The Valve Wizard
Single-ended (SE) power output stages are probably the simplest form of power amplifier. They are usually used for relatively small amplifiers, e.g., less than 15W, and are invariably cathode-biased. Higher powers are obtainable with either very large power valves, or by using multiple valves in parallel, but beyond about 15W it is usual to use the more efficient push-pull system.
Initial Criteria: The principle of operation for the cathode-biased single-ended output stage is somewhat simpler to understand than that of the push-pull amplifier, as a SE stage is similar to a typical pentode stage used in preamplifiers. Its only real difference is in using a transformer for an anode load, rather than the resistor that you'd see in a preamplifier stage.
The first two things to consider when beginning to design are: What sound are you looking to get from the power amp, and how much output power do you want?
If we decide that we would like the stage to contribute an aggressive character to the sound of the amplifier as a whole then the EL34 is a good choice, and should deliver around 8W to 11W at a reasonably low HT of 250V and somewhat more at higher voltages.
Transformer Impedance: When selecting a transformer it is necessary to know what HT voltage is going to be used (at least roughly). Referring to the data sheet, we can see that an EL34 can be operated from a very wide range of HT potentials. Other single ended EL34 designs commonly use between 250V and 400V. The lower end of the range will suit lower transformer impedances, and vice versa. In the following example we'll use 300V.
Transformer manufacturers generally state that an output transformer will show 'x' primary impedance with 'y' secondary load. For example: 5k primary impedance with an 8 ohms secondary (speaker). This is derived from the voltage and current ratio of the transformer, which are inversely proportional to each other. That is to say; if the voltage is stepped down, the current must step up:
It's easy to see that a transformer that exhibits a voltage and current ratio of 20 will have an impedance ratio of 400. This means that connecting a speaker of 8 ohms to the secondary will reflect an impedance of 3.2k to the primary. Doubling the speaker impedance to 16 ohms would also double the primary to 6.4k. (This is a useful trick that may allow you to obtain your ideal primary impedance by connecting the transformer to a speaker impedance other than the rated value.)
Because the grid curves of a pentode allow the signal voltage to swing almost to 0V on the anode, and because we would like to run the stage approximately centre biased, there is a rule of thumb we can use to find a suitable transformer impedance:
With our HT of 300V, and taking the data sheet value for maximum anode dissipation as 25W;
It is usually the case that there will be no 'off the shelf' output transformer that suits our ideal impedance exactly, so we would draw some load lines to find a transformer that is suitable. Plotting several load lines will show you how much you can afford to 'fudge' the impedance value to suit your power supply, or what transformers are available. For this example we will assume that the nearest transformer available with a higher impedance than we calculated is rated at 4k, 10W. Draw load line:
As you can see from the blue line, the load line is first drawn in the normal way, but this will not be the load line that the valve ends up operating on, it simply shows us the gradient of the load.
Choosing a bias point: Because we are using a reactive load rather than a resistive one (i.e., a transformer and not an anode resistor), the bias is not chosen in the same way as for a preamp stage.
If you are wondering why it appears that the signal voltage can now swing higher than the HT voltage, it is because this is exactly what happens! Inductances abhor changes in current. When current through the transformer increases it stores energy, which is released when the current falls again, allowing up to twice the HT voltage to be developed. Because of this, the HT in a Class A amp must never be more than half the maximum peak anode voltage rating of the valve, given on the data sheet. For the EL34 this is 2000V so we are well within safe limits!
Screen Voltage: The screen voltage is usually set by a dropping resistor in the HT supply (Rg2) (see the section on
smoothing and filtering), or a choke, plus a small screen-grid stopper. This will place the screen voltage at roughly the same voltage as the anode, or a little lower. Guitar amps usually sound best when the quiescent load line passes slightly below the knee of the curves. It is this interplay of load, anode and screen voltage that is the essence of pentode design.
We already know the quiescent anode current will be 75mA, so we can expect 75/7 = 10.7mA of quiescent screen current. We will assume the preamp in this amplifier draws an additional 5mA.
The total current through the screen-grid dropper (Rg2) is therefore 15.7mA.
As mentioned, the quiescent load line will usually pass slightly below the knee, which is find for clean amplification. However, when it comes to overdrive it is a BAD IDEA, because once the operating point swings up to the 0V grid curve, the screen current rapidly increases. If the operating point hangs around this point for too long (as it does during clipping) it can easily cause the screen to overdissipate and be destroyed. To avoid this, a screen-grid stopper is added, which forces the screen voltage to drop as the screen current rises, limiting the dissipation. As the screen voltage drops, all the grid curves get squashed down, and as a rule of thumb we would like the knee to meet or pass below the load line under these dynamic conditions. This is known as 'sliding-screen' operation, and requires a certain amount of estimation and educated-guessing as we shall see.
Firstly we must know what voltage we need the screen to sag down to, and to do this we use the mutual characteristics graph. Unfortunately
the mutual characteristic graph provided in the data sheet does not
show screen voltage extending as far as zero grid volts. However, we
can guess that if we want the zero volts curve to squash down to where
the -8V line is initially, then the -8V grid line will move down to roughly
where the -16V grid line is currently.
Now well introduce a big fudge factor and say that when the anode swings close to zero, all the current is stolen the by the screen (OK that isn't strictly true, but it'll do for now). From the load line, the peak anode current is about 150mA. Use Ohm's law to find the minimum value of screen-grid stopper:
This resistor will also drop the quiescent screen voltage by 470 * 0.0107 = 5V, which is negligeable.
Biasing: Now we know the screen
voltage will be 300 - 7.4 - 5 = 288V we could re-draw the new anode characteristics to find the bias
voltage. However, a quicker way is simply to use the mutual characteristics
graph again: We know our quiescent anode current will be 75mA, and our
screen voltage is 300 - 7.4 - 5 = 288V, and this indicates a grid-to-cathode voltage
of about -17V (blue dot), which is our required bias voltage. The total cathode
current will be equal to the quiescent anode current plus the screen current, making 86mA in total. Use Ohm's law to calculate
the value of cathode resistor (Rk):
Cathode bypass capacitor: As with most single ended stages, fully decoupling the cathode will maximise gain by preventing internal feedback and so maximise output power and input sensitivity too (making the valve easier to overdrive).
The grid-reference resistor (Rg1) can be found by consulting the data
sheet for the maximum allowable value in cathode bias, which will usually
be less for a power valve than a preamp valve. For the EL34 the maximum
value given is 700k, and we would probably use 470k.
Reactive Load: It is worth noting that an output transformer is reactive and so has a rising impedance with frequency, and is also coupled to a loudspeaker. A loudspeaker, particularly one designed for guitar amp use, does not exhibit a constant impedance across its frequency range. Because of the combination of capacitance, inductance and resistance that makes up a loudspeaker's impedance and the fact that it is deliberately tuned to produce a frequency response that will sound good with electric guitar, the impedance will vary quite considerably from the average quoted value. This has the effect of turning our straight load line into an ellipse, which will vary with frequency and go beyond the maximum anode dissipation curve. This is not a problem though, because on average the valve will still operate on the straight load line we drew.
The graph below shows a load line with a screen voltage of
250V, and how it will in fact be an ellipse. We can see that the input
sensitivity is just over 20V p-p. At full output before clipping, the
maximum anode current is about 140mA peak (50mArms) and the maximum
anode voltage is about 540V peak (191Vrms). This gives an average power
output to the load of 0.05 * 191 = 9.5W (and an anode efficiency of
You should now be able to see that using a transformer with a lower primary impedance would permit a higher screen-voltage (and therefore more headroom) because the load line would be steeper, but would force us into cold Class A operation unless we lowered the anode voltage. Conversely, a higher load impedance would require a lower screen-voltage (less headroom), but would allow a higher anode voltage while still operating in centre-biased Class A. It is through drawing load lines in this way that a good-sounding and safe combination of all three can be found.
Remember though, the load line drawn is only correct provided the right impedance speaker is plugged in. Connecting a higher impedance speaker will cause the load line to rotate anti-clockwise around the bias point, possibly causing screen-grid failure due to passing below the knee of the grid curves (although if you're lucky, the screen resistor will fail open first). It can also cause arcing in the transformer due to much higher anode voltages being developed when the valve is overdriven. Connecting a lower impedance speaker will have the opposite effect; the load line will become more steep, pushing the valve into cold Class A operation which may or may not cause over dissipation of the anode (thankfully it usually doesn't). It is therefore always safer to plug in a lower impedance speaker than a higher one, if you have to.
Many thanks to Zoe and Iain Hartney for their contribution to this tutorial.