DESIGNING A REALLY GOOD 300B POWER STAGE

Andre Jute

To design your own amplifier from scratch or seriously to modify a design by someone else you have already built or bought, you need a few methods and a little mathematics. The techniques are not onerous--working in the flesh with high voltages should be far more frightening--and the math to design a resistor-capacitor coupled or transformer coupled amplifier is also pretty simple once you discover a few shortcuts, which I shall shortly demonstrate for you. There are of course esoteric complications with which the truly knowledgeable may, if meanspirited, humiliate the aspirant. But as long as you stay within the widely accepted margins of good design, you can ignore many of them.

 

If you intend to take up amp design as the consuming hobby of the rest of your life, the one indispensible book is Langford-Smith's The Radiotron Designer's Handbook, 4th edition, which runs to 1500 pages and can get pretty heavy but does not overlook any of the minutae.

 

The method of tube amp design offered in this chapter will, I hope, be more accessible to the modern amateur designer and DIYer.

 

This chapter and the next two offer the minimum amount of information required to design your own complete resistance-capacitance (RC) coupled SE amplifier from scratch.

 

Design procedure

A tube amplifier consists of a signal chain and a power supply chain which act as one unit to amplify a signal of a few millivolts to such a level that the output transformer can convert the resulting much larger voltage into enough current to drive a loudspeaker satisfactorily. How this amplification function is performed is called the "transfer function" of the amplifier and is evaluated in frequency and power bandwidth, in flatness of response, and of course in decibels of gain.

 

The amplifier is designed backwards from the interface of the output transformer with the loudspeaker and, unless you can afford custom transformers, is designed around output transformers, mains transformers and chokes (collectively the "the transformers" or "the iron") known to be available.

 

Describing the power supply of a hi-fidelity amplifier as part of its transfer function means precisely what it says: everything is connected; that also applies to every single other part. Since all parts of the amp interact with all other parts of the amp, the design may have to be done iteratively by cut and fit methods until you have gained a good deal of experience. Designing an amp is also much more of an art than a mere engineering exercise, so experience counts double or treble.

 

If you design an amp for yourself, you should design it to suit your favourite speakers or some speakers you know you will buy or build. There is no point in building an amp in isolation from the rest of your chain just because it is the fashionable topology of the week.

 

Let us say that the speakers you want to drive have a nominal impedance rating of 8 ohms and that you have calculated that they require a maximum of 3W to drive them. Refer to Section 102 The Myth of the Watt for several mutually reinforcing methods of determining how much power your speakers really need, as distinct from what the manufacturers say they need, often a grotesquely inflated number.

 

Output tube and load

With the power requirement and the speaker load known, you can start designing the signal cascade. A cascade is a series of tubes each amplifying a signal a little more, or even a lot more. Each tube and its surrounding components from its grid resistor to just before the grid resistor of the next tube is called a "stage" in the cascade. Confusingly many important calculations take the grid resistor of the next stage into account rather than the grid resistor of the stage being calculated.

 

A 3W single-ended output requirement is a doddle. We could do it with 2A3 but I like the 300B so that is what we choose.

 

At this point it helps, unless you can afford to have custom output transformers made, to know what primary impedances are available over the counter. For most power tubes you want an output transformer (OPT) with a primary impedance (Zpri) of about four to ten times the plate resistance (Rp) of the chosen power tube, which you also find on the tube spec sheet. Lower Zpri multiples of the plate resistance deliver more power but also more distortion; the higher multiples offer less distortion but also less power. Approximately four times plate resistance is chosen because at this multiple there is a reasonable balance between distortion and power output. Load multiples of plate resistance higher than four pay a substantial price in power for an increasingly marginal improvement in the distortion figure. Most audiophiles call a halt to the search for lower distortion at a multiple between five and eight.

 

The plate resistance of a 300B and its eponymous imitators is usually around 680-720 ohms. We are thus looking for an OPT with Zpri in the region of 2.5Kohm to 7.2Kohm. Those of us who are not power hogs or utterly obsessed with chasing irrelevantly vanishing transistor-land distortion numbers will usually find happiness when loading 300B somewhere from 3Kohm to 6Kohm.

 

The Lundahl 1623-SE can be wired on the secondary to reflect impedances of 1.6-3.0-5.6Kohm onto the primary. (This is the correct way to make a multi-use output transformer; actually tapping the primary is an egregious practice for reasons we don't have the space to go into here.) The two useful ones for SE 300B are 3.0Kohm, which is pretty much a default 300B load, and 5.6Kohm, which is near enough the upper limit of 8x plate resistance. It has different power ratings at these impedances ranging from 13W to 50W, so our desired 3W will never drive it into saturation.

 

Power tube operating points

There are several ways you can choose operating points for the power tube.

 

You can apply Ohm's Law to calculate operating points from knowledge of the tube's maximum power dissipation, within the envelope of its maximum plate current and voltage, all of which is information usually found on the spec sheets.

 

Or many tubes have one or more sets of suggested operating conditions on the spec sheets, and you could choose one of those without doing any calculations of your own. In section 114 there is an awful warning tale about what happens to people who pick operating points off the sheets without first understanding that the assumptions under which the factory data are given have nothing to do with audio, and would in fact be quite unrecognizable to modern tubies..

 

Or you could do it visually, on the diagram published for the tube which shows the plate current drawn against the plate voltage at any level of grid bias. Such a set of curves allows you to determine all the operating conditions of a tube with the aid only of a ruler, a pencil and a very little mental arithmetic. I strongly recommend this method, not least because it helps the amateur visualize what is happening inside his precious tube.

 

For the 300B Western Electric published a huge numerical table of many operating conditions, which also applies to the modern production WE300B. STC published another for the 4300, their version of the 300B, of which the modern Chinese 300B is a copy. Study these tables until you grasp the relationship between impedance and distortion, and also the relationship between voltage/current and output power.

 

Now forget the tables, and forget whatever you've read about other people's operating points; some of them parrot these old tables without any investigation or thought. Those tables are based on measurements made under assumptions common at the time, one of which was that 5% distortion would be acceptable to everyone. (The same applies to almost all tubes, not just 300B!) The 5% is no longer true, and hasn't been since 1947 when Olson discovered that critical listeners found distortion objectionable when it reached 2.5% in an amp with a bandwidth stretching only up to 15kHz. Today, with a more sophisticated audience and a wider bandwidth by at least a third, the discrepancy between the tube producers' wishful thinking and consumer reality might be much larger than it was in 1947.

 

The curves are the only true authority!

 

Drawing the maximum dissipation curve

Refer to the 300B Ep-Ia (plate voltage-plate current) curves you downloaded from the internet in Section 112. Work with me on the transfer curves.

 

Here's a Blue Peter moment, one I made earlier:
113KISS300Boperatingpoints.jpg

for you to download for reference. Do note that it doesn't use the numbers I tell yout o work with in this section; I want you to draw your own lines on a sheet of transfer curves because only practice brings true understanding.

 

First, recollect that power (W) is voltage multiplied by current (VA). Therefore current in amps is power in watts divided by voltage. This knowledge permits you to draw a maximum power dissipation curve as VA (volt-ampere) points. For the 300B the maximum permissable dissipation (Pw or Pdmax) is 40W. Thus at 300V on the plate (Eb) it must not draw more than 40W/300V = 0.133A or 133mA of current (Ia).

 

If you calculate Pw/Eb = Ia (eg. 40W/400V= 100mA) for every 50 or 100V across the bottom of the page (the plate voltage, Eb) and draw it directly on the sheet, that is accurate enough because you won't in any event go near max dissipation. (I haven't drawn it on 113KISS300Boperatingpoints.jpg  because I will go nowhere near it. If you want to see a dissipation line set at 80% of Pdmax or 32V, check 112KISScurves.jpg again; it's the thick yellow line.) Just to be absolutely clear: You must not operate any tube above its maximum dissipation rating. The entire signal swing (we'll come to it) must fall under the maximum dissipation curve, besides not causing any other limitation from the spec sheet to be exceeded.

 

In fact, operating the tube at maximum dissipation is not recommended either. It may be built like the proverbial Australian brick outhouse and give years of service at maximum dissipation. Or it may not. In any event, it is good engineering practice to derate components from their maker's proudest claim in order to ensure the minimum of breakages. Anywhere from 60% to 80% of the permitted maximum seems to me conservative. For a 300B that is 25W-32W.

 

Perhaps you want to draw your chosen dissipation curve as well. You do this by picking a percentage of full dissipation, say 80%, translating it into power (32W out of a 300B's maximum of 40W for instance), and repeating the process described above to draw a curve parallel to and below the maximum dissipation curve.

 

Whoa! You may now wonder what is all this talk of 25W-32W when we are talking about getting much less than 10W of amp-driving power. That is because a power tube used in single-ended applications (by definition Class A operation) is only 25% efficient. The other three-quarters of the power in the maximum dissipation you will permit it will be consumed as heat, quite literally dissipated. In practice other losses, compromises and design decisions usually result in realized, usable power in the order of nearer 20 per cent of dissipation.

 

The loadline

The load angle of your output transformer is the change in plate voltage divided by the corresponding change in plate current or -RL=deltaEb/Ia. All the minus sign means is that the slope is negative, i.e. that the line falls from top left to bottom right. Since our standard schematic on which we will draw it comes only one way, the loadline we draw will always have a negative slope, so you can ignore such hairsplitting niceties. Another one is that transconductance (gm) is usually given with a negative sign preceding it; that too is irrelevant for our purposes though rendering these things shows respect for the language of electrical engineers.

 

Okay, back to business. Since your OPT primary Z is normally fixed by what is available, the formula is more conveniently written as RL*deltaIa=deltaEb, which in English reads as: multiply the output transformer primary impedance in ohms by an arbitrary amount of current in amps to discover how much the plate voltage will move because of it. Thus if your OPT primary Z is 3000 ohms, multiplying it by 150mA or 0.15A tells you the plate voltage will move 450V because of the 150mA change in its current.

 

Lay a ruler on the Ia-Eb lines at the load angle of your output transformer. In our example the ruler would cut the vertical current or Ia zero line at 150mA and the horizontal voltage Eb zero line at 450V. Anywhere along this line the load will be 3000 ohms. Even better, at any point on any line precisely parallel to this arbitrary loadline the load will also be 3000 ohms. On 112KISScurves.jpg the lower turquoise line represents my ruler (what primary impedance am I working with when my ruler cuts the scales at 100mA and 560V?) before I slid it up.

 

Grid bias and design centre values

Note that there are also diagonal lines on the table, curved at their bottoms. These represent the negative grid bias voltage, which must be as large or larger than the signal we shall put on the grid of the 300B to keep the tube operating in class A1 by preventing it ever going into the positive grid bias region and drawing current on the grid.

 

Along the loadline represented by your ruler you may choose any operating point of voltage/current/grid bias at which the dissipation is not more than 40W (max for the 300B; cf the spec sheet) or such lower level you have chosen to ensure long tube life. I repeat: 60% to 80% of maximum dissipation or 25W to 32W is a good choice.

 

The operating point is a design centre value. When WE says the maximum plate V is 450, they mean at quiescence i.e. no signal, which is usually near or on the halfway mark along the negative grid bias, and it follows that in fact the tube is theoretically good to 900V at maximum swing (zero current) even if you may not put more than 450V into it at the no signal condition. There is an unspoken practical qualification to the last sentence: "as long as you do not exceed any of the other maximum ratings." It is generally assumed that you will not operate the tube at more than one maximum rating at any one time.

 

Zero current means the tube "cuts off". You don't want to go that far. Serious distortion will result.

 

Note that the response curves for each negative bias condition curl at their bottoms.

 

You don't want to go there either if you don't have to: non-linear distortion.

 

Also, the zero negative bias voltage line is not a good place to be too near to, as many valves start drawing grid current well into the negative grid area. That too makes an unacceptable sound at the extreme, though the overload condition is gradual and some listeners are more sensitive to it than others.

 

Choosing your operating point

You now have a trapezoidal box outside which you should not, cannot or do not want to operate the power tube. You can draw horizontal, vertical and diagonal lines on the schematic to represent these limits.

 

You want to start operating your tube on the loadline a little to the right of the 0V grid bias line to ensure class A1 output. You want to stop operating it at a point before the response becomes non-linear in the region of a curved section of a grid bias line, or, worse, cuts off because it can draw no current.

 

This current cut-off point can be extended by sliding your ruler up while holding it at the same angle so that at any plate voltage you are using higher current and somewhat lower bias into the same load. Slide the ruler, still standing in for your loadline, until it touches your chosen dissipation level and note that at this point the distance between the zero bias line (or some line you have drawn to the right of it and parallel to it to distance your ears from grid current) and the furthest portion of straight, equidistant bias curve the loadline crosses is longer than it can possibly be at any lower point.

 

Now choose the negative grid bias voltage which represents half the bias voltage change between the peak to peak signal swing end points, and there is your voltage at the plate (350V) and plate current (72mA), and negative grid bias (-72V), all ready to be read off.

 

Choosing a specific output transformer

We now know that of the three current capabilities in the Lundahl LL1623-SE OPT group we want the Lundahl LL1623-SE/90mA, the nearest higher capability to the 72mA at the operating point. The alternatives available, 120mA and 180mA would be too much. If you choose too little current capability the OPT will saturate with DC current before maximum power; if you choose too much the OPT will be operated outside its most linear region (this is what the experts and poseurs mean when on the newsgroups they refer to 'running below the BH knee' or 'not getting over the knee'--they are not sadomasochists).

 

The true power output

VA is only apparent power, of which about three-quarters will be dissipated as heat: that is the price of class A sound! We need to discover the true power the tube will deliver via the transformer to the speaker. We also need to know if our operating point will deliver more distortion than we can tolerate.

 

Calculate the true power output and distortion by measuring on the curves, extending them upwards as required because their truncation at the top of tube diagrams includes another implied and untrue assumption, viz that the tube is perfectly and symmetrically linear about its design centre.

 

The output power is the product of voltage swing and the current swing (in whole amperes!--72mA is 0.072A) divided by 8. The voltage swing is 540V-120V = 420V. The current swing is 150ma - 10mA = 0.140A. Thus we can calculate 420*0.14/8 = 7.35W. The output transformer should be rated for at least twice this power so that it offers an instantaneous 100% overload capability. At 3Kohm the Lundahl OPT we have chosen is rated at 25W, so it embraces us with a huge safe margin.

 

Distortion

The 2nd harmonic distortion, as a percentage, is

((((Imax + Imin)/2)-Io)*100)/ (Imax-Imin)

where Io is the current at your chosen design centre operating point Q; it is known as the quiescent current, sometimes rendered Iq. In Class A single-ended operation we usually disregard third harmonic distortion. With this method third harmonic is not likely ever to get into your aural threshold because you will be able to see something is wrong on the curves long before you hear it in a built amp.

 

In this case the formula works out to 1.43% second harmonic distortion. Don't let it worry you. We cannot drive the amplifier (as conceived, two stages total and with the transformer settings above) to full output even if we wish to.

 

But even that is irrelevant. What really counts in any amp is whether the first watt is good. In a low-powered tube amp, matched to suitable speakers as we intend to do here, that first watt walks ten feet tall because it falls in the most linear region of the tube's transfer function, where the distortion is much less.

 

The 300B cathode resistor and humbuster

While we are here, we may as well calculate the rest of the network around the 300B. The cathode bias resistor should put a negative voltage of -72V on the cathode to prevent the signal ever swinging into the positive grid area. The plate current determined above is 72mA. By Ohm's Law, the resistance required is the voltage drop desired divided by the plate current (R=Vd/I) or -72V/0.072A=1000 ohms, a convenient value!

 

The power dissipated in this resistor will be, also by Ohm's handy Law, W=I*I*R or 0.072x0.072x1000=5.184W and for safety we normally specify a rating twice or three times that: 15W will do anywhere else but the cathode resistor for a power valve is such a critical component that 25W or even 50W would be a superior choice.

 

The resistors and the potentiometer in the humbuster network have their ratings calculated by the same formula but with normal multipliers of 2x or 3x for a safety margin. Thus the 100 ohm potentiometer will dissipate 0.5184W and should be rated at 2W, and the 100 ohm resistors branching out from it, splitting the current between them, can be 2W for convenience.

 

The 300B cathode bypass capacitor

We'll bypass the cathode resistor with a capacitor. The larger the capacitor is, the deeper the bass. I don't bother with the math, because multiplying by pi (3.142-something) is beyond my mental arithmetic after too many years of computers. (When I sit in boring concerts I design amps on the screen of my Apple Newton - - I am an old-fashioned sort of guy - - and do the arithmetic on the slide rule bezel of my watch.) Anyway, I have long since had it imprinted on my consciousness that if the product of the resistor in ohms and the capacitor in microfarads (uF) is around 50,000, the stage will be flat down to 32Hz, and if the RC product is around 100,000, the stage will be flat down to 16Hz. Thus, for a 1Kohm resistor setting the cathode bias, choose a 47uF (or 50uF) or 100uF bypass cap according to whether you want to bypass to 32Hz or 16Hz, and be done with it.

 

The rule of thumb is that the reactance (Xc) of the cathode bypass capacitor must not be more than 10% of the resistance of the cathode resistor. Reactance is merely the resistance to electromagnetic flow of a capacitor; it is frequency-dependent. Capacitive reactance is easily calculated as

Xc= 1/(2*pi*f*C)

where pi is 3.142, f is the lowest frequency you want to pass without attenuation, and C is the capacitor in farads (one microfarad = one-millionth of a farad). The reactance of a 50uF cap at 32Hz is 99.5 ohms, and the reactance of a 100uF cap at 16Hz is also 99.5 ohms, in each case less than 10% of the 1Kohm cathode resistor.

 

The reason for rolling the power tube off quite high at the low frequency (LF) end is that a driver in a horn speaker is unloaded below its nominal resonance in free air. Feeding a Lowther horn driver a lot of power at much under 36Hz is ill-advised.

 

The more uptight among electrical engineers can become pretty hot under the collar about this sort of shortcut. They would prefer to make a complicated dynamic model in which the various resistances with an influence, such as for instance the cathode's internal resistance, are all taken into account. That is interesting if one has the time and a powerful computer, but we once did all the math for over 90 stages in cascades for over thirty amps consecutively through our proto shop, and the shortcut in 95% of cases was closer than 5% to the dynamic model prediction; the actual empirical choice after testing was predicted by the shortcut in the same 95% of cases. A tube amplifier is not rocket science so those margins of error fall well within the margins of even the best available caps. Don't waste your time with the heavy math where it doesn't matter, unless of course you like heavy math for its own sake.

 

From plate voltage to supply voltage

The voltage to be supplied to the OPT by the power supply is the design centre plate voltage (Ep or Eb) we have read off the diagram, plus the voltage drop for the negative bias, plus the voltage drop over the DC resistance (164 ohms for the chosen transformer) of the OPT primary. The latter voltage drop is the product of the primary DC resistance and the plate current draw, 164x0.072 or near enough 12V, so the B+ for the power tube circuit must be 350+72+12V or 434V.

 

All that remains is the 300B's grid leak resistor, and that we can set the permitted maximum of 250K though we may have to alter it when we design the previous stage in the cascade, called the driver. (It doesn't matter too much if you use 270K; it's common enough practice nowadays. If you want to be precise and can't find a 250K resistor, use two 500K in parallel.)

 

Compromise and iteration

We have now arrived at the sort of 300B output stage for which when built into an amp you can pay a lot of money in a boutique or a bit less but still substantial sums by mailorder from Taiwan or China. It's an impressive amplifier and with the right speakers does its job superbly. Only one person in perhaps a hundred thousand will ever hear an amplifier this good.

 

At this point you have had a go on your own after the last section and in this section you and I have worked out way through the design of a good standard 300B power stage. (By >standard< you will of course understand that the elite prefers not to attract attention to themselves for fear that the government will tax their innocent pleasures.) This output stage is in fact from a design I published in the mid-1990s which was built with a two-stage 6SN7 voltage chain by quite a few audiophiles of widely varying skill levels. Their speakers were reported to require half a watt to 6W after generous allowance for transient peaks, a breeze for this design which with the 3K load is good for 7W.

 

This is a near-universal 300B for all seasons, as blameless as a single-ended amp ever gets to be. For engineering respectability it was necessary to go there first; if you have never had a 300B, or if you had a cheap one with mickey mouse tubes and Chinese iron, you must build this one as a baseline of excellence before you can move on to ultrafidelity. Otherwise, what will you compare your experience to?

 

But, good as it is, it is only one half of what I promised. What we will design next, an ultra-fi 300B amplifier, is something much more uncompromising, much more tailored to a cultivated taste, much less respectful of the lowest common denominator of engineering fashion that rules in transistor amps. In short, the The KISS Amp 300B Ultrafi will elevate taste above mere silence. It makes sacrifices to hedonism, and I don't mean silver wire rubbed on the thighs of virgins, I mean in conceptual engineering.

 

That requires a boost into lateral thinking mode.


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All text and illustration is Copyright © Andre Jute 2004

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