Uf = 0 turns of the heater and stops operation. Perhaps you meaned something different?
I have doubts that PC88 will oscillate at 3GHz, even in this configuration. Did you actually measure the oscillation frequency?
The PC88 was designed for the old TV UHF tuners, and it has the maximum oscillation frequency at about 1.2 GHz.
http://www.electrojumble.org/Tuners01.pdf
Sad to say, I can remember all those tuner models!
I also think you are pushing your luck to get a PC88 much beyond 1GHz and in any case the PC86 was the one designed to be an oscillator. Those 'bottles' had a very short life expectancy, possibly becauase they were buried under so much shielding and ran red hot. If you have a salvaged one, treat it with suspicion, it has seem more than a few days use it will have deteriorated already.
Brian.
It might work but I see a potential problem with making the grid more positive with respect to the cathode. It will behave like a diode and the extra voltage may force too much current to flow between the grid and cathode. Typically, when that happens you see a glow in the gap between them and the cathode coating gets damaged.
'Uf' is only the heater voltage "U" being a reference to Voltage and "f" for filament. It can be either polarity if it makes the construction easier. If you try passing signal current through the heater you should expect some instability and long delays before the frequency stabilizes.
Brian.
Yes, the answer is: build it, and measure it.
As was already stated, those tubes have very short life even in normal conditions, but when you push to their limits with 20mA-40mA grid current, they die even sooner.
https://upload.wikimedia.org/wikipedia/commons/3/33/Barkhausen_Kurz_PC86.jpg
This was the reason, when the first hybrid TV sets appears (valves+transistors), the first block that was replaced by transistors was the VHF/UHF tuner.
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