Single-Ended Bottcamp
I sat in a waiting room, notepad and pencil and calculator at the ready, with about half an hour to kill. I decided to design a small, single-ended OTL headphone amplifier for 300-ohm headphones, such as those from Sennheiser. I was thinking that the amplifier needed be portable and should run off a 12Vac wallwart. In other words, small enough to take to work or place next to a laptop at Starbucks.

The background idea was that smart phones, laptops, and MP3 players all assume 16-ohm to 32-ohm headphones, which means they only put out a peak-voltage swing of about 1V. Sadly, 300-ohm headphones need more voltage to dance; hence the need for a headphone amplifier that offered more voltage gain, but at less peak current flow. In other words, this is a nice fit for tube-based designs, as tubes are current limited, not voltage limited. So, how much peak voltage swing do we need?

Decades ago, I attach the scope probes to the output of my headphone amplifier and listened to my Sennheiser HD580 headphones at the highest SPLs that I could tolerate. I saw that peaks of 3V showed up on oscilloscope screen. Well, we only need divide 3V by 300 ohms to find the peak output current swing, which is only 10mA, which is well within the limits of a 6DJ8 or ECC99 or 5687. Of course, many other audio-signal triodes, such as the 6SN7 and 12AU7, can deliver this much cathode current, but due to their higher plate resistances (rp), they require higher B+ voltages. For example, a 6DJ8 with a cathode-to-plate voltage of 62V and cathode-to-grid voltage of 0V draws 20mA, but a 6GC7 or 6SN7 needs a voltage of 160V do the same. In other words, we seek low rp and high transconductance (gm).

Here is the formula for the required B+ voltage, when the cathode is at ground potential (0V):

      Vb = 2Iq(rp + Rload)

If you are wondering why I specified a current draw of 20mA, when the peak current swing is only 10mA, the answer is that a cathode follower loaded by a 10mA constant-current source must idle at 10mA and swing 20mA at peak output, as it must not only pull up against the 300-ohm load, but also the constant-current source (CCS), making a total of 20mA, 10mA for the load and 10mA for the CCS. When the output swings down to -3Vpk, the cathode follower has ceased to conduct altogether and 10mA constant-current source does all the tugging down against the 300-ohm load.

This is the cathode follower output stage. The constant-current source is set to the desired idle current; in this example, 10mA. The next step is to determine the required cathode voltage. Normally, we use the following formula to find the needed cathode voltage to establish a desired idle current with a predetermined B+ voltage.

      Vk = (Vk-p - Iq ·rp) / (mu + 1)

Where mu is the triode's amplification factor. But this won't necessarily give us enough voltage headroom to both drive the load impedance and not run into the constant-current source's minimum voltage drop, which cannot be zero volts. Speaking of the constant-current source, we can use the famous LM317 voltage regulator.

Since so little current is required and so little voltage dropped across the IC, we can forgo giving it a heatsink. The LM317's data sheet shows the following graph of the voltage drop versus device temperature with various current flows.

Note that this shows the voltage drop across LM317's input to output pins, not from ground to the input pin. In other words, we must add 1.25V to the shown drop-out voltage. For example, with 25C and 20mA, we get a drop-out voltage of about 1.5V, to which we add 1.25V, bringing us to 2.75V. This voltage must be added to the peak output voltage swing (3Vpk), which gives us the require cathode voltage, 5.75V. To be extra safe, add another volt, 6.75V.

The output coupling capacitor formula is easy enough. With a load impedance of 300 ohms, any coupling capacitor value 30µF and up is usable. In fact, since the cathode voltage is so low, we could use a non-polarized electrolytic capacitor bypassed with a small-valued film or PIO capacitor. The next voltage to be calculated is the grid-bias voltage.

Remember that grid-bias voltage is relative to the cathode, not ground. We return to the formula for finding the cathode voltage:

      Vk = (Vk-p - Iq ·rp) / (mu + 1)

If we do the math, we get a result of -0.9V, which we then add to the previous voltage of 6.75, leaving us with 5.85V relative to ground potential. The B+ voltage must be at least equal to 5.85v + 62V, if we are using a 6DJ8 triode. Are those results set in stone, inviable and sacrosanct? No, not even close. What we have is a good first approximation of what is needed. It does, however, save us a lot time just striking out at random voltages and part values. This is why the backs of envelopes and pencils exist. When I got home, I ran SPICE simulations on this design, using my calculated voltage as guides.

The above proved the most promising, within reason. What sort of reason? For example, we do not want the cathode follower's 6DJ8 triode to dissipate too much heat, and we want to make sure that the constant-current source draws a bit more than 10mA to ensure a clean negative output voltage swing. At the same time we want to give the input triode a fairly high plate resistor value and cathode-to-plate voltage. Thus, the 100Vdc B+ voltage.

This is an OTL amplifier that uses negative feedback, which sets a fixed gain of 1:3 or +9.5dB. How much negative feedback? The open-loop gain is 1:18.8 or +25.5dB; subtract the closed-loop gain and we get 16dB of negative feedback. In SPICE simulations, the performance was admirable—well, at least in terms of THD, output impedance, and bandwidth. In terms of PSRR, which is critical in a headphone amplifier, not so much, as it was only -28dB at 100Hz. I figured it was time for me to apply some of my signature Aikido Mojo.

With the added Aikido-Mojo 768k resistor and 10µF capacitor, the PSRR improved by -40dB, bringing it down to -68dB. That's a one-hundredfold decrease. Bear in mind that this is the raw PSRR, absent any further noise-reduction ploys, such as chokes, RC filters, power-supply regulation …

With 1Vpk of output at 1kHz, the THD is about 0.1% in SPICE simulation.

At full output, i.e. 3Vpk, the THD rises to 0.46%, but still retains the lovely single-ended cascade of harmonics.

The problem with using a 6DJ8 as the output triode is that the high idle current flow of 10mA takes a bite out of the 6DJ8's longevity. In other words, if we use a triode with greater plate dissipation, such as the ECC99, we can expect a much longer tube life. Another issue might that although 3Vpk of output voltage swing delivers nine times more power into the 300-ohm headphone than the 1Vpk that smartphones put out, it may not still be enough. It we increase the potential output voltage swing to 6Vpk, the output stage now delivers 36 times more power. We could double on 6DJ8 triodes in the cathode follower stage or use two ECC99 triodes.

The LM317-based constant-current source now draws 21mA of current, so each ECC99 triode draws 10.5mA. The cathode follower cathode voltage has been upped to 9.2V due to the increase output voltage swing of 6Vpk. What are missing from the schematic are the negative-feedback loop and some Aikido Mojo.

The 10k and 91k resistors set a gain of 1:6 or +15.6dB. The 931k resistor and 10µF capacitor inject a sampling of the power-supply noise into the 6DJ8's grid, resulting in the Aikido-Mojo boost in PSRR. Here is the PSRR graph.

A PSRR of -66dB at 100Hz is excellent for any tube circuit. The distortion was super low with 1Vpk of output.

Note the relatively strong 2nd harmonic. At full output, the distortion rises, but still maintains the sweet single-ended cascade of harmonics.

By the way, the output impedance in SPICE simulations was 15 ohms. We finally arrive at the actual circuit that I sketched out in that waiting room.

Click on schematic to see enlargement

This is a hybrid headphone amplifier, as the tube-based input stage has been replaced by a transistor-based bastode differential amplifier. The negative-feedback loop no longer encompasses the output coupling capacitor, so I decided to radically increase the coupling capacitor value. In addition, this topology does not invert. Since we no longer have a tube-based grounded-cathode amplifier input stage, I wondered if we could use a 6DJ8 and a lower B+ voltage.

Click on image to see enlargement

Note the 100Vdc B+ voltage, which results in a plate dissipation of only 0.87W for each 6DJ8 triode. Moreover, two 6DJ8 tubes have roughly the same combined heater-element dissipation of one ECC99, 4.6W versus 5W. The 10µF input coupling capacitor might be overkill, but when driving transistor bases a low-input impedance is desirable. Of course, the solid-state signal source (the smartphone or personal music player or DAC) will offer a low input impedance, but a 0.1µF input coupling capacitor would present an impedance of 79.6k at 20Hz; in contrast, the 10µF input coupling capacitor, only 79.6 ohms.

(The reason polarized-electrolytic coupling capacitors used in CD players and DAC and other solid-state audio are often 33µF to 470µF in value is not to extend the low-frequency bandwidth but to reduce the capacitor's distortion. The greater the electrolytic coupling capacitor's capacitance, the lower the distortion. Non-polarized-electrolytic coupling capacitors are inherently low-distortion.)

Interestingly enough, the 6DJ8 beat the ECC99 in SPICE simulations, delivering lower distortion.

At full output, 6Vpk, we get the following:

Nice. Let's assume that reality will prove ten times worse; nonetheless, the THD would only rise to 0.1% from 0.01%. The output impedance is less than one ohm, the result of the super high gain from the transistor-based bastode input stage. Here is the PSRR graph:

No doubt some are wondering about the 1mA constant-current source, asking where I can buy one of those. Rather than buy, it's better to build.

This constant-current source works extremely well. The way it works is simple enough: the MJE350 PNP transistor exhibits a base-to-emitter voltage of 0.59V, which we use as free voltage reference. The top transistor controls the bottom transistor's current conduction—but in anti-phase. When the top draws more, the bottom draws less, and vice versa, i.e. conversely.

If the voltage drop across the 590-ohm resistor exceeds 0.59V, the top MJE350 responds by increasing its conduction, thereby forcing the bottom MJE350's base to see higher voltage, which in turn causes the bottom MJE350's emitter to follow, reducing the voltage drop across the 590-ohm resistor. In other words, this circuit strives to constantly maintain a fixed 0.59V voltage drop across the 590-ohm resistor; and a constant voltage drop equals a constant-current draw. If we desire a 10mA current draw, we reduce the 590-ohm resistor value to one tenth or 59 ohms.

Now for Something Different
Because I can never stop exploring alternative circuit variations, I wondered if a better place for both constant-current sources might be above the triodes. In other words, we would replace the cathode follower with a grounded-cathode amplifier. With two constant-current sources shielding the triode plates, no Aikido Mojo is needed. Here is what I came up with:

We see two grounded-cathode amplifiers in cascade. The input signal enters the left triode's grid, where it gets both amplified and inverted at that triode's plate. This signal is then passed on via the 0.1 µF coupling capacitor to the right triode's grid, whereupon it is once again amplified and inverted, with the two inversion series yielding no phase inversion at the output. The 470-ohm cathode resistor and the 1.05k resistor and 10µF capacitor define a negative-feedback loop. To see this works just imagine forcing a positive voltage pulse on the output.

The positive pulse is both relayed and attenuated by the negative-feedback loop to the input triode's cathode. Signals enter a triode's cathode are amplified but not inverted at its plate, as the triode now functions as a grounded-grid amplifier. The non-inverted and greatly amplified pulse is then fed into the right triode's grid, forcing much greater current conduction from this triode, thereby pulling down its plate voltage in response, bucking the positive pulse with a negative one. Negative feedback in a nutshell. If we substitute the pulse with distortion generated by the amplifier circuit itself, the distortion fails to match the input signal, so the same mechanism works to erase the distortion. Speaking of distortion, here is the SPICE-generated Fourier graph:

The THD is about 0.1%. The relatively strong 2nd harmonic bestows a slight warmth. At full output, which is only 3Vpk, due to the 13mA constant-current source, the harmonics take on that single-ended cascade so prized by our ears.

Note that the negative feedback, however, does not extend down to DC, as the two internal coupling capacitors break the DC connection between the triodes. This means that at extremely low frequencies there is negligible negative feedback and, thus, high gain, roughly equal to mu ², where mu is the triode amplification factor; in the case of the 6DJ8, about 1:1,000 or +60dB. Is this a problem? Not really, as the 0.1µF coupling capacitor limits the amount of low-frequency signal that appears at the second triode's grid.

Okay, what if we take this potential problem and turn it into an asset? How so? We juggle the two internal capacitor values to create a bass boost.

Note that the 0.1µf capacitor was replaced by a 1.1nF (0.0011µF) capacitor and the 10µF by a 3.9µF capacitor. These values create a +6dB bass hump at 20Hz.

With rare exception, most headphones droop at the low frequencies, giving them their signature thin sound. Will this feedback-based low-frequency boost create extra distortion? It certainly will at 20Hz, if for no other reasons that we have greater gain and less negative feedback; but once the frequency plot flattens, not really.

Interestingly, the SPICE Fourier analysis is sensitive to phase shift, whereas a THD meter isn't. In other words, we need not worry.

Returning to the circuit, note the other changes, such as the 330µF non-polarized electrolytic capacitor and the lower plate voltage on the output triode. Since we put in place a bass boost, we should ensure a low output impedance for the headphones, which the bigger capacitor helps ensure. At the same time, however, we run into the problem that non-polarized electrolytic capacitors top out at 100Vdc; thus, the lower plate voltage.

Another issue might be our desire for greater output voltage swing. The easy workaround is to use two 6DJ8 triodes in parallel in the second stage. A three tube headphone amplifier would look cool, but might make the heater power supply a tad more difficult.

Music Recommendation: Demo-Grade Bass Tracks
I never met an audiophile who didn't hunger more and better bass. I was going to qualify this first sentence with a "male" audiophile who… but then I remember that back in the 1970s, when audio was king, that I heard loudspeakers with over ripe bass described as "seduction speakers," as women were said to swoon to powerful, deep bass. Okay, we all like good bass—and some of us are willing to pay obscene amounts of money to get it. Once we have, we need to show it off. Thus, the following list of ten excellent bass-demonstration tracks.

The first track I just discovered at a friend's house, "Chocolate Chip Trip" by prog-rock band Tool on their album Fear Inoculum.

Do not expect to be hammered in the beginning, as that track, like many other bass showcase tracks, saves the heavy ammo for the end. Asides from great bass, the track delivers an astoundingly huge stereo image.

Just about any album by Mickey Hart qualifies as a bass-extravaganza. On his album Ramu, I quite like the track "Nacare."

Good bas doesn't mean just organ pipes and big drums, as it also refers to the ability to impart a sense of the music hall's size. In fact, the near silent portions of some albums, such as the recording of Benjamin Britten's Noye's Fludde allows us to sense extent of venue; absent deep bass, we cannot hear dimensions.

Returning to Mickey Hart, his album, In the Groove, departs from his other albums by not so much delivering massive bass, but high-quality bass, bass good enough to hear the room acoustics. For example, the tracks "Storm Drum" and "Drops" do a great job of portraying a near ominous if not menacing huge chamber.

Of course, I cannot forget to mention his most famous album, Däfos, whose track "The Gates of Däfos," is often described as "the drum equivalent of a piano falling down a flight of stairs."

One last Hart album has to be mentioned, Planet Drum (25th Anniversary). I often play the track "Temple Cave" to test my systems bass (and imaging).

Another go-to bass album is Inlakesh's The Gathering, any of whose track count as demo-grade, but I truly like the first, "Forest Gathering." Mercy. That's some drum.

I have recommended the following album, Lou Harrison's Drums Along The Pacific, before, but I didn't single out one track whose first note hits our ears like a sonic karate chop, "Song of Quetzalcoatl, for 4 percussionists."

Another great plucked string bass extravaganza is Cassandra Wilson's track, "Strange Fruit," from her album New Moon Daughter.

I can probably come up with another ten bass-worthy tracks, but this should hold you for now.

//JRB

AI Summary
The AI assistant within Adobe Acrobat created the following summary.

The paper discusses the design and specifications of a portable single-ended OTL headphone amplifier for 300-ohm headphones.

Design of a Single-Ended OTL Headphone Amplifier

The text discusses the design considerations and calculations for a portable single-ended OTL headphone amplifier suitable for 300-ohm headphones. ​

• Designed for 300-ohm headphones like Sennheiser HD580. ​
• Aims to provide higher voltage swing than typical smartphone outputs.
• Peak voltage swing needed is 3V, resulting in a peak current swing of 10mA. ​
• Utilizes low rp and high transconductance triodes like 6DJ8 or ECC99. ​
• The formula for required cathode-to-plate voltage is provided: Vk-p = 2Iq(2rp + Rload). ​

Constant-Current Source and Voltage Calculations

The text explains the use of a constant-current source and the calculations for necessary voltages in the amplifier circuit. ​

• LM317 voltage regulator is used for the constant-current source. ​
• Required cathode voltage calculated to be 6.75V for safe operation. ​
• The output coupling capacitor should be at least 30µF for a 300-ohm load. ​
• Grid-bias voltage is determined to be -0.9V, leading to a B+ voltage requirement of at least 67.75V.

SPICE Simulations and Performance Metrics

The author shares results from SPICE simulations, highlighting performance metrics of the amplifier design. ​

• Open-loop gain is 1:18.8 (+25.5dB) with a closed-loop gain of 1:3 (+9.5dB). ​
• PSRR (Power Supply Rejection Ratio) is -28dB at 100Hz, indicating room for improvement. ​
• THD (Total Harmonic Distortion) is about 0.1% at 1Vpk output, rising to 0.46% at full output (3Vpk). ​

Enhancements with Aikido Mojo

The text describes the implementation of Aikido Mojo to improve PSRR in the amplifier design. ​

• Aikido Mojo improves PSRR from -28dB to -68dB, a significant enhancement. ​
• The design includes a 768k resistor and a 10µF capacitor for noise reduction. ​
• The THD remains low at 0.1% with 1Vpk output, maintaining desirable harmonic characteristics.

Alternative Tube Choices and Output Voltage Swing

The author explores using different tubes and configurations to enhance output voltage swing and amplifier performance.

• ECC99 triodes are suggested for longer life and higher output swing. ​
• Increasing output voltage swing to 6Vpk delivers 36 times more power into 300-ohm headphones. ​
• The design can utilize two 6DJ8 triodes in parallel for increased output. ​

Hybrid Headphone Amplifier Design

The text presents a hybrid amplifier design that combines tube and transistor technologies for improved performance. ​

• The input stage is replaced with a transistor-based bastode differential amplifier. ​
• The design operates at a lower B+ voltage of 100V, reducing plate dissipation. ​
• The 10µF input coupling capacitor is used to ensure low input impedance. ​

Constant-Current Source Construction

The author details a method for building a constant-current source using transistors. ​

• The MJE350 PNP transistor is used to maintain a constant 0.59V drop across a resistor. ​
• Adjusting the resistor value allows for setting the desired current draw (e.g., 10mA). ​

Innovative Circuit Variations and Bass Boost

The text discusses innovative circuit variations, including bass boost features in the amplifier design.

• Grounded-cathode amplifiers are used with two constant-current sources for improved performance. ​
• A bass boost is created by adjusting coupling capacitor values, resulting in a +6dB boost at 20Hz. ​
• The design maintains low output impedance while addressing potential distortion issues.

Recommended Bass Demonstration Tracks

The author provides a list of tracks ideal for showcasing bass performance in audio systems. ​

• "Chocolate Chip Trip" by Tool is highlighted for its impressive bass and stereo imaging. ​
• Mickey Hart's albums are recommended for their bass-heavy tracks, such as "Nacare" and "Temple Cave." ​
• Other notable tracks include "Blue Bossa" by Brian Bromberg and "Strange Fruit" by Cassandra Wilson, showcasing high-quality bass. ​

 

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