There is more to truth than flat, but if it's not flat, it can't be truth. Impedance can literally impede the sonic truth.
Robert E. Greene
TAS Issue 71 May/June 1991
1 For comparison, a 0.05 ohm output impedance would give a variation of only 0.09 dB in this situation. These dB numbers come from the formula for the externally applied voltages by taking 20 times the log of the ratio of the external voltages for the two different external resistances =20 log ((1 +(Ro/ RE1))/(l +(Ro/RE2))). The 20 instead of 10 is because power is proportional to voltage squared.
2 A big impeadance peak at a certain frequency means that at that frequency the speaker draws very little current for a given voltage. If the speaker has the ideal flat sonic response to constant voltage then at an impedance peak frequency, the speaker is producing its specified sound level with very little power input. (Recall that power = voltage times current.) Lots of sound from little power means resonance!
3 Complex in the mathematical sense of using complex numbers, as well as complex in the vernacular sense of complicated. The technically inclined have probably noticed already that the completely precise form of all this would be most easily expressed in terms of impedances as complex numbers. More on this later.
Why Amplifiers Don't Always Sound Right : Output Impedence and All That
TAS 71 - May/June 1991 Robert E. Greene
What a perfect amplifier would sound like is not easy to say. But what it would do is easy to describe: It would generate an exact, enlarged replica of its input voltage at its output terminals, no matter what was connected across its output. As such, this is impossible, because voltages cannot be maintained across a short circuit; therefore a shorted amplifier won't be able to replicate its input voltage. So we have to restrict our attention to reasonable loads, not too close to short circuits. But even in this case, there are reasons why real amplifiers aren't quite perfect. Some of the reasons are complicated. Some of them are arguably not yet understood. But there is one reason for imperfection that is comprehensible and also important in practice: this is the matter of what is called output impedance. Exactly what this is and how it affects amplifier sound is what this article is about.
As an amplifier is played and voltages are generated at the output terminals, current runs via the speaker cables through the speakers. Without current, there would be no power, hence no sound. The current for one channel runs from one amplifier output terminal to the other, which way varying as the signal changes. If output current is running from terminal A through cable and speaker and then another cable to terminal B, then current must run inside the amplifier from terminal B to terminal A. This has to happen because current cannot accumulate anywhere. But there is resistance to current flow: The cables and the speakers have resistance; so does the amplifier. The current flow from one terminal to another inside the amplifier encounters resistance, too. This internal resistance is called the output impedance of the amplifier. In transistor amplifiers it is usually low, on the order of 0.05 ohms. In tube amps, it is usually much higher, more like 0.5 to 1.0 ohms, or even more.
In effect, each channel of the amplifier is driving two loads in series; the external cable plus speaker load and the output impedance load. Some of its total voltage is used up on the internal, output impedance load. There is a formula for this. If V TOTAL is the total voltage, RE is the external load, and Ro the output impedance, then the voltage applied to the external load is:
But the details of the formula don't matter here. All you need to know is the general idea.
If output impedance is small compared to the external load, almost all of the total voltage goes to the driving of the external cable-plus speaker load. But if the external load has resistance (impedance) that is small enough to be anything like the same size as the amplifier's output impedance, then quite a lot of the total voltage goes to driving the internal load and so the external load gets correspondingly less of the total voltage.
Suppose the total voltage signal is an almost perfectly amplified replica of the input. (This is what happens in real amplifiers-the total is right, not necessarily the external part of the totaL) Suppose also that the fraction of the total lost in the internal resistance of the amp is always the same, say five percent of the total. Then the cable-speaker combination always gets 95 percent of the total. But 95 percent of a perfectly amplified signal is still a perfectly amplified signal; it's just at a lower volume. So there is no problem with the internal voltage drop in the amp as long as it is a constant fraction of the total.
The internal voltage drop will be a constant fraction of the total as long as the ratio of speaker-plus-cable resistance to output impedance is constant. But here is a difficulty: Real speakers almost always have a resistance (impedance) that depends on frequency and so varies according to frequency. At some frequencies, the impedance may be low; at other frequencies it will go up to much larger values. There is no way an amplifier designer can anticipate these changes in a detailed way, because they are different for different speakers. Speaker designers try to be careful not to let the impedance of their speakers go too low: Ultra-low impedance demands too much current from the amplifier. But they seldom manage to make their speakers' impedance constant.
As a result of the unpredictably fluctuating speaker impedance, the actual frequency response of an amplifier into a real speaker, not an idealized constant resistance, is usually not flat. The way this problem is supposed to be handled is for the amplifier to have really low output impedance; then the internal voltage loss in the amp is small. Even though it changes with frequency, it always stays a small percentage of the signal, so the externally applied voltage always almost equals the voltage total-and it is the total that is the almost perfect replica of input in real amplifiers. So everything is fine as long as output impedance is really low.
Watch out, though. Some amplifiers, including almost all tube amps, don't pull this trick off. An output impedance of 0.5 ohms is pretty low for a tube amp, actually. But it is not really low enough to make the amp nearly flat into speaker loads. Suppose your speaker's impedance fluctuates from, say, 4 ohms to 20 ohms as frequency varies. That kind of variation is very common, almost a general rule for multidriver box speakers on account of crossovers, resonances, etc. But even this will make frequency response vary greatly using that 0.5 ohm tube amp. The response is about 0.8 dB higher at the 20 ohm frequencies than at the 4 ohm frequencies. That kind of variation is definitely audible. A 1 ohm output impedance will give a 1.5 dB shift in this situation.1 And you wondered why trying a tube amp in your system changed the sound so much?
This already bad situation becomes even worse when one confronts an amplifier having substantial output impedance with one of those speakers with an impedance dropping abruptly to 2 ohms or even 1 ohm in certain frequency ranges, but with a higher impedance in other frequency ranges. Low speaker impedance demands lots of current from an amplifier, but that is just a matter of having a big enough (and stable enough) amp to play loudly without driving the amp into current limiting. All a speaker with, say, a 2 ohm impedance at all frequencies needs is a big stable amp, and then, no problem. The problem arises from variation in impedance and most especially deep dips in impedance at some frequencies.These graphs show some examples:
It is worth noting that upward jumps in impedance from, for example, a reasonable level of 4 ohms up to 8 ohms, have less impact on frequency response than the dips in impedance to really low levels. With an amp of 1 ohm output impedance again, a 4 ohm speaker impedance has the speaker seeing 0.8 of the total voltage; the 8 ohm speaker impedance gives 0.889 of the total voltage. The dB difference is 0.9 dB-audible but not nearly so bad as the 4 dB difference we found in going from 4 ohms down to 1 ohm of speaker impedance.
The following table shows how far down in decibels the voltage at the speaker terminals willi be from the total voltage generated by the amplifier, as determined by speaker impedance and amplifier- output impedance together with cable impedance. Across the top are four possibilities for output-plus-cable total impedance. Vertically, seven possible speaker impedances are listed. The table entries are the decibel drops. To find variations of voltage as speaker impedance varies, you take differences. For example, with 0.5 ohm output impedance (plus cable imped. ance), the voltage difference from a frequency where speaker impedance is 2 ohms to one where speaker impedance is 15 ohms is 1.94 - 0.28 = 1.66 dB. The lower speaker impedance, I 2 ohms in this case, always has the lower voltage; so the 2 ohm frequency is down 1.66 dB I relative to the 15 ohm frequency.
Even extremely large peaks in speaker impedance aren't that bad, comparatively, in their effect on frequency response. The speaker cannot see more than the total voltage, no matter how high its impedance. So in our example of a 4 ohm speaker with 1 ohm output-impedance amp, a huge peak in speaker impedance would just take us from 80 percent to 100 percent of the total, about a 2 dB change. That's still not as bad as the 4 dB in dropping from 4 ohms to 1 ohm. However, enormous speaker impedance peaks at certain frequencies are symptomatic of resonances,2 either electrical or mechanical, and these are sometimes undesirable even though they may not be observable in frequency response terms. But that is another story.
Even with speakers that have reasonable impedance behavior themselves, there are additional things to worry about. Some amps change output impedance with frequency, compounding the speaker impedance variation difficulty. Moreover, any cable impedance (resistance or inductance or capacitance) actually counts as part of the output impedance of the amplifier as far as what voltage signal the speaker terminals "see." And it is the speaker terminal voltage that determines what you hear!
Speaker Cables
Few speaker cables have any substantial amount of resistance in the ordinary Ohm's Law sense. But you should certainly be very cautious about using ones that do. (Roughly speaking: forget such cables-they can't work right.) What many cables do have is enough inductance or capacitance to be a problem. When you look at the "specs" of inductance or capacitance for cables, the numbers don't sound like much. But the effect varies with frequency. A little bit of inductance that won't have much effect at midrange or low frequencies turns into a much larger obstruction to the high frequencies. For example, one microhenry is, in a sense, equivalent to 6 milliohms at 1 kHz-not much, really. But at 20 kHz, it is equivalent to 120 milliohms or 0.12 ohms, an amount comparable to the output impedance of the amp itself. Similarly, capacitance in amounts which won't do much in the midrange and highs would cause a substantial roll-off of the deep bass if it were in the series, like the bass-blocking capacitors on the input to the electrostatic speakers. But cable capacitance is in parallel, not in series, so it too rolls off the highs. But it turns out that for speaker cables, inductance is far more significant than capacitance. ( For iterconnects, it is the other away around.)
The whole business of the interaction between the resistance, inductance, and capacitance of cables and the frequency balance the speaker sees is a little bit complicated. (Ordinary resistance combined with inductance does not just add up the resistance and the ohmequivalent of the inductance, for instance.) I am going to save this stuff for a later article. When it comes to that, I oversimplified a bit in talking about the output impedance of amplifiers, too, by lumping resistance, inductance, and capacitance together as total impedance. But the essential points remain valid and we avoided any complex math.3
Leaving further technical details for later, we still have the basic picture: The only hope for flat response into a real-world speaker is low output impedance for the amplifier and low impedance for the cables-low resistance, low inductance, and low capacitance. There is more to truth than flat, but if it's not flat, it can't be truth. Impedance can literally impede the sonic truth.
Robert E. Greene
TAS Issue 71 May/June 1991
1 For comparison, a 0.05 ohm output impedance would give a variation of only 0.09 dB in this situation. These dB numbers come from the formula for the externally applied voltages by taking 20 times the log of the ratio of the external voltages for the two different external resistances =20 log ((1 +(Ro/ RE1))/(l +(Ro/RE2))). The 20 instead of 10 is because power is proportional to voltage squared.
2 A big impeadance peak at a certain frequency means that at that frequency the speaker draws very little current for a given voltage. If the speaker has the ideal flat sonic response to constant voltage then at an impedance peak frequency, the speaker is producing its specified sound level with very little power input. (Recall that power = voltage times current.) Lots of sound from little power means resonance!
3 Complex in the mathematical sense of using complex numbers, as well as complex in the vernacular sense of complicated. The technically inclined have probably noticed already that the completely precise form of all this would be most easily expressed in terms of impedances as complex numbers. More on this later.
