cap decoupling of triodes /intro

This is the lecture I held at the 2015 European Triode Festival (ETF). It is about new insights, new graphs and new formulas that I developed during 2015 for cap decoupling of resistance-loaded triode gain stages. There will be four blog posts covering it—here we go.

A small note upfront: occasionally in this series I will refer to designers and design practice. My insights in these matters are straight from my career as an interaction architect; in no way do I want to imply that I am an audio designer. (However, I did do an earlier ETF talk about applying my design nous to understand audio design.)

What I will present in this series is not a rehash from the books; it is my personal journey that I undertook this year, investigating this topic. Up to this year I had been using a math graphing program (grapher.app, as found on every Apple mac), plugging component values into a circuit transfer function and checking the resulting response curve, until I got what I wanted:

This is a cut-and-try approach, as is using a circuit simulator (SPICE), or breadboarding a circuit—measure the response, then swap parts—or listening and swapping parts.

At the beginning of this year I wanted to move beyond cut-and-try and take control of the issue. I wanted to understand how this works and clear formulas to work with. To be able to do quick back-of-the-envelope designs and to be able to work forward and backwards (i.e. from results back to design choices). I used my trusty math grapher to conduct my investigation.

before we start

This series does not exist in the vacuum of the absolute truth, but inside a value system. I better present that first. For starters there are the levels of effectiveness of audio design changes:

10.0 circuit architecture/topology;
01.0 component values;
00.1 component quality.

This list says that one can expect 10 times more noticeable results from topology changes, than from component values changes. Aand these values changes are again 10 times more noticeable than component quality changes. Now before you protest, there is one extra rule:

kaboom! enough errors at a lower level can destroy all your work.

Thus if you pick parts that are made of pure poison, you will get crappy sound, even if your topology is cool and your component values bang-on. And if your component values are off-the-wall, then it does not matter how inspired your topology is.

Here is a design thing: a long time ago I learned that the hand of the master can be seen in the big plan (circuit architecture/topology) and in the finessing of the details (component quality); the mid level (component values) is the journeyman level, easily learned in the first couple of years.

It happens to be that this whole series is about this journeyman level. We will not go into topology changes; there will only be triodes loaded by resistors and decoupled by one or two capacitors. Also we will not go into component quality, especially not with caps (oilers vs. plastic vs. ’lytics).

(but I will confess that I have a hidden agenda: I started this investigation to find out what the lowest cap value is that I can get away with, hoping that it would turn out to be so low that I can easily use some ‘nice caps.’)

imho

The second part of the value system is based on one of my earliest experiences with modding tube amplifiers. I had obtained this 60s Philips amplifier and did not have clue what to mod. However, my friend Daan van Egmond had given me some Audio Amateur issues and it seemed that just about every article said: ‘beef up the caps.’ And so I did; I beefed up the B+ cap of the input stage, by a factor of five. Old and new caps were of the same quality.

I switched on the amp, no blue smoke, played some music and for the first two minutes I was in awe with the new, rock-solid bass that I heard. After those two minutes I also heard that my treble was now… distorted; what used to sound like hi-hats now sounded like spray cans being triggered.

So I changed it in the opposite direction: half the original cap value. Wow, the mids and up had obtained this new free and flowing quality, but… the bass was now more wooly—compared to the original situation. I lived with that result for quite a while.

the bigger the better

Thus this series will be very much based upon the assumptions that—

• there is a right-sized time constant (R×C) that strikes the right balance between bass and treble;
• if the time constant of the circuit turns out to be smaller than 70%, or larger than 140%, of what you intended, then you failed because you are half an octave—or more—off; losing either in bass or in treble quality;
• when designing a full-range amplifier the question becomes ‘how much can you give up on bass and/or on treble’—you cannot have it all;
• when designing amps for use in multi-amp systems that this is all about optimisation: for bass in woofer amps, treble in tweeter amps, and something well-proportioned in relation to the pass-band in mid amps.

(I have been asked how time constants can have an influence on the treble quality. My current thinking is: look at a graph of a cap (dis)charging through a resistor. There is simply a maximum to the slope of the current, ^∂I⁄_∂t, which governs the maximum of amplitude×frequency that can be passed by that RC. The larger the time constant, the lower that maximum is. If it is too low, then you’ll get slew distortion.)

getting started

It is time to start rolling. First, each of us has to pick a bass cut-off frequency, ƒ_-3dB, to design with. I think we all can name some numbers we have used one time or another, but I want to do something else.

Here is another design thing: experienced designers move straight past what people say they want, find out what people need and design for that. It is a key to success. I’ll give you a method to do this for yourself, in this matter.

Before we get to ƒ_-3dB, we will first determine ƒ_interest; the lowest frequency that really matters to you. And instead of getting all philosophical about it, I suggest that you set it to the low-frequency limit that already exists in your system. This limit can be set by the source material, or by your front-end, but I will concentrate here on the most likely candidate: your speakers (in your room).

Thus if you have a pair of Klipsch La Scalas—

and their literature says (probably optimistically) that they go down to 51Hz (-4dB), then you can win more than two octaves of treble quality when you let go of 20Hz and settle for ƒ_interest = 51Hz.

I have these speakers, Spendor SP1/2—

and if I could convince myself to let go of the mythical 20Hz (hey, this is not easy) and align myself with its ‘typical in-room response: -6dB at 45Hz,’ then I can win more than an octave of treble quality.

Even with a Tannoy Canterbury—

—literature says 28Hz (-6dB). Still half an octave of treble quality can be won there.

summer of love

So now we all have a ƒ_interest in mind, tuned to everyone’s unique situation. The next step is now to pick a ƒ_-3dB that respects this ƒ_interest. Now where it comes to respect, there are two opposing philosophies.

The first philosophy is law and order. The bass is going to be completely authoritative and unflappable. This position will be represented by Mr. law & order himself, Richard Nixon:

I will use a ƒ_-3dB that is 10 times lower than ƒ_interest as a Nixonian position in this series.

The other philosophy is love and high(s). It is about liberating the mids and up, and kaleidoscopic experiences. Maybe it is even about getting high. This position will be represented by hippies:

I will use a ƒ_-3dB that is equal to ƒ_interest as the hippie position in this series.

Hippies to the left of you, Nixon to the right; now tell me, where do you stand in this matter?

You will fall somewhere in between these two extreme positions. Only experience can tell you where that is. No experience? Have I got a short-cut for you!

Ages ago (at a previous ETF in Denmark, go figure) my friend Christian Rintelen—former editor of the enthusiast magazine HiFi Scene Schweiz—told me that when you meet a person who has worked for years on their hi-fi system (building or buying) and have gotten to know their character (takes five minutes), then you will know what that system sounds like, before ever hearing it. The system will reflect the character of its owner.

And now we can apply this in reverse. Think of what you voted in the most recent elections. It is not for nothing that I just placed hippies on the left and Nixon on the right. Where your vote sits in the local political spectrum gives you a good starting value for how you like to respect ƒ_interest.

And with that, we got the result for this instalment: a ƒ_-3dB that is based entirely on the fundamental limits of your system, and your own character and principles.

doggy bag

Here are the take-home points of this instalment—

• This series is about the journeyman level of audio design: getting the component values right.
• Bigger is not better for time constants; the challenge is really much more about precisely positioning a pass band—of quality.
• Using ƒ_interest, you can win a lot by being reasonable.
• After deciding where you stand between hippies and Nixon, you can find your own ƒ_-3dB.

And that’s all. Next up: part two, where we will cut straight to triodes, resistors and caps.