October 2013

Vacuum Tubes Part 3
Continuing Grey Rollins' vacuum tube analysis.
Article By Grey Rollins

Note: Part 1 is here and part 2 is here.

  Okay, so far we have an amplification stage with a modest amount of gain. That's a good start, but it is not yet a complete preamp. Why? After all, the voltage swing is there and the current is okay, so what's the problem? Well, the output impedance is high and that leaves it at a disadvantage when driving interconnects and such. There are several potential solutions to the problem, but the classic one is to add a cathode follower.

The amplifier circuit we've been looking at is technically called a common cathode circuit. It receives a signal at the grid and gives its output at the plate (or anode, if you prefer). The cathode follower (officially known as a common anode circuit), like the common cathode, takes its signal at the grid, but the output is taken at the cathode, not the anode/plate. This leads to several differences. The common cathode circuit has plenty of voltage gain, some current gain, and high output impedance. The common anode circuit has no voltage gain (if you want to get picky, it actually loses a tiny amount of voltage gain), but in return it offers current gain and a low output impedance.

I don't know about you, but the first time I looked at a cathode follower, I was a little unnerved — how does the thing bias? Won't it... I dunno... blow up, or something? Not to worry, the cathode follower knows what it's doing. Look at it this way — if the grid is held at the plate potential of the preceding stage, then you know that the cathode will be within a few volts of that. In our current circuit, the grid's going to be around 150V. Take the value of the cathode follower's resistor and plug it into the Ohm's Law formula: 150V / 47k = 3.2mA. Which, interestingly enough, is the same as the current for the first stage.

Before going any further, I'd like to note that I'm going to skirt another controversy. The classic cathode follower bothers some people because the resistor at the bottom is a passive component and doesn't contribute to the current flow at the output. All I'm going to say is that there are more complicated follower circuits that address their concerns, but that the vast majority of classic tube circuits use ordinary cathode followers and it hasn't hurt their reputation a bit; they sound just as good as ever.

While you can set up a cathode follower's grid with a DC blocking cap and a pair of resistors arranged as a voltage divider, it's much easier to bias it by tying the grid directly to the preceding stage's plate. Simple, elegant, and it disposes of three parts. A win-win proposition.

The cathode follower does have one quirk. Since its cathode is at a relatively high voltage relative to ground, it can arc between the cathode and the filament, which in many circuits is referenced to ground. There are two common solutions. One is to reference the entire circuit's filament supply to some voltage other than ground, using a voltage divider. The other is to use a separate heater supply for the cathode follower (referenced to a higher voltage) and leave the rest of the filaments at ground potential. I tend to use separate filament supplies, which has the added benefit of spreading out the filament current demands over more than one transformer. That can be a great benefit if you're using more than one or two tubes in a circuit. Yes, it makes the circuit a little more complicated, but it's not that bad. A 6SN7's filament requires 600mA at 6.3V — small transformers like that may already be in your junk box, waiting for an opportunity to earn their keep.

So how do you proceed if you want to use the filament winding on the transformer you already have, rather than run multiple filament supplies? The first step is to look up the relevant spec for your chosen tube. In the case of the 6SN7, the rated maximum heater/cathode voltage is 100V. The first stage cathode is near ground, so we'll round that off to 0V. The second stage, the cathode follower, has its cathode near the plate voltage of the first stage, which we're going to say is around 150V. Let's split the difference and raise the filament supply to 75V, which means the first stage sees 75V between the heater and the cathode — comfortably within range. The cathode follower's heater will see the difference between the heater at 75V and the cathode at around 150V, which leaves 150V – 75V = 75V, also within spec. So, something like a 51k resistor from ground leading to a 150k resistor to the rail will do the trick. You can tie either side of the filament supply — or the midpoint, if you're using an AC filament supply — to this reference. Easy. Just keep the heat dissipation in the voltage divider resistors in mind and you'll be fine. The 51k resistor will need to dissipate a little over 0.1W, so a 0.5W part will be fine. The 150k part will take about 0.3W, which isn't too bad for a 0.5W resistor, but I'd use a 1W, just to be on the safe side. You won't have a problem in the first year or two if you use a ½W, but if you look at older equipment you'll sometimes see scorched circuit boards from years of exposure to high temperatures. Occasionally the resistor will burn out. Since we're building these circuits for ourselves the extra few cents for a 1W resistor is trivial. If this was a commercial effort the bean-counters would give us hell, but we'll take the long view and thumb our noses at them.

The one remaining thing to cover is that the first stage of this preamplifier — the common cathode part — inverts phase. The output of a common cathode circuit goes the opposite direction of the input. If the signal at the grid swings negative, the output goes positive and vice versa. The easiest solution to this is to reverse the leads at your speaker. On the other hand, if your power amplifier happens to invert phase, then the two inversions will cancel out and all will be right with the world — you can hook up your speakers normally. In case you were wondering, the cathode follower does not invert phase. A lot of circuits add a common cathode stage simply to re-invert the signal. Yes, it works, but unless you need that gain, you're going to have to burn it off again in some manner. All is not lost, however. There's another circuit that will allow you to have your cake and eat it too, but we'll leave that until later.

A couple of notes for those who want to experiment:

-- Higher bias (which you get by lowering the value of the cathode resistor) is a good thing as far as sound quality and the ability to drive other circuits, but watch the plate dissipation on your tube. Calculating the plate dissipation is not hard. Measure the voltage drop across either the plate resistor or the cathode resistor and divide by the value of the resistor. This will give you the current running through the tube; it will be in the milliamp range. Then measure the voltage from the tube's plate to cathode and multiply that by the current you just calculated. I'd suggest staying below 75% of the rated plate dissipation.

-- Be aware that the tube will “push back” as you fiddle with it. Let's say that you're running a tube at 1mA and you want to double the current to 2mA. You might think that halving the cathode resistor would do the trick. It won't work out that way. You'll end up with something less than the intended 2mA because the tube's characteristics will change.

-- Keep the plate at around ½ of your rail voltage. It's easy to forget that if you're increasing the bias, the voltage drop across the plate resistor will increase. Let us assume that you're running a 300V rail and a 150k plate resistor with 1mA across it. Then you decide to increase the bias from 1mA to 2mA. Let's do the math: 2mA * 150k = 300V. Yikes... you just put the entire voltage across the plate resistor — there's no room left for the tube!

Of course, it doesn't work that way in the real world. As noted above, the tube will push back and it, the plate resistor, and the cathode resistor will reach an accommodation where some of the voltage actually does appear across the tube. The real reason you want to run the plate at about half of the rail is to maximize the linear voltage swing. Imagine that the tube took up 295V of the 300V rail. As the output tries to swing positive, it will only be able to go 5V before it hits the rail, but it has 295V of potential negative swing. This asymmetry will cause distortion. You don't have to get too crazy about it — after all, you're not going to try to swing +150V at the output of a preamp — but it will matter a lot if you're trying to build a power amp and want a clean output from your driver stage where the voltage swing will be in the hundreds of volts.

-- A more subtle point is that increasing the current through the tube will reduce the voltage spread between the grid (which is at ground potential, i.e. 0V) and the cathode. The tube will behave wonderfully at idle, when there's no signal, but once you start playing music through it, the signal will drive the grid positive, at which point the grid will start to attract electrons. This is called grid current and a small amount is okay — in fact, some portion of the electrons will always hit the grid no matter what you do — but it's not a good idea to intentionally push the tube into conduction at the grid. Tubes have a limit as to how much of this sort of thing they can take and it also tends to get non-linear pretty quickly.

Have some idea as to how big a peak signal you expect at the grid and try to set the grid voltage at about half that value. In other words, if you're expecting a signal with 2 volts peak-to-peak, then set your cathode at least 1V (i.e. half of the 2V value) above the grid to allow the positive half of the signal room to move.

-- What if you've got a junk box power transformer that you would like to use, but try as you might, you just can't hit 300V (assuming that's your target voltage); your power supply obstinately refuses to go any higher than, say, 275V. So near and yet so far... arrrgh! Do you have to drop the money to buy a new transformer? Good news — the answer is no. Tube circuits are marvelously forgiving. Go ahead and build the circuit as-is. You then have three options: a) enjoy the music (er...that sounds familiar...where have I heard that phrase before?), b) do a little fiddling to optimize the circuit for the target (consider increasing the bias current a smidgen to take advantage of the newly-available heat dissipation due to the lower voltage at the plate), or c) go with (a) and listen to the circuit while you save up for a new transformer. Your choice. I would not suggest going below 200-225V. The circuit will work, but if you're getting that low you might want to think about using the 180V portion of the table. Again, do not exceed the rated voltage for the tube. You can use lower voltages, but if you're thinking about increasing the voltage, take a look at the tube's specs first.