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NEGATIVE FEEDBACK

    Negative feedback, or as I believe it should be called, inverse feedback, is a hotly debated issue. There are those who understand the principles and are for it, and those that understand the principles and are against it. There are those that don't fully understand the principles and due to a well meaning imagination (myself included in the imagination department) overemphasize in their minds what is actually happening in the circuit employing inverse feedback.

    We will discuss here what inverse feedback is and the benefits and new problems it causes and how we can overcome them.

WHAT IS INVERSE FEEDBACK?

    Simply put, it is the addition of the input signal with a slightly smaller amount from the output. What I mean by this is that if the input signal is 1, then the inverted signal from the output is reduced to about 0.9 before it is added to the input signal. In essence the amplifier still amplifies by the same amount, but now the input signal is reduced by a factor determined by the feedback network.

    The feedback network is, in its simplest form, a resistor from the output connected to a junction of a resistor and an active input component (the cathode or grid of a tube, the emitter or base of a transistor, the source or gate of a FET). The resulting combination makes a voltage divider that lowers the inverted output signal level before adding it to the input signal.

WHAT ARE THE BENEFITS?

    The result of feeding a signal from the output of the amplifier to the input is a reduced singal that also includes the distortion that the amplifer makes, but inverted. The resultant output then becomes a smaller signal than what would have been without inverted feedback but with the distortion greatly reduced. This is one of the benefits of inverted feedback. The shape of the signal out before inverted feedback can be analyzed as having  harmonic distortion. So harmonic distortion is reduced.

    Another benefit of inverted feedback is a consistent amplification along the frequency bandwidth. In its open loop form, or without inverted feedback, the frequency response curve could resemble the Appalachian mountains. While this would be a bad design, the use of inverted feedback would make the frequency dependent curve flat. It is like taking a paper silhouette of the mountains and with a scissors cut along the horizon below the lowest point. What results is a low level plateau. This has the effect of maintaining a constant frequency/ampltude relationship and increasing the effective response range.

    So instead of having an amplifer with a frequency response curve of 50-10,000 hertz +/- 4 dB variation at the -3 Db points of roll off, we have an amplifier with a response of 10-30,000 hertz +/- 0.5 dB variation between the -3dB roll off. The latter is much more desirable.

    There is another problem that occurs in an amplifier that is known as intermodulation, or IM distortion. This is where two signals of different frequencies combine to make a third and fourth signal, called sum and difference signals. If I put a signal of 1 kilohertz and 3 kilohertz into my amplifier, they can combine to make four and two kilohertz signals. This is the result of adding and subtracting the two frequencies (this is also known as heterodyining). Inverted feedback reduces the amplitude of these unwanted signals to insignificance because, like the other distortions, it is now added to the original signal which didn't have them to begin with, but inverted.

    In a push pull amplifier, inverse feedback also helps to reduce or virtually eliminate crossover distortion.

WHAT ARE THE DRAWBACKS?

    This is where the debates come in. Before we get involved in where I stand on the issue, we will discuss them.

    The first one is what is called transient intermodulation, or TIM distortion. This is the result of the inverted feedback signal being delayed by the passing of the original signal through the amplifier. Every amplifier delays the signal somewhat. In tube amplifiers this could be due to two things, capacitors and transformers. These devices have a tendency to shift the phase of the signal resulting in significant delay. The tubes themselves introduce delay but at a much lower rate. The delay from them is most noticeable way beyond the audio spectrum.

    What happens is the output signal could be delayed (worst case scenario) up to as much as 130 degrees or more. This can translate into up to a few milliseconds. When a signal is introduced into the amplifier, the amplification is at full open loop gain for those few milliseconds (again, worst case scenario). So the signal produces a spike. This is the transient intermodulated signal. Transient because it only occurs at the first instance of a signal, thereafter not existing for the duration of that signal. The problem with this is that an audible hashiness could be heard when the signal is pulsed, like the hitting of a tympany or kick drum (these examples are used because of their fast attack times).

    In the case of TIM distortion, the two ways of eliminating it are not to use inverted feedback, or make an amplifier that is faster. In other words an amplifier that has what is known as a high slew rate.

    Slew rate is the rate that voltage changes over time. The output voltage to be exact. For instance, a slew rate of 10 volts per millisecond is alot slower than 10 volts per microsecond. This can be demonstrated by injecting a perfect square wave into an amplifier. If the amp has a slow slew rate, instead of the on edge going straight up it will appear sloped. A higher slew rate will produce a straighter up slope. It is this slope that makes the TIM. So the amp with a slew rate of 10 volts per microsecond may still have TIM, but it will be so small in amplitude and so small in duration (tantamount to high in frequency) that all that is needed is a small value capacitor in the output  to filter it out. Chances are your speaker's crossover network has enough capacitance to do the job. Heck, the wire may have sufficient capacitance to filter it out.

    Another factor involved in this TIM issue is what we call in digital technology propagation delay. But this can easily be minimized by using fewer components, as many purists (present company included) are fond of. That is one reason why tube amps are so appealing.

    The propagation delay brings to mind another possibly imagined problem. When a signal is fed the inverted signal from the output, that inverted signal is also "amplified" through the amplifier,therefore having another chance to be fed back. One could imagine this to occur indefinitely, causing a blending of the signal, making it sound blurred or smeared. Admittedly I had thought the same thing for a long time. I had to then seriously rethink the issue.

    For one thing, the inverted feedback is, while reducing the original signal by a factor determined by the network, also reducing itself to a very great degree. To put it mathematically, if the distortion is 10% of the output signal and the output signal is 10 volts, then the distortion is 1 volt. If the input signal is 1 volt, then the gain is abviously 10 (actually it is a bit more. I think the formula stipulates a +1, for an actual gain of about 11. this is why I say the inverted signal is about 0.9 volts). The feedback network is reducing the ouput by about a factor of ten. So, the inverted feedback is getting a signal of close to probably about 0.9 volt  including the 1/10th of the distortion that is only 10% of the output, or 0.09 volts. This will then reduce greatly the distortion at the output.

    So let's say that the output now has the inverted feedback with it. Because the amp makes the positive form of it, it is significantly reduced. Let's say that the amp with inverted feedback is now claiming a ditortion rating of 0.5% When the output is fed back this time, the inverted feedback that was already there is now further reduced. Let's do the simple math. The output is now 0.5% of the total output (a relatively bad rating). With an output of 10 volts, the portion of it that was the inverted feedback is now 0.05 volts. Fed back it is further reduced to 0.005 volts. This is virtual oblivion and most certainly inaudible.

    So if this endless feedback is occuring, it is doing so at such a low level, several levels of magnitude lower, so as to be totally insignificant, therefore no more damaging to the sound quality as noise is.

    The other fact here is that the output must follow the input. By the time the first iteration of inverted feedback gets to the output, the signal has changed such that its significance no longer exists. So it essentially dissapears. This is my humble opinion.

USING INVERTED FEEDBACK

    The use of inverted feedback is 1) a personal decision and 2) a tricky one. When I first tried inverted feeedback it was on my solid state tube amplifier. I did not like the effect that it had on bass at the time. It made the bass sound blended as was mentioned above. It got deeper to be sure, but I was looking for that triode with no NFB sound and that is what I got without NFB. It wasn't until about two years ago when I had my amp professionally FFT analyzed that I revisited the possible use of NFB. The amp had a 4% THD rating. I then experimented with different positions of the NFB loop. There were four different ways to accomplish this. One of them sounded great. The others reduced the effect of tubelike sound I had desired. It turns out that the gentleman who tested my amp, being a tube amp engineer himself, also came to the conclusion that placement of the NFB loop is critical and requires experiment and listening. My amp was reduced to about 0.2% distortion and still sounded great.

    There are several ways to employ inverse feedback. Actually, I think I can only recall two. Globally and locally. What this means is that I can have feedback at each stage of the circuit or from the output of the entire circuit back to the beginning. If memory serves, the inventor of inverse feedback proposed local feedback, where three circuits with a gain of 10 that each had NFB would have greater linearity and stability than two circuits with the same total gain without NFB.

    The benefit of using local NFB is the virtual elimination of TIM. Also, each stage can be tailored to give precise gain. Therefore the entire circuit can have the gain desired as designed. Each stage will have a very low level of distortion. The total result might be as good as the final result of global feedback, if not better. Some may say that that is not true because the next stage will multiply the previous stage's distortion product however minimal by the factor of the stage.

    Let's examine that one mathematically. If the distortion product of stage 1 is 0.2% of the output, and the output is amplified 10 times, then does it really mean that the 0.2% now becomes 2.0%? Absolutely NOT. The proportion of distortion to signal remains the same. If the input signal is 1 volt then the distortion will be .002 volts. After amplification the distortion will be 0.02 volts. But the signal will be 10 volts. It is still 0.2%. So an amplified signal of 0.2% distortion, assuming no further distortion, will merely be a larger signal with 0.2% distortion!

    One could in essence make several stages with local NFB and then use one global NFB loop to further reduce distortion. Or one could leave out that loop and have a decent sounding amp with no more than 0.5% distortion (from a preamp). This is not a shabby response, considering that many very high tech recording studio tube amps have this rating.

ALTERNATIVE DISTORTION REDUCTION DESIGN TECHNIQUES

    There are alternatives to NFB for the reduction of harmonic distortion. Simply put, the trick is to minimize the nonlinearities. This can be painstaking because for one thing one needs to know precisely where to bias the tubes to get the most linear region involved. Then set up the tubes circuitry to use each stage's curves to in effect cancel out the previous stage's curves. One example of this is to use a direct coupled cathode follower. Steve Bench has demonstrated this on his site where he measured the performance of the various types of circuit topologies. I use the cathode follower version myself on my single ended tube amp  circuit. The sound is not quite what the prototype was with a single triode (not as bottom end "warm"). It is brighter sounding than the single triode circuit. But it is far more revealing and clean. I do not regret the decision to use it. Steve measured about .05% distortion at about a 10 volt output signal level. He makes the statement that because the cathode follower's curves are inverted, they in effect cancel the non-inverted curves of the first stage. This is a form of inverse feedback that has no phase or propogation delay, eliminating any TIM distortion. In the amp the output stage is a single 6L6, so I employ NFB to reduce the distortion products that it and the transformer introduce.

    Another circuit that is used is the ltp (long tailed pair) phase splitter better known these days as a differential amplifier. This reduces, virtually eliminates, even order distortion. Most tube afficionados claim that this is not a good thing. I tend to agree. I believe that a proportion of the harmonic products needs to be maintained, even if the distortion products are reduced to nil, in order to maintain that natural sound that tubes can bring.

    Another method is to reduce the number of components along the signal path. I design my tube amps with no cathode bypass. I believe that it is this cap that is responsible for some forms of IM distortion and the so-called tube squishing everyone believes in. So viewing the circuit you will see no bypass caps. Some may say that this increases the impedance to the output, but NFB is supposedly there to decrease output impedance anyway so...

    Some engineers actually use solid state components to maintain bias on the tubes. These components become what are known as constant current sources. But, in my opinion this reduces or circumvents the whole reason we love the sound of the triode to begin with. If we have a constant current, then what we have is a response curve like that of the pentode anyway. If we notice, the pentode's plate current goes up quickly, then sharply goes to the right, maintaining the same (or within a few tenths of a milliamp) current from some low voltage all the way up to B+. So why bother. Hence why I used the circuit I did.

    These are but a few non inverse feedback methods.

CONCLUSION

    My conclusion to the issue of inverted feedback is that if you wish to use it, find the best location that sounds good to you. My personal rule of thumb is that if the source is a low impedance then the point of the input should also be a low impedance. And inversely (no pun intended) if the source is a high impedance the point of inverse feedback should be a high impedance.

    For example, the feedback taken from the output transformer secondary should be fed to the cathode of the voltage amplifier tube (unless a differential amplifier is used as the first stage and not a splitter. In this case there is no choice). If it is taken from the plate of a tube it should go to the grid of the input tube. This should give the best sound. The key here is experiment and listen.
 

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