Which way is better to feed the heaters of a vacuum tube on a guitar amp, AC or DC?
With the same transformer, is it possible to change between AC and DC supply for the heaters?
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There are two types of heaters. In one, the cathode is a hollow cylinder and the heater is inside the cathode but electrically isolated from it and everything else. In the other type, the cathode is a wire with at least two connections. Current is passed thru this wire to heat it while its common mode voltage is driven with whatever signal is supposed to be on the cathode.
In the first type, the heater can be driven by AC or DC. It doesn't matter as long as the RMS voltage is right. Common voltages were 6.3 V and 12.6 V. This type has the advantage that since the heater is completely isolated from everything else, it can be driven directly be a separate secondary of the power transformer just for that purpose. The downside is that it takes more power to keep the cathode at the proper temperature.
The second type must be run from well-filtered DC. Since the cathode has some resistance end to end (it must to dissipate power), there will be a voltage difference end to end proportional to the heater current. This will show up in the output signal if it varies. This type of tube was usually used where power usage mattered, like in battery operated equipment. Usually there would be a separate battery for heating the cathodes. The heater voltage was often 3 VDC in these tubes, since that was two ordinary cells in series.
The normal rating for vacuum tube heaters is 6.3 volts and 12.6 volts. The 12.6 heaters normally give an option for a centre tap so they can be connected as two 6.3V.
There was always a debate about which was best A.C or D.C. but the original amplifiers were wired as A.C.
The perceived benefit of rectifying was to reduce hum but the rectified power still contained a large AC component at 100/120 Hz.
The other answers are correct; tubes can be heated with either AC or DC. Traditionally AC was used for economic reasons - it saved the expense of a rectifier - except in low power (battery) equipment - which wouldn't apply to a guitar amp.
Now with AC heating, there will be some small variation in cathode temperature across the AC cycle, and this modifies the emission characteristics. In a push-pull amplifier, everything cancels out under small signal conditions and the amp sounds quiet and clean, but under heavy load (where one valve is conducting hard and the other is off) this contributes some intermodulation products.
Hi-fi amplifiers minimise the audible effect using negative feedback, and modern ones can afford (especially at those prices!) to use regulated DC heater supplies; but that's not what you are designing : these imperfections are partly responsible for the grungy guitar amp sound.
So I would use an AC heater supply as a deliberate part of the design, especially if you are trying to achieve something like the original guitar amp sound.
In most amps, valves can be heated with AC or DC. Tapping the heaters may be important since the heater filaments can act like a diode if the cathod is some volts above heater potential (which is the case most of the time with auto bias) and induce AC hum in you beloved signal.
Make the heaters center tapped +15V above low signal tubes' cathode can prevent this problem to appear. Be sure to respect maximum cathod to heater voltage given by the data sheet for all your valves when you design the heater circuit.
A vacuum tube device's heater filament can be supplied with either DC or AC, the tubes work the exact same way with either type of supply: The heater is simply using the power for resistive heating.
The voltage to be supplied would also be the same, i.e. if a tube is rated for 12 Volts, then one uses 12 Volts DC or 12 Volts AC.
On the second part of the question: To take the AC output of a transformer and convert to DC, an additional bit of circuitry is required: A rectifier (either a bridge rectifier or a half-wave diode) followed optionally by a capacitive (or sometimes an LC) filter, then perhaps a voltage regulator, depending on what purpose the rectified power is to be used for.
For heating coils in vacuum tubes, there is no benefit to rectifying the AC supply, just use the AC.