• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

General rule of pentode screen grid wiring

I'm familiar to some degree with triode circuitry but pentodes and beam tetrodes are new to me. And I'm confused by the screen grid wiring despite I understand its role. Data sheets usually specify limiting values of the screen current and also give graphs of screen current relationship to other working point parameters. And usually they also give some examples of biasing for different modes of operation with screen voltages (!) specified.
So in general how to deal with screens? I know that to work as a shield the screen must be held at a constant voltage and properly decoupled. So should I look for specific voltage or specific current or both? My understanding is that I have to limit the current and the voltage will set where it wants to which means connecting the screen to some high voltage supply (in most simple form to the plate supply) via resistor (and decoupling it).
 
For voltage amplifiers; the lower the screen voltage, the better, compatible with grid current. For example, grounding cathode and supressor directly, and biasing the grid by contact potential using 10megohm, will be self adjusting to about 30V. So, a high value resistance of 2.2M will let you an auto bias method with large amplification and low distortion. Most pentodes have 4:1 plate to screen current ratio. So, taking into account you can manage screen and load resistors to get about 250 to 300 times gain in one stage.

For power pentodes, usually they run screen and plate at same voltage excepting horizontal deflection tubes which run screens in the rangevof 150DCV or the like.

Proper decoupling of screen grid is sometimes necessary, othe not so. You can manage the screen grid as an output electrode (for example in Phantastrons and Sanatron circuits) or as an input one as in ultralinear circuits. As screen draws current, input impedance is limited to some k depending on passive and tube parameters.

For more data, look at this:
https://ax84.com/archive/ax84.com/static/rdh4/chapte12.pdf
Pages 16 and following (for AF voltage amplifiers).
 
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Screen voltages are also dependent on the operating mode.

Example, 807 Beam Power tube
Maximum Specified screen voltages:
300V Beam Power mode
400V Triode Wired mode
Unspecified: about 350V Ultra Linear mode

Depending on your circuit, Your Mileage May Vary.

Hint: A screen (g2) that has a constant voltage acts very much like a Plate does.
As the grid, g1, goes from negative with respect to the cathode, and signal swings g1 voltage all the way to equal to the cathode voltage, the screen draws max current (just like a plate current is max there). That applies to A1 and AB1 operation.
(A2 and AB2 draw more screen current and more plate current).