The general small-signal model of a tube is pretty much outlined at the link Madmanguruman posted: a current source in parallel with a plate resistance and the associated inter-electrode capacitances.
For non-linear time domain analysis, the situation is more complicated as outlined here. As the article states, it's possible to derive a mathematical model of a triode or pentode based on the Langmuir-Child law, but that model doesn't accurately represent the real behavior of a tube in certain areas of its operation. The best models are "phenomenological" i.e. designed to fit a tube's actual performance curves as closely as possible without regard to underlying physics.
There is a program I've used available that will let you take published tube curves, fit the model to the curves, and then spit out a SPICE subcircuit. It works well for triodes, I don't know if it can be used for pentodes though. There are also many, many ready-to-run SPICE models of varying quality for a variety of different tubes on the web.
Certainly possible. The classical way is to overload a pentode amplifier stage and measure the way the anode current drops as the signal level increases. So the anode current is a maximum at zero signal, and progressively (but non-linearly) reduces as signal level increases.
You will find a schematic on page 5 of this manual for a precision audio test set, the (1960s) BBC Designs Department ATM/1, which was usually partnered with the TS/10 Wien bridge oscillator. Beautifully made, and a few still around when I joined thu BBC in the 1980s - though you only used it if someone else was using the EP14... I had the opportunity to buy one after they were all retired.
The relevant circuitry is V4 (rectifier), V5 and V6 on the schematic (p.5) - V6 is a barretter (??? a voltage stabiliser), providing a stable voltage (130V I think) to the screen grid. As the anode and screen grid share the cathode current, this is important to getting the law right. (V6 can probably be replaced with zener diodes, if you don't mind a little passive silicon!)
V5 (CV454) is a 6BA6 in my example.
Note the adjustments R51,R52 for "zero" and "law" - there is a strict calibration procedure against known reference levels to get the law accurate enough for broadcast work. Best description of that procedure I can find online is here.
For a VU meter you will have to adjust the attack and decay time constants (R35,C15,R37) to slow the metering down - increasing R35 to about 100k may be a good start, as this is a Peak Program Meter not a slow (averaging) VU meter, designed to measure short term peaks which could overload a transmitter.
Also, as "zero" corresponds to full current and "max" to zero current, this circuit assumes you can ask the meter manufacturers (Ernest Turner) to make you a right-hand zero meter! If you can't, and don't have as eclectic a junk box as mine, the simplest solution is to mount a regular meter upside down...
Source : archive of old BBC equipment manuals and select "ATM1".
Best Answer
To complete Nils’ answer, in audio applications, transformers are needed to adapt the low speaker impedance (generally between 4 or 16 ohms) into a load suitable to power tubes (generally several kilo ohms). As the output power raise, the biggest transformers need to be. In the case of a single ended output stage, they must use class A mode. A constant current goes through the transformers and does saturate its core. They need to be air gapped hence over sized to provide a reasonable primary inductance while standing the constant current.
This is one big reason why an output watt is so much more expensive with tubes as compared to transistors. In hi-fi applications, the output transformer is responsible of the amplifier’s output bandwidth limitation (and phase twists) due to stray capacitances and leak induction. In the other hand, it provides a galvanic protection to the (maybe expensive) speaker system.
For a stereo amplifier, that makes at least 3 transformers (1 power supply, 2 output) that need not to induce noise into each other. As tubes use high voltage (up to several kV sometimes) self-inductances are often used in CLC cells to filter the 100Hz ripple out of the power diodes. They have values from several Henrys up to dozens of Henrys and are as big as a transformer adding a bit more weight to the whole.
That is why tube amplifiers are -- most of the time -- so heavy.