sound practices reading club /4

Now that we know where we are coming from, acquired an attitude and wired our minds, we are going to get hands-on today: a double feature of an article showing some practical circuit calculations and an inspiring article that references it.

First up is from the archives: Making Use of Load Lines from sound practices issue 2, written, in 1955, by Norman Crowhurst. In it, he describes first the way to draw and calculate the DC operating point of a resistance loaded gain stage. Then he shows how the AC load line is superimposed on that and dynamic operation is checked and actual gain calculated. Then we are told that really the whole procedure works in the opposite direction.

teaser quote: ‘[…] the neat little table of tube characteristics does not tell the whole story. The best link between theory and practice, which enables the prospective designer of an amplifier to come fairly close to the right answer the first time, is the use of graphic tube characteristics and the drawing of load lines.’

a gift from Joe Roberts, SP editor: from the sound practices CD, here is the original article.

pop quiz

Can we find out more about the unnamed tube he is using here in his example? Yes we can. In figure 2:

• by drawing a horizontal line at 6mA, we see it cuts the zero and -1 volt grid lines with 50 volts in between. So one volt on the grid swings 50V on the plate, maximum: µ (amplification factor) is 50.
• by drawing a vertical line at 150 plate Volts, , we see it cuts the zero and -1 volt grid lines with 3.8 milliAmperes in between. So one volt on the grid swings 3.8mA on the plate, maximum: gm (transconductance) is 3800 micromhos.
• by following the slope of the -1V grid line between 150 and 200V, we see that the plate current goes up by 3.8mA: rp (plate resistance) is 50 / 0.0038, about 13 kiloOhm.

These numbers matter when selecting tubes or working out circuits with them:

• the µ is the maximum voltage amplification possible. depending how you hook it up (resistor loaded; choke loaded; active load) you will get 50–100% of the µ. From that you can select the tube with just the right µ for your needs.
• the plate resistance determines what values of resistor/choke/active load you can use on the plate and what value of loads (either the next stage or a speaker via an output transformer) you can drive with that.
• transconductance completes the picture: µ = rp * gm. The three values are interconnected this way at any given point in the curves. Transconductance is used for more tricky calculations than we are doing right now. Note that when selecting tube types, really high transconductance is a warning sign: those tubes are usually not very linear (bendy, unevenly fanning out plate curves) and have a lot of spread in characteristics tube–to–tube because everything is very closely spaced inside the tube.

practical note: the formula in the first column of page 2 for the parallel resistances should be R = (R2 * R4) / (R2 + R4).

Also, the formula given for the kathode bypass cap C2 is a bit too simple. This cap really has to work against a combination of plate resistor R2, plate resistance rp and kathode resistor R3. [correction, 25-2-16:] Finally, the correct formula for calculating the kathode bypass cap is available. It took me years, but at the end I could not take it any longer that all of tube literature had no (correct) answer to this question.

The second article is from SP16: MV45 Convertible written by Steve Berger. The pattern that emerges in this article should be familiar by now: a combination of musical and technical goals, attitude and inspiration, and making it work on a existing chassis. This time, Steve’s way. Read Dorwin Gregory’s consumer-side review if you like to.

teaser quote: ‘My point is that, it’s not the recording, it’s where the recording takes you that is the most important thing. These machines can, in the hands […] of the right person, be transportation devices, even time machines.’

my take

Crowhurst’s article is the practical side of what jc wrote two weeks ago: ignore the tube manual’s suggested operating points, do your own empirical research. Here is where the fun starts. Working with the curves and taking available B+, needed gain and voltage swing into account, you try to set up a dynamic load line in the part of the tube curves where they are straight, parallel and equally spaced. That’s where triodes are superbly linear.

Steve Berger did the same for his MV45. Note that the first tube in this amp is set up by the 14k on the plate and the 2k5 in series with it to B+, it is 16k5 that you use to play around with in the 5687 curves. Now here is a snag: Steve chose not to bypass the kathodes of the first and second stage. That saves him and Dorwin having to listen to two more smearing capacitors connected to a very sensitive terminal of a tube. But nothing comes for free.

The result is that Steve has set up the MV45 stages for DC exactly according to the Crowhurst article, but for AC the connection is lost. With an unbypassed kathode resistor, rp is increased by (µ+1) times that resistor, µ is unchanged and from µ = rp * gm, gm is reduced proportional to rp’s increase. The result is that for AC the curves look significantly different and a graphical way of exploring how the stage will work is no longer possible.

After picking up a datasheet via tdsl.duncanamps.com we see that the 5687 is, at 16mA where Steve is using it, a tube with µ of 17.5 and an rp of 2k5. For the first stage rp becomes 2k5 + (17.5 + 1) * 82 = 4k, for the second stage it is 2k5 + (17.5 + 1) * 470 = 11k2. The former being a 60% increase in rp, the latter a massive 350%. That makes it no longer the low rp driving tube Steve selected it for.

Now go and read the articles, see you next week.

ps: read about the classic 45 in issue 5: Meet the Tube: the 45.