|John Broskie's Guide to Tube Circuit Analysis & Design|
Yes, it's been a long time. Battling to refuel on all the parts needed for kits have taken up most of my time. It hasn't been easy sourcing parts. For example, the 2.5" tall heatsinks that are part of many kits are no longer stocked by the vendor I used, except by special order of 3,000. That's a lot of heatsinks, a crazy amount, so I had to hunt down another source. And so it has gone with many other critical parts.
The 12B4 is a great little triode that has a small but supremely devoted following—and with good cause, as it is both inexpensive and great sounding. An inspection of the 12B4's specifications reveals that it is not your typical audio triode.
Note the peak cathode current and peak plate voltage limits and it maximum plate dissipation. This is one robust little tube. Also note that each 12B4 tube only holds one triode. Thus, in order to use the 12B4 in an Aikido stereo line stage amplifier would require eight 12B4 tubes. Ouch. That's a lot of tubes. On the other hand, in the CCDA (the constant-current-draw amplifier), only four 12B4s would be needed for stereo use.
Quick CCDA Overview
A line stage is needed either to boast a weak signal voltage sufficient to drive a power amplifier to full output, or to deliver current sufficient to drive a high capacitance load (such as long stretches of interconnect). Just how much gain is needed for a line amplifier? Let's begin the answer with the observation that most line amplifiers have too much gain. (After all, many audiophile run passive line-stage setups, which offer no voltage gain.) While this extra gain impresses the audio neophyte who marvels at the power implicit in the distorted thunder that a mere one quarter twist of the volume knob provokes, it ultimately only subtracts from the useful range of turn on the volume and usually only worsens the signal-to-noise ratio of the line stage. If 20 to 30 dB of gain is too much, how much then is best? The answer will depend on each system. A safe guess, however, would be 6 to 20 dB of gain, which translates into 2 to 10 times the input signal.
Calculating the gain from a CCDA amplifier is easy, when the cathode resistor is left un-bypassed, as the gain roughly equals half the mu of the input triode used. For example, the 12B4 presents a mu of 6.5, so the gain will equal about 3 (+9.5dB) at the output, not 3.5 that 6.5/2 implies due to gain loss from the cathode follower.
Gain = muRa / (rp + Ra + [mu +1]Rk)
And since we wish to split the B+ voltage at the input tube's plate,
Ra = rp + (mu + 1)Rk
Thus, the gain formula reduces to
Gain = muRa / 2Ra
which further reduces to
Gain = mu/2
Unlike the Aikido circuit, which delivers a perfect platform for tube rolling, as vastly different tubes can be swapped in and out of the board (say a 6AQ8 and 6H30) without having to change the resistor values, the 12B4 CCDA requires more care in selecting resistor values. The problem is the daunting array of different possible B+ voltages and idle currents. For example, a 12B4 CCDA might run a B+ voltage of only 100Vdc or as much as 300Vdc. Moreover, the plate resistor cannot be the little 1/2W devices that the Aikido freely uses, but big 2W (or 3W) power resistors, which are hard to find and expensive. The solution the problem of too many resistor combinations is to let the idle current move, but lock the plate and cathode resistor values. A triode with a cathode and plate resistors acts like a resistor, not a perfect resistor, but a fairly good one.
As the graph reveals, a 12B4 triode with a 1000-ohm cathode resistor (no plate resistor) behaves much like a 9.4k resistor. (By the way, note the much improved linearity over the plate curve lines, albeit at the cost of greatly increased plate resistance and reduced transconductance. Adding a plate resistor also makes the triode behave more like a good resistor.) The formula for the effective resistance is:
R = rp + Ra +(mu + 1)Rk
The upshot is that if we chose plate and cathode resistors values to work at the middle of possible B+ voltages, these same resistors will still split the B+ voltage across a wide range of B+ voltages. In other words, we can use a wide range of B+ voltage with the same cathode and plate resistor values. In general, the following formula is a good starting point:
Rk = (Ra – rp) / (mu + 1)
12B4 CCDA PCB
The added diode is also essential, as it protects the second triode at startup, when the cathodes are cold and the cathode follower’s cathode sits at 0V and its grid sees the full B+ voltage—never a good idea, as the cathode can see portions of its surface ripped away by the huge voltage differential. C1 & C2 are the output coupling capacitors. C3 and C4 are power supply filtering capacitors which, with resistor R8, define a simple RC filter. R5 (the extra cathode resistor) is optional, although highly recommended, as it buffers the cathode follower’s output from heavily-capacitive loads and it increases the cathode follower’s linearity, but at the cost of increased output impedance.
The 12B4 CCDA board holds two coupling capacitors, each finding its own 1M resistor to ground. Why? The idea here is that you can select (via a rotary switch) between C1 or C2 or both capacitors in parallel. Why again? One coupling capacitor can be Teflon and the other oil or polypropylene or bee’s wax or wet-slug tantalum…. As they used to sing in a candy bar commercial: “Sometimes you feel like a nut; sometimes you don't.” Each type of capacitor has its virtues and failings. So use the one that best suits the music; for example, one type of coupling capacitors for old Frank Sinatra recordings and the other for Beethoven string quartets. Or the same flavor capacitor can fill both spots: one lower-valued capacitor would set a low-frequency cutoff of 80Hz for background or late night listening; the other higher-valued capacitor, 5Hz for full range listening. On the other hand, each coupling capacitor can feed its own output, for example, one for low-frequency-limited satellites and one for subwoofers. Or if you have found the perfect type of coupling capacitor or the perfect small bypass capacitor, the two coupling capacitor could be hardwired together on the PCB (via a jumper across the capacitor pads).
The GlassWare Select-C selector switch and PCB makes wiring up a 12B4 board an easy task, as the two coupling capacitor outputs from each channel of the 12B4 CCDA attach to the small PCB and the two outputs leaving the switch allow choosing between coupling capacitors C1 or C2 or both C1 and C2 in parallel.
I know many will never avail themselves to the two-capacitor setup, which is their great loss, as it is my favorite feature. Much like having a gearbox in a race car, having the ability to switch between output capacitors is essential. Often a certain recording cries out for a countervailing sonic overlay. For example, a recording from the 1970s may sound brittle and hard but using an oil coupling capacitor undoes much of its harshness; or a recording may sound too diffuse, too soft, which can be sharpened with a Teflon capacitor.
12B4 CCDA B+ Power Supply
An analogy can be made between cars and a tube line-stage amplifier. A race car runs high revs and high horsepower and it is obscenely expensive, noisy, unreliable, and glorious to behold. A family’s commuter car is cheap, quiet, reliable, and boring. Running high voltage and high current will make for a short tube life and a wonderful sound. Running low voltage and low current will greatly extend tube life and save money on part cost. For example, a typical 200V capacitor is much more volumetrically efficient and cheaper than a 400V capacitor. Thus, running a lower B-plus voltage allows us to increase greatly the total capacitance in the power supply, at a lower cost, which will lower power-supply noise at the output. Unlike the Aikido circuit, which nulls its power-supply noise at its output, the CCDA circuit only offers a -6dB reduction of power-supply noise at its output. Because of the CCDA's poor PSRR figure, I would replace resistor R17 with a choke (must be mounted off the PCB), as it could greatly reduce the amount of ripple going into the R8/C5 RC filters.
My recommendation is to use a power transformer with a 120Vac secondary that will establish a 165V to 170V raw DC voltage after the rectifiers, which will then fall to about 120V to 150V after the two RC filters; and to run the 12B4s under a high idle current, say 23mA (Rk = 220, B+ = 140V, Ra = 3k). I like using two power transformers: one for the heater regulator and one for the B+ power supply. It is easy to buy a 12.6Vac @ 3A transformer and a 120Vac @ 200mA transformer, but difficult to find a single transformer with both of these secondary voltages. In addition, I like using my staggered AC switch to turn on the heater power supply first, before bringing up the B+ voltage.
Or use a 240Vac secondary that will establish a 330V to 340V raw DC voltage, which will then fall to about 250V to 300V after the RC filters; and to run the 12B4s under a lower idle current, say 15mA (Rk = 1150, B+ = 300V, Ra = 10k).
Resistors R8a & R8b are in parallel and they form the series resistor in the RC power supply filter with capacitors C4 & C5. Resistor heat equals I² x R (and V²/R); for example, 20mA and 5k will dissipate 2W.
12B4 PCB Heater PS
Since one triode’s cathode sits close to ground potential and the other close to half the B+ voltage, the heater-to-cathode voltage established differs between triodes. The safest path is to reference the heater power supply to a voltage equal to one fourth the B+ voltage that appears after resistor R9; for example, 75V, when using a final 300V B+ voltage. The ¼ B+ voltage ensures that both top and bottom triodes see the same magnitude of heater-to-cathode voltage. The way to set up this voltage relationship is with the following circuit:
The heater's power supply power transformer must offer at least 1.8 times more current than the heaters will draw. For example, four 12B4s will draw 1.2A @12.6v, so the heater power transformer must be able to sustain an AC 2.16A current draw (2.5A is good choice). In addition, with sine waves, the AC voltage equals the peak voltage divided by the square root of 2, i.e. 1.414. Thus, a 10Vac sine wave peaks at 14.14V; a 6.3Vac, 8.9V. In other words, a sine wave that peaks at 14.14V will produce the same amount of heat in a resistance as a 10Vdc voltage source would produce in the same resistance; thus, we label the 14.14Vpk sine wave as being 10Vac. Thus, in order to get the 16Vdc raw DC voltage that a 12.6V heater voltage regulator requires an input voltage equal to remainder of 16V minus the rectifier loss (about 2V) divided by 1.414, which is roughly 12.6Vac. The 12B4 CCDA heater power supply can be setup in a voltage doubler configuration, wherein a 6.3Vac @ 4A winding is used to establish a 12Vdc output.
12B4 CCDA PCBs and Kit
The perfect operational amplifier is easy to define: infinite bandwidth, infinite input impedance, infinitely low output impedance, infinite gain, infinite slew rate, and an input and output voltage swing limits equal to its power supply rail voltages. Well, in point of fact, today’s solid-state Op-Amps come very close to this ideal.
Yet, when it comes to high-end audio, the Op-Amp is a marketing liability, as discrete components are seen as the expensive, difficult, and more desirable alternative. Why? Where to begin. As amazing as are modern solid-state Op-Amps, they must by necessity entail compromises in their construction; they are tiny after all. For example, the internal resistors are microscopic and, thus, dissipation limited, as are the transistors. In addition, the internal capacitors are crummy beyond belief. Moreover, because of their small size and because battery-powered applications demand it, they run on embarrassingly low currents, often only a few milliamps, sometimes less than 1mA for the entire Op-Amp; considering that every Op-Amp holds at least three stages, that means that each stage only gets the smallest trickle of current.
In sharp contrast, an operational amplifier based on discrete components can be as big and powerful as we desire. We can use 2W resistors and huge Teflon capacitors and massive heatsinks and robust high-voltage power transistors. But we must pay in cost, effort, heat, and cubic inches. And if we wish to jettison all practical constraints, we can build a tube-based Op-Amp. The only problem with an entirely tube-based Op-Amp is that it will prove difficult to design a version for use with a bipolar power supply. (If only there was a P-version of the triode.) The easiest workaround is to design a hybrid OpAmp. I can hear many asking, How many stinky transistors (or MOSFETs) will be needed? Not to worry, just one.
Before going any further forward, let's review some Op-Amp basics. The inverting amplifier configuration inverts the input signal's phase so that it is amplified 180° out of phase at the output. In other words, a positive input voltage results in a negative output voltage. The ratio between resistors, R1 & R2, sets the gain of the inverting amplifier. For example, if R1 equals 10k and R2 equals 100k, the resulting gain will be 10; thus, if +1Vdc is presented to the input, -10Vdc will come out at the output.
This is the preferred configuration for an Op-Amp. The rule is: Whenever possible—invert. The advantage the inverting configuration bestows lies in that input signal enters the Op-Amp at a zero voltage, zero impedance point, the conjuncture of the two feedback resistors and the inverting input. This means that unlike the non-inverting amplifier configuration, which must deal with the entire voltage swing of the input signal, which can cause non-linear effects because of the moving of the input bias voltages and compressing of voltage headroom as the input signal swings from one extreme to the other, the non-inverting amplifier inputs are comfortably at the same bipolar power supply midpoint. Also, unlike the non-inverting amplifier, the gain of this amplifier can be set to less than unity, unity, or greater than unity. (Not all IC Op-Amps, however, are unity gain, or close to unity gain, stable. Check the Op-Amp spec sheet for more information.)
Now, we can move on to the tube hybrid OpAmp shown below.
This Op-Amp holds no internal coupling capacitors, being DC coupled throughout; the 1µF coupling capacitor at its output is almost, but not quite, optional. But I am getting ahead of myself. So let us begin at the top triode's grid. If this grid sees a positive input voltage, the triode will increase its current conduction. Because the triode's plate sees a fixed DC voltage, the only element that can move with the input signal is the cathode. Because the cathode resistor is not bypassed, the input signal the grid sees will be superimposed upon the cathode resistor, although attenuated quite a bit. In other words, the triode is configured inside a cascode topology, which will serve to preserve much of its transconductance. For example, if the triode's effective transconductance reduces down from, say, 10mA/V to 3mA/V because of the unbypassed cathode resistor, then a 1Vpk input voltage will prompt a 3mA increase in current conduction; a -1Vpk voltage, a 3mA decrease in current conduction.
Note that the signal developed across the 1k resistor is the result of multiplying the triode's effective transconductance against the resistor's resistance. The larger the resistance, the higher the gain. And, unlike the grounded-cathode amplifier, the resulting gain can easily exceed the mu of the triode. In addition, since the triode's plate is locked tightly in place, the triode cannot develop any dreaded Miller-effect capacitance, ensuring a wide bandwidth. The PNP transistor could easily be replaced by a high-voltage P-channel MOSFET (or FET). So what's not to like? Unfortunately, plenty. But it will have to wait until next time.
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