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I think it would be useful to discuss the concept of bias as it pertains to guitar amplifiers. I have read some articles saying that you should always rebias your amplifier when you change the power tubes--and some even say you should do this even if your amplifier is cathode bias (a.k.a. self bias). So, starting with the most basic:
What is bias? When should re-biasing my amplifier be considered? Can I re-bias my amplifier myself?
There are many methods of biasing.
Those applied to the preamp tubes generally use cathode bias which is a small resistor with optional capacitor in parallel. What this does is effectively create a voltage source in series with the cathode with raises it above ground. This has the same effect as lowering the grid voltage below ground by the same amount.
By reducing the capacitor size or even eliminating it you introduce negative feedback. This reduces the gain but increases the linearity of the signal. The capacitor fixes the voltage which ultimately depends on the quiescent current.
The standard resistor value is about 1.5k which puts the grid about 1.5V below the cathode(or the cathode 1.5V above the grid). A normal 12AX7 can take a grid input from about 0 volts to -4 volts. Below about -4 volts the tube will cut off as it cannot turn off any further. 0 volts on the grid allows current to flow and anything above this allows even more. 0 volts on the grid on a cathode biased tube is really the negative of the cathode bias.
So if you have 1.5V on the cathode due to cathode bias putting 0 volts on the grid will set the tube to be somewhere between completely on and completely off. You find the right amount to give you the most gain and the most linearity and the lowest noise. If your guitar signal's transients are too large then they will clip(the tube can't turn off any further no matter how large the signal is). This is how we get pre-amp distortion but we do it by sending in a larger signal than we normally should. For your first tube you do not want this unless you want to get distortion from your clean sound. You can change the grid resistor from about 0 ohms to 3k ohms and still get a good usable signal. To my ears the best value sounds around 1.5k.
The other method is to use fixed bias which applies the voltage to the grid directly. This is just another way to do the same above but it doesn't have any feedback capabilities and is easier to adjust(since you don't have to change out a resistor). In this case though the voltage doesn't depend on the quiescent current which means you don't have to calculate or probe it.
For power amp tubes, one has exactly the same type of concept since they are just "bigger" pre-amp tubes. (A pentode is a triode with 2 extra grids but otherwise functions along the same lines)
A power amp tube is generally biased using fixed bias because you don't want it to change that much(big changes in current going through it = big change is cathode bias) and you want as much gain as you can get(cause that's the whole point of a power stage).
The same kinda principles apply but in a power stage the grid can swing usually to around -80V for the grid instead of -4 for a triode. This means the bias is much lower(around -40V).
Changing the bias effects the location on the operating point of the load line. This effectively sets up the "operating current". It is important only in that the tube has a maximum power output it can handle. When running a tube in linear mode almost any location can work as long as your operating within spec. The problem is that when you want maximum gain and your input is large you start getting near or into the non-linear regions of the tube. This is where biasing can be important and can be different for two tubes.
Effectively the load line is given by I = (Vcc + u*Vg)/R
The two extremes are when I = 0 and when Vg = 0. Note that when I = 0 we have Vg = -Vcc/u. This means that for smaller u we have larger possible grid voltage swings. This is why you generally want to use a lower gain tube as the input such as the 12ay7. The problem is these are dual triodes and it will effect the 2nd tube two which may be used for more gain. This will reduce the overall distortion of a hi-gain channel which may not be desirable. This can be fixed by changing the circuitry since all tubes have enough gain to drive any stage.
For example, the input tube takes a signal about 1Vrms and outputs a signal(theoretically) of 100Vrms(for u = 100 such as a 12ax7). This drives the input grid of another tube. But the grid can only swing from about 0 to -5V. So we have way to much gain for it. Therefore massive clipping would occur. Attenuation is needed. So even a u = 40(12ay7) would work except that it would be attenuated by the same divider. If we changed the divider circuit we could recover the lost gain and not lose possible power(which ultimately comes from the power amp tubes but they have to be driven by a large enough signal to get that power).
Mostly that stuff above is for pre-amp tubes and even though the same thing applies to power amp tubes you generally focus more on power amp tubes for a few reasons.
Power amps generally are in class AB push pull. This means that you have two tubes working against each other which removes the current in the transformer(for dc anyways). If the tubes are not balanced you'll get current in the transformer which can burn it up.
Power amps are bias effects how "hot" the tubes run. The hotter the better up to a point before the tubes melt. Some amp manufacturers intentionally run the tubes very cold to save money(they extend the life of the tubes that they ship them with).
Power amps are the workhorses of an amp that actually give the amp it's power gain rather than just voltage gain. If the bias is too low then the current will be too large through the tubes but also through other components which may gradually fail over time causing other components to fail more.
Tubes must be unbalanced slightly as to reduce crossover distortion. This is nasty distortion that is prevalent at lower volumes. This is one of the reasons running a push-pull amp as loud as possible gives the best sound as the crossover distortion is masked out.
For power amp tubes you can rebias them and even balance the tubes if they are unbalanced(not a great way but better than nothing but generally requires extra work to do so). You can make your tubes hotter or colder to improve the sound.
There are many things you can do to an amp to make it sound better. "Stock" amps generally are designed to increase lifespan and profit margins rather than tone.
Biasing an amplifier basically means adjusting the current that flows through the tubes to match the tubes' operating parameters and the particular sound you want to get out of the amp.
You can do it yourself, but from what I'm reading, you need to have a decent understanding of electronics. Replacing tubes in your amp will likely mean you will need to re-bias it.
I found "The Last Word On Biasing" and "What does adjusting tube amp bias mean?" helpful in explaining what biasing is and how it works.
"How to bias a Deville amplifier" is a little information on changing tubes and bias on a Fender Deville amp.
It taught me a fair bit, and I know a limited amount on the specific area of tubes.
Hope this helps
Not all tube amps need/should be re-biased when changing tubes. E.g. Mesa/Boogie amps have pre-set bias and need some sort of modding in order to change it. The tubes should be bought as a matched set though.
