what factors control gain in a triode preamp stage?

[Groover]

a simple triode stage has a cathode resistor (Rk), maybe a bypass cap (Ck), a plate resistor (Ra), and a supply voltage (B+).

Can the gain of the stage be increased by changing a) Rk? b) Ra? c)B+?
Is there an upper limit to how much increasing Ck will increase gain?

NOTE of course I realize that the tube type is a factor, but let's keep that a constant for the sake of this discussion.

[tubeswell]

The the plate resistor, cathode resistor (and bypass cap), and HT voltage, are means to an end. The HT sets how much overall power the stage will have, and to a point the plate resistor and cathode bypass cap set how much gain the stage will have, and the cathode resistor sets the operating point/bias of the stage.

The amplification factor of the triode itself is determined by:

plate resistance - the resistance that the triode presents to AC (determined by how much the plate current varies with variations in the plate voltage); and

transconductance (how much the plate current varies with variations in the grid voltage); and

amplification factor (how much the plate voltage changes with variations in the grid voltage) and is the product of the plate resistance and the transconductance.

The amount that a stage amplifies is also affected by the stage's input impedance and its output impedance. These interact in conjunction with (other) loads from (either) your guitar pickup, or the stage in front, or the stage behind, or the output transformer load (which also incorporates the speaker impedance), depending on where the stage is in the amp. Typically the higher the output impedance of the previous stage etc is compared to the input impedance of the next stage, the more AC gain will be attenuated. Conversely, the lower the output impedance is of the stage before, compared to the input impedance of the stage after, the more the signal will be preserved. The vol and tone controls in a pre-amp are an elaborate example of contribution to the output impedance for the stage in front of them. They load down the stage and affect the integrity of the signal. A TMB tone stack does this more than a simple vol control (or a simple interstage voltage divider). That is why there is a DC coupled pair (with a cathode follower) driving a TMB tone stack in a tweed bassman (i.e. it provides better signal integrity because the output impedance is really low so it can drive the tone stack better), or a recovery stage after the TMB tonestack in a blackface amp.

Now triode stages with resistive loads have a DC load line and an AC load line. The DC load line sets the operating point/bias. The AC load line is critical in determining gain of an overall pre-amp, because AC is the thing that we are trying to amplify. The AC gain is different/less than the 'DC gain' (as shown on a static plate characteristics graph), because AC gain is affected by the output impedance of the stage before and the input impedance of the stage behind.

Triodes also have inter-electrode capacitance, which in conjunction with the input impedance of that triode, affects the frequencies that will be amplified by that stage. Similarly, the size of the coupling capacitor in an AC coupled stage, interacts with the plate resistor, the plate resistance, and the grid load resistance of the next stage - to affect the frequencies amplified to the following stage.

That's all the key bits (I think).

[d95err]

Here's a very good article on the triode gain stage:
Designing Common-Cathode Amplifiers

[Merlinb]

Can the gain of the stage be increased by changing a) Rk? b) Ra? c)B+?
Is there an upper limit to how much increasing Ck will increase gain?

The upper limit for gain is :

A(max) = mu * Ra / (ra + Ra)

Increasing Ck simply allows lower and lower freq's to reach this full gain, as shown below

Assuming the cathode is bypassed, increasing Ra has the greatest effect in increasing the gain, for example:


The B+ has very little effect on gain, except at stupidly low voltages where gain will start to decline.