|John Broskie's Guide to Tube Circuit Analysis & Design|
29 October 2016
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One realization hit me hard, however, after finishing my last post: it is a lot easier to write about an event like the RMAF than to write about circuits. Much easier. In other words, my already moderate respect for the minor-rivulet—stream of any sort is too at odds with reality—audio press grew even more moderate. (Is such a thing possible? Can one be more moderate?) Of course, green grass always appears easier to cut and maintain on the other side of your own fence. Sometimes, however, it actually is easier to cut and maintain, particularly when it is made of Astroturf.
A decade ago, while enjoying a fine Indian dinner with an audio-magazine editor, I listened to him bemoan the flood applications he received from would-be audio-equipment reviewers—most of whom, he informed me, were lawyers. He had a point. You borrow new audio stuff, you write about new audio stuff; if you say nice things, you might get to keep the audio stuff or procure it on the cheap.
In contrast, each circuit and schematic is a like a Chinese wood-piece puzzle that must be carefully taken apart, piece by piece. (And should the circuit prove novel, i.e. strikingly new, then no fallback resources are available, such as Wikipedia or electronic textbooks.)
Back in the day when Audio magazine was sold in the magazine racks at super markets and the description of "mainstream" actually applied, I thought that the magazine should hire a circuit editor/reviewer, so that each product being reviewed would also receive a schematic review, where someone (dare I say it, someone like me) would comment on the actual circuit, offering praise, condemnation, and potential modification as needed. Yes, yes, I know that it would never happen, as just about all audio-gear manufacturers imagine that their products are as precious as the Hope Diamond and as unique as a snowflake, designs so revolutionary that armed guards must protect the valuable schematic from the prying eyes of industrial spies. Sure. Of course, a few manufacturers do know the sad truth that exposing their schematic to scrutiny would reveal how desperately monotonous and tedious their design is. Who after all wants to be seen naked by the world? Much better to let the fancy enclosures and fanciful ad copy hide what resides inside. We always read that the codpiece will make a comeback soon; in high-end audio it already has.
In short, writing my last post felt like a vacation, although attending the RMAF felt more like hard work. Paradoxically, creating a new circuit feels like a trip to Disney Land, while drawing its schematic, running SPICE simulations on it, and writing about the circuit feels like hard work.
Well, why do I need to use signaling symbols before writing about the cathode-coupled amplifier circuit? My words might only deliver an overview of existing practice, of what is found in old electronic textbooks, the stuff most tube practitioners already know. Alternatively, my words might describe minor modifications to the standard cathode-coupled amplifier or, indeed, major reformations and overhauls of the circuit. What do you think of these three icons for textbook, modifications, and new approaches?
Of course, I might cover all of the above in a new post. In fact, I plan on doing all three in this post, my thirteenth post on the topic of the cathode-coupled amplifier topology.
The textbook overview of the cathode-coupled amplifier is simple enough: the input triode is configured as a cathode follower, while the output triode is configured as a grounded-cathode amplifier.
Since the cathode follower offers no signal gain, why not take it out, leaving only the grounded-grid amplifier? The answer is that the grounded-grid amplifier is difficult to drive, as its input impedance is low and the cathode is not likely to be at ground potential. Thus, a cathode follower was used, as it input grid presented a nearly-infinite impedance and could easy be tied to ground potential. Of course, other buffer circuits could be used to drive the grounded-grid amplifier; for example, a White cathode follower or emitter follower would also work. We could also use an isolation transformer, which would eliminate the need for a negative power-supply rail and large shared cathode resistor or constant-current source.
An added advantage to using an isolation transformer is that the grounded-cathode triode could be connected to a negative power-supply rail, but without incurring the usual power-supply-noise problems.
Another possibility is to use the transformer coupling along with an inductive load for the grounded-grid stage.
The inductor load displaces so little voltage, assuming a low-DCR, that we can use the same valued cathode resistors.
Hybrid Cathode-Coupled Amplifiers
The PNP transistor drives the cathode while presenting a low-impedance input to the input cathode follower. Note how this circuit is the exact opposite of a current mirror, as the current variation is not mirrored, but inverted. In other words, as the input triode draws more current, the output triode draws less current.
By adding a zener, we can lose the plate resistor and capacitor. Remember that without a plate resistor, the input triode sees a much larger cathode-to-plate voltage; thus, its cathode voltage must be higher in order for it to draw the same amount of current as the output triode.
Note the replacement of the cathode resistor by a constant-current source, which will allow for larger output voltage swings and lower distortion.
Still, the big question to answer is why bother with this hybrid solution? The answer is that the negative power-supply rail can be much lower than typical, with as little as -5V sufficing, rather than a few hundred negative volts. More importantly, we can use dissimilar triodes, such as the 12DW7, which holds 12AX7 and 12AU7 triodes.
The 12AX7 triode draws only 1mA, while the 12AU7 draws 5mA. The 12DW7 tube's heater is powered by the -12V power-supply rail. The 100k and 33k resistors form a feedback pair that establishes a gain of 4 or +12dB. As it stands, this is a fine little tube-based line stage amplifier, as +12dB of gain is usually all that is needed these days. Of course, the 12k cathode resistor could be replaced by a constant-current source, such as the famous LM334 or a FET-based alternative.
Just how well does the above circuit perform in SPICE simulations? Here is the answer.
Translated into THD, the answer is below 0.01% distortion. Not bad. More importantly, note how there is 2nd harmonic and that is pretty much it. Amazing performance for one tube and not much more. Housed in a $600 enclosure, adorned with fancy knobs, accompanied by Dueland or Mundorf coupling capacitors, and sporting a $5,000 price tag, this simple line stage amplifier would be the envy of your friends. On the other hand, for less than $400, using excellent but less expensive parts, you could build the same line stage amplifier.
Another way to think about this circuit is treat this circuit like a tube-based OpAmp. Often we need a small amount of fixed gain and not much more; for example, you might need to drive passive filter or boost an old tube-based tuner's output. The Circuit's PSRR comes in at about -18dB and its output impedance is about 2.2k. If we desire the lowest noise and output impedance, however, then something like the following is the better way to go.
The ECC99 and 12DW7 should share a 12V heater power supply that is voltage referenced to +60Vdc. The Aikido cathode follower output stage strips away the ripple form the output signal. The 100k and 20k resistors set the gain to 4.
Or, we can use the PNP transistor a bit differently.
The transistor and cathode follower create a push-pull buffer, which can aggressively pull the grounded-cathode amplifier input up and down.
As you can see, there are many ways to drive a cathode. Indeed, a complete mini power amplifier could be used, such as an OpAmp.
Why would anyone want the above circuit? Here is a possible example: you have a single-ended output stage whose output triode requires +/-80Vpk grid-voltage swings to achieve full output. The above circuit could easily deliver those voltage swings; in addition, those swings would be low-distortion, low-output-impedance, and wide bandwidth. Moreover, the OpAmp offers low-noise and performs an auto-bias on the triode, keeping its plate centered on 200V at idle. The load that the OpAmp must drive would be equal to (Ra + rp)/(mu + 1) in parallel with Rk. If the OpAmp is not up to the task, then the following design would unburden the OpAmp. (Most modern OpAmps are up to the task, which explains why they are found in so many headphone amplifiers.)
The PNP transistor presents a much lower input impedance than the cathode.
Are we done? No. We are never done. For example, we could add some Aikido Mojo thus:
By injecting a small portion of the B+ noise into the triode's grid, we create a power-supply-noise null at the triode's plate, thereby giving the OpAmp less work to do.
How about wrapping the OpAmp's negative feedback loop around the entire amplifier, so the output tube and output transformer would be included? I wouldn't, as we would be likely to run into too many phase shifts. On the other hand, we could get away with two feedback loops.
The output stage gets its own negative feedback loop, as the output transformer's secondary attaches to the output tube's cathode. Note the 32V DC offset at the output, but the speaker is safe, as the transformer's secondary should present a very-low DCR. (If a negative bias voltage were used in place of the constant-current source, then the DC offset would almost entirely disappear.)
How does this feedback loop work? Imagine a positive pulse created by pushing the woofer; this pulse would force the output tube's cathode to become slightly more positive, which would effectively make its grid more negative, which would decrease the tube's current conduction, which would be reflected through the output transformer as a negative output voltage swing, thereby countering the positive pulse. Degenerative feedback, in other words. Understand that we must pay a price for this feedback loop, as the input signal to the output tube must be much larger. For example, if the peak output swing into the speaker is 16Vpk, then the output tube will needed to see +/-48Vpk swings at its grid.
Cathode-Coupled Amplifier PSRR
One big problem is that when the power switch is flipped on, the negative power-supply rail voltage is likely to develop almost instantly, while the triodes are still waking up and not conducting. A big problem this, as the grids will be 200V more positive than the cathodes, which can easily lead to cathode damage, as the huge voltage differential can strip away sections of the cathode's surface. The solution is simple and cost less than a dime:
Under normal operation, the cathode is always at some positive voltage, so the diode falls out of the circuit, as it is reverse biased. It only conducts, when the triodes are cold or missing from their socket. In all the following schematics, mentally add the diode; I left it out to aid clarity of topology.
The second problem worthy of an unhappy face is that the bipolar power supply ripple gets imprinted on the output signal.
Not all the positive rail ripple leaks through, only about 50% of it. Adding a constant-current source, paradoxically enough, will only make the PSRR figure worsen, not improve.
My solution, actually just one of my many solutions, is to use two long-tail cathode resistors and bypass one of them with a large-valued capacitor. This was a trick I came up with over 30 years ago to quell the power-supply noise leaving a differential amplifier.
What is going on is that the bipolar power supply ripple is equal in magnitude but out of phase between positive and negative rails. (Or, at least it should be; the balance between the two rails can be thrown off by loading one rail more than the other.) The two cathodes are tied together and follow the grids, so almost no ripple appears at the cathodes. Thus, the 4.99k resistor must see almost all of the negative power-supply rail ripple, which will induce a varying current flow through the resistor, which in turn travels up and through the triodes and their plate loads. (Imagine that the two 10k plate resistors are in parallel, creating a 5k resistance.)
Well, as the positive bipolar power supply ripple pulls upward in voltage, the negative bipolar power supply ripple pulls down in voltage, so the increased current flow through the 4.99k cathode resistor will also flow through the plate resistor, causing a greater voltage drop across the resistors, which will result in the plate voltage remaining constant. Magic. Aikido mojo magic.
Another way to achieve the same bipolar-power-supply-noise null is as follows.
All the DC current flows through the 10.1k cathode resistor, while only AC current flows through the 9.76k cathode resistor. In AC terms, the two cathode resistors are in parallel and the same bipolar-power-supply-noise null obtains as before. As the 10.1k cathode resistor is the only cathode resistor that will get hot, it must be a high-wattage type. So what advantage does this alternative arrangement offer? The large-valued capacitor terminating the 9.76k cathode resistor will likely be an electrolytic type. Electrolytic capacitors are complex devices that exhibit effective series resistance (ESR), effective series inductance (ESL), and leakage current. Thus, placing these failing off to the side might improve the overall functioning. On the other hand, if a high-value, high-quality film (or high-quality electrolytic) capacitor was used instead, then both variations should work identically.
Another approach is to inject a portion of the positive rail ripple into the grounded-cathode triode's grid.
The gain remains at 4, or +12dB, as the feedback network remains in place, but the PSRR is greatly improved. In the SPICE simulations, a 6DJ8/ECC88 tube was used. Different tubes and different feedback resistor values will require a different ratio of positive rail ripple to be injected. In other words, expect a lot of work. The workaround to extra work might be to make a universal setup that always creates a power-supply-noise null, regardless of the tubes used or feedback ratios. The following circuit allows twice the ripple to be present on the negative power-supply rail than on the positive rail, which was achieved by using twice as big an RC-filter capacitor on the positive rail.
Most OpAmps suffer from a poorer PSRR figure for their negative power-supply connection than their positive connection.
Thus, some high-end audio gear use asymmetrical power supply reservoir capacitor values, so that a much greater amount of capacitance in the negative power-supply rail is used to overcome the imbalance in PSRR between the positive and negative power supply connections.
But in this Aikido-mojo version of the cathode-coupled amplifier, the positive rail gets the added capacitance. Great are we done now? No. We are never done. The huge problem with this solution is that electrolytic capacitors are famously off their stated value, with low-voltage electrolytic capacitors often holding more capacitance than they are labeled and high-voltage electrolytic capacitors holding less. Even if you carefully measured the electrolytic capacitors, they might drift of value over time. The better approach is always to vary the resistors rather than the capacitors.
The top RC filter holds a 2k resistor, while the bottom RC filter holds a 1k resistor. Note the differing voltage drops and the twice as big ripple on the negative power-supply rail. Also note that the 100µF capacitors must be matched (and should be identical capacitors). Just how well does the above circuit work over a bandwidth of 10Hz to 100kHz? The following SPICE-generated graph tells all.
Note that the most important frequencies to look at are 100Hz and 120Hz, as those two are where most of the power-supply ripple will be found. Not bad, as well over -100dB of PSRR is shown. Of course, the larger the power-supply capacitors, the deeper the attenuation.
An Odd Catch from the Past
As I looked over the schematic, my first thought was bewilderment, as I had thought that the big decade for blowing pot and dropping LSD was in the 1960s, not the 1950s. Why? As a cathode-coupled amplifier circuit, this circuit was stupendously stupid. But then, it's not really a cathode-coupled amplifier circuit. Well, what is it then? This patent refers not to a phase preserving cathode-coupled amplifier, but a phase inverting grounded-cathode amplifier which employs positive feedback and which must be entirely enclosed within a larger negative feedback loop.
It is, in other words, an attempt to create the electronic equivalent of a perpetual-motion machine. Back in the fifties, when electrical engineers were drunk on negative feedback, the notion arose that if an amplifier could give rise to infinite gain, then that infinite gain could infinitely power negative feedback, resulting in zero distortion and zero output impedance. The only problem was that gain, like anything else of value, is all too finite. The only way left to get more gain, once the limits imposed by limited transconductance were hit was to employ positive feedback, which would yield crazy high gain, crazy high and crazy distorted gain—but that was okay, as the crazy high negative feedback ratio would erase the distortion. Yeah, sure. It didn't.
Norman Crowhurst did his best to explain how the plan was just an electronic ponzi scheme, but few listened. In his own words, from the third chapter of his book, Understanding HiFi Circuits.
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