At this point, one should be sure to make a distinction between a triod and a penthod, they are rather different animals!
A penthod is pretty much a current source when Looking at the device from a load side. The translation of tube current to anode voltage is relatively simple - multiply the current by the load impedance, thus the gain is A = gm * ZL (ZL is the load impedance).
The triode does not look like a current source, its output resistance is not that high thus the gain is
A = (mu * ZL)/ (Rp + ZL) where Rp represents the tube impedance.
When talking about linearity, the first thing to observe is what takes place is to look at the relationship between grid voltage and anode current. Say we take the EF804 that was mentioned earlier. Clearly the curves show much better linearity near 0V grid voltage, and as one goes to more negative grid voltage, the curves (grid voltage vs, anode current are EXTREMAL non linear.
But the above does not mean that one can get best linearity operating near grid at 0V. Operating near V grid = 0V means much higher tube current which does impact things -
more current means a higher dissipation and heat, and it may require lower loads to avoid operation at very low anode voltage, where the tube encounters another type of non linearity. Either way (high current and low load or low current and high load, or operating between), one ends up with limited gain.
Now, lets get some perspective. Say we take an open loop (no feedback) EF804 operating at say 140V anode voltage, with a grid bias of say 3V (pretty typical). Say we input a grid voltage of 1KHz sine wave with 1V peak.
At no signal Vg = -3V and Ia = 1.5mA
At positive peaks, Vg = -2V and Ia = 3mA
At negative peaks, Vg = -4V and Ia = 0.5mA
So the AC signal positive peak is 3-1.5 = 1.5mA
The AC signal negative peak is 1.5-.5 = 1mA
Now draw a sine wave where the negative peaks are 66% of the positive peaks. The distortions are HUGE! we are not talking about .001% linearity. We are not taking 1% linearitry either. We are talking about huge non linearity!
In fact, I do not believe the eye can see a difference between a .001% and a 1% curve, they both look like a stright line. The EF804 Vg vs Ia curves look like way over 10% distortions for a 1V peak signal. Open ended tubes are highly non linear, and of course, like all devices, they will get more linear when the input signals get to be very small.
So what does one do? One weighs the many variables (including heat and reliability) and one optimizes a circuit by considering various trade offs, no different then the design of any circuit. When it comes to linearity, one can trade off some (or all) of the open loop gain of a device for linearizing the circuit. Say one has 60dB of open loop gain AOL (gain of 1000), and a certain amount of distortion POL (percent distortions open loop). The device also has a certain given bandwidth BWOL (open loop bandwidth in Hz).
One can keep the circuit as open loop with AOL, POL and BWOL (gain distortions and bandwidth under open loop conditions).
Or one can apply negative feedback. Applying negative feedback WILL REDUCE THE GAIN OF THE CIRCUIT. The more feedback, the lower the gain. If the feedback amount is say 10dB, the "left over gain", the circuit gain with feedback is 60dB - 10 dB = 50dB (open loop gain - feedback = closed loop gain). If the feedback is say 30dB, the close loop gain is 60-30 =30dB. If the feedback is 60dB the closed loop is 0dB (gain = 1, no gain)as is the case with a follower circuit.
So why waste the open loop gain? The reason is - one gets an improvement in BOTH distortion and bandwidth. Say the open loop gain was 60dB, the distortion was 10%, the bandwidth was 10KHz. With feedback of say 40dB (100), we end up with circuit gain of only 20dB, but the distortion is down from 10% to
10/100 = .1%, and the bandwidth of the closed loop circuit went way up as well...
So it is about the circuit design and tradoffs one makes.
But the facts are:
While one can get a lot of open loop gain from cascading devices, tubes are expansive and most designs do not use a lot of tubes to raise the open loop gain, therefore the distortions tend to be higher, especially at signals higher then a few millivolts.
Having less devices in the circuits would be great if the devices were perfect to Begin with. In fact, going for less distortions would take a gradual step by step buildup, many stages in series. In my above example, one can not get a 60dB
and .1% in one step, because the single device yields 10% at 60dB. But 3 stages of 20dB each, with 40dB negative feedback per stage will almost get you there and 4 stages with 45dB feedback in each, will yield even better linearity.
Now, .1% is still a lot of distortions in my book, and the above was just an example. There are many people in audio that like tube sound, and are willing to accept and acknowledge the reality, that tubes circuits have distortions. In fact many people openly state that they like the coloration (distortion) due to 2nd harmonics and so on.
But here I saw some comments by some claiming that tubes are linear.
The facts are: Tubes are not linear. Transistors are not linear. Fets are not linear. The nature of the non linearity of tridoes, penthodes, bipolar transistors FET's are all different. Those devices all have huge device to device tolerances, temperature dependent behaviour... At the end of the day, it is the circuit that counts. One can choose to retain some of the open loop device characteristics in a circuit, and in that sense, a tube will sound different then a FET and a FET is different then a bipolar. That is because a square law is different then an exponential curve, the "inter electrode" capacitance in a semiconductor changes differently in a semiconductor then in a tube, and so on. But At the end of the day, it is the circuit that counts.
Like the tube sound? That is OK with me. You want to claim that tubes are less noisy and distort less then transistors? I have an issue with it - tubes and transistors distortions and noise should not be examined out of the context of real circuits, and there are many different circuits and component values that make for different outcomes.
Regards
Dan Lavry
www.lavryengineering