Did Leo Fender use math?

[Helmholtz]

I'm sure Leo was familiar with the standard tube literature of the time like tube manuals (e.g. the RC-19), the RDH4 or Terman's book and used the formulas given there. Also certainly knew how to use a slide rule.
Now, would you call applying simple formulas math?
Filling in numbers is quite different from deriving a formula or solving an integral or differential equation.

[Chuck H]

I'm sure Leo was familiar with the standard tube literature of the time like tube manuals (e.g. the RC-19), the RDH4 or Terman's book and used the formulas given there. Also certainly knew how to use a slide rule.
Now, would you call applying simple formulas math?
Filling in numbers is quite different from deriving a formula or solving an integral or differential equation.

Indeed! IMHE making a design work is just work. The math isn't typically that complicated given that we have tube data, spec sheets for components and ohms law. Leo used what was available at the time to do the best he could. The numbers that needed to be crunched were already defined. So it was more a matter of doing the work than discovering theorems.

[J M Fahey]

I am *certain* Leo used Math, and quite advanced type.
Not a formal Engineer but he was *a Tech* and a *designer*, he couldn't go far without it.

Notice he hardly ever used datasheet examples, if at all.
*All* his power amps *abuse" tubes ... all of them.

Typical datasheet examples suggest 300V plate, maybe 350, and 250V screens for 6L6 (just check them), he regularly used > 420-430V, sometimes higher, scary 400V on screens.
And they survived reliably, for many years.
You do not get there by blindly going wild and praying.

What I am also quite certain is he didn't use Calculus.
Surprise surprise: you don't really need it.

Straightforward designed is achieved by using regular "4 operations" plus squaring or square roots (to solve power, dissipation, impedance, etc.)
or the secret weapon: **graphs**
Which also solve many other branches of Engineering, as in plane wing design, airflow, motor power, torque, fuel consumption, complex Chemical reactions , epoxy curing times ...
*anything*.

Graphical calculation is *powerful* because you can accurately design stuff for which (think about it), no mathematical model has yet been found/created.

But you can vary parameters, measure results and plot them on a sheet of paper..

I do it all the time to design with "mystery tubes" (often TV tubes) for which no model exists because nobody cared and nobody expects to use them.in.Audio.

For example, when everybody was desperate in 2019-2020 because tubes all but disappeared and few left were sold for outrageous prices, I bought 1000 ECC189 @ 50 cents each.

There are datasheets but expecting it's "normal" use: VHF cascode TV tuners, with one triode getting 90V and the other 160V

I measured my own and have been using them happily.

As a side not, Leo must have not studied Calculus (because he didn't need it) but he studied and was certified as an Accountant, who *do* use a lot of Math.

Anybody deciphering complex and obscure IRS rules and regulations "is" a Genius in my mind.

[mozz]

Where is that picture of his shop, you can see scopes and signal generators. That to me is the same as using math.

[Mick Bailey]

From Wikipedia "In 1928, Fender graduated from Fullerton Union High School, and entered Fullerton Junior College as an accounting major, though he continued to work with electronics."

[Chuck H]

FWIW Leo didn't just START making Fender products. It was a gradual process bourn from his radio and amplifier repair shop that he ran for many years. Prior to that he had been contracted by some bigger venue recording acts to build PA systems. Something that wasn't available off the shelf in those days. He eventually saw that a profit could be made by building and selling amplifiers from his shop. Most were PA amps at first and then he and a partner (Doc Kauffman?) worked out designs for lap steel guitars and the "woody" amps. Leo always had credited engineers close at hand. Some employed by Fender and others just associates. I don't know how many were electronic engineers and the way the story is told in most articles you'd have to think Leo did everything by himself. He was known to be a workaholic but such a notion is ridiculous. Certainly he was no slouch having done a lot of custom design, repair and service and learning enough from that to develop a marketable product all before ever starting Fender. So no, he wasn't an engineer. But you can bet he used math.

[J M Fahey]

Almost forgot: his right hand Forrest White WAS a graduated Engineer, came straight from an Aerospace company (way back then it was a Defense company which had been building plane parts for USAF during WW2 ) and organized everything from parts stock and ordering to quality control to internal Factory workflow to ..... in a modern Factory way.
In fact, much of Fender legendary reliability comes from his "good build practice" ideas.

[Chuck H]

Sorry for this... I'm about to p!$$ in the bunchbowl

Just try telling any TrainWrech enthusiast that Ken Fischer wasn't an "engineer" As far as I know he wasn't by any scholarly credential but he had a long history building radios and troubleshooting for Ampeg in their hey day. That is to say, he had a head for it even though he couldn't show you papers to prove it. I'm not an engineer either, but, I do enough amp design that after evaluating the performance of Ken's circuits I almost can't believe how eloquent they are for the task at hand. That is to say that the tonal reputation of those amps is strong and he did it with fewer components than anyone before or since. It absolutely wasn't by accident. And my understanding is that while he could do any critical evaluation called for, he often didn't. For him the circuits were so basic that he didn't have to so he tuned his circuits by ear with a nod toward knowing how to not blow things up. I expect Leo had some of that mojo too and the engineers on staff were there to bounce ideas off of and/or consult on occasional intricacies. But that's just my guess. That said...

There are definitely a couple of clunky things done in Fender amp circuits. The most prominent and ubiquitous would be the BF/SF reverb coupling circuit. What a noisy piece of doo doo. And yet the Fender reverb sound is the benchmark. So I digress.

EDIT: Also FWIW, Ken had access to many amp designers with engineering credits as well. Though the information was usually flowing the other way since Ken had already built his reputation in mods, repair and builds. But Ken only made a hundred amps! Leo built an empire!!! So of course he aligned himself with people that could and would help. Two sides of the same coin.

[Justin Thomas]

Ken had gone to the RCA electronics school, same as Jess Oliver & numerous other amp people back in the day. I don't recall if I read it in the Ampeg book or Dave Hunter's interview with Ken, but I do know Ken Fisher had "some sort of schooling," and IIRC Ampeg paid for it for him.

I think a lot of great amp designers (I did not say "famous" so some of y'all here go into this category) know SOMEthing of the tech, more or less, degree or not. The thing that sets them apart is a willingness to go beyond "the book" when it matters & when to stick to good practice (mainly construction & preventing self-immolation of said amp).

Myself? I could stand to learn & do more math, but I can swap a part quicker than I can do an ohm's law calculation. I just do enough math to not cook transformers & the rest is "like, you know, whatever!" None of my customers have called about blown-up amps yet so I must be doing SOMEthing right.

Jusrin

[Helmholtz]

The most prominent and ubiquitous would be the BF/SF reverb coupling circuit. What a noisy piece of doo doo.

Not sure what you mean.
Could you elaborate?
What would you change?

[Helmholtz]

Now we have over 20 answers, but still no explanation from the OP why the issue matters to him.

[Chuck H]

Now we have over 20 answers, but still no explanation from the OP why the issue matters to him.

I thought the same thing. And I think I get it. The earliest vintage circuits are very close to what was found in standard circuit documents at the time. So designing those amps looks a lot like the "put part A into slot B" method was used. Then later as the circuits became more specialized there are some seemingly constant methodologies. Like Fenders ubiquitous 12ax7 triode amplifier stage of 100k plate, 1.5k cathode bypassed by a 25uf cap. These values were used almost regardless of plate voltages or specific circuit impedances. Whereas other manufacturers 12ax7 triode stages varied A LOT even stage to stage. So it looks like less evaluation was done by Fender.

To be clear "I" don't feel this way. I have a very different interpretation. Just saying that I can understand where the notion came from.

[Helmholtz]

I thought the same thing. And I think I get it. .....

Yeah, but that would be the technical background.
What I meant was, why would he like to know.
Maybe something like "do I need to learn math to become a good amp designer?"

[Chuck H]

Not sure what you mean.
Could you elaborate?
What would you change?

To be clear I do think that the Fender circuit has good signal performance. It's just noisy. Any hum might be attributed more to grounding specifics than the circuit itself? But it may also be that the reverb level is reamped twice before the PI so any hum analogous to the reverb recovery stage, which is amplifying a very low level signal from the tank, is amplified again. Every Fender amp reverb I've used had more hum than I was happy with which gets louder as the reverb level is increased.

And then there's the dry signal pad divider of 3.3M to 4.7M with the 470k/100k pot as the shunt. This high resistance/impedance circuit adds johnson noise to the dry signal.

So there's hum and hiss. I think it's interesting that Fender abandoned the 6G16 Vibroverb circuit in favor of the later circuit. The 6G16 pads the dry signal with a split plate load so there's a lot less series resistance. I used something similar to the 6G16 reverb circuit in the first reverb amp I built. There's no hum advantage but there is less hiss. And I actually AB'd both Fender coupling methods when I built that amp and chose the one I liked best for noise and performance.

The last reverb amp I built is very different. I coupled the channels and reverb to a virtual earth circuit and used a dual gang pot for the reverb level control that simultaneaously acts as a standard, voltage divider type volume control and adjusts the series resistance to the VE circuit. This way there is no actual padding of the dry signal, just a unity gain stage and amplification is still achieved for the reverb signal. It works just great with a lot less noise. For tonal reasons I have the recovery stage partially bypassed but this circuit still hums less than any Fender amp. Like I mentioned, this may have to do with grounding specifics for the Fender amps.

Rather than make you figure it out the hard way I'll just clarify this amps features. It switches between being a Fender type amp and a Vox type amp with a front panel switch (no footswitch for this). It has only one set of tone controls on the panel but two tone stacks wired on dual gang pots. This way I get the tone I want from either "channel" but I don't need two rows of knobs. It's not so much a two channel amp as a two voiced amp. With reverb and a bias wiggle trem. The reverb works great. I'm less exited about the trem. It's ok but I want it to be better. I'm not sure a bias wiggle trem is the best circuit for tubes with high-ish voltage and fixed bias.

[J M Fahey]

"Like Fenders ubiquitous 12ax7 triode amplifier stage of 100k plate, 1.5k cathode bypassed by a 25uf cap. "

Well, *that* comes straight from the datasheet, go figure.
Check RCA, Sylvania and other old datasheets.
Probably Philips too, about ECC83.

Why it's universal use?
You don't mess with what works fine..
In any case, it's not a full design but a "gain block".
If it works fine, why change it?

On the other side, competitors slightly changed some values, say Peavey 150K plate resistors, more to state "hey , I am not blindly copying Fender" , than any real need.

I can justify 220k plate resistors in high gain amps trying to get a couple extra dB.