$\require{color}$

# The Cathode Follower

## Intro

If there’s one thing I really hate about tube articles, it’s the unnecessary use of technical terms such as transconductance and parasitic oscillation. In this article I intend to break down the design of a cathode follower without using all the technical terms only an expert designer knows about.

## Tube Choice

We first need to choose a tube. For most applications, we want a tube with high current capabilities. Sure, we could design a cathode follower using a 6SN7 or 12AU7, and many people have, but frankly I’m not sure why. The linearity will be better, but the whole purpose of a cathode follower as an output stage (emphasis because there are other applications, such as for a current source) is to pump out current into our load. If you take a look at the OTL amps on the market that are made for headphones, they primarily use the 6080 or 6AS7 tube. It has very good current capabilities, and runs at pretty standard voltages of 100-300V. So, let’s use this tube for demonstration purposes.

## Bias

Now comes the tricky part, kind of. First, we can draw a load line, just as we would with a simple cathode biased gain stage. Convince yourself (through the datasheet) that the steeper the line, the more current swing we can get. Mark an arbitrary bias point, and draw two load lines through it, one really steep and one very flat (it doesn’t even have to intersect the axis for the purposes of seeing the difference in current). Now look at how much current is gain moving 1V up on the grid lines. It should be pretty clear that steeper lines give more current out.

So, let’s take a look at the datasheet and pick a bias point. It should be known that I am incredibly lazy and as a result, I pretty much always use 250V. This isn’t exactly ideal for this tube, but who cares, it’s a blog post, not an actual build.

We are looking at a bias pretty close to maximum power, but that’s okay, since we want a beefy buffer, we don’t mind driving the tube pretty hard. Here is where the math comes in, but don’t worry, it’s simpler than you might expect.

We have 140V on the plate @70mA, so we know we must be dropping the rest of the B+ across the cathode resistor.

$R_c\cdot .07\text{A}=250\text{V}-140\text{V}=110\text{V}\hspace{10mm}R_c=\frac{110}{.07}=1.5k\Omega$

We know the grid needs to be -60V with respect to the cathode, so with the cathode at 110V, we need our grid at 50V. We could achieve this using two different methods: fixed bias or self bias. In fixed bias, we use an external supply to set the grid voltage, while in self bias, we use a potential divider. I opt for the potential divider, because it is much cheaper and still extremely effective. We need 50V on the grid, and we want no less than 1mA flowing idly for stability, so we know we want 250K total resistance. For a potential divider

$V_g=\frac{R_{bottom}}{R_{bottom}+R_{top}}\cdot V_{B+}=50\text{V}\hspace{7mm}\text{and}\hspace{7mm}R_{bottom}+R_{top}=250k\Omega$

We get that $R_{top}=200k\Omega\hspace{7mm}\text{and}\hspace{7mm}R_{bottom}=50k\Omega$

And that’s it folks, a simple cathode follower, such as the one seen in the Bottlehead Crack (even though the Crack uses something like 150-200V), which sounds pretty good in my opinion.