cap decoupling /5 : ultrapath

‘What about ultrapath?’ an engineer and tube enthusiast asked me, in reaction to earlier instalments of this series. ‘Yeah, what about it?’ I thought. I just wasn’t very interested. That is, until a couple of minutes later I started thinking of current paths and I realised I had the method at hand to deal with this topic in a structured and comprehensive way. Ah, then I am interested.

personal note: this blog post sat as a draft in my editor for half a year because within days of starting writing it, it was ballooning out of proportion. I did not know what to do with it for a long while. At the end I decided to finish it and publish it in one piece, because the topic of ultrapath does not deserve a series of posts. If this post is too much of a book chapter for you, then just check out the short version circuit analysis, the verdict of how each circuit scores and take away the doggy bag at the end of this post. Here we go—

In this instalment I will look at a number of claims that are made (or, at least I think they are) for ultrapath connection of capacitors:

1. you avoid using a kathode capacitor;
2. you can use smaller-value caps, maybe even ideally-sized;
3. only one capacitor is in the signal path; a chance to optimise its quality and use cheap and ugly for the other ones;
4. a hum/noise cancelling setup can be created.

Now, let’s look at them current paths.

the general case

This generalised schematic covers a whole lot of triode stages with gain:

• usual suspects for the plate load are: a resistor, choke, or active load/CCS;
• Z_filter is part of the B+ filtering; usuallya resistor, choke, or CCS/electronic resistor (see part 2);
• common options for coupling are:
• R-C (coupling cap to grid resistor);
• L-C(coupling cap to grid choke);
• DC (i.e. a piece of wire, no connection to reference/ground then);
• a little less common: a level-shifter (some silicon or a VR tube set up to drop a fixed number of volts between the plate and the receiving load).
• common examples of a receiving load are:
• grid of a tube;
• input terminal of something made out of silicon;
• an RIAA network;
• tone controls/tone stack
• a cable, followed by the input of the next ‘box’ in the signal chain.

That makes for at least 180 different circuits we are looking at here, in one swoop. If this is a little too abstract, think of the plate load and Z_filter being a resistor, R-C coupling and a tube receiving load and you got this familiar sight:

currents here, currents there

There are three AC current paths that make our generic circuit work. The first one is what I call the generator current:

This is how the tube works; varying the current through the plate load. To complete the circuit, the path between B+ (above the plate load) and the kathode needs to be closed for AC.

Next, what drives the receiving load, through the coupling? First up, it is the tube:

If the coupling is connected to reference/ground then current has to return from there to the kathode. Certainly this is the case for the current driving the load. Combined, this is the signal-kathode current. To complete the circuit,the path between reference/ground and the kathode needs to be closed for AC.

What also drives the receiving load, in parallel to the tube, is the plate load:

This is the signal-B+ current. To complete the circuit, the path between reference/ground and the B+ (above the plate load) needs to be closed for AC.

no excuses

Now, we got to have a serious talk about these currents, because I can see some of you thinking ‘some of these are negligible, I don’t have to take care of all of them.’

Concerning both signal currents (B+ and kathode), the signal is the current and the current is the signal. If you really did your best and managed both signal currents to become zero, you would have also killed the music: zero signal.

The generator current does not reach the receiving load. Can you hear it, then? Maybe not. But any funkiness in the generator cycle is sure to show up in the signal currents.

Some of you may have also noticed that when the plate load becomes really large (for all frequencies, so we are talking CCS), then both the generator and the signal-B+ currents becomes really small—but not zero. You do not have an open-circuit (for AC) plate load. I think it is safe to say that we all do not do TeraOhm (one million MΩ) CCSes, either (I do believe some people on this planet can build a TeraOhm CCS, but surely they do not read this humble blog). However, I would not miss the clue that reference/ground to kathode becomes in this case the most-exercised current return.

Thus we have to take care of all three currents, always. If we do not take care of them, they will take care of themselves, with anarchic results. We would have lost control then, of the behaviour of the circuit. Especially the two currents involving B+ have plenty of opportunity to get back there via other routes—with extra impedances and frequency dependent filtering along the way.

love triangle

You may have noticed the repeats in the current path descriptions. Indeed, the three return paths form in a neat triangle:

Anything with low AC impedance can connect these three, but since this series is called ‘cap decoupling’ we are going to do it conventionally: with capacitors.

In general, these three required connections can be provided by a belts-and-braces three caps hookup that implements the triangle:

But we can also be a bit frugal and note that in this triangle configuration, any of the connections can be provided by the series connection of the other two (e.g. you can also get from B+ to reference/ground by hopping via the kathode). In other words: two caps are enough.

There are three configurations with two caps. The first one is the conventional one:

yeah, yawn.

Then there is what I call ultrapath-A:

and ultrapath-B:

That’s right, ultrapath configurations consist in general of two caps, simply because there are three current paths to take care off. Ultrapath claim number three—only one capacitor is in the signal path—looks, in general, unattainable.

In just a moment, we will check out how these four variants differ.

one on one

Have a look again at that triangle image above. When we define ‘kathode = reference/ground’ (i.e. connect the kathode directly to ground and bias our tube via its grid), then the green path disappears and the other two become one and the same thing: a path between reference/ground and B+ (above the plate load). Now all current returns can be handled with one capacitor and no kathode capacitor is needed:

It is cool to see how this single capacitor ties the whole circuit together. But not all is rosy. We have already experienced once how the requirements of B+ filtering leads to a B+ cap that is 10–100 times too large for its job of closing the current paths.

note: this type of circuit can also be achieved by nearly shorting the kathode (for AC) to reference/ground, e.g. with a battery, diodes, or a very small resistor (see part 3).

And now the other side of this coin: when you use aconventional kathode resistor, you will have to use a kathode capacitor (or else degenerate). You will notice that on all of the schematics that follow in this blog post there is a kathode cap. Yes, also in all the ultrapath ones.

This settles claim number one for ultrapath: avoiding a kathode capacitor is not a trait of ultrapath; it is only related to (not) using a conventional kathode resistor.

the big, fat exception

So far, so general. Then I noticed that there is topology that does not fit this mould. It is not an obscure one:

Transformer coupling! Z_filter is the same array of options as in the general case. The options list for the receiving load is that of the general case, plus one: loudspeakers. That is then an additional 18 circuits joining our survey.

Notice how two boxes are missing from the image above? That is because plate load and coupling are now one and the same thing: the transformer. This unification has an interesting side effect. There is only one current path:

The generator current is the signal current. I must say that this single, pure current path makes transformers even more sympathetic to me than they already were. It also means we have found the potential to realise claim number three for ultrapath: only one capacitor is in the signal path.

I say ‘potential’ because there are a couple more mundane tasks to take care off here: filtering the B+ and keeping the kathode at reference/ground for AC. And thus we can roll out another four cap configurations. There’s three caps:

conventional:

ultrapath-A:

and ultrapath-B:

These four variants will also be checked out, below.

spoiler: also for transformer loading the rule is: if you use a conventional kathode resistor, you will end up with a kathode capacitor (or else degenerate)—see below.

voodoo child

And just when you thought the streets were safe… there is yet another odd one out. It is the love child of the general case and the big, fat exception. I will unveil that one when we are through with checking out the eight cap variants we have rounded up, up to now. We will have then the understanding to swiftly deal with it.

conventional caps

Let’s get started with evaluating cap configurations. We lead off with the general case:

short version: not much to say here, simply the baseline for our comparison.

the (slightly) longer version: With our newly-won insight we can say that the two caps directly take care of both signal currents, B+ filtering and AC kathode grounding. The generator current takes the back seat and goes trough both caps.

transformer

short version: again, simply baseline.

the (slightly) longer version: knowing that there is only one generator/signal current path to deal with, it is slightly annoying that it has to go through both caps.

ultrapath-A

The general case:

short version: the kathode cap gets connected to B+; same value as a conventional-caps C_k; theoretically, a smaller C_k value can be achieved; full B+ noise gets injected into the kathode, leading to a lot more noise.

longer version: it may sound a bit flippant, but ‘kathode cap gets connected to B+’ immediately puts us on the right track. Look at the image above and the one ‘2 up’—for ‘conventional caps, general case’. The following description is true for both of them: as the impedance of C_k rises, more current goes trough the kathode resistor, creating a voltage that is amplified by µ+1 by the tube, degenerating it.

For C_k on its own, the formulas for the stage response are the same here as for conventional caps.

Now, what is different is that for conventional caps C_k works in series with the B+ cap (C) for the generator current and thus has to be compensated (read: increased) for that. For ultrapath-A, no such compensation is needed. It is worth noting that our experience up to now has been that this increase is mostly insignificant, because C is really (too) large: 10–100 times its ideal value (i.e. just big enough for the rp, plate load and ƒ_-3dB). There is only going to be a noticeable reduction in C_k when C < 10C_ideal, and only a significant one when C < 4C_ideal.

Thus ultrapath claim number two—smaller-value caps—is theoretically true, but in practice insignificant.

buzz

We do have a noise problem here. The full hum, noise and signal induced fluctuations of the B+ are coupled by C_k into the cathode, for the whole audio bandwidth. How much more noise is that? Our baseline is ‘conventional caps, general case’—

noise_conv = rp / [rp + Z_plate load] × noise_B+

The tube and the plate load form a impedance divider. Note that it is good for this spec to have a large-value plate load.

For ultrapath-A the B+ noise is fully amplified by the tube—taking the plate load into account—and added to the conventional noise:

noise_ultra-A = [rp + (µ+1)Z_plate load] / [rp + Z_plate load] × noise_B+

Comparing the two, the noise increase is—

ultrapath-A/conventional = [rp + (µ+1)Z_plate load] / rp

This quickly spins out of control for even moderate plate loading and moderate µ (e.g. loading = 2× and µ=20; increase = 43, i.e. +33dB). note: high µ and/or high-value plate loads (choke, CCS) are severely punished.

You may now think ‘I can grit my teeth and deal with an extra portion of noise.’ Well, maybe. But what is also increased by the same amount—in multistage amps—is negative feedback in the bass region (sounds bass-shy) and susceptibility to motor-boating. Nobody likes motor-boating.

Thus users of ultrapath-A in general-case circuits have to really filter the B+, a lot to counteract that noise increase we just calculated. You really want to be carful about the drastic measures you are going to take for that. Note that both signal currents go through the B+ cap (C). Also, a huge single time constant in your B+ filtering will make a slight compressor out of your stage. I advice to use a two-stage B+ filter, with identical time constants, to provide what you need.

The verdict; achieving the ultrapath claims, when compared to conventional caps:

1. (avoid kathode cap): false—nothing to do with ultrapath;
2. (smaller-valued caps): theoretical (for C_k); insignificant in practice;
3. (one cap in signal path): false—not for general case; 3 current paths;
4. (hum/noise cancelling): quite the opposite; it’s a noise explosion.

This circuit is really a trouble magnet. It is educational and prepares us for what comes next, but I do not know why anyone would use this.

transformer

short version: the kathode cap gets connected to B+ and it is the only one you will hear; the rest is quite like the general case, but ‘only’ µ times more noise than conventional.

longer version: potential unlocked! Only listening to C_k; its sizing as a kathode cap guarantees that all the audio you are interested in flows through it. That sizing of C_k is the same a for the general case, above. Thus is not going to be a beautiful C_ideal (just enough for rp, Z_primary and ƒ_-3dB) in size. It is going to be µ+1 times larger, plus some extra to compensate for the kathode resistor.

Also here C_k does not need to be compensated for C, offering a theoretical chance to reduce its value compared to a conventional cap hookup.

buzz

The noise problem is also definitely there, but slightly different that for the general case.

With a transformer, the signal is not mustered between plate and ground, but over the transformer primary. Our baseline is ‘conventional caps, transformer’—

noise_conv = Z_primary / [rp + Z_primary] × noise_B+

You would expect Z_primary to be larger than rp, mostly a lot. This is thus worse than ‘conventional caps, general case.’

For ultrapath-A the B+ noise is fully amplified by the tube—µ+1 times—but now the difference is taken with the top of the primary (i.e. 1 - (µ+1)= -µ), and that is put in an impedance divider between rp and Z_primary:

noise_ultra-A = µ × Z_primary / [rp + Z_primary] × noise_B+

Comparing the two, the noise increase is—

ultrapath-A/conventional = µ

That is simple. And completely independent of rp and Z_primary. Still a bad increase of hum, noise and signal induced trouble. B+ filtering needs to be increased by a factor µ. Correct, you are not listening to C, but watch out with ballooning the time constants. Again, a two-stage approach.

The verdict; achieving the ultrapath claims, when compared to conventional caps:

1. (avoid kathode cap): false—nothing to do with ultrapath;
2. (smaller-valued caps): theoretical (C_k); insignificant in practice;
3. (one cap in signal path):true; but see the postscript at the end of this post;
4. (hum/noise cancelling): still the opposite; it’s a noise µ-tiplier.

You can win one-cap purity here, at the cost of extra B+ baddies, or extra B+ filtering.

ultrapath-B

The general case:

short version: the B+ cap gets connected to the kathode; its calculation is the same as for the conventional case; if C_k is a lot larger than C, then not so much B+ noise gets injected into the kathode.

longer version: why can’t C not be ideal-sized, you know, just big enough for the rp, plate load and ƒ_-3dB? Why is it treated and calculated as a (usually) much larger B+ cap?

Well, C may look really appealing to us, allowing a direct and elegant path between the kathode and the B+. But the electrons passing the kathode do not care; they take any path possible, inversely proportional to the impedance of each path.

Thus the electrons will happily take a path through C_k, then through reference/ground, some other cap—or a couple in series—to B+; then through Z_filter, to land at the top of the plate load. The combined series capacitance along this route does not matter that much. It can be smaller or larger than C (also by an order of magnitude) but that only determines the current ratio of the two paths.

The only thing that can stop this current taking all kinds of wild paths through the circuit is Z_filter. As long as the impedance of C is quite smaller than Z_filter, C is the only path for all generator current. Taking also into account that C—in series with hopefully much larger C_k—has to do the B+ filtering job, it follows that C is calculated exactly as for conventional caps.

less buzz

This configuration also injects noise in the kathode, but it can be a lot less if you make C_k a lot larger in value than C. The two caps form an impedance divider, reducing noise by C/(C + C_k). The noise increase is then—

ultrapath-B/conv = C/(C + C_k) × [rp + (µ+1)Z_plate load] / rp

You really want to be careful about the drastic measures you are going to take for making C_k a lot larger. Note that both signal currents go through the C_k.

The verdict; achieving the ultrapath claims, when compared to conventional caps:

1. (avoid kathode cap): false—nothing to do with ultrapath;
2. (smaller-valued caps): the opposite; C_k will be naturally a lot larger
3. (one cap in signal path): false—not for general case; 3 current paths;
4. (hum/noise cancelling): the opposite; the maximum obtainable is just a little noisier.

A second miserable performance of ultrapath with general-case circuits; again just a learning experience for what is next.

transformer

short version: the B+ cap gets connected to the kathode; same value—or slightly larger—as for the conventional case; this C is the only cap you will hear; make C_k µ times larger than C and win a whole lot of B+ noise rejection, at the cost of losing control of the time constant of the stage (overdamping).

longer version: the stars seem to finally align here. As long as C is sized as a B+ capacitor, no generator/signal current will contemplate going anywhere else as through this cap. We are then in the same territory as ‘kathode shorted to reference/ground; only one cap’, with its inherent problem: the requirements of B+ filtering leads to a B+ cap that is 10–100 times too large for its job of closing the current paths.

Nothing is perfect. Usually C_k controls the time constant of the stage; by taking C_k out of the equation the inductance of the transformer will dominate the time constant (overdamping).

no buzz

Have a look at this model for our triode and transformer:

From the bottom up, we see the triode modelled as a voltage generator—controlled by the grid and kathode—in series with its dynamic plate resistance; then the transformer with its primary impedance; finally on top the B+ as a generator of some noise.

Would it not be good if the signal caused by changes in V_grid made it through the transformer and nothing else—certainly not the noise on the B+? Well, we can give that our best shot.

If the triode generator could replicate noise_B+, then the whole string would see this noise; at the top, the bottom and at the point where the transformer meets the tube. And then the transformer would see the same noise_B+ at both ends of its primaries… and ignore it.

This noise rejection is independent of the actual rp and Z_primary, and of how these change with signal level and frequency. I think that’s very cool.

How do we get noiseB+ in the triode generator? By feeding a 1/(µ+1) version of it into the kathode. This happens in the ultrapath-B transformer circuit when C_k = µ × C. Although you won’t ‘hear’ C_k—non of the audio signal passes through it—it does not mean you can use any kind of junk there. The two caps have to form a pretty good impedance divider over a large frequency range, also for ultrasonic noise. Thus C_k has to be of a quality comparable to C. A brute-force way of doing this is to use for C_k µ times the cap you use for C.

reality check: I do not expect that a perfectly noiseless amplifying stage can be achieved here. First of all there are other noise sources than B+ (e.g. the heater/filament); then there is the fact that compared to a resistive divider—where a pot can provide the final percents of getting it bang-on—achieving a precise ratio of two capacitances is more laborious; last, two non-identical (physical geometry, materials & construction) tracking each other over a large frequency range is not a matter of course.

But nonetheless there will be a good deal of B+ noise rejection and this is an interesting tool to use in your designs. In general it allows you to use lean and quickly-recovering power supply, while not having to suffer the hum and noise—and in multi stage amps shelved bass or motor-boating.

The verdict; achieving the ultrapath claims, when compared to conventional caps:

1. (avoid kathode cap): false—nothing to do with ultrapath;
2. (smaller-valued caps): the opposite; C_k will be larger than conventional;
3. (one cap in signal path): true; but watch that C_k quality; but, but see the postscript at the end of this post;
4. (hum/noise cancelling): true.

You can win one-cap purity and B+ noise rejection here, at the cost of an over damped stage and finding a larger kathode cap that is as good as that kathode–B+ one.

three caps

The general case:

short version: added a bypass cap (C_u) for the generator current; every current path goes through all three caps; reduction in C and C_k cap values is possible; kathode noise injection: just like ultrapath-B.

longer version: finally a chance to introduce an ultrapath capacitor (C_u); up to now we have just been shuffling the other two around. Although there is now a dedicated capacitor for each of our three current paths, it does not mean that the electrons think that is an offer they can’t refuse. Again, they will just let the impedance numbers speak and split up accordingly.

Thus if you employ a super-beautiful C_u of 4µF (maybe a close to ideal value), and C and C_k are normal 47µF electrolytics (that is, 23.5µF in series), then 4/27.5 = 14.5% of the generator current will go through the beautiful C_u, and the rest (85.5%) through both electrolytics. I guess the best you can say is that C_u works as a bypass cap for the generator current.

Of the two other currents, the signal-kathode current goes (92.7%) through C_k, in parallel with ‘C_u & C in series’; the signal-B+ current goes (92.7%) through C, in parallel with ‘C_u & C_k in series.’ I think introducing C_u did not actually improve this situation.

Except that there is potential to reduce the values of C and C_k, by introducing C_u; maybe cut them in half or even more. That asks for a C_u that is really large in value compared to C and C_k. That is however in conflict with the fact that here we are again injecting noise into the kathode—exactly like for ultrapath-B—thus you would like C_k to be much larger than C_u. Satisfying both of these drives the value of C towards zero and at the moment it is zero, you have landed exactly in ultrapath-B territory.

The verdict; achieving the ultrapath claims, when compared to conventional caps:

1. (avoid kathode cap): false—nothing to do with ultrapath;
2. (smaller-valued caps): possible; however mutually exclusive with the ability to limit the noise increase;
3. (one cap in signal path): false—not for general case; 3 current paths go through all 3 caps;
4. (hum/noise cancelling): the opposite; the maximum obtainable is just a little noisier, but no small caps then.

Three strikes: out! It seems that ultrapath was not made for general case circuits.

transformer

short version: added a noise-eliminating cap (C_u); make it C_k/µ and win a whole lot of B+ noise rejection. The generator/signal current will go through all three caps.

longer version: We can now start to be very philosophical and try to derive what are the optimal cap values for this trio. Or we can simply recognise how you would get here: you have a conventional-caps transformer circuit with some well chosen C and C_k values, and now you either have too much hum or even motor-boating, or everything is fine but you would like to achieve a more nimble power supply (e.g. one filter stage less, or lower time constants).

I said ‘well chosen’ because what we will do next is a ‘garbage in, garbage out’ process. So I expect you calculated your C and C_k well (stay tuned to this series for that) or tuned them by ear; not that you swiped them from someone else’s schematic.

The simplest thing to do next is to build on what we just learned for ultrapath-B and add a C_u that is simply µ times smaller in value than C_k—done.

But then, I asked myself: could the addition of C_u mean that C and C_k can be smaller? So I solved the equations. Starting with the conventional B+ and kathode capacitor values (C_conv and C_k-conv), and the tube’s µ, the formulas for C, C_u and C_k are:

C = [µ+1 - C_k-conv/C_conv] / [µ+1 - C_k-conv/(µ+1)C_conv] × C_conv

C_u = (µ+1)/µ × (C_conv - C)

C_k = µ × C_u = (µ+1) × (C_conv - C)

Yeah, the one for C is pretty opaque, right? I thought I make some graphs to see how these formulas work out:

(x: C_k-conv compared to C_conv, 0 is equal, far-left is 0.1, far-right is 10—technically log(C_k-conv/C_conv);
y: µ, 3 at the bottom, 100 at the top, purple lines (from bottom) at: 4, 8, 20, 50—technically log_33.33(µ/3))

We see here plots of how C compares to C_conv (C/C_conv). The left-most one shows everywhere this is 0.91, the next one is 0.82, from there on it is the E6 series, from 0.68 to 0.1. The last one (red) is where C=0. Yes, as can be seen from the first term in for formula for C, when C_k-conv = (µ+1)C_conv, C becomes zero; i.e. from there on one has landed in ultrapath-B territory. The other two formulas confirm that.

In general the graph shows that only in the bottom-right corner there is a significantly reduced value of C (compared to C_conv) to be won. A lot of caps come in E6 values, so the first significant reduction is one step down in E6 (0.68), the third line from left. The first two lines, from left, are really baby steps. Thus only for low µ (3–8) and relatively large C_k-conv (> 1.5 × C_conv) is it worth checking the formulas. In all other cases, use the simplest thing (just insert a C_u = C_k/µ).

Looking at the graph for both C_k and C_u does not change that sobering thought:

In orange we see two curves for C_k compared to C_k-conv (C_k/C_k-conv). The top one is for 0.91 and the bottom one for 0.82. Yes, only baby steps; a three caps setup does not significantly reduce the value of C_k.

In black we see the straight, parallel, evenly-spaced lines for the value of C_u, compared to C_conv (C_u/C_conv). It is all E6 series, with the left-most being 0.01 and the rightmost is 1. Small C_u values are found in the top-left area, where insignificant changes in C and C_k values are found.

The verdict; achieving the ultrapath claims, when compared to conventional caps:

1. (avoid kathode cap): false—nothing to do with ultrapath;
2. (smaller-valued caps): possible; the optimum is cutting the B+ cap almost in half;
3. (one cap in signal path): false; the current goes through the triangle of three caps;
4. (hum/noise cancelling): true.

This looks like a useful tool to me for tuning (output) transformer stages.

voodoo child, slight return

There is one more thing to deal with: parafeed. This is our love child: mostly a general-case circuit, but the coupling is via a transformer—as well as a cap—and that introduces traits of transformer circuits. With the options for plate load, Z_filter and receiving load the same as for the general case, plus the ‘loudspeakers’ receiving load option from transformer coupling, it adds another 54 circuits to our survey, for a grand total of 252 circuits.

What the parafeed transformer brings to the table is galvanic separation from the receiving load. This gives us the freedom to connect the ‘other end’ of the transformer primary (i.e. the primary end not connected to the tube plate) in three different places.

Before I go through the parafeed circuit variants, first some words on where to connect the parafeed cap; at the plate, or the other end? What is better is certainly not the topic of this blog post. So I say—

1. just use the hook-up you believe to be better;
2. or, if you really must: test it. Live with one variant for a month (so you forget you are testing); then the other variant, also for a month; after that you change it back to the first variant and you either now know which one is better, or you go back to point 1 on this list.

In the drawings below I have put the parafeed cap at the plate end for simplicity’s sake.

grounded parafeed

The first variety of parafeed we’ll look at is the conventional one, where the other end of the primary is grounded:

Really, really conventional. In fact, it is so conventional that it is indistinguishable from the general case circuit. By looking at the currents—generator, signal-kathode and signal-B+—we see exactly the same triangle of return paths, between B+, kathode and reference/ground:

And because of that, all our analysis of the general case is also valid here: there is no benefit in using any ultrapath variant.

kathode-return parafeed

The second variety of parafeed looks more tricked out; the other end of the primary is returned to the kathode:

(somehow the triode ended up looking like a stack of pancakes, sorry)

Looking at the currents shows quite a different picture:

Reference/ground is out of the game. The signal-kathode current (green) goes though a self-contained current loop, closed by the parafeed cap. When the plate load is not a resistor, but a choke or a current source, then this current is the major one; the most important. This self-contained loop looks quite ideal.

But there are also the two minor currents: generator and signal-B+. Here, their return paths are one and the same: from kathode to B+. It looks very appealing to use a capacitor from kathode to B+; to use one of the ultrapath variants. Alas, all of the noise injection problems described for the general case and ultrapath-A/B and three caps are also valid here. If you still want to use any of the ultrapath hookups, then the cap sizing is the same as for the general case.

The verdict: you get a very elegant major current loop, but I would use conventional caps for noise reasons, even if that means that your minor currents go through both B+ and kathode caps.

B+-return parafeed

The third variety of parafeed looks a bit odd; the other end of the primary is returned to B+:

It is quite a demonstration of how parallel parafeed is. Looking at the currents, it doesn’t seem we gained anything here:

OK, reference/ground is out of the game again; there is one elegant, self-contained current loop, but it is a minor current: signal-B+; the major signal-kathode current and the generator current share one return path. So what is the big deal here?

The big deal is that the output signal is mustered between B+ and the plate, just like for normal transformer circuits. This means that the hum/noise cancelling trick of ultrapath-B and three caps also works here:

The cap sizing, and quality, is the same as for transformer circuits.

The verdict: you can achieve hum/noise cancellation here with ultrapath-B or three caps, but you will be listening to the B+ cap (and the other two for three caps).

transformer(less)

You might think by now ‘is there no way to profit from ultrapath without using a transformer?’ Well, let’s see. Avoiding a kathode cap has nothing to do with ultrapath and one cap in the signal path is definitely tied to the single current path of a transformer; good luck obtaining that in another way. That leaves hum/noise cancelling and smaller-valued caps.

In the instances where we had success in hum/noise cancelling, it was because the output signal is mustered between B+ and the plate. Hmmm, there is a general way to do that:

This will do hum/noise cancellation and with three caps you might get smaller-valued caps. The cap sizing, and quality, is the same as for transformer circuits.

‘Ugh’ you say, ‘an op amp!’ Well, the symbol just stands for any type of differential-input amplifier—a long-tail pair of tubes would do fine. ‘Ugh push-pull!’ you say. If you take the signal of the plate of the ‘minus’ tube of your diff-pair (the one connected to the triode before them) and let the ‘plus’ tube (connected to the B+) alone, to do its noise-cancelling job, then I would be proud to call it a single-ended solution. This could be cool for a phono stage; making it quite quiet with a loosely filtered B+ supply.

doggy bag

Here are the take-home points of this instalment—

• If you use a kathode resistor, then you will need a kathode cap to avoid degeneration. Ultrapath does not change that fact.
• General case circuits are not improved in any way by any ultrapath variant.
• Transformer loaded circuits react with pros and cons to ultrapath:
• ultrapath-A: one cap in the signal path, at the cost of µ-tiplied noise (but, see postscript below);
• ultrapath-B: one cap in the signal path, hum/noise cancelling, at the cost of overdamping and a larger C_k (but, see postscript below);
• three caps: hum/noise cancelling, at the cost of listening to all three caps.
• Parafeed circuits are tricky voodoo children. B+-return parafeed can be made hum/noise cancelling with ultrapath (also, see the acknowledgement below).
• A general triode stage followed by a differential stage can be made hum/noise cancelling with ultrapath.

And with that, I’m done. Stay tuned for more cap decoupling posts.

acknowledgement: John Broskie’s tubecad article on ultrapath was of help while preparing this blog post. Make sure you read it, if alone for his insight on the realities of capacitor values. Also, he shows how to make a kathode-return parafeed stage with ultrapath-A hum/noise cancelling.

postscript: over on audio asylum this post featured in a discussion. Also shown there is an image by Lynn Olson of ultrapath-A, transformers. It makes clear that in the Texas-sized blog post above I have only looked at the output loop(s), and not at the grid input loop of our tube stage. Since I always work according to the principle that currents flows in/out of a grid, it means that for the two variants that I labeled ‘one cap in the signal path’—ultrapath-A&B, transformers—the grid input loop goes through the ‘other cap’ and you will hear that one too. Not that loud, though, because the ‘crud’ of the kathode cap(s) appears on both the grid and the kathode, and is not amplified by the stage—it appears with µ=1 on the plate. But I do admit this is the end of the ultrapath ‘one cap in the signal path’ argument.