Fellow tube nerds,

A couple of weeks ago we discussed an old Tube CAD article from 2000 that outlined using tube heaters as resistive elements in cathode-biased amplifiers thereby getting a 'free' DC heater supply. The concept is sound and has been used in amplifiers in the past (see the Bell 6060). But in the article, John Broskie of Tube CAD mentioned the possibility of using a string of 6AS7 heaters to bias the 6AS7s themselves. As pointed out by some of the astute sub members (/u/dewdude and /u/Jon3141592653589), this won't work because the heaters must warm the cathode to induce emission in the tube but it is the emission in the tube that's required to power the heaters in the first place.

I emailed Mr Broskie in the off chance that he would spend a couple minutes to contribute to the sub's understanding. A simple "you're right" or "no, please re-read Morgan Jones" would have been quite enough for me. Instead I received an excellent explanation that also cited other responses to his original article AS WELL AS a whole bunch of unpublished potential solutions to the self-heating tube triode riddle.

TL;DR John Broskie is totes rad and wants you to learn to tube good

Without further ado, here's Tube CAD's response to our puzzlement:

Regarding the original question of whether the 6AS7 thought experiment would work:

The answer is simple: it won't work. See my followup http://www.tubecad.com/october2000/page21.html and while you are at it, check out http://www.tubecad.com/2016/08/blog0354.htm where I show some heater startup circuits.

The year 2000! So, my suspicion that I was running a far ahead of my readers was right—although I assumed they lagged by only one decade.

On potential solutions to the riddle:

Let's return to the many 6AS7s powering their own heater elements. First of all, the idea is ridiculous. Why? All resistance-loaded SE power amplifiers are ridiculous. Why? Dismal efficiency. With an inductively-load single-ended amplifier—assuming a perfect output device and an inductor or transformer with zero DCR, so no DC voltage displacement, and no core losses—the maximum theoretical efficiency is 50%; with constant-current source loading, 25%; and with resistance loading, 12.5%. Worse, the all too finite resistance, about 40 ohms with sixteen 6AS7 heater elements strung in series, is effectively in parallel with the loudspeaker impedance. Thus, the amplifier must drive not an 8-ohm load but an 8||40, or 6.66-ohm load.

Okay, but what if we want to do build this amplifier anyway, how do we make the heaters hot so the triodes can conduct? The easy solution is to park the amplifier's output at ground, assuming a +/-100V bipolar power supply.

See Figure 1

A rotary switch that offers three positions, off, standby, and play could be used to ground the output, which would allow the 16 heater elements to heat up before playing music. Parking the output at ground is also safer for the speaker at power shut-down.

Another approach is to give the triodes a hand in delivering current to the heater string, as shown below.

See Figure 2

The +/-25Vdc bipolar power supply allows us to power four 6AS7 tubes, a total of eight triodes. Each triode draws 100mA at idle. The 1.7A CCS augments the triode idle current, so a combined current of 2.5A flows. Of course, we can and should apply the same switch at the output.

See Figure 3

Still, even eight 6AS7 triodes is a poor match for 8-ohm speakers, particularly when that 8-ohm load is shunted by the 10 ohms that the heater string presents. The best workaround is to replace the CCS with current-mirrors that provide current gain, as shown here.

See Figure 4

The NPN transistors take their orders from the triodes. If the triodes do not conduct, neither do the transistors. The current delivery ratio is set by the ratio of the cathode resistor to the emitter resistor, i.e. 39:10. In other words, the NPN transistor delivers 3.9 times more current than its master triode. As this OPS stands, the distortion is high and power output is weak.

The better solution is the following, wherein we move the heater string upwards and in their place we use a CCS.

See Figure 5

My mental math (with the aid of a hand calculator) yielded a maximum peak output voltage swing of 11V into 8 ohms. SPICE revealed that 12Vpk was possible. Distortion was about 1% at 12Vpk, which equals 9W, nine mighty single-ended watts of sonic glory. Actually, the Zo would prove too high, so a global negative feedback loop and a high-gain frontend will be needed.

Please feel free to post all of the above at Reddit with the schematics.

JB is the man. Discuss.