Which brings up an interesting point - shielding. Shielding a signal wire is most commonly taken to mean running a coaxial wire with the signal on the central conductor and the shield connected to ground. The shield does in fact keep any other signals out side the shield from touching the central conductor by shunting those signals to ground. However, it does it by completely enclosing the signal wire in an enveloping parallel (ack! there's that word again!) sheath. As you might expect from the earlier comments on parallel wires, a wire with a shield completely surrounding it has a lot of capacitance to the shield. Indeed, coaxial cable often has specifications on the capacitance per length of cable. Good cables can be down in the range of 10-15pF per foot. Bad cables can be significantly more. Put a couple of feet of bad shielding cable on a grid signal, and you're losing treble. Better than oscillating, but not perfect by any means.
Wiring capacitances - how much matters?
It's easy to calculate how much is too much for audio purposes. There are two important cases - a capacitor in parallel with a resistor and a capacitor in series with a resistor. We don't consider inductors and capacitors because
- there's at most one real inductor in essentially all amps - and that's in the power supply; lots of tiny parasitic ones, though
- parasistic wiring capacitances are so small that they are swamped by parallel real capacitors, and series real capacitors are so much larger that the real capacitor is effectively a short circuit.
Fortunately, we can calculate the frequency where the capacitor and resistor interact the most very easily. This is the frequency where the capacitor's impedance equals the resistance, or F = 1/ (2*pi*RC). To a first approximation we can consider every frequency below this to be unaffected by the resistor, and above it to be unaffected by the resistor.
Guitar amps are a special case of audio amplifiers. Hifi amps have to handle 20kHz, and some purists would insist that 40kHz is a minimum. However, the best wound guitar pickups pretty much cut off above 7kHz and our speakers don't put out much above 4kHz. Even for fuzz-box generated hash, there's not much happening above 10kHz. To make some sense of the huge numbers of variables, we'll have to make some assumptions. The capacitances we calculate may be wrong by a factor of two either way, but then calculating capacitances between free-swinging wires is prone to some error anyway. We'll at least be close enough to know where to dig deeper if we need to.
For a resistor, the "significant capacitance" is C = 1/ (2*pi*Rf), or at 10kHz, C= (15.9/R) uF. If the resistor in question is a 1M resistor, the capacitance will be C = 15.9pF. So a resistor between 8 and 32pF makes a "significant difference" to a 1M resistance. We can see then that the higher the impedances involved, the smaller the capacitance that makes a difference to tone. Likewise, the lower the resistance, the bigger the capacitance must be to make a difference.
One "resistance" we don't see listed on schematics also has a big effect - the equivalent plate resistance. Since we already know that the higher the resistance, the smaller the capacitance that has an effect, we'll consider two high-end examples - the 12AX7 plate and a small-signal pentode plate resistance. The 12AX7 has a plate resistance of about 60K under the conditions it's most often used in preamps. This resistance is effectively in parallel with the plate resistor, so the parallel combination makes for a resistance of about 37.5K in the very common instance of a 100K plate resistor.
We can quickly see then that the wire coming from a 12AX7 plate may have a 37.5K source resistance - that is, it can supply current exactly like a perfect voltage source with a 37.5K resistor in series with it. This wire couples the signal it carries to every conductor anywhere near it - and is loaded by every conductor near it through the parasitic capacitances. If the wire is run right along the chassis, insulation actually touching, this is just like a capacitor to ground connected to the wire. If that capacitance is more than 424pF, then we lose treble above 10kHz, and the amp starts to sound a little dull. We've lost some high-end tone.
If there are 10Vac of signal on that plate wire (not at all unusual), and it runs near a wire connected to an input tube's grid, Then to couple in a feedback signal equal to a typical guitar signal of 100mv, we only need a capacitor of C=15.9/100M uF = 0.159pF - YIKES!! A SIXTH OF A PICOFARAD!!!! We suddenly see how oscillations start - a grid wire too close to a plate wire and a bit of bad luck on the phasing and the amps starts screaming at 100kHz.
OK. So now we know what we're playing with. A fraction of a pF can give us oscillations, but we need something between 8 and 400pF to start cutting treble off, depending on the circuit.
 Here's some detailed considerations on the implications:
The picture shows a somewhat representative tube amplifier voltage gain circuit. The "real" circuit is shown in black, and the parasitic capacitances are shown in red. The excess capacitors may come from wires or PCB traces, doesn't matter which.
Cp1 shunts signal away from the grid when its impedance is less than Rsrc. Cp3 shunts amplified signal around the plate resistor Rp, and Cp2 leaks inverted and amplified signal from the plate to the grid. Every single one of these results in treble loss. Cp2 is the worst because its real value is "amplified" by the voltage gain of the stage. It can be modeled by another capacitor in parallel with Cp1 of Cp2*voltage gain.
So how much capacitance matters?
Cp1 and Cp2: for a representative Rsrc of 35K (typical of a 12AX7 plate with a 100K plate resistor), when the sum of Cp1 and Cp2 times the voltage gain is Cep=1/(2*pi*35K*20kHz) = 227pF, this "dulling capacitor" is eating half the signal. If we assume that all of this is from Cp2, and a voltage gain of 30 for the stage, then the max capacitance we can stand for Cp2 is 7.5pf. As we know from the calculations above, either PCB land or #22 wires are both about .3 to 0.4pF/inch, so we can stand a maximum of about 18 inches of absolutely parallel run wires before we start getting treble loss even at 20kHz. That's a lot! Even when we correct for our assumption that Cp1 and Cp3 didn't matter, allowing for a fifth of the capacitance to be in them, we would be safe with 12-15 inches of parallel, side by side signal run. While the laced-and-bundled stripboard techniques might do this, it's unlikely to be a real problem. Good stripboard and good PCB construction will not even come close.
On Rp, Cp3 could be C= 1/(2*pi*100K*20kHz) or C=79.5pF before we'd get treble loss at 20kHz. That's 227 inches of paralleled wire.
For Rk, there can be no effect if Ck is part of the circuit. Cp4 is completely swamped by Ck. If there is no Ck, the gain of this stage will start rising at the frequency F=1/(2*pi*Rk*Cp4), or for ballpark values, F=1/ (2*pi*1500*7pF) = 15.1MHz!! The tube itself will be cutting off at that frequency. So wiring capacitance from this source has no effect on the frequency response of this tube.
 Between two stages the picture changes a bit. This illustration shows two stages, one following the other, but connected with a feedback capacitor that we'll assume was caused by bad wiring. The signal at the second plate is in phase with the signal at the first grid, and considerably larger. If each stage has a gain of 30, the second signal is 30*30= 900 times as big as the input signal. For a 0.1V signal, we'd see 90Vac of signal on the second plate if it was not otherwise limited.
The feedback through the parasitic Cfb is limited by the plate resistance of the second triode, maybe the 37.5K of a 12AX7, and is divided down by the other capacitances at the grid of the first triode, Cgeq, and by any loading at the input other than the grid leak resistor. Let's take worst case, the input open.
Unless we've done something special to make Cgeq smaller, it's probably on the order of 2-3pF. Let's see what Cfb makes the loop gain one, so this thing oscillates. We'd have to have a feedback loss of 900 to make this true, so the impedance of the parallel combination of Rgrid and Cgeq have to equal 1/900th of Cfb's impedance. At frequencies below F=1/(2*pi*1M*3pf) = 53kHz, the impedance is dominated by Rg, and decreases above that. Phase shift also accumulates above that, so let's take the resistance as the limiting resistance. To get oscillation, the impedance of Cfb has to be no more than 900 times Rg, so Cfb=1/(2*pi*900M*10kHz) = 0.018pF. ACK!! 18 FEMTO-FARADS???? HOW DOES THIS THING EVER WORK AT ALL??
It works at all because that picture does not show the whole story, of course; it's too simplistic. There are other parasitics that are not shown in this picture that actually raise the needed coupling well above the 18 fF level. The phase shifts and leakages we've blithely ignored, as well as the parasitics from the first tube itself enter into it as well. However, the math complexity goes right through the roof, so it gets to being a poor illustration, lost in the complexity.
It makes a great morality play for keeping your input and output wires well separated though, doesn't it?
This is actually one of the places that PCB construction would be a big help. The Cfb path would likely be much nearer other signal traces and especially ground traces, which would eat a lot of the feedback signal.
 Parasitic capacitance effects on the tone stack
--- coming ---
How to do PCB construction wrong
This is easy. Just use the technology in ways that ignore the mix of strong points and failings that every technology has. Some examples of WRONG techniques:
- Using a PCB designer that is not experienced with analog circuits, or worse yet, an automated layout program that is intended primarily for laying out digital circuits. This gets you the tiniest possible PCB - with all the worst aspects of the technology for analog circuits.
- Using too-thin PCB materials, possibly combined with using too few mechanical supports. This lets your PCB flex and either crack the thin traces or break solder joints to heavy parts.
- Mounting input/output jacks and other connectors on the PCB - this lets the regular mechanical stress of insertion/removal flex the PCB
- Mounting preamp tube sockets on the PCB with no reinforcement so tube insertion/removal stresses and can crack board lands and solder joints.
- Mounting controls on the PCB, or worse yet, mounting the PCB to the chassis through controls soldered to the PCB - there is always some mis-fit between the PCB and the chassis. Using controls to mount the PCB to the chassis builds in a mechanical stress. Using both controls and other mechanical mountings lets both the mountings stress the PCB.
- Mounting power tubes to PCB's - ACK!! They're big, they're heavy, they get removed and reinserted, they're hot; about the only thing worse would be ...
- Mounting transformers to PCB's without special reinforcement.
Unfortunately, PCB technologies are most cost efficient when everything is connected to the PCB, which encompasses all the things you can do wrong. So you get a clear conflict between cost efficiency (that is, the manufacturer making money) and long term reliability.
How to do PCB construction right
Don't let the boards flex
- Use thick enough board material - 1/8" instead of the normal 1/16" should be enough
- Stiffen and reinforce the board if it's large - say, over 5" in any dimension; use lots of mounting points to the chassis and reinforcement wherever stress is unavoidable.
- Mount any modestly large/heavy components to the board with mechanical restraints that take the stresses off the solder joints. Component leads for anything bigger or heavier than about a 5W power resistor or a 1" by 2" capacitor must not be relied on to hold the component physically.
- Mount mechanical components which will be moved, stressed, adjusted, etc. off the board and connect with flexible leads; this includes pots, jacks, switches, and tube sockets. The flexible leads don't transmit the stress to the board.
Don't let the boards get too hot
- Glass-epoxy board materials softens and begins to char at temperatures easily generated by power resistors and power tubes. Mount these items off the board or provide special thermal shielding.
Don't use solder as a mounting glue
- Wires coming into the PCB should terminate in either plated-through holes, eyeletted holes, or stress-relieved connectors. Otherwise, any wire movement stresses the solder holding the wire in and the bond of the wire pad to the base PCB material. This can crack the solder joint, or it can crack the copper foil itself.
- Repetitive stress on solder joints eventually causes the joint to fail - this happens with switch and pot mountings, as well as places where heated parts cause thermal expansion stress.
Don't treat high impedance analog signals the same way you do low-impedance digital signals.
- Be aware of the parasitic capacitances that exist in wiring, and route sensitive lines in the shortest, most direct path possible, NOT paralleling other low impedance lines that could couple noise, hum, or feedback signals into it.
- Keep parallel runs of non-related signal lines to a minimum
- Use interspersed ground lines to "decouple" parallel traces where needed.
- Like good PTP practice, lay out the circuits so that trace/wire lengths are minimized, and the signal flow is from small to large. Keep outputs well separated from inputs.
PTP Wire Amp Myths You'll Hear
PCB's use traces to connect components that add a small degree of capacitance between the parts which changes the tone/sound
It is correct that PCB's use thin copper traces to connect parts and that there is capacitance between all the traces. However, the implication that point to point wiring does NOT have such parasitic elements is completely false. Point to point wiring uses "wires" to connect components; these "wires" also add a small degree of capacitance between the parts. In fact, for some instances, hookup wire can have MORE wire-to-wire capacitance per unit length than PCB traces. There are no wires that *don't* have self inductance, capacitance, resistance and all the other ills that every electronic part is heir to. Which has more? It depends... you have to know the mechanical specification of exactly where every part is in relation to every wire and the chassis to compute the capacitance for either traces or wires. A well designed PCB with attention paid to where the traces go may have bigger or smaller capacitances to other traces and parts.
As to this necessarily degrading tone - almost always no. The capacitances may or may not have any audible effect, and if there is an effect on the tone, it may or may not be positive, or may or may not be swamped out by the actual parts instead of the wires/traces. The only way to tell is to figure out what the capacitances actually are and see if it makes a difference - what's the capacitance of a signal wire lying against the chassis for 6"? Is it more or less than the capacitance of a PCB trace for 6"? Hmmm... can't tell without measuring and seeing what this capacitance couples together in the amp.
Companies used to use carbon comp resistors which yield a richer, more complex tone.
Ah, yes. The old "They don't make them like they used to". They really don't make them the same any more - thank God. Resistors used to be 20% tolerance, drifted another 5-10%, and had a "hole in the middle" where all the ones that did by accident get within 5% and 10% of the nominal value had been selected out. A 20% resistor was guaranteed to not be any closer that 11% to the nominal value because all the 10% and better ones had been selected out by the manufacturer. Old carbon comp processes had build in distortions, rectification effects, and so on. Process control is much better than it used to be. The differences in carbon comp and modern film resistors are real, but that whole thing is a topic for another article. Suffice it to say that just because it's carbon comp, it's not tone magic. Carbon comps were the cheapest available resistors in the "golden age", and were used for that reason. Leo Fender was a businessman, not a guitarist.
The quality of the parts has been reduced / Companies used to use better quality caps.
Another one. This one is pure nonsense. Modern capacitors are more stable, more consistent, have closer tolerances, lower drift with time and soldering, and so on.
Ah, but the old paper capacitors were tone magic/mojo magnets/whatever.
Nonsense. Old paper capacitors had higher ESR and ESL than some modern capacitors, lower than others. It's entirely possible to get *better* modern caps and then add resistors to "ugly them down" to what the older caps did. You do have to know what you're doing, though.
Modern parts that cost next to nothing when bought bulk quantities are loaded by computers.
Leo Fender would have jumped on that!! He'd have loved it. As it was, he used the cheapest parts and labor that would produce his amps reliably enough to sell well. Leo was a businessman, not a guitarist.
Cheaper parts and pcb's lead to an amp or effect that sounds stiff, lifeless or one dimensional compared to the earlier ones
Huh? Why? What parts affect the tone? This is a form of creeping superstition. Most audio research indicates that the terms "stiff", "lifeless", "tiring", and so on are associated with low levels of intermodulation distortion. This is a circuits thing, not a wiring thing, no matter how it's done.
Handwired, point to point will always sound better than any stock PCB amp.
Lets face it, in the 50's and early 60's amps were wired point-to-point, because it was cheap...the skilled labor required to solder wires to the turrets was cheaper than buying PCB making equipment, which was still experimental at the time. But there's no real evidence that you can't do as well or better with a PCB. And the PCB's will come out the same way, every time. No little lead dress problems making some of your amplifiers oscillate when the rest of them are OK. |
