You usually can't - not without risking lots of problems. Think about it: in most tetrodes, the control grid (g1) is designed to be operated negative of the cathode, with the screen grid (g2) some hundreds of volts positive. Also the control grid of almost every tetrode is designed with a much smaller power dissipation than the screen grid, and will handle much less current. If you simply strap all available grids together, as you're proposing (Fig 1), and apply RF drive, g1 will get much more drive voltage and current than it needs, and g2 will get much too little. In most cases the result is an excessive drive requirement, poor intermodulation performance, damage to the control grid and dramatically shortened valve life. That's the simple explanation. For full details, consult the characteristic curves of the tetrode you're proposing to use, and see what happens to the two grid currents across the whole drive cycle.
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