Grounded Cathode Amplifier

So you learned that a tube uses a voltage signal at the grid to control the flow of electrons from the cathode to the anode.  I bet you think you’re ready to party, don’t you?

But the flow of electrons is current and what we really want is to embiggen the little voltage signals that CD players, DACs, and phono preamps put out.  How does the current flowing from the cathode to the anode become voltage?  Well, the tube needs a load.  A big, hot load.  You naughty, naughty hobbyist.

Let’s look at a really simple tube scenario and deconstruct it a bit.  You see that resistor (squiggle) at the bottom?  That’s the cathode resistor (Rk).  Ignore it for now.  You see the other resistor at the top?  That’s the load resistor (Rl).  Let’s talk about what happens to this resistor when the tube is doing its thing.

Our imaginary tube grid is letting 15mA (.015 A) of current through with a voltage source of 300V and a 10,000 ohm resistor as a plate load.  What is the voltage across the plate’s load resistor?

V = I * R

.015 amps * 10,000 ohms = 150 volts

Now what if the grid lets through a little more current, like 20mA, what is the voltage across the plate load resistor?

.02 amps * 10,000 ohms = 200 volts

So the little signal voltage on the grid that determines how many electrons get through also affects how much voltage appears across the plate load resistor.  If you connect something else in parallel to the plate load resistor, it too will see that changing voltage. To see how much amplification you get from a grounded cathode amplifier, you’ll need to understand a little bit more about how they are biased.

The Maths

Where the voltage amplification is A, the load resistor is Rl, the cathode resistor is Rk, the plate resistance is Rp, and the Mu is Mu.

For bypassed cathode resistors:

A = Mu * Rl / (Rp + Rl)

And un-bypassed cathode resistors:

A = Mu * Rl / (Rp + Rl + (Mu +1) * Rk)

That’s tube amplification in simple terms.  If you want an exhaustive description and even more maths, read TubeCad’s explanation.  Most of the rest of tube audio is just keeping the finicky little bitches happy and and not blowing them up.