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About Negative Feedback

FractalAudio

Administrator
Fractal Audio Systems
Moderator
In 1927 Harold Black invented the negative feedback amplifier. This was a pivotal discovery in electronics and solved a variety of problems in amplifiers. The major problems it addressed are:
- Linearity
- Bandwidth and frequency response
- Input Impedance
- Output Impedance

Conventional amplifiers of the time suffered from poor linearity: the output was distorted; poor bandwidth: the frequency response was limited; poor input impedance: the input impedance was too low (or too high depending upon the amplifier type); and poor output impedance: the output impedance was too high (or too low depending upon the amplifier type.

Negative feedback solved all these issues. It increased the linearity thereby reducing distortion. It increased the bandwidth and improved the input and output impedance.

The fundamental theory behind negative feedback is subtracting a percentage of the output from the input. This "error signal" is fed back to the input inverted (out of phase), hence the term negative (as in subtraction) feedback.

One of the concepts of negative feedback is "gain reduction". Negative feedback achieves its attributes by subtracting the error signal from the input which decreases the gain of the amplifier. The amount of gain reduction is given by 1/(1 + AB) where A is the open loop gain of the amp and B (beta) is the feedback amount, both in V/V (for voltage amplifiers). If the open loop gain is very high the gain of the amplifier is almost entirely specified by the feedback. Op-amps work on this principle. For example if the open-loop gain is 1,000,000 and the feedback is 10% (0.1) the closed-loop gain is 1M / (1 + 100K) ~= A/(AB) = 1/B = 10. Therefore the closed-loop gain is the inverse of the feedback amount. Tube power amps have far less gain than this so the calculations are more complicated. A typical tube power amp has an open-loop gain of around 30.

The amount of feedback determines how much each of the above attributes are improved. Nothing comes free though as negative feedback inherently lowers the gain of the amplifier.

Many guitar amps employ negative feedback although some do not. Examples that do include Fender, Marshall and Boogies. Examples that do not include Vox, Matchless and the modern modes of a Dual Rectifier. This feedback is known as "global negative feedback" and is employed in the power amp. There are no known guitar amps that employ global feedback in their preamps although individual triode stages often employ some negative feedback. Some guitar tube amps employ local negative feedback in the power amp as well in an effort to further linearize the power amp. This can be accomplished using an ultra-linear transformer (which effectively uses the screen grid as a negative feedback input) or by using feedback around each power tube.

Let's examine each of the attributes and the effect negative feedback has in relation to a guitar amp:

Linearity
The transfer function of a tube power amp is quite nonlinear. A typical power tube has a roughly x^(3/2) response which is quite a deviation from linear. By feeding back an error signal the input to the power amp is "pre-distorted" thereby making the transfer function more linear. This reduces harmonic distortion. This also reduces gain. The result is that the transfer function more closely follows a straight line. However eventually no amount of feedback can correct the nonlinear response when the amp hits its limits of operation, i.e. clipping. So the transfer function becomes more linear but transitions into clipping faster. An amp with no negative feedback will have some amount of distortion even at low signal levels. This distortion will increase as the amp is driven harder and eventually the amp will enter saturation (clipping) but this occurs relatively smoothly. As we increase the negative feedback the distortion at lower levels is reduced but the amp enters saturation more abruptly. This makes clipping more harsh sounding.

The Axe-Fx models this behavior exactly by actually employing a digital replica of the power amp complete with adjustable negative feedback. This is in contrast to other products which model the power amp as a waveshaper.

Frequency Response
The frequency response of a tube power amp is also quite nonlinear. The bandwidth is limited by the transformer and other components. The frequency response itself deviates significantly from a straight line due to the influence of the speaker impedance. A tube power amp has a very high output impedance. Therefore the frequency response follows the impedance of the speaker. This results in a peak at the low frequency resonance that can be 20 dB or more and a rising response due to the voice coil inductance that can be 10 dB or more at 10 kHz.

Negative feedback forces the frequency response towards an ideal, flat, infinite bandwidth response. The more negative feedback, the wider and flatter the response. However, guitar players like the nonlinear frequency response. The speaker impedance effectively "scoops" the response giving a warmer and more lively tone. This can be addictive but also can cause the tone to get lost in the mix as the midrange frequencies are attenuated.

Input/Output Impedance
Negative feedback also forces the input and output impedance towards ideal values. For a voltage amplifier this would be infinite input impedance and zero output impedance. The output impedance is intrinsically related to the flattening of the frequency response described above. For a guitar amp the increase in input impedance increases the effective load that the preamp sees and can result in wider frequency response out of the preamp.


The Damping Parameter
The Axe-Fx II allows the user to fine-tune the amount of negative feedback in the power amp via the Damping parameter. The term damping refers to the fact that increasing negative feedback lowers the output impedance and therefore "dampens" the response of the speaker. Power amps often specify their output impedance in terms of "Damping Factor" which is the ratio of the load impedance to the output impedance. The higher the damping factor the less the speaker impedance influences the frequency response.

Let's examine what happens as you adjust the Damping parameter.

As we increase the Damping we increase the negative feedback. This does several things:
1. LOWERS THE GAIN of the power amp. This causes the power amp to not distort as easily since the signal is amplified less and therefore it won't clip as easily.
2. Increases the linearity of the power amp. This reduces harmonic distortion but makes clipping "harder" as the transition to clipping is more abrupt.
3. Flattens the frequency response. This makes the frequency response more linear and widens the bandwidth. The peaks in the frequency response due to the speaker impedance are flattened and broadened.

As we decrease Damping we decrease the negative feedback which does:
1. Increases the gain of the power amp. The causes the power amp to clip more readily.
2. Decreases the linearity of the power amp. This increases harmonic distortion and softens the transition into clipping.
3. Increases frequency response distortion. The response becomes more scooped and the bandwidth is reduced.


Many guitar players like the sound of amps with no negative feedback. The Vox AC-30 is the classic example of an amp with no negative feedback. The power amp distortion is soft and the scooped response along with lots of harmonic distortion give a bell-like tone for high frequencies and warm low frequency response. The drawback to this is that the low end can get muddy as the low frequencies clip readily due to the frequency response distortion. These types of amps typically do not work well for high-gain tones although there are notable exceptions, i.e. the Dual Rectifier which uses a high-power power amp and bass reduction in the preamp to compensate for the increased bass response.

Fender and Marshall amps (and their derivatives) use varying amounts of negative feedback. The amount of feedback in Marshall amps was all over the map in the early years and seems as though the builders didn't really adhere to rigorous documentation and revision control. As such there can be quite a bit of variation in the sound of these early Marshalls.

So what is the correct amount? There is no definitive answer however there are some guidelines. For more vintage tones less Damping is typically desirable. This gives softer power amp breakup and more "baseline" distortion. For modern, high-gain tones more Damping may be desirable as these tones typically rely on preamp distortion and the power amp is desired to be neutral (which many players describe as "tight"). As stated before the Dual Rectifier in modern modes is a bit of an enigma. The power amp in this mode uses no negative feedback. You can hear this as an increase in volume when you flip the switch to Modern (remember that negative feedback reduces the gain so turning it off will increase the gain).

I have read some users recommending increasing the Damping to reduce the amount of power amp distortion in, for example, Fender models. I do not endorse this viewpoint. The distortion is primarily reduced because the gain is reduced but the power amp will sound more "sterile" due to the increased linearity and flatter frequency response. A better solution is to simply lower the Master Volume. This drives the power amp less while retaining the baseline harmonic distortion, softer transition into clipping and more scooped frequency response.

Modification of the error signal is commonly employed in guitar amps. This was first employed as the ubiquitous Presence control. The presence circuit reduces the amount of feedback at higher frequencies. Since the gain of the power amp is inversely proportional to the amount of feedback, reducing the amount of feedback over only a certain range of frequencies will therefore increase the gain of the amp at those frequencies. The presence control therefore boosts high frequencies. This concept was extended to low frequencies via the Depth or Resonance control. Basically these controls are bass and treble controls for the power amp but operate by reducing the feedback for those bands. On most amps setting these controls fully CCW will basically remove them from the circuit. Turning them CW will reduce the feedback in the prescribed bands thereby increasing the gain of these bands. An exception are Boogie (Mark series) power amps. The presence control in these amps is more complex and the flattest frequency response is achieved with the knob set to noon. Turning the knob CCW will reduce the treble response. Turning it CW will increase it.

Note that these all interact with the Damping control. To hear this reduce the Damping to a value just greater than zero. Note that the Presence and Depth controls will have almost no effect. This is logical since B (beta) is nearly zero and we can't reduce it further.
 

xpenno

Power User
Superb post, very interesting and informative read. I have a JVM that I added a selector switch that allows me to take -ve feedback from early plexi, though stock, EVH plexi, JCM800 and no -ve feedback. It's a very cool upgrade indeed. I tend to keep out of the advanced menus these days but I might have a play :)

Cheers

Spence
 

FractalAudio

Administrator
Fractal Audio Systems
Moderator
Superb post, very interesting and informative read. I have a JVM that I added a selector switch that allows me to take -ve feedback from early plexi, though stock, EVH plexi, JCM800 and no -ve feedback. It's a very cool upgrade indeed. I tend to keep out of the advanced menus these days but I might have a play :)

Cheers

Spence
That would be exactly analogous to the Damping parameter. I don't have precise numbers though. Also, I have no idea what "early Plexi" would be, LOL. I've seen Plexis with 47K from the 16-ohm tap (lots of feedback) and some with 100K from the 4-ohm tap (very little feedback). The models in the Axe-Fx are based on my actual Plexis. I have a 1972 50 watt and a 1968 100 watt. I also have a 1987x which is one of the re-issues but I don't consider that a "real" Plexi.

My JCM800 has 100K from the 4-ohm tap so the Damping is very low. That's partly the reason these amps are so loud. The low feedback gives the power amp more gain.
 

xpenno

Power User
That would be exactly analogous to the Damping parameter. I don't have precise numbers though. Also, I have no idea what "early Plexi" would be, LOL. I've seen Plexis with 47K from the 16-ohm tap (lots of feedback) and some with 100K from the 4-ohm tap (very little feedback). The models in the Axe-Fx are based on my actual Plexis. I have a 1972 50 watt and a 1968 100 watt. I also have a 1987x which is one of the re-issues but I don't consider that a "real" Plexi.

My JCM800 has 100K from the 4-ohm tap so the Damping is very low. That's partly the reason these amps are so loud. The low feedback gives the power amp more gain.
From your post it sounds like they vary by quite a long way. I have to say that I'm going from other people experience and not that of my own, they speak about pre 70's super leads as have 47k resistors which gives them the warmer sound, as they head into the 70's they seemed to increase to around 74k, the JVM has an 80k resistor the EVA plexi reportedly has a 137k and the JCM800 around 176k. As I say, that info has come from others and is not my own findings, either way it's a fun parameter to play with as it affects the tone and response of the amp greatly.
 

pima1234

Fractal Fanatic
I've read a lot about tube amps (and am glad to be done with them, honestly), but I continue to learn more thanks to Cliff's posts in this section.
 

Fabio KTG

Fractal Fanatic
Whenever I read one of Clif's posts, I now quickly scan it for incomprehensible words. If I read more than 2 in a sentence, I know my brain will turn to mush, so I just nod, agree and pretend that I have an ounce of understanding.

Which I don't.
 

Stratoblaster

Fractal Fanatic
Thanks for the interesting read. One of the things I like about the Damping/negative feedback advanced controls is how you can really fine tune the onset of distortion and how fast/hard the power amp transitions into clipping, especially since most of the amps/tones I use have high MV settings. Along with other advanced parameters (Transformer Match, etc.) there are many options for tailoring the power amp distortion characteristics. Great to have so many options.
 

dkenin

Inspired
Perfectly written! I've scoured the internet for a definition of negative feedback with regard to the amp sound, but always just got mathematical equations. Thank you so much for shedding light on this. I can't wait to play with the control instead of shooting in the dark with this parameter.
 

VegaBaby

Fractal Fanatic
super interesting read.

I believe some of the Suhr amps have variable Negative Feedback installed in the back of the amp for adjustment. very easy to get a more "brown" sound with lower settings of -ve Feedback and slighltly cleaner and more modern with higher settings of -ve Feedback.
 

Marky

Inspired
Awesome post Cliff. Love reading things like this. Good to have insights to how real tube amps work and to then understand all the controls that we have at our disposal in the Axe-Fx.
 
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