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Nelson Pass 10/10/09
Every audiophile understands the concept of the =E2=80=9Csweet = spot=E2=80=9D, that happy=20 balance of conditions that elicits the best possible sound. It can be a=20 particular listening spot, the best positioning of loudspeakers, or the=20 fortuitous combination of components which complement each other = perfectly. It=20 should be no surprise that the desire for the best performance takes the = search=20 for the sweet spot into the interiors of the components themselves.
This article will concern itself with finding the sweet spot for = each gain=20 device in audio amplifiers. It is a commonly held belief in audio that = the best=20 amplifiers are composed of one or more active gain stages, each made as=20 intrinsically linear as possible before negative feedback is applied to = further=20 improve performance.
Taken to the extreme, linear stage =3D good / negative feedback =3D = bad. The=20 latter half of that statement is the subject of controversy, but there = is no=20 argument about linear stages being good. Achieving intrinsically = low=20 distortion in active devices (tubes or transistors) is usually not easy. = We can=20 use good parts, see to it that they have adequate voltage and current = available,=20 and use them in topologies that play to their strengths. These are the = basics,=20 and this is what you generally see when you examine schematics of = popular=20 amplifiers.
However each individual device has a sweet spot where its = performance is the=20 best, often dramatically better, and finding that sweet spot is a = powerful=20 technique for maximizing the performance. I am writing about this = because=20 over the years of communicating with DIYers and many professionals I = have=20 discovered that this is a poorly understood concept, and I have seen = many=20 circuits which have failed to take advantage of it.
For every gain device, there is a number which characterizes the = amount of=20 gain. When we talk about distortion we are talking about the alteration = of the=20 amount of gain in the device as the conditions change. The gain of a = tube or=20 transistor is altered primarily by changes in voltage across the device, = current=20 through the device and the temperature of the device. Changes in any of = these=20 conditions changes the gain, and all gain changes make the distortion. = More=20 precisely, they are the distortion.
Of course the concept of a sweet spot depends on having an idea what = of what=20 constitutes the best performance. It could be that you want the lowest = measured=20 distortion, a particular mix or phase of harmonics in the distortion = waveform,=20 the greatest efficiency, greatest power or simply the best subjective = experience=20 when you listen to it. The sweet spot is whatever you want =E2=80=93 = after all, you are=20 the designer.
I Brake For Tutorials
If you don=E2=80=99t mind a little basics, =
let=E2=80=99s look at=20
examples of gain devices in generic circuits, starting with a =
triode:
This illustration shows simplified examples of the two most common = of gain=20 stages using any kind of gain device, and the device pins are the Grid, = Cathode,=20 and Plate. In both cases the input signal appears at the Grid and = variation of=20 voltage between the Grid and Cathode causes a change in the current flow = from=20 the Plate to the Cathode. (All the examples you will see are simplified, = and=20 omit DC bias that may be present on the pins except for the V+ = supply).
In Common-Cathode mode, the tube develops both current and voltage = gain, and=20 the output is taken off the plate, inverted in phase and usually = increased in=20 amplitude.
In Common-Plate mode, the tube seeks merely to have the Cathode = voltage=20 follow the Grid voltage, so the output voltage is ideally the same as = the input,=20 but with some current gain. That is why it=E2=80=99s called a = follower.
For both modes we would normally look for the sweet spot, the = conditions=20 giving the best performance, by varying the values of the supply V+, the = value=20 of the load resistance, and the bias current through the device. = Inevitably=20 there will be some combination of these which is the best. Sometimes one = of the=20 circuit conditions is fixed =E2=80=93 often it is the load value, in = which case we vary=20 the other conditions =E2=80=93 the supply voltage and the bias.
In all of the examples we will look at later, I have chosen to = simply look=20 at Common-Plate (or Common-Drain / Common-Collector) performance, but = the same=20 ideas apply to Common-Cathode (or Source or Emitter) operation.
Actually, Common-Drain circuits would seem to offer the least =
opportunity=20
for improvement - as followers enjoying 100% degenerative feedback, they =
already=20
have a much lower distortion character than Common-Drain circuits. But =
we will=20
see that even they can be improved, often dramatically, if you find the =
sweet=20
spot.
Here=E2=80=99s the example of the JFET counterparts to the =
tube circuits seen=20
above:
Here the pins are Gate, Source, and Drain. In the Common-Drain = follower, the=20 input voltage pretty much follows the output voltage, and in the = Common-Source=20 amplifier, the output is inverted and has both voltage and current gain=20 available.
Here=E2=80=99s the MOSFET example, and it has the same pin =
designations as the=20
JFET.
And last,
And last, here is the example of a bipolar transistor, where the = pins are=20 Base, Emitter and Collector:
The choice of a particular type of gain device - tube or transistor = - is=20 often arbitrary, but ideally it plays to the particular strength of the = device=20 for a given application. In principle you can substitute one type for = another,=20 but as a practical matter, there is usually a good reason for the = selection of=20 one over the others.
It=E2=80=99s doesn=E2=80=99t matter in terms of the idea of finding = the sweet spot =E2=80=93 the=20 terrain changes at bit, but the game remains the same.
{pagebreak}
For any of the above circuit types and devices, if you start with = reasonable=20 textbook values for the circuit, you will get reasonable performance. If = you=20 start to play with the values a little bit, you will find that the = performance=20 changes for better or worse. Often you will find a combination of = voltage and=20 resistor values which give a lot better than the generic performance. = That=E2=80=99s the=20 sweet spot.
If you have a distortion analyzer, you could simply run through the = range of=20 combination of values and select the result you like best. If you simply = want=20 good measurements, you might be able to stop there. If you are looking = for=20 better subjective performance, you might find this a good place to start = your=20 listening.
What creates the existence of the sweet spot in gain devices? To see = where=20 this comes from, we will look at the characteristics of some tubes and=20 transistors.
Let=E2=80=99s start with a simple big triode, the 300B. This curve = shows the Plate=20 to Cathode current as a function of Grid voltage, with each curve = representing a=20 fixed value of plate voltage.
Looking at this curve, we see that the lines are curved =E2=80=93 = the more current,=20 the faster they rise. Below is a different view of the same character, = but with=20 the current plotted as a function of the Plate voltage with each line=20 representing a fixed value for Grid voltage.
These lines are also curved with a shape very similar to the =
previous=20
graph.
A perfectly linear tube will have these lines in both graphs=20
perfectly straight and equally spaced. Any deviation from that would be=20
distortion. Looking at the curved lines, we can see that there is quite =
a bit of=20
distortion.
For a given Plate voltage, the current increases exponentially with = the Grid=20 voltage, in what is known as a square law characteristic, resulting in = second=20 harmonic distortion. For a given Grid voltage, the current increases=20 exponentially with the Plate voltage, also a square law and also = creating second=20 harmonic distortion.
In this curve the Y axis is still the plate current, but the X axis = is now=20 the Plate voltage, and each line represents the Grid voltage. It looks = familiar=20 =E2=80=93 just as the plate current is an exponential function of Plate = voltage, it is=20 also an exponential function of the Grid voltage. This is a particularly = important observation with respect to finding the sweet spot.
{pagebreak}
Ordinarily in a tube amplifying an AC signal, a positive change in = Grid=20 voltage causes an increase in Plate current and is accompanied by a = decrease in=20 Plate voltage. The gain due to Plate current increases, and the gain due = to=20 Plate voltage decreases. The opposite happens when the Grid voltage goes = negative.
These two gain variations tend to cancel each other, resulting in = more=20 constant gain and lower distortion. If you choose your conditions so = that the=20 simultaneous gain increases and decreases are equal, you can lower the=20 distortion a lot.
This technique is often referred to as load-line cancellation. It is = called=20 that because the range of the device=E2=80=99s operation sits on a line = in the transfer=20 curve, and the particular shape and position of that line results in = minimum=20 distortion.
By some criteria, this would be the sweet spot. At this point you = will=20 probably find that your second harmonic has largely disappeared and you = are left=20 with some third harmonic. This is because you can=E2=80=99t completely = cancel two square=20 law distortions without leaving a cubic trace =E2=80=93 the third = harmonic.
So how much distortion reduction are we talking about? On a clear =
day, we=20
can think in terms of a 90% reduction, as seen in the following curve, =
where a=20
triode follower is operated at a high plate voltage giving the upper =
blue=20
distortion curve. Without changing the load or the current, I simply =
reduced the=20
Plate voltage until
the gain dependence on Plate voltage matched the =
gain=20
dependence on Plate current (as determined by lowest distortion at 1 =
volt) and=20
ran the red curve.
I think we can agree that this is a significant reduction, roughly=20 equivalent to what we would see with 20 dB of negative feedback, except = that we=20 have not attached a negative feedback loop and the output gain and = impedance of=20 the circuit remain about the same.
Because of the square law characteristics of the devices, the = primary=20 distortion is second harmonic in content, and when we cancel two second=20 harmonics we find that the remainder is a third harmonic. The original = second=20 harmonic looks like this on an oscilloscope viewing the output of a = distortion=20 analyzer:
After cancellation, the harmonic content looks like this:
If your criteria instead is a particular harmonic content and/or = harmonic=20 phase, a deviation from this point in either direction will give you = second=20 harmonic back with its phase depending on which way you went, and you = can tweak=20 this in relation to the amplitude of the third harmonic if you like.
There is a reason why triodes are popular in single-ended = applications =E2=80=93=20 their gain dependence on Plate voltage is quite strong and makes for = easy=20 load-line cancellation.
Load line cancellation is available in the other types of gain = devices,=20 including pentodes, JFETs, MOSFETs and bipolar transistors, but they = take more=20 subtle advantage of load-line cancellation. In many cases it is easier = to find=20 the sweet spot with push-pull operation. We will see real world examples = of both=20 single-ended and push-pull later, but first we will consider the = characteristics=20 of the other devices.
This technique also applies to pentode tubes, although it will not = be quite=20 the same. The transfer curve of the pentode is much the same with regard = to grid=20 voltage, but the current variation due to Plate voltage is different. = Here is=20 the transfer curve of a pentode:
Here we see a family of curves which indicate that the gain=20 (transconductance) increases exponentially with Plate current, but has = less=20 variation with respect to Plate voltage as compared to the Triode. You = can still=20 vary the voltage, current and load parameters to find the sweet spot, = but it=20 will be in a different place.
JFETs have the exponential current vs Gate voltage but enjoy a wider = variety=20 of transfer characters situated between triode and pentode and are = generally=20 well suited to exploit the concept of a sweet spot in single-ended Class = A=20 circuits.
JFETs come in both enhancement mode and depletion mode, the primary=20 difference being the DC voltage required on the Gate to turn them on. = Depending=20 on the dimensions of the Gate structure on the chip can exhibit pentode = or=20 triode characteristics, or an in-between =E2=80=9Cmixed = mode=E2=80=9D.
Following is the curve of an enhancement mode power JFET:
And here is the curve of a depletion mode power JFET:
You will note that these aren=E2=80=99t the tiny little signal JFETs = that everyone=20 is accustomed to. These are examples of the new generation of high power = JFETs=20 coming out of the labs. In the 1970=E2=80=99s when Yamaha and Sony = produced power JFET=20 devices for use in their own amplifiers it created some excitement among = audiophiles. Unfortunately it seems that they were ahead of their time, = and now=20 those parts are quite rare.
Fortunately totally new devices show promise in modern power = amplifiers both=20 as switches and linear amplifying parts =E2=80=93 tomorrow=E2=80=99s = transistors (at tomorrow=E2=80=99s=20 prices).
For power JFETs the Ids dependence on Vds is partly a function of = the Gate=20 channel depth on the chip. The pentode-like character is seen in high = current=20 power =E2=80=9CVertical=E2=80=9D JFETs and the triode-like character is = seen in SITs, (Static=20 Induction Transistor).
The enhancement mode power JFETs do well in single-ended Class A=20 applications and can take advantage of load-line cancellation, and my = samples of=20 depletion mode JFETs have a more pronounced voltage dependence, and are = thus=20 even more interesting.
Here is an example of a JFET follower whose characteristic is mostly = =E2=80=9Cpentode-like=E2=80=9D. The upper curve reflects the distortion = at V+ voltage near the=20 device rating, and the lower curve shows the distortion cancellation = available=20 by searching for the =E2=80=9Csweet spot=E2=80=9D at a lower supply = voltage. You can see that at=20 1 volt, the distortion has been reduced by about 85%.
Alternatively we could have adjusted the bias current or the load=20 resistance, and we also could have tried for best performance at some = higher=20 voltage that 1 volt.
This example was of one of those =E2=80=9Clittle=E2=80=9D JFET = devices, but it works with=20 parts of all sizes. The thing to remember is that this cancellation is = there=20 somewhere, and you might want to go looking for it. Also keep in mind = that the=20 sweet spot is a bit different for every part, even within the same part = types,=20 and you will want to consider expending the effort for each individual = part if=20 you want the absolute in performance.
This is important when you change out tubes in an amplifier, as = every=20 tube-o-phile knows they are all different. Setting them to a generic = bias=20 current does not guarantee the sweet spot for a given tube. You might = want to=20 consider how you can vary the supply voltage and the bias while = evaluating the=20 performance.
Below is an example of a power MOSFET=E2=80=99s transfer curve:
Power MOSFETs have a character somewhat similar to a pentode. The = Plate has=20 been replaced by the Drain, the Grid has become the Gate, and the = Cathode is now=20 the Source. We see from this diagram that the gain increases with Ids = but there=20 is not a lot of dependence on Vds above a few volts. At just a of couple = volts=20 we operate in what is known as the =E2=80=9Clinear=E2=80=9D region of = the MOSFET, where there is=20 strong dependence. You can work the load-line in this region = effectively, but it=20 is not a popular technique for a number of good practical reasons. = Fortunately,=20 for many MOSFETs operating in Class A, the distortion of the current = transfer=20 curve is low enough that you can still find the cancellation for a = pentode type=20 voltage characteristic =E2=80=93 just go looking for it.
And of course, someone is going to ask, =E2=80=9CWhat about bipolar = transistors?=E2=80=9D It=20 so happens that bipolars have a sweet spot also. Here is an example of = the=20 current gain figure of an ordinary NPN transistor vs Collector = current.
There is also a dependence on Vce known as the Early effect, a = slightly=20 straight line dependency increasing with voltage. As with other devices, = finding=20 the sweet spot for a bipolar device means locating the point where these = variations result in distortion cancellation.
Here we see the gain vs current curve of an NPN power transistor = showing=20 some gain dependence vs Collector current. Above a couple of volts, the=20 variation is much less and forms a fairly linear straight line with = voltage.
Of course you can work these two curves. The following distortion =
curve=20
shows
a follower circuit like the others, but with a bipolar =
transistor. The=20
blue line is with a high supply voltage, and the red is the reduced =
voltage. The=20
reduction in distortion is less dramatic, but it=E2=80=99s still about 7 =
or 8 dB=20
better:
{pagebreak}
Of course, single-ended Class A is not the only way to operate gain = devices.=20 Large reductions in distortion can be had by operating gain devices in=20 push-pull, where two similar devices operate in balanced opposition such = that=20 their second harmonic characteristic is naturally cancelled. Below on = the left,=20 you see a pair of JFET followers operated push-pull:
So where=E2=80=99s the sweet spot for this sort of circuit? = It=E2=80=99s there if you go=20 looking for it. The following sets of curves show three techniques for = getting a=20 pair of these devices into the sweet spot.
First off you can take the =E2=80=9Cregular=E2=80=9D follower shown = above and simply vary=20 the supply voltages a bit. The curve below shows distortion for two = examples,=20 the upper blue curve being with two equal supply voltage values. The = lower red=20 curve shows what can happen if you vary only one of the supply = voltages:
Here=E2=80=99s a technique we use at Pass Labs =E2=80=93 the use of = some single-ended bias=20 in a push-pull output stage to reduce distortion. The distortion curve = below=20 shows what you can get if you simply put a small value current source in = parallel with one of the JFETs as shown on the middle circuit. The = current=20 source displaces the bias current values on the JFETs until they achieve = a more=20 perfect distortion cancellation:
There is yet another way, shown by the circuit on the right in the = diagram,=20 which involves the use of a trim potentiometer instead of the Source = resistors=20 of the =E2=80=9Cregular=E2=80=9D circuit.
Here we see that a simple adjustment of the pot can drop the = distortion by=20 90% without having significant effect on the other aspects of = performance.
{pagebreak}
There is one last important variable affecting performance and the = location=20 of the sweet spot =E2=80=93 temperature. All of these gain devices have = transfer curves=20 which are some function of the temperature of the device. All those = transfer=20 curves I have shown you will be different if you vary the = temperature.
Conceivably you could adjust for the sweet spot by varying the = temperature.=20 More practically, you will want to see to it that our circuits have = reached=20 their ordinary operating temperature before adjusting for the last bit = of=20 performance.
{pagebreak}
So what do you do if it=E2=80=99s impractical to find the optimal = load-line in a=20 given circuit? Occasionally the sweet spot occurs at voltage values that = are=20 impractically low, or at currents that are higher than a device can = handle for a=20 given voltage. Here are three things that a designer can do to get into = the=20 zone.
The first is cascoding, where the gain device is coupled with a = Common-Gate=20 / Common-Grid / Common-Base (depending on the type of device!) tube or=20 transistor which adds practically no influence of its own but which = allows a=20 more arbitrary DC and AC voltage across the gain device. Here are a = couple of=20 examples, using JFETs in both Common-Drain and Common-Source = circuits.
The top JFET is the cascode device, and its Source voltage, which = will be=20 seen by the Drain of the JFET below it, is set by Vref. The idea is that = the=20 cascoding device provides a =E2=80=9Cvoltage umbrella=E2=80=9D for the = gain JFET, and all manner=20 of voltages can appear at the output of the circuit while the gain = device sees=20 all, a portion, or none of it.
It=E2=80=99s pretty easy to get into the sweet spot using a cascode, = and if you want=20 to explore this in some more detail, I recommend Zen Variations 9, which = you can=20 download from www.passlabs.com. There we explore getting the lowest = possible=20 distortion from an amplifier using a single stage with a power JFET = having a=20 high current rating, but a low voltage and dissipation rating.
Another thing you can do to get into the zone of the sweet spot is = to=20 parallel devices. There are times when the load is too low (and you = can=E2=80=99t change=20 it) or the voltage is too high, but often you can mitigate this = situation by=20 operating devices in parallel. This way you can limit the dissipation of = each=20 device, and the load appears as a multiple of the number of devices.
A third thing you can do is to use a transformer, which can allow = you a=20 flexible range of voltages and currents through the device while = delivering the=20 appropriate values to the load. Tube amplifiers do it all the time, and = it gives=20 the extra flexibility that then allows you adjust for the sweet = spot.
{pagebreak}
All the loads we have examined are resistors. Many times that is all = we need=20 to work with anyway, but when it comes to loudspeaker drivers and = passive=20 crossovers we have to contend with loads which are also reactive and = which vary=20 in impedance. This can be a problem when the load-line that gives best=20 performance depends on resistance. A reactive load will take it out of = the sweet=20 spot.
This is particularly true for tube amplifiers operating single-ended = Class A=20 without feedback =E2=80=93 much of the performance depends on triode = load-line=20 cancellation. These amplifiers are particularly appreciative of = resistive loads,=20 and if you have this situation, it=E2=80=99s worth considering ways to = flatten the load=20 impedance, giving a more resistive load for the amplifier.
There is another solution to this problem if you employ cascoding. = Referring=20 again to Zen Variations 9, we see there is a technique, which I have = dubbed=20 =E2=80=9CCascode Modulation=E2=80=9D, in which the gain device can be = made to see controlled=20 load-line voltage variations which are only a function of the output = current,=20 and not related to the output voltage. In this way, the sweet spot is = preserved=20 into any load reactance or impedance, and it is very easily dialed in by = adjusting a couple of resistor values. In the example of ZV9, we get a = 90%=20 improvement in distortion by simply attaching the cascode=E2=80=99s = voltage to a=20 different spot, without changing any values or any other = characteristics.
{pagebreak}
So there we have it. As an audiophile you want the best performance, = and you=20 probably aren=E2=80=99t above spending money and trying tweaks of = various sorts to help=20 you get it. But there are real improvements that can be had without = extra=20 accessories or emptying your wallet.
Amplifying circuitry can be made better without more complexity and = without=20 more feedback. The best part of this for do-it-yourselfers is that these = are=20 things that can be done on your own bench, costing mostly just the time = it takes=20 to tweak the circuit and evaluate the results. Moreover, this approach = is not=20 seen on the factory floor =E2=80=93 for most manufacturers it=E2=80=99s = simply too time=20 consuming to do, and the rest probably never heard of it.
So here=E2=80=99s your chance to make simple high quality audio = amplifiers better=20 than ever. Buy yourself a cheap used distortion analyzer and go for = it.
Copyright 2009 Nelson Pass
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