I just wanted to submit my understanding of distortion mechanisms to "peer review" so that I and others might benefit by the collective wisdom of the DIY Audio fora. In other words what do you think of this analysis? I would like you to correct errors and expand the discussion. Please note that I am looking at the mechanisms that produce distortion and how to prevent their generation. I do not cover methods used to correct or cover up distortion that is already produced such as feedback, feedforward, and masking.
Basic Overview
I will proceed under the assumption that distortion in electonic circuits is due primarily to non-linear transfer functions in the various devices both passive and active. For example even a resistor can be said to have a transfer function which converts voltage to current or current to voltage according to the transfer function defined by R=E/I. Thus if R varies according to current through it, voltage across it, temperature or anything else there will be some distortion. If the change in R is rapid enough to affect the audio signal then there is the potential for an audible distortion product. For example if the temperature of a resistor is completely stabilized so that the resistance is other than the value intended then the transfer function is distorted but not in a way that would be audible unless it effected some other device (e.g. throwing the bias of a transistor out of whack). If however the temperature and this R varied at say 100Hz then audible distortion (motor boating) would result.
This type of analysis can be used with any device whether passive or active. We are most often interested in the distortion produced in active stages since these situations are assumed to produce most of the audible distortion in the final circuit. The distortion in an active stage can be divided into output side and input side and I will look at these seperately.
Output Side Distortion Products
Here I am assuming that the primary distortion source is the fluctuation of the devices transfer function due to current. I am open to the idea that voltage across the device is a significant factor as well and would appreciate any experiences in this area.
In tubes and FETs the effect of interest is a change in transconductance with changes in plate or drain current respectively. In BJTs the effect would be changes in forward current gain with changes in collector current. Distortion reduction would therefor seem to be afforded by;
1. Selecting devices with smaller varience of transfer function. The the BJT with the narrowest range of hFE variation over the anticipated signal excursion would be preferred from the perspective of minimal distortion.
2. Designing the stage to produce the minimum variation in device current for the needed signal amplitude.
Choosing the appropriate device is relatively straight forward if we keep in mind that there is some interaction between the bias point and the linearity of the transfer function. Thus a device may be very linear in part of its operating region and very non-linear in other parts.
It appears that the sucessful reduction in distortion afforded by the use of active loads may be due primarily to the reduction in device current swing.
My Understanding of CCS Loads
My understanding is that a constant current source load reduces distortion by just such a reduction in current variation. With a resistive load on a BJT in CE configuration the actual load (i.e. loudspeaker or next amplification stage) is effectively in parallel with the load resistor. Thus the signal current (i.e. AC) is divided between the load resistor and the actual load. Thus the device has to produce more signal current than is needed by the actual load. When using a CCS load the current through the active load can not increase or decrease in response to the signal so that all of the signal current goes to the actual load. Therefor the device produces less current variation for a particular signal at the actual load.
This also implies that the highest practical input impedence in the following stage is desireable to reduce the signal current requirements.
Input Side Distortion Products
This side of the issue I am not as clear on. Any variability in device bias caused by the input side of the stage will have a negative effect on distortion but I suspect that there are more non-linearities associated with the input stage than I am aware of.
One obvious source of distortion would be any variation in input impedence. For example for a BJT any drop in the input impedence would increase the base current and thus the collector current causing distortion of the output. An increase in impedence would have a similar affect in the other direction. Much of the variability in the device itself would already be accounted for in the transfer function (hFE for the BJT) but reactive elements would probably not appear in curves unless they were generated at a significant AC frequency. Input capacitance is probably especially significant in devices like MOSFETs.
The input bias circuitry should therefor be chosen not only for the highest practical input impedence but also with the least variable impedence with respect to input signal conditions.
Passive Devices
The most troubling passive devices are likely to be reactive elements. Capacitors should be chosen for most stable capacitance values over a wide range of voltages and AC currents. I suspect that variation due to voltage is the primary effect. Where one has a choice in where to place capacitors it would seem that doing so at the lowest possible signal levels would improve distortion due to non-linearity in capacitors.
Similarly with inductors my guess is that smaller variation in inductor current will produce the best distortion results.
Well What do you think? Where have I missed the boat?
Basic Overview
I will proceed under the assumption that distortion in electonic circuits is due primarily to non-linear transfer functions in the various devices both passive and active. For example even a resistor can be said to have a transfer function which converts voltage to current or current to voltage according to the transfer function defined by R=E/I. Thus if R varies according to current through it, voltage across it, temperature or anything else there will be some distortion. If the change in R is rapid enough to affect the audio signal then there is the potential for an audible distortion product. For example if the temperature of a resistor is completely stabilized so that the resistance is other than the value intended then the transfer function is distorted but not in a way that would be audible unless it effected some other device (e.g. throwing the bias of a transistor out of whack). If however the temperature and this R varied at say 100Hz then audible distortion (motor boating) would result.
This type of analysis can be used with any device whether passive or active. We are most often interested in the distortion produced in active stages since these situations are assumed to produce most of the audible distortion in the final circuit. The distortion in an active stage can be divided into output side and input side and I will look at these seperately.
Output Side Distortion Products
Here I am assuming that the primary distortion source is the fluctuation of the devices transfer function due to current. I am open to the idea that voltage across the device is a significant factor as well and would appreciate any experiences in this area.
In tubes and FETs the effect of interest is a change in transconductance with changes in plate or drain current respectively. In BJTs the effect would be changes in forward current gain with changes in collector current. Distortion reduction would therefor seem to be afforded by;
1. Selecting devices with smaller varience of transfer function. The the BJT with the narrowest range of hFE variation over the anticipated signal excursion would be preferred from the perspective of minimal distortion.
2. Designing the stage to produce the minimum variation in device current for the needed signal amplitude.
Choosing the appropriate device is relatively straight forward if we keep in mind that there is some interaction between the bias point and the linearity of the transfer function. Thus a device may be very linear in part of its operating region and very non-linear in other parts.
It appears that the sucessful reduction in distortion afforded by the use of active loads may be due primarily to the reduction in device current swing.
My Understanding of CCS Loads
My understanding is that a constant current source load reduces distortion by just such a reduction in current variation. With a resistive load on a BJT in CE configuration the actual load (i.e. loudspeaker or next amplification stage) is effectively in parallel with the load resistor. Thus the signal current (i.e. AC) is divided between the load resistor and the actual load. Thus the device has to produce more signal current than is needed by the actual load. When using a CCS load the current through the active load can not increase or decrease in response to the signal so that all of the signal current goes to the actual load. Therefor the device produces less current variation for a particular signal at the actual load.
This also implies that the highest practical input impedence in the following stage is desireable to reduce the signal current requirements.
Input Side Distortion Products
This side of the issue I am not as clear on. Any variability in device bias caused by the input side of the stage will have a negative effect on distortion but I suspect that there are more non-linearities associated with the input stage than I am aware of.
One obvious source of distortion would be any variation in input impedence. For example for a BJT any drop in the input impedence would increase the base current and thus the collector current causing distortion of the output. An increase in impedence would have a similar affect in the other direction. Much of the variability in the device itself would already be accounted for in the transfer function (hFE for the BJT) but reactive elements would probably not appear in curves unless they were generated at a significant AC frequency. Input capacitance is probably especially significant in devices like MOSFETs.
The input bias circuitry should therefor be chosen not only for the highest practical input impedence but also with the least variable impedence with respect to input signal conditions.
Passive Devices
The most troubling passive devices are likely to be reactive elements. Capacitors should be chosen for most stable capacitance values over a wide range of voltages and AC currents. I suspect that variation due to voltage is the primary effect. Where one has a choice in where to place capacitors it would seem that doing so at the lowest possible signal levels would improve distortion due to non-linearity in capacitors.
Similarly with inductors my guess is that smaller variation in inductor current will produce the best distortion results.
Well What do you think? Where have I missed the boat?
Hi mashaffer !
Distortions are a very complex thing !
And yes, resistors do distort, not only by heating up. That's why there
are these expensive metallicfilm resistors.
BJTs, FETs and Tubes do distort different, mainly due to complete
different transfercurves.
You shouldn't take look too much at the hfe in BJTs, you can easily
use a currentrange where hfe is "linear". The worst thing is the Vbe-
curve. (Relation between vbe and current) This curve is far from linear.
Depending on the form of this curve different harmonics are generated.
That's one of the mainreasons for css, if current does not change,
vbe and hfe does not change, but only if Vce does not change.
To keep Vce stable, you can use cascodes and so on...
There are also principles to eliminate some of the distortions, even
after they have already been created.
And now its getting really difficult...
Mike
Distortions are a very complex thing !
And yes, resistors do distort, not only by heating up. That's why there
are these expensive metallicfilm resistors.
BJTs, FETs and Tubes do distort different, mainly due to complete
different transfercurves.
You shouldn't take look too much at the hfe in BJTs, you can easily
use a currentrange where hfe is "linear". The worst thing is the Vbe-
curve. (Relation between vbe and current) This curve is far from linear.
Depending on the form of this curve different harmonics are generated.
That's one of the mainreasons for css, if current does not change,
vbe and hfe does not change, but only if Vce does not change.
To keep Vce stable, you can use cascodes and so on...
There are also principles to eliminate some of the distortions, even
after they have already been created.
And now its getting really difficult...
Mike
Hi!
...like your thoughts.
Regarding BJT output stage in class AB I read that the best idle current depends on the picked emitter resistors
.... may be it is an old story to you, but found it quite
interesting...
It was assumed to have a perfect voltage drive fom the VAS for a complementary BJT voltage follower and the idea was that the nonlinearity of NPN side should compensate with PNP side.
If perfectly voltage driven then the output impedance of a BJT follower is theoretically approx. 25mV/A. ==> the lower the current the higher the output impedance.
Considering one half of a complimentary BJT follower, we would get
Rout= Re + 25mV/A.
If both sides are taken into account both Routs are in parallel.
If now an AC current is drawn, then one side will show an increasing impedance while the other side will lower its output impedance.
The author proposed to adjust the idle current to a value that results in 25mV voltage drop at each emitter resistor.
At zero output current then the output impedance would be
1/2 (Re+ 25mV/I_idle).
The max. output impedance will happen at the point where one BJT is cut off and here the output impedance would be Re+25mV/2I_idle, which is about 1.5 times higher than at zero current. At higher currents the output impedance would decrease again asymthotically to the value which is observed at zero current.
Distorsion of capacitors:
One reason for distorsion is also mechanical movement of the plates / foils. The AC currents cause mechanical forces to the electrodes, which causes some small vibrations.
If the distance between the electrodes is changing, then also the capacitance is changing, resulting in distorsion.
A simple test for this is to apply a reasonable high AC voltage in the frequency range 500Hz...1000Hz and listen to the capacitor. The louder types may generate more distorsions from this mechanism.
I think this is mainly applicable for film/foil caps, because in ceramic or electrolytic caps the distorsions might be dominated by several other effects.
Distorsions in inductors are a mess except air wound coils.
As soon as iron, ferrite, metal powder, cool µ, etc. is used...
....I stop thinking about theory on distorsions and proceed to trial and error... of course an air gap can help.....
Bye
Markus
...like your thoughts.
Regarding BJT output stage in class AB I read that the best idle current depends on the picked emitter resistors
.... may be it is an old story to you, but found it quite
interesting...
It was assumed to have a perfect voltage drive fom the VAS for a complementary BJT voltage follower and the idea was that the nonlinearity of NPN side should compensate with PNP side.
If perfectly voltage driven then the output impedance of a BJT follower is theoretically approx. 25mV/A. ==> the lower the current the higher the output impedance.
Considering one half of a complimentary BJT follower, we would get
Rout= Re + 25mV/A.
If both sides are taken into account both Routs are in parallel.
If now an AC current is drawn, then one side will show an increasing impedance while the other side will lower its output impedance.
The author proposed to adjust the idle current to a value that results in 25mV voltage drop at each emitter resistor.
At zero output current then the output impedance would be
1/2 (Re+ 25mV/I_idle).
The max. output impedance will happen at the point where one BJT is cut off and here the output impedance would be Re+25mV/2I_idle, which is about 1.5 times higher than at zero current. At higher currents the output impedance would decrease again asymthotically to the value which is observed at zero current.
Distorsion of capacitors:
One reason for distorsion is also mechanical movement of the plates / foils. The AC currents cause mechanical forces to the electrodes, which causes some small vibrations.
If the distance between the electrodes is changing, then also the capacitance is changing, resulting in distorsion.
A simple test for this is to apply a reasonable high AC voltage in the frequency range 500Hz...1000Hz and listen to the capacitor. The louder types may generate more distorsions from this mechanism.
I think this is mainly applicable for film/foil caps, because in ceramic or electrolytic caps the distorsions might be dominated by several other effects.
Distorsions in inductors are a mess except air wound coils.
As soon as iron, ferrite, metal powder, cool µ, etc. is used...
....I stop thinking about theory on distorsions and proceed to trial and error... of course an air gap can help.....
Bye
Markus
From a practical standpoint, Biasing a BJT to where the Q-point moves only very little along the AC load line will produce low distortion, especially in a diff. amp. Current source and current mirror circuits are nice
This keeps the output load Z linear and input current more linear with Hfe. wirewound resistors can have an inductive componant, but heat will cause white noise in resistors and other devices. Heat is a function of current, not voltage. I guess all those electrons slamming into the atoms of the resistive material creates noise. Using low current and less electrons, low noise devices will help reduce this noise.
Solid state devices add odd harmonic distortion to the signal, like it wants to create a square wave. A circuit can be built to generate these high frequency odd harmonics at 180 degrees so that they cancel out and signal is not distorted.
This keeps the output load Z linear and input current more linear with Hfe. wirewound resistors can have an inductive componant, but heat will cause white noise in resistors and other devices. Heat is a function of current, not voltage. I guess all those electrons slamming into the atoms of the resistive material creates noise. Using low current and less electrons, low noise devices will help reduce this noise. Solid state devices add odd harmonic distortion to the signal, like it wants to create a square wave. A circuit can be built to generate these high frequency odd harmonics at 180 degrees so that they cancel out and signal is not distorted.
Douglas Self research
Hi all, please do not miss this site:
Douglas Self Audio Amplifier Institute
Very good reading, from Douglas Self who is in my view a real engineer-designer, who doesn't resort to witchcraft & mystification, but to plain facts.
Regards, AudioGuy.
Hi all, please do not miss this site:
Douglas Self Audio Amplifier Institute
Very good reading, from Douglas Self who is in my view a real engineer-designer, who doesn't resort to witchcraft & mystification, but to plain facts.
Regards, AudioGuy.
If your goal is to get very low distortion without negative feedback, then your probably stuck with making a tube amp. Even this will not give you any power efficiency considering the tube. If you want to operate a transistor over a range, voltage vs current range, and without distortion noise this range is going to be very small to be without feedback or any correction circuitry.
It is very important for solid state.
Of corse if you used 400W of power to produce 10W of music, it may be possible.
It is very important for solid state.
Of corse if you used 400W of power to produce 10W of music, it may be possible.
Regarding the need for feedback...
But would the feedback need to be inter-stage? In other words if I used local feedback (partially unbypassed emitter resistors and/or collector-base feedback on common emitter stages) could I not improve the linearity of each stage without using multi stage FB?
But would the feedback need to be inter-stage? In other words if I used local feedback (partially unbypassed emitter resistors and/or collector-base feedback on common emitter stages) could I not improve the linearity of each stage without using multi stage FB?
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