Calcs for op amp loading vs THD?

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atavacron

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Jan 28, 2009
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What data am I bringing in to a rough estimation of whether an amp can drive a particular load at a particular output level without veering into distortion? And what is the math thereafter? Looking at any data sheet, you have the RMS vs. THD+N plot, the short-circuit current, and what else? Without expanding the question to in-loop buffering or parallel amps (or negative impedance for that matter!), maybe a good place to start would be “I see that OPAXYZ with a 65mA short circuit current can output 7V into 600R at .XXX% THD+N, but what can it output into 400R without the THD+N curve taking off?”
 
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I'm not aware of any such calculations. Distortion in amplifiers almost always traces back to what part of the ohmic region of transistors is being exercised. When the amp reaches a point where it cannot supply or sink more current, that is usually because some transistor has reached the edges of it's ohmic region. This is where currents change sharply and thus is a source of distortion. So THD depends largely on the design of the amp and particularly the output stage. Although consider that if the amp is actually clipping and negative feedback is being used (which is basically always in the case of an op amp), THD is going to go through the roof regardless of the circuit design.

Note that plots of THD vs Output Voltage and Output Voltage vs Output Current and similar might not give you the insight you're looking for. For example, if you look at the Output Voltage vs Load Resistance plot in the TI TL072 datasheet, it has a very smooth curve but this provides absolutely no indication as to what THD would be. The TL072 has a 128R resistor in series with the output which is going to cause a significant voltage drop but also push the internals out of their linear region and result in probably significant THD over much of output swing shown in the plot. So one thing to look at in the datasheet would be to see what sort of series resistance it has on the output. If it's small, that means the amp is more stable under load, has better drive and probably just a better output design.

update:

As an example NJM4556 has very good drive capability (frequently used as a headphone amp) so it's plots are probably a good indication of what to look for:

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There is no indication in the datasheet as to what the series resistance is but my guess is it has to be pretty low if it can do double zero THD at 1Vrms into 200 ohms. That's pretty great actually.
 
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There is no indication in the datasheet as to what the series resistance is but my guess is it has to be pretty low if it can do double zero THD at 1Vrms into 200 ohms. That's pretty great actually.
There's a big difference between a TL0 and a NJM455x. The former's output protection is just this 128 ohms resistor in series, so the current limitation happens much more smoothly than the latter, which has much smaller resistors in series and relies on clamping transistors to limit current abruptly.
In particular, when the protection is "re-entrant" - meaning it protects sooner when the Vce voltage is high, inserting a resistor between output and load actually increases the output capability.In particular, it's the case of the 5532. Inserting a 47r resistor actually gives better drive for an 8-ohm load than a direct connection.
 
There's a big difference between a TL0 and a NJM455x. The former's output protection is just this 128 ohms resistor in series, so the current limitation happens much more smoothly than the latter, which has much smaller resistors in series and relies on clamping transistors to limit current abruptly.
In particular, when the protection is "re-entrant" - meaning it protects sooner when the Vce voltage is high, inserting a resistor between output and load actually increases the output capability.In particular, it's the case of the 5532. Inserting a 47r resistor actually gives better drive for an 8-ohm load than a direct connection.
Yeah, I think I know what you mean. The 47R allows more of the amp output swing to be exercised without triggering output protection and more voltage equals more power?

So can the 47R be inside the feedback loop? It seems that might be better for THD (provided parasitics don't get involved). And it would also help adjust power for different headphone loads.
 
Yeah, I think I know what you mean. The 47R allows more of the amp output swing to be exercised without triggering output protection and more voltage equals more power?
Correct. Of course it sepends on teh structure and the protection scheme.
So can the 47R be inside the feedback loop?
Yes.
It seems that might be better for THD (provided parasitics don't get involved). And it would also help adjust power for different headphone loads.
That subject came when I designed headphone diistribution systems. In order to cater for the various impedances, I chose to put the resistor outside the FB loop, so the level would not change as drastically between an 8 ohm and a 600 ohm headset. Distortion was not as much a concern as preserving audition.
 
That subject came when I designed headphone diistribution systems. In order to cater for the various impedances, I chose to put the resistor outside the FB loop, so the level would not change as drastically between an 8 ohm and a 600 ohm headset. Distortion was not as much a concern as preserving audition.
Seems to me having it inside the FB loop would have the same effect but give you much lower output impedance and maybe less distortion.
 
Seems to me having it inside the FB loop would have the same effect but give you much lower output impedance
No, having it in the FB loop would maintain constant gain, resulting in higher power on lower loads. Having it outside the loop makes the effective power less dependant on headphone impedance.
and maybe less distortion.
There was a time when headphone outputs were taken from a power amp's output via a resistor. When I was working for a HiFi company, that's how it was done and nobody ever complained.
Headphone designers were much aware of that, and took the necessary precautions that it implied (low Qms and Ls).
Current headphones are quite different, because they are meant to be driven from a low-Z source.
 
No, having it in the FB loop would maintain constant gain, resulting in higher power on lower loads. Having it outside the loop makes the effective power less dependant on headphone impedance.
If the op amp can put out say 10 Vp, the two scenarios are the same:

Iphones = Vp / (Rbuildout + Rphones)
Pphonees = Iphones * (Vp * Rphones / (Rbuildout + Rphones))

8ohms: 10 / (47 + 8) * (10 * 8 / (47 + 8)) = 0.264 W
600ohms: 10 / (47 + 600) * (10 * 600 / (47 + 600)) = 0.143 W

The above calculations are the same with Rbuildout outside or inside the FB loop.

When the output of the amp is 10V, you have the same amount of current through the 47R + Rphones regardless of gain.

So I'm not sure what you mean about gain. I don't see how gain has anything to do with what sort of power that can be delivered into the phones with a given supply.
 
So I'm not sure what you mean about gain. I don't see how gain has anything to do with what sort of power that can be delivered into the phones with a given supply.
Let's say the amp with zero-ohm output Z delivers 1V. With 8 ohms it's 125mW, with 600 ohms it's 1.5mW, a ratio of 75.
The one with 47ohms source impedance delivers 2.6mW into 8 ohms, 1.4mW into 600. A ratio of less than 2.
With a headphone distro system, you have people that come with their own headphones, the first thing they do is plug in. If the last user has cranked up the level for his 600 ohms headphone, the newcomer with its 8 ohm headphone gets blasted.
 
Distortion is something very, very difficult to predict and compute analytically because it involves non-linear equations and models. What you are asking is not trivial; it's something that has been keeping many great minds occupied for decades. Some very important mathematical schemes have been developed, for example, by using Volterra series it is possible to model the non-linearities of amplifiers including their memory effects (the inclusion of the effect that capacitive and/or inductive elements have in the signal). They are quite cumbersome to do by hand though. From Volterra Series an interesting tool has been developed, which has applications in high-frequency amplifiers, they are called the "X Parameters". RF/Microwave power amplifiers are purposely heavily driven into their non-linear range (aka make them distort), so analyzing their distortion behavior is really important.

Audio doesn't work this way since you don't want to purposely drive the amp into distortion as in the RF world (unless you are building a Fuzz pedal or something), so, perhaps it could be more interesting and relevant to analyze audio amplifiers in what some call "weak non-linearities", that is, if you think of 'non-linear' as a clipped sine wave almost turned into a square wave, and 'linear' as a pristine sine wave with no distortion, 'weakly non-linear' is somewhere in between, but much more tilted towards the pristine sine wave side response than to the square wave. Those sort of models make use of polynomials which have low-valued coefficients for the quadratic and higher order terms (hence its name weakly non-linear, since the linear terms dominate).

In my opinion, as Abbey suggests, all calculations must be made in the computer world in tandem with real measurements. You can propose a weak non-linear model, measure a particular op-amp vs loading and try to fit your model into the measurements. It is more of an academic exercise to study how a particular op-amp distorts rather than something practical for everyday DIYing. In the case of loading, the non-linear components would appear primarily due to the output stage distortion. Again, it is very interesting if you are someone like me who is into academia or research, don't know how useful this would be to a DIYer though.

That being said, some op-amp datasheets do provide measurements of THD vs loading, they are not very comprehensive, usually 600 ohms and 2K will be the reported results. As a general rule, you don't want to go below 600 ohms, and 600 ohms is where an op-amp will distort more when considering full voltage swing. Of course, if you are not outputting full voltage swing, you can go much lower than 600 ohms.

I guess that, for some raw calculations, what you can do is to check the THD measurements and look at the swing values they used, for example, if they used 600 ohms and +/- 12V swing, you can divide 12/600 = 20 mA, and extrapolate to different values of loading/voltage. For example, if you use 1 V into 50 ohms, 1/50 = 20 mA, you are using the same current, and the distortion values MIGHT be similar to the values reported for 12V and 600 ohms. I emphasize MIGHT since I already mentioned that there are other factors being involved and the linear relationship I just described might not be valid. Measurements must be carried out to check if your predictions were right or completely off-target.
 
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Let's say the amp with zero-ohm output Z delivers 1V. With 8 ohms it's 125mW, with 600 ohms it's 1.5mW, a ratio of 75.
Again, you're talking about gain. The operator doesn't care about volts on the output. They just adjust the level pot to produce the right loudness. So gain and voltage does not matter.

What matters is the power delivered with the knob at a certain position and, unless I'm missing something, that is defined by current and load. And the current into the load for a given supply is always going to be Vsupply / (Rbuildout + Rload) regardless of the buildout resistor being inside or outside the FB loop.
 
Again, you're talking about gain. The operator doesn't care about volts on the output. They just adjust the level pot to produce the right loudness. So gain and voltage does not matter.

What matters is the power delivered with the knob at a certain position and, unless I'm missing something, that is defined by current and load. And the current into the load for a given supply is always going to be Vsupply / (Rbuildout + Rload) regardless of the buildout resistor being inside or outside the FB loop.

You're missing the fact that "Vsupply" is higher when the 47R is inside the feedback loop. Since the opamp raises the voltage at its output pin to compensate for the loss across that 47R such that the full 1V appears across the phones. With the 47R outside the loop, thereby forming a voltage divider with the phones, the voltage across the phones is reduced to 145mV.
 
Again, you're talking about gain.
And you're talking about maximum power.
The operator doesn't care about volts on the output. They just adjust the level pot to produce the right loudness.
I gave you an example of a very common situation where the operator adjusts the level after he's been blasted.
What matters is the power delivered with the knob at a certain position and, unless I'm missing something, that is defined by current and load. And the current into the load for a given supply is always going to be Vsupply / (Rbuildout + Rload) regardless of the buildout resistor being inside or outside the FB loop.
I gave you a pretty good example in post #10. The power delivered by amp with the extrernal resistor is more constant vs. headphone impedance. Now, it's certainly not all, ignoring headphone sensitivity, but it offers a certain degree of protection to the bearer's ears.
 
for some raw calculations, what you can do is to check the THD measurements and look at the swing values they used, for example, if they used 600 ohms and +/- 12V swing, you can divide 12/600 = 20 mA, and extrapolate to different values of loading/voltage. For example, if you use 1 V into 50 ohms, 1/50 = 20 mA, you are using the same current, and the distortion values MIGHT be similar to the values reported for 12V and 600 ohms. I emphasize MIGHT since I already mentioned that there are other factors being involved and the linear relationship I just described might not be valid.
That’s the direction, basically. So let’s take an OPA1611, for example. Short circuit current of 30mA IIRC. 10V RMS into 600R. 10/600 = 16.7mA. I know that a 5532, with similar drive, shouldn’t push less than 500R. 10/500 = 20mA. So for a general purpose op amp, is the rule of thumb something like “two-thirds of the rated short circuit current”?

Looking at the OPA210 (it’s really the best gen purp BJT out there for everything but mic amps), with a 65mA short circuit and a 7V output into 600R before THD takeoff, that’s 7/600 = 11.7mA. It’s not a headphone driver so that’s the closest heavy-load spec one can extrapolate from the data sheet. I have an application where I need to guesstimate the lowest resistance it can drive at 1.75V, which is 12dB down. 1.75V/150R = 11.7mA. Sounds pretty reasonable, same current, more than enough for any oddball low impedance low noise circuit path. Am I missing anything?

What if we push it harder?

7V/600R = 11.7mA
7V/323R = 21.7mA (1/3 of short)
7V/215R = 32.5mA (1/2 of short)
7V/162R = 43.3mA (2/3 of short)
 
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You're missing the fact that "Vsupply" is higher when the 47R is inside the feedback loop.
You misinterpreted my defition of "Vsupply". Vsupply does not refer to the output of the circuit at whatever point. Vsupply refers to the voltage of the power supply which is generally a fixed voltage. Power supply voltage is going to define what power can be dissipated in a power amplifier application.

Putting Rbuildout inside or outside the FB loop has no effect on making "effective power less dependant on headphone impedance".

The only difference is the gain of the amp itself. With Rbuildout outside the FB loop, the 47R does not impact gain. With Rbuildout inside the FB loop, the gain is higher because of the voltage divider created by the 47R and Rphones.

But again, the listener does know or care what the gain of the amplifier is.
 
That’s the direction, basically. So let’s take an OPA1611, for example. Short circuit current of 30mA IIRC. 10V RMS into 600R. 10/600 = 16.7mA. I know that a 5532, with similar drive, shouldn’t push less than 500R. 10/500 = 20mA. So for a general purpose op amp, is the rule of thumb something like “two-thirds of the rated short circuit current”?

Looking at the OPA210 (it’s really the best gen purp BJT out there for everything but mic amps), with a 65mA short circuit and a 7V output into 600R before THD takeoff, that’s 7/600 = 11.7mA. It’s not a headphone driver so that’s the closest heavy-load spec one can extrapolate from the data sheet. I have an application where I need to guesstimate the lowest resistance it can drive at 1.75V, which is 12dB down. 1.75V/150R = 11.7mA. Sounds pretty reasonable, same current, more than enough for any oddball low impedance low noise circuit path. Am I missing anything?
No, if you reach short circuit current you are far too deep into the no-go zone in terms of distortion. I would base the assumptions on the THD measurements rather than on the short circuit current. Short circuit current just tells you the max current the op-amp can provide before going into protection mode, it doesn't tell you anything about distortion.
 
You misinterpreted my defition of "Vsupply". Vsupply does not refer to the output of the circuit at whatever point. Vsupply refers to the voltage of the power supply which is generally a fixed voltage. Power supply voltage is going to define what power can be dissipated in a power amplifier application.

Putting Rbuildout inside or outside the FB loop has no effect on making "effective power less dependant on headphone impedance".

The only difference is the gain of the amp itself. With Rbuildout outside the FB loop, the 47R does not impact gain. With Rbuildout inside the FB loop, the gain is higher because of the voltage divider created by the 47R and Rphones.

But again, the listener does know or care what the gain of the amplifier is.
The resistance outside the FB loop does impact gain, not the gain of the op-amp, but the overall gain, what it is sometimes referred to as "Transducer Gain", although the latter assumes matched impedances, but the concept is the same though.

In any case, I don't know what this pissing contest has to do with the OP.
 
I would base the assumptions on the THD measurements rather than on the short circuit current. Short circuit current just tells you the max current the op-amp can provide before going into protection mode, it doesn't tell you anything about distortion.
Yes. I elongated the post just now to demonstrate why I was referencing the short circuit current in that sentence. It was just a touchpoint, not a calc.
 
Yes. I elongated the post just now to demonstrate why I was referencing the short circuit current in that sentence. It was just a touchpoint, not a calc.
I understand, I know of no rule of thumb to base on the short-circuit current to determine a safe operating point for low distortion. Since the protection circuit of many op-amps is different and may start influencing the output sooner than in others, and in different ways, my only suggestion would be "well bellow the short circuit current".
 

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