Design Of A Single Ended 2A3 Valve Amplifier - Part 2

In part 1 we looked at design of the 2A3 output stage of this amplifier, that was a very, very long time ago. Now we'll look at the D3a driver.

The Driver Stage

Output Stage Recap

Design of this driver stage is very similar to the output stage, but with slightly different goals. The purpose of the driver is to drive the output valve's grid, so let's have another look at the 2A3 anode characteristic curves to remind ourselves - here's the datasheet graph to which I added the safe operating zone.

If you remember, our operating point is 250V and 60mA, with a grid bias of -43.5V.

As this is a class A1 design the 2A3's grid should remain negative at all times (i.e. to the right of the red curve) so for full output the grid swings down from its bias point of -43.5V to 0V (and up to -87V). The driver is a common cathode stage, so the driver needs to swing + and - 43.5V on its anode, which is coupled to the 2A3 grid via a capacitor. Capacitors block DC voltage - we'll talk about this capacitor later.

Driver Stage Considerations

So how do we choose the driver? There are a number of considerations but if we want to use a single stage before the 2A3 then ideally we need to swing the + or - 43.5V from a standard 2V RMS input, such as a CD player. 2V RMS equates to 2 x square root of 2 x 2 = 5.66V peak to peak so + and - 2.83V. So in rough terms the driver needs a gain of 43.5 / 2.83 = 15.3. In reality a valve's datasheet amplification factor won't be fully achieved, maybe only in the region of 70%.

And we perhaps might prefer a little more sensitivity than + or - 2.83V, and + or - 1V gives us plenty of "welly" on the volume control. So let's aim for an overall gain in the region of 40.

It's not just a question of choosing a valve with the appropriate amplification factor, it has to be able to actually swing those volts too! And ideally we'd like it to have plenty of headroom i.e. some more swing in hand so it's not up against its limits and clip.

We also want to minimise distortion so might want to aim for areas of the anode curves with equally spaced grid voltage curves. (However, as the amplifier is the result of two stages, both stages have to be considered together as a combined system if we want to fine tune minimum distortion. But that would need some test equipment and is beyond the scope of this blog.)

And of course we need to obey the safe operating characteristics of the valve.

The D3a

So back to the D3a. It's a "special quality" pentode that was used for telecommunications. Here's the datasheet. Pentodes are generally newer than triodes (which is somewhat relative these days!) but can make good drivers as they typically have higher gain than triodes. Sometimes too high. But they can be wired as triodes with lower gain, and some think they can sound better this way.

Not all pentode datasheets contain triode connected info but fortunately the D3a does. Looking at page 3 the triode amplification factor is given as 77, so ~70% is a real world gain of about 50, which is nice. Now let's look at the second graph on page 7 for the average anode characteristics.

The curves look rather like the 2A3, but the values of voltage and current are very different. That's because this is a signal valve rather than an output valve.

The Operating Point

So let's look at the operating point and start with the safe operating requirements, see page 5 of the datasheet. Helpfully the maximum anode power dissipation of 4.5W is already shown on the datasheet graph. In addition we want to stay to the right of the 0V grid line, and not exceed the maximum anode voltage of 220V and maximum anode current of 30mA. So here's the graph again, with the safe operating zone shown.

Now we can choose our operating point. We want to swing 2 x 43.5 = 87V peak to peak on the anode, and we want a nice place on the grid voltage curves with equal spacing to minimise harmonic distortion. But also, unless we're going to have a separate power supply we need to bear in mind the B+ supply voltage that we determined in our output stage design.

Now if we go back to our 2V RMS input voltage from a CD player, which is 5.66V peak to peak, if we look at the curves above we can't adequately bias our valve for this swing - the grid voltage curves only go as far as -3V. In reality we would need a meatier driver.

But it's not necessary to swing the full 5.66V - music rarely reaches the full 2V RMS. If we go for 2V peak to peak then the amp will have decent sensitivity. So let's bias the valve to the right of the 1V curve. This does mean of course that there is the potential danger that at full bore the amp could overdrive, but in reality the volume control would never be turned up that high to permit the full 2V RMS swing in a well balanced setup system.

Now it's an iterative process of looking at operating point and anode loadline. An operating point of 150V and 20mA, which is a grid voltage of approximately -1.38V, looks a decent compromise. You can see I've sketched in the approximate -1.38V line at the operating point.

Loadline and Anode Load

When we looked at the output stage we went with the datasheet loadline of 2500 ohms, which is approximately 3x the anode resistance. Our choices for a driver are slightly different as the higher the load resistance generally the better as it will tend to reduce distortion. But the higher the load resistance (i.e. the larger value of the anode resistor) the more voltage will be dropped across it, which in turn means the higher the required B+ voltage.

The datasheet for a triode connected D3a gives the internal resistance as 1900 ohm. If we apply the 3 x rule: 3 x 1900 = 5700 ohms. So we're looking for a resistor of at least 5700 ohms, and ideally we want to use a standard value with suitable rating. So 6800 ohms looks pretty good, and the power dissipated in it will be the current squared x the resistance, so 0.02^2 x 6800 = 2.7W. We derate by 3 x to 5 x, so we actually want a 6800 ohms resistor rated between 8W and 13W, maybe a nice 12W Mills again.

The loadline is shown in magenta, and the thicker section shows the swing about the operating point - up to a maximum of -2.56V where the maximum allowable anode voltage of 220V occurs. As the grid voltage can swing up from -1.38V to -2.56V (1.18V) it therefore swings down to -1.38 - -1.18 = -0.2V.

Now if we look at the anode voltages at these points on the grid voltage we can see the anode voltage will swing up to 220V and down to 75V i.e. -75V and +70V from the operating point. Ideally those values would be the same as the difference reflects a little distortion - that's the consequence of unequally spaced grid lines. But a difference of 5V is pretty good in reality.

If we now think back to our 2A3 we need + and - 43.5V swing on its grid, and the D3a as we have it configured here can swing +70V and -75V, more than actually required. But as most music is recorded with less than 2V RMS, in reality we'll be able to use more of the volume control, without needing a pre stage. And if the music is too loud so the driver stage starts to clip it will sound a little unpleasant and the volume will inevitably be turned down.

Cathode Resistor

Nice and easy, we want to raise the cathode to 1.38V to achieve the correct bias and there will be 20mA through it, so using our friend, ohm's law, R = V / I = 1.38 / 0.02 = 69 ohms. Let's say 68 ohms as a standard value. Power dissipated through the cathode resistor = 0.02^2 x 68 = 0.03W, so we can happily use a half watt rated resistor.


Cathode Resistor Bypass Capacitor

Right, time for some more maths again. First let's work out the cathode resistance (check back to the 2A3 page for more explanation):

rk = (ra + Rl) / (mu +1) = (1900 + 6800) / (77 + 1) = 112 ohms

So R = 1 / ((1 / rk) + (1 / Rk)) = 1 / (1/112 + 1/68) = 1 / (0.0089 + 0.0147) = 42.4 ohms

As this is a driver stage and earlier in the reproduction chain we should aim for a much lower f-3 frequency than the output stage as once the bass frequencies have been lost they can't be magiced back. 1Hz isn't unusual.

And therefore C = 1 / (2 x pi x f-3 x R) = 1 / (2 x 3.142 x 1 x 42.4) = 3754uF.

Which is a big capacitor. But I had some Panasonic 2200uF electrolytics which gives an f-3 of less than 2Hz. Still lots of uF, but not unreasonable.

As the voltage at the cathode is approximately 1.38V a capacitor rating of 5V is fine.


Grid Leak Resistor

The datasheet suggests 500k ohms as a maximum, I went with 100k ohms, 1W is more than adequate.


Grid Stopper and Screen Tie Resistors

There are two more resistors that are very important. The first is called a grid stopper and is soldered as close to the valve socket pin for the control grid (G1) as possible. This stops valves oscillating. Higher gain valves, like the D3a have a habit of oscillating which is a bad thing. You might not audibly recognise oscillation but it will affect the sound to some degree. Sometimes it can be present but at very high frequencies, much higher than we can hear, but it can still have an affect on the music. A value somewhere between 300R and 2200R usually does the job. I used 1000R, and half a watt will be adequate.

The other resistor ties the screen grid (the middle of the three in a pentode) to the anode. This is what make the valve work like a triode rather than a pentode. 1000R half watt again.


Capacitor Coupling the Two Stages

Now we have the basic design of the driver stage we need to consider how we couple the driver stage to the output stage. The signal is taken from the anode of the D3a so we know the voltage there is 150V (our D3a operating point) plus the voltage we have raised the cathode by (1.38V) so ~151V. If we were to attach the anode of the D3a directly to the grid of the 2A3 there would be 151V on the 2A3 grid, which would be a very bad thing. Remember, from our 2A3 design there's 0V on the grid, -45V relative to the cathode, so applying 151V wouldn't do the 2A3 any good at all.

So we need a way to ensure this doesn't happen. The three usual methods are capacitor coupling, interstage transformer coupling, and direct coupling. Capacitor coupling is the most common, and for good reason; it's the easiest to implement. And whilst some say other methods sound better others are inclined not to agree; you need to build for yourself and see what you think. Capacitor coupling works in this application because capacitors block constant voltage but allow changes in voltage to pass, so using a capacitor blocks the 151V but allows the signal to pass to the 2A3 grid. We just need to work out how big a capacitor we need.

Whilst almost any capacitor would block the 151V on the D3a anode the coupling capacitor forms a high-pass filter with the 2A3 grid resistor, so if the value is too low the f-3 corner frequency could be too high and we would lose our bass again.

The high pass filter capacitor value is given by:

capacitance (farads) = 1 / (2 x pi x corner frequency f-3 (hertz) x resistance (ohms))

C = 1 / (2 x pi x f-3 x R)

Using the 40Hz f-3 we designed the 2A3 stage for gives:
C = 1 / (2 x 3.142 x 40 x 100000) = 0.4uF

0.4uF isn't a common value, but 0.47uF is. And it has the advantage that as it is slightly larger it drops the f-3 frequency to around 34Hz. Whilst beneficial as it drops the high pass filter a few Hz it also doesn't compound high pass filters at the same frequency, which wouldn't be ideal in some respects.

But you could also choose to use a 1uF coupling capacitor which would drop f-3 to 17Hz. This is perhaps a nicer place to be, but it requires a bigger value capacitor, and some audibly prefer smaller. More capacitance generally costs more too.

There is roughly 151V across this capacitor so the capacitor needs a higher voltage rating. Generally, you want to be using a nice film capacitor here. Some swear by paper in oil, others prefer PP. But most film capacitors used in valve amplifiers are rated for 630V, some 250V, so more than adequate.

Volume Control

This just leaves the volume pot. There is a balance to be struck here, 50k is pretty good but others can be used.

And now it's confession time. It's so long since I first started preparing these two blogs I've lost the drawing file somewhere on an old computer which had the circuits and values :-(. But if you've made it this far then you have enough persistence to fill the values in for yourself :-). So no final glory shot of the full amp circuit, but who knows, maybe in another seven years I might do a blog about the power supply...

Design Of A Single Ended 2A3 Valve Amplifier - Part 1

This is a simple single ended valve amp I "threw together" a couple of years ago. It was meant for a colleague to try valves at home, but never found it's way out of the house. It's been in the project room ever since (as attested by the obligatory dust to be found in all the best male domains) and makes a particularly good match for the Quasars.

There's nothing fancy about the design - a triode strapped D3a pentode capacitor coupled to a 2A3, both in self bias with AC heating. The HT power supply is a simple LCLC passive filter with a GZ37 rectifier. Here's the audio schematic without part values, all straight forward stuff.

But it has decent parts and sounds very good. Surprisingly good really. Not the best amp I've built (that's a copper GM70 SE amp, but that's another story), but it fits in a single chassis which makes a change from most of my more recent builds... And I haven't felt the need to replace it which speaks volumes. And in the spirit of openness here's a photo of the inside just to prove how thrown together it was. I certainly wouldn't encourage anyone to study my wiring!

The chassis was actually recycled from my very first amp build - a Bluebell Audio 2A3 Loftin White built 10 years ago. Parts were supplied by Philip Ramsey using Shishido san's circuit. I just needed to drill a few more holes to accommodate different output transformers, chokes and a volume pot.

Preamble over, let's talk about the design. Bear in mind this is intended to be a simplified explanation of simple valve amp design - if you want the in-depth theory there are many good sources, try Valve Wizard's website or Morgan Jones Valve Amplifiers. I would also highly recommend reading Gordon Rankin's write up of his Bugle 45 amp - a great amp and really good design primer. First though, recognition must go to Nick Gorham as it was a circuit he posted that inspired me to build this.

The Output Stage

The usual place to start when designing a valve amplifier is the output valve, in this case a 2A3. By looking at the datasheet we can see whether it's likely to be suitable for our system, or what we might need in our system to make it "work". Assuming we have some reasonably efficient speakers a 2A3 makes a lot of sense.

Anode (Plate) Characteristics

Let's look at the anode characteristics graph on the datasheet

This graph shows a series of curves representing the relationship between voltage across the valve and the current through the valve for different grid voltages. Let's consider the classic 2A3 operating point, i.e. how the valve is "set up": 250V, 60mA, -45V on the grid. If we look back at the first page of the datasheet we're even told what might be a good operating point ;-). So looking at the graph above, 250 plate volts and 60 plate milliamps just happens to intersect with where a line representing -43.5 grid volts would be. (Okay, that's not quite -45V but it represents the lower limit of the AC heating, 2.5V.)

If for instance you maintained 250V across the valve but went with -35 grid volts you'd draw around 115mA. And burn out your 2A3 pretty quickly. So we need to check that our proposed operating point is within the valve's rating, and for a class A1 amplifier the datasheet tells us that we shouldn't go above 300V across the valve, and we can plot this line on the graph.

The datasheet also tells us we shouldn't let the anode (plate) dissipate more than 15W. So we can add this to the graph too as a curve with a series of points where voltage x current = 15W.

To draw the 15W curve we could plot a point at 100V and 150mA (which is 15W) say, and another at 200V and 75mA (= 15W), and another at 300V and 50mA (also = 15W), and so on for as many points as we feel necessary. For safe operation of the valve we need to operate in the area of the graph below the curve.

As we're designing a class A1 amplifier the grid should always remain negative relative to the cathode too, so we also need to be to the right of the 0V grid line too.

And if we plot all three on the same graph we find the acceptable area of the curves that we want to work within, the green shaded area below.

 And 250V anode voltage and 60mA is right at the limit of this region, thus maximising the power obtained from the valve. In general it's usual to maximise the power obtained from a valve, if you're lucky enough to have rare old monoplates you might choose to be a little kinder to them and maybe run them at 50mA instead...

Loadline

The next thing to consider is the loadline, an example of which is also shown on the datasheet, rather conveniently. It's the sloping straight line labelled "LOAD RESISTANCE = 2500 OHMS", centered about the -43.5V grid line, ranging between 0 grid volts and -87 grid volts. This loadline represents the load resistance of the output transformer, which in the case of the datasheet is 2500 ohms. But why 2500 ohms? You could just leave it to the RCA engineers and accept they knew what they were doing, which they most certainly did, but the longer answer is it's a compromise.

What do we want from our amplification stage? Usually we want to maximise power and we want to minimise distortion. The relative importance of the two depends on what we're trying to achieve, but as this is an output stage we want a good balance of the two.

If we consider distortion we can see how linear the valve is (or isn't) at our operating point by looking at how evenly spaced the grid lines are along the load line. Between 0V and -60V the spacings look fairly even, but beyond -60V the grid lines tighten a touch. So when the music signal is larger than + or - 15V (so lower than -30V and higher than -60V) the distortion will increase.

In general, if we wanted to reduce distortion we could increase the load resistance which would flatten the loadline i.e. make it closer to horizontal. But if we do this we will lose some power. And that's the compromise. We're considering the classic 2A3 operating point, and there's good reason for doing so as it's a good balance.

The rule of thumb for an output valve's load resistance is 3 x the anode (plate) resistance. So if we look at the datasheet again, the plate resistance is given as 800 ohms, which multiplied by 3 gives us 2400 ohms, or our 2k5 output transformers. 3k5 output transformers are often seen used in 2A3 schematics and trade a little output power for slightly lower distortion.

If we look back at our graph of anode characteristics with our limiting conditions marked on we can see the loadline is right at the very top of the 15W line. In fact part of the loadline actually crosses the 15W line but it's transient and overall the valve dissipates 15W.

Cathode Resistor

Okay, that was a bit heavy, sizing the cathode resistor is much easier now we've decided how we want to operate our valve. As we're designing a simple valve amplifier we're going to use self bias. We know that there will be 250V across the valve and we need to bias the grid at -45V relative to the cathode. Ohm's law is our friend

voltage (volts) = current (amps) x resistance (ohms)

or

V = I x R

Rearranging Ohm's law gives us R = 45 / 0.060 = 750 ohms. The datasheet suggests 750 ohms, there's a surprise!

We also need to calculate the power rating of the resistor.

power (watts) = current (amps) ^2 x resistance (ohms)

or

P = I^2 x R

(Blogger doesn't seem to allow superscript for the squared term)

Which gives us P = 0.060^2 x 750 = 2.7W

But we must derate this as a 2.7W resistor (even if we could find such a thing) would burn up very quickly. Typically we derate by 3 to 5 times, so our 2.7W becomes 8.1W to 13.5W. Even at 3 x derating the resistor will get very hot and I prefer to go to 5 x if I can find something suitable. In this case I would go for at least 12W, maybe a nice Mills if you're feeling flush.

Our output stage is starting to take shape now. Under the cathode we have a 750 ohms 12W resistor which raises the potential at the cathode to 45V. As there's 250V across the valve (i.e. between the cathode and anode) there will be 250 + 45 = 295V at the anode.

Cathode Resistor Bypass Capacitor

If we don't use a capacitor to bypass the cathode resistor the stage will have lower distortion and higher headroom, but more importantly for an output stage it will have a small fraction of the gain. This is why common cathode stages usually have a cathode resistor bypass capacitor. Calculating the size is a little involved.

capacitance (farads) = 1 / (2 x pi x f-3 (hertz) x R (ohms))

or

C = 1 / (2 x pi x f-3 x R)

f-3 is the frequency at which bass will have rolled off by 3dB. 3dB represents a halving of the bass output in this case so we need to set f-3 somewhere below the frequency at which we want full bass output. If we want full bass output down to 40Hz, not unreasonable for an output stage, let's set f-3 at 20Hz.

R, unfortunately, isn't simply the value of the cathode resistor. It's actually the cathode resistor in parallel with the cathode resistance, rk.

cathode resistance = (anode resistance + load resistance) / (amplification factor +1)

or

rk = (ra + Rl) / (mu + 1)

So rk = (800 + 2500) / (4.2 +1) = 3300 / 5.2 = 634.6 ohms

And therefore R = 1 / (1 / 634.6 + 1 / 750) = 344 ohms

Finally we can calculate the value of the cathode resistor's bypass capacitor

C = 1 / (2 x pi x f-3 x R) = 1 / (2 x 3.142 x 20 x 344) = 23.1uF. So we'd choose 22uF as it's a commonly available size. If you had a 47uf capacitor to hand then f-3 would be 10Hz. And 10uF would give a f-3 of 46Hz. I had a couple of 100uF capacitors handy so used those.

As you can see, if we had simply used the value of the cathode resistor, Rk, instead of R then we would have made the cathode bypass capacitor more than twice the size it actually needs to be.

As there's 45V at the cathode the capacitor needs to be rated higher than this. 50V is perhaps a little too close for my liking and I would choose at least a 63V rated capacitor and possibly 100V.

Grid Leak Resistor

We're nearly there now, just the grid leak resistor to specify. It's purpose is to tie the grid to ground and provide the cathode bias via the cathode resistor. The datasheet usually specifies a maximum value, in our case 500k ohms. Higher isn't necessarily better, but it can't be too low otherwise it would draw significant current and we want to keep the current draw under a milliamp. 100k is a reasonable value for the 2A3, and 1W should be more than enough as it should see very little current.

Final Output Stage

And here it is, our finished output stage. If you're wondering why there are two resistors between the cathode resistor and the cathode, this is in lieu of a humpot. A humpot allows any hum caused by AC heating of the valve to be minimised. But instead of a hum pot two resistors will put the cathode resistor at the centre of the potential difference between the two ends of the filament. In practice 2A3s are virtually hum free with decent construction of the amp and I've never felt the need for a hum pot.

In a later blog I'll look at design of the driver stage.