John Broskie's Guide to Tube Circuit Analysis & Design

06 May 2007

Common-cathode (a.k.a. cathode-coupled) amplifier
I am a big fan of the common-cathode amplifier (also known as the “cathode-coupled” or “grounded-grid” amplifier—no thanks to Bruce Rozenblit, whose taxonomic howler has made already murky waters murkier still). This topology offers low distortion, no phase inversion at the output, and a wide high-frequency bandwidth.  This last characteristic is due to a very low input capacitance for the input, as no Miller-effect capacitance is created. Additionally, a negative feedback loop can readily be applied, because of the inverting, high-impedance input presented by the rightmost triode. The down side to the circuit is the usually used high-voltage negative power supply rail and the issue of dissimilar grid or B+ voltages, as the input triode’s plate connects to the B+ directly, whereas the output triode’s plate sees a plate resistor between its plate and B+.

I do not want to recap the basics of the circuit any further here, as I have covered that aspect of the topology before. See blog 42 for more background. (I suffer from a quirk: I cannot stand anything I have written--well, I can't stand it right after I have written it, to be exact. After I have finished writing, I always feel that I have done no more than just sketched out the roughest first draft and that a lot more work is needed. But after a year or so passes, I look back on the once-hated piece of writing with a small smile. So it was when I reread blog 42: “not bad, not bad at all” was my fond observation.)

The last blog entries mentioned the trick of making cathode followers on the cheap. Long story, short: don't use a negative power supply. Instead, rely on a low-mu triode and a high B+ voltage to allow a higher cathode voltage and, in turn, a larger-valued cathode resistor, largely bypassing the need for a negative power supply rail. Well, the same trick can be applied to a common-cathode amplifier, as shown below:

The 5687’s low mu (about 17) and the B+ voltage of 300V requires a -15V grid-to-cathode voltage to maintain an idle current of 10mA. A 1Vpk input signal is only 1/15th as large, which means that the triode will only have to undergo a small change in current conduction to accommodate the input signal (10mA/15). So, while a negative power supply and a much larger cathode resistor will produce less distortion, the 1,500-ohm cathode resistor isn’t that much worse. (1,360 ohms is shown in the schematic, because the 12AX7’s current conduction must be factored in the resistor’s value.)

Note that 5687 triodes are not used throughout; instead, a 12AX7 receives its input signal at its cathode from the input 5687’s cathode. Then this bottom 12AX7 is loaded at its plate by another 12AX7, which helps lower its distortion, as the symmetrical loading offers a countervailing twist to an already twisted active circuit element.  [I changed my mind; see Blog 107 for details]

The rest of the topology falls into place, with the second 5687 delivering a low-distortion and low-output-impedance in the cathode-follower-based output stage. The output triode's cathode resistor is made up of three sub-resistors, which works as a voltage divider to present the feedback to the bottom 12AX7’s grid. The total gain is roughly +20dB (1:10); the open-loop gain is closer to +34dB (1:50).

Much like the Aikido circuit, this line stage amplifier will require a heater power supply that is referenced to ¼ of the B+ voltage, in this example, +75V. The power supply must be well-filtered or regulated, as this topology does not enjoy any Aikido techniques to sidestep the power-supply noise. Still, this is an interesting circuit and I wish I had time to throw a working example together. Of course, the 5687 and 12AX7 are not the only tubes that can be used; two 5687s or two 6SN7s can be used instead, or a 6BX7 and 6SL7 might make a good pairing as might a 5751 and two 12B4s. In fact, a negative power supply rail can be added or, what might be better still, a FET-based constant-current source could be used, which would not require the bipolar power supply. (The source resistor's value must be adjusted to yield an idle current of 11mA through the FET.)

Wait a minute. How does this circuit sound? Well, with the right records or CDs, it sounds a lot like Beethoven or Chopin or The Beatles or John Coltrane or Rosa Passos. No, no, not what is it playing, but What does IT sound like? Oh, I misunderstood. It sounds as clear as “Those eyes, with clearest substance crystalline,” as Barnabe Barnes put it in his sonnet number 103. But then, the more I think about it, Shakespeare, as always, said it better, as we read in his 103rd sonnet:

Alack, what poverty my muse brings forth,
That having such a scope to show her pride,
The argument all bare is of more worth
Than when it hath my added praise beside!
O blame me not if I no more can write!
Look in your glass, and there appears a face
That overgoes my blunt invention quite,
Dulling my lines and doing me disgrace.
Were it not sinful then, striving to mend,
To mar the subject that before was well?
For to no other pass my verses tend
Than of your graces and your gifts to tell;

In other words, I lack the skills to describe such audio perfection, so rather than "doing me disgrace" or having my words mar a perfect sonic presentation I leave it to you to listen and tell us what it sounds like.


Slew rate
Before moving on to plate-follower topology, let’s look into an important design issue when designing any follower circuit. Yes, it sounds like heresy, but a cathode follower often stumbles when asked to drive a large capacitance. Quickly charging and discharging capacitance requires current, not just low output impedance. For example, a 12AX7, when used in a cathode-follower circuit, presents an output impedance of about 600 ohms, which seems plenty low for driving a 1,000pF load, as these two values seem to imply a -3dB frequency of 265kHz.

Here is an example of how the math will lead you astray (or should I have said too little math...). Yes, 600 ohms shunted by 1,000pF does equal a 265kHz transition frequency, if the amplifier driving the 600-ohm resistance is burly enough to supply the needed current. How much current? It depends on how much voltage you wish to swing; 10Vpk into 1,000pF at 265kHz requires 16.7mA; 10kVpk into 1,000pF at 265kHz, on the other hand, requires 16.7A. (Hold a tiny 1,000pF capacitor in your hand and imagine dumping 16.7A of current into it.)

In fact, the 12AX7-based cathode follower, with an idle current of 1mA, can only swing 10Vpk into a 1,000pF load up to 16kHz, thereafter it is slew limited and it distorts grossly. Remember, slewrate equals current divided by capacitance, SR = I/C. Now, a 12AX7-based plate follower will suffer the same fate with an idle current of only 1mA, as the same physics apply.

Plate followers
The plate follower (a.k.a. anode follower), like the common-cathode amplifier, is a much-too-overlooked circuit. In many ways it is the inversion of a cathode follower: where the cathode follower takes its output at its cathode, the plate follower takes its output at is plate; where the cathode follower preserves the input signal’s phase, the plate follower inverts; where the cathode follower delivers an output signal close to, but never equal to or greater than unity, the plate follower can readily impart a gain of unity or greater than unity; and where the cathode follower presents an ultra-high input impedance, the plate follower offers an impedance equal to its series input resistor, which is usually lower rather than higher, so as to ensure a greater high-frequency bandwidth, due to Miller-effect capacitance.

I know that more than a few readers are thinking right now that, other than the higher gain, the cathode follower has it all over the plate follower, as the cathode follower is simpler, uses fewer parts, does not invert the phase, and offers a high input impedance. While there is a lot truth to that position, the complete story is a bit more complex. For example, one liability the cathode follower faces is that its cathode is often floating far above ground, which makes referencing its heater to ground problematic, if the maximum cathode-to-heater voltage is exceeded. Moreover, the plate follower’s seeming liability of inverting the phase is not always a liability, as sometimes it is essential. In addition, the plate follower can easily be reconfigured as a mixer circuit or summing circuit by just adding a second input resistor; and its two feedback resistors allow easy frequency-selective attenuation or boost. In other words, the plate follower offers quite a bit more flexibility, which the cathode follower denies us. For example, what if we do not want 100% feedback, but only 15%? With a cathode follower we are out of luck, but with a plate follower, we need only set the appropriate feedback resistors ratio.

So, what can be done to improve the plate follower? Since the simple plate follower is—at heart—a grounded-cathode amplifier with a feedback loop, we can use the same techniques that improve a grounded-cathode amplifier’s performance. For example, the plate resistor can be replaced with an active load, as shown below. This modification yields a lower distortion and a better PSRR figure, as the active load effectively equals a much larger impedance than the plate resistor offered.

(I get depressed thinking about the 90% of tube fanciers who will label the above circuit as an SRPP, but at least I know that all the regular readers of this blog know much better, seeing immediately that this circuit functions in a pure single ended fashion, with no pushing and pulling.)

Since we have moved onto two triodes, let see how many two-tube topologies can be rendered as plate followers. As shown below, a cascode amplifier can be retrofitted and transformed into a plate follower type circuit. Is this a good idea? I am not sure. The elimination of Miller-effect capacitance is a great advantage, as is the preservation of the bottom triode’s transconductance. But would two triodes in parallel work better? More experimentation is required

Of course, the SRPP is never far from most solder slingers thoughts. (Do you note some exasperation and/or fatigue on my part? It just seems that whenever I look in Japanese audio magazines or at reader-sent-in schematics, I see gratuitous SRPP circuit thrown in. About five years ago, one fellow wrote to me, complaining that his line stage amplifier developed far too much gain. I was wasn’t surprised, as he had cascaded two SRPP circuits, one 6DJ8-based SRPP amplifier after another. Why? More is better, I guess. And at least ten tube fanciers have told me that they love my Aikido SRPP design! I wonder how many believe that any time one triode sits atop another an SRPP is created. Far too many, I am sure. Because the SRPP demands the least thought, it is the most popular tube topology, which also go a long way to explaining why I am so sick of it.)

Two triodes are put to good use in the augmented plate follower, as shown below. The input triode provides gain and the output triode offers low output impedance and low distortion. Dissimilar triodes would make excellent candidates for this circuit, such as the 6DE7, 6DR7, 6EA7, 6FR7, 6GF7, or 12DW7, particularly if high-gain and low output impedance are required.

If the feedback resistors are removed, the circuit looks similar to the constant-current draw grounded-cathode amplifier that I like so much, as shown below.

This arrangement draws a fairly constant current, which greatly eases the power supply’s workload. Adding the two feedback resistors gives us the following circuit.

I know that the extra cathode resistor is bothering a few of you, but I would never build this circuit without it, as the small-valued resistor does wonders to improve the output tube’s linearity and it buffers the cathode follower’s cathode from excessive load capacitance.

What else can two triodes do? The following circuit is an interesting example. The underlining configuration for the input tube is cascode, as the top triode sees a fixed cathode-to-plate voltage and the current variations that flow through it are relayed to the load resistor through the transistor. The output tube’s circuit topology is simply a variation on the grounded-cathode amplifier, albeit with a bipolar power supply. Expect a lot of open-loop gain, as the cascode will develop a high gain which the grounded-cathode amplifier will further amplify.

No doubt that a fistful of three-triode plate follower topologies can be devised, but I am jumping ahead to four-triode designs. the Aikido amplifier accepts the feedback loop gracefully and adds its superb power supply noise rejection and low distortion and output impedance.

  And the XPP amplifier benefits from the feedback loop, as its output impedance runs quite high without it. Bare in mind that the XPP amplifier does not produce a gain any higher than what the output tube’s amplification factor. Thus, a 12AX7 input tube will not add much more open-loop gain than a 6CG7 would produce. In other words, the XPP circuit is more of an output stage than a complete amplifier.

The Gomes amplifier also uses four triodes and it falls somewhere in between an SRPP and the XPP amplifier in functioning. Its gain, however, is more dependent on the input stage’s gain. For example, a 12AX7 input tube will add much more open-loop gain than a 6CG7 would produce.

If we subtract the push-pull operation from the Gomes amplifier, we get something like the following.

Ideally, in the SE+ plate follower, the output stage works in pure single ended operation, as the two feedback resistors, Rfb2 and Rfb3, notch out any drive signal, leaving only the output distortion as an input signal for the rightmost bottom triode’s grid, which will become inverted at its plate, reducing distortion at the output.

The trick is to get the resistor ratios suitably adjusted, which means that this plate follower variation must work into a specified load impedance (or the ratios will be thrown off).


Next time
I think that we are ready to move on to the No-Gain—No-Pain circuit and its variations next time.




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