The Valve Wizard

The cathodyne phase inverter is similar to the cathode follower in design, but the total load resistance is divided in two and shared between the anode and cathode. It has been used in many popular guitar amps including the Fender (push-pull) Princeton, most Orange amps and several Ampegs. However, it does carry something of a bad reputation among builders. It is true that without due care and attention the cathodyne can give some fairly ugly overdrive tones, but this is avoidable, if we are willing to abandon a couple of the 'traditional' design attitudes.

First, let's look at how it works. When current through the valve falls, voltage drop across the anode load also falls and anode voltage therefore rises. At the same time, voltage drop across the cathode load falls and cathode voltage therefore also falls. Because the same current flows through both anode and cathode loads, the signals generated across them must also be equal in magnitude (if we use equal loads), but out of phase with each other. The circuit is also known as the 'split load' or 'concertina inverter' because the shape of the output sine waves resemble a concertina's bellows.

The main drawback of the cathodyne is that its gain is limited to slightly less than unity to each output. However, when preceded by a typical gain stage the combination will provide about twice the overall gain of a long tailed-pair using the same valves, usually with better overall balance too.
Another common criticism of the cathodyne is that its output signal swing is less than that of a long-tailed pair into the same load. Of course, by using a somewhat larger load we can easily obtain as much swing as a typical long-tailed pair would give, or nearly so, so this is rather a moot point.

Any valve could make a good cathodyne. Low ra valves like the ECC82 will give a greater swing into lower loads and are easier to DC couple to the previous stage, but if we want a lot of gain from the previous stage then an ECC83 / 12AX7 is the obvious choice.

The gain of the cathodyne to one output is the same as that of the cathode follower, being:
A = mu .R / [ra+R(mu+2)]
where R is the total load resistance of Ra + Rk. However, for most valves this can be be approximated using the simple equation:
A = mu / (mu + 2)
Using the ECC83 we can expect the gain to be around 0.99 to each output.

The cathodyne operates under 100% internal feedback, like a cathode follower, so it is extremely linear before clipping. Therefore, when choosing a load we are really only concerned with output signal swing. If the power valves are sensitive types like EL84s or 6V6s, then we don't need huge amounts of swing and a total load around 47k to 100k would probably do. If we need to overdrive bigger valves like EL34s then 200k is probably in order.
For example, the load line below shows a total load of 200k, or in other words, the anode and cathode resistors are 100k each. We can see that the total output signal swing is 250Vp-p, but this is shared between the anode and cathode, so we will obtain 125Vp-p from each output.

Biasing: As with any stage, centre biasing gives maximum headroom. The curves show that the valve should reach cut-off around -4V, so for centre biasing we would choose -2V (green dot). Of course, you could bias hotter or colder as you see fit.
With the bias point shown above, the anode-to-cathode voltage is 200V, and the remaining voltage (HT-Vak) is shared equally across the two load resistors. Therefore we can expect the cathode voltage to be (300-200)/2 = 50V. The same conclusion could have been arrived at by noting that the anode current is 0.5mA. Since Rk and Ra are both 100k, the voltage across each much be: 0.0005 *100k = 50V.
The necessary grid voltge must be 50+(-2) = 48V. Or we could just call it 50V, which would be close enough. In fact, as a rule of thumb you may assume that the grid voltage of a cathodyne will be about 1/4HT for typical operation. This could either be applied directly to the grid via a potential divider, or we can make a cathode-biased version. Both types are shown in the image below.

Cathode biasing: Since we need a bias of -2V, and the anode current is 0.5mA, use Ohm's law to find the bias resistor, Rb:
2 / 0.0005 = 4000 ohms
So anything from 3.3k to 4.7k would be worth trying. In some hifi amps Rb will be bypassed to ensure perfect balance, but this is unecessary for guitar purposes. Of course, as with a cathode follower, a bias of -2V does not mean that the stage will overdrive if we input more than 2Vpk, the stage has roughly unity-gain remember!

Grid-leak and Input Impedance: In the cathode-bias version, the grid-leak resistor is boot-strapped, so it can be made smaller than usual to reduce inherent noise. The actual input impedance will be
Zin = Rg / [1 -( Av * (Rk / (Rk + Rb))]
So if we use a grid-leak of 470k, input impedance is:
Zin = 470k / [1 - (0.99 * (100k / (100k + 3.9k))]
= 9966k, or nearly 10Meg!
This is very high, so would present very little load to the preceding stage. In fact, a grid leak as low as 200k or even 100k could be used if we were very particular about minimising noise.

The input capacitor blocks the high DC potential at the grid from reaching previous stages. Since the input impedance is extremely high, we would need a really small capacitor to attenuate bass, which would create a high-impedance node that would be rather sensitive to electrostatic noise. Therefore it is better to use a 'normal' sized coupling capacitor (1nF to 22nF say) and use small output coupling capacitors instead, if we want to reduce bass.

Balance and Output Impedance: Provided the outputs are loaded equally, balance of the stage is perfect (despite the 'apparent' difference in output impedances- internal feedback forces them to be the same!). If the outputs are not equally loaded (as when the following stage is overdriven) the cathodyne will no longer be balanced, and other strange things can happen (see below).
When equally loaded, the output impedance from anode and cathode is roughly 1/gm, the same as a cathode follower.

When unbalanced, the anode output impedance can be approximated as:
Zout(anode) = Ra

Cathode output impedance can be approximated as:
Zout(cathode) = (Rl + ra) / (mu+2)
But these are extremes. As far as any 'normal' design is concerned, we usually assume the output impedance of a cathodyne is negligible, like a cathode follower.

Avoiding unpleasant overdrive tones:
Because the cathodyne operates under heavy internal feedback, strange things happen during overload conditions, and this is the main complaint about 'ordinary' cathodynes. Firstly, when the cathode output begins to overdrive the power valve, grid current in the power valve can cause the cathode voltage of the cathodyne to become clamped, so it looks like the cathodyne suddenly has a bypassed cathode! This causes the gain at the anode to suddenly increase, causing a negative 'gain spike' at the anode. This is shown in the upper photograph, and I originally called this 'nipple distortion' for obvious reasons... Fortunately, most push-pull amps are class AB, so this spike won't usually be amplified by the corresponding power valve since it is already in cutoff when the spike occurs. However, if you are building a class A amp then the spike can be avoided by using unusually large grid stoppers on the power valves, around 100k say.

The much greater problem with the cathodyne occurs when it is itself overdriven. Because it has such a large cathode resistor only a little grid current is required to 'jack up' the cathode voltage. When driven very hard this can cause an inverted copy of the cathode signal to appear at the anode, effectively creating a sort of full-wave rectified or frequency doubled signal at the anode. This is shown in the lower photograph, and it is usually this which causes the ugly 'blatting', 'swirling' or 'grainy' sounds sometimes heard in amps using this kind of phase inverter. Fortunately, the cure is simple. We add a large grid stopper to the cathodyne, to keep this grid current in check. A value of 100k to 1Meg is usually necessary. Before you worry, this will not affect the treble response though, because the cathodyne only has unity gain! Therefore it's input capacitance is extremely low, at about 2*Cga + Cgk, which is only 4.8pF for the ECC83! This is the real 'secret' to obtaining a smooth, consistent sound from the cathodyne, no matter what kind it is. If you are using a cathodyne always give it a nice big grid-stopper. The tonal reward is startling!!! Yes I know Leo Fender didn't use any, but he wasn't designing amps to be overdriven, and this is the 21st century.
Believe it or not, the long-tailed pair can also suffer from both of the above mentioned effects (but by different mechanisms), but it is much rarer.

The image [left] shows an example of a DC coupled cathodyne with arc-protection and grid-stopper to prevent frequency-doubling. In this case a small amount of quiescent grid-current flows in the cathodyne. The grid-stopper also serves to bring the grid voltage down to a more suitable level for biasing the cathodyne, so it is doubly useful!