What is meant by Vf?
Vf is the filament voltage of a vacuum tube.

Some tubes, especially those intended for battery operation, had a single wire that was both the cathode and the heater.  This was often called the filament.  The differential voltage controlled the heater, and the common mode voltage the cathode.  Some types had a center tap to more easily set the common mode voltage in the middle of the cathode.

Look up a 1H4 as a example of about as simple a triode as there is.  The filament has no center tap and requires 2 V at 60 mA thru it for it to work as the cathode.  In contrast, the 3V4 is a power pentode meant for battery operation and has a center-tapped filament.  This is the type of tube you would have found in the audio output stage of a small portable radio.

Other types of tubes had a separate heater that was not electrically connected to the cathode.  For those, there was a separeate heater and cathode, so Vf was not used.