Crossovers for Class-D Amplifiers
In Post 635, we saw my crossover design for use with those class-D amplifier that could handle low-impedance loads (actually, most class-D amplifiers can). The class-D part was important, as the design exhibited deep dip down to 2.66 ohms at high-frequencies, which would trouble most class-A and class-AB power amplifiers. The schematic was accurate, both in layout and in part values, but it failed to provide the driver polarity markings, without these marking the inner workings made no sense. Oops! Here is the corrected schematic:

The dual-voicecoil driver (DVC) must have one of its voicecoils—the one that is in parallel with the tweeter—wired in opposite phase to its other voicecoil. Why? The out-of-phase voicecoil counters the high-frequency signals as it cancels the in-phase high-frequency signal the other voicecoil sees. Think of it as a free low-pass filter. By the way, we should add a Zobel network across the DVC and tweeter to null the DVC voicecoil's inductance (Le).

In fact, we should place a Zobel capacitor and resistor across both DVC voicecoils, but not across the woofer, as its Le works with us, as we subtract its Le from the calculated inductance. Ideally, DVC drivers with low series inductance would be used, but as so few DVC drivers are available, we must take what we can. Okay, I must add a further qualification to the last sentence, as many DV subwoofer drivers are made, but few DVC woofer-midrange drivers are made. Let's look at a two-way version (without any Zobel network), as it reveals how we cheated the system.

The only crossover shown, the capacitor and inductor, is a 2nd-order Linkwitz-Riley high-pass filter for a 4-ohm load. Where is the DVC woofer's crossover? It uses the high-pass filter and its one out-of-phase voicecoil to create the lumpy 1st-order low-pass filter that results in a flat-phase, transient-perfect crossover that still offer 2nd-order protection to the tweeter. This is a huge freebee, which is only possible due to the proliferation of cheap, small class-D amplifiers. Such a setup could prove a huge boon in car-audio and powered-loudspeaker systems, where a midrange-tweeter driver replaces the typical 1-inch dome tweeter. Speaking of fullrange drivers, I mentioned that speaker catalogs are replete with DVC subwoofer drivers, so why not use one with a fullrange driver?

For example, a 5-inch fullrange driver and a 6-to-8-inch DVC subwoofer would make a felicitous pairing, as the fullrange driver on its own stubbles at deep bass reproduction. Internally, the enclosure holds a divider that gives each driver its own sealed internal air volume. Note the wonderfully non-parallel walls. (The driver magnet structure itself serves to break up the rear wall reflections.) Here the crossover values for a 300Hz crossover.

I omitted Zobel networks for greater clarity. In my Post 636, I pointed out:

By the way, class-D power amplifiers all hold output inductors and shunting capacitors, as the high-frequency switching noise must be filtered away.

From International Rectifier's (Infineon Technologies) PDF, AN-1198 Class D audio amplifier ICs - Bridging class D amplifiers, we read:

Since the typical IR Class D amplifier design does not include the output LC filter in the feedback loop there will significant changes in the overall frequency response of the circuit with variations in the load impedance presented to the circuit. The output filter is usually designed to give minimal peaking at high frequencies but in some instances a small amount of peaking of 1 or 2 dB at 20 KHz may be tolerable, especially since most people cannot hear over 15 KHz and a higher Q output filter may lead to more attenuation of the output voltage ripple at the switching frequency. It is generally desirable to have at least 40 dB of attenuation or more at the average switching frequency of the amplifier. The IR Class D circuit is self ‐ oscillating so its switching frequency can vary over a fairly wide range. Most designs target a switching frequency of around 400 KHz so in order to have 40 dB (100X) of switching ripple attenuation with a second order filter the cutoff frequency should be at around a decade lower or 40 KHz typical. The ideal output filter would be maximally flat and would exhibit a Butterworth “critically damped” frequency characteristic. If the phase linearity was important then a minimum phase filter such as a Bessel filter could be used instead but it would impart a drooping frequency response to the high frequency response depending on where the filter cutoff frequency was located.

Well, what if we forgo the cheesy output inductors and capacitors and use high-quality (purposeful, more useful) inductors and capacitors instead? In other words, why not include the necessary inductor and capacitor within a passive crossover, moving the 40kHz low-pass filter down to, say, 400Hz? For example, here is a 3rd-order Butterworth low-pass filter:

The RC filter (R1 and C1) are tuned to the crossover frequency, while the output inductor and capacitor are also tuned to the crossover frequency, but with a Q of 1, which multiplied against the input low-pass filter's Q of 0.707, yields a final Q of 0.707. If a 2nd-order Linkwitz-Riley low-pass filter is desired, we simply omit capacitor C2, as all the math remains the same. Actually, I take that back, as we could subtract the woofer's Le from inductor L1's value.

For a 1st-order low-pass filter, we can omit both L1 and C2, as the woofer's Le would probably be sufficient to filter away the 400kHz switching frequency. This would work well with a bi-amplified system, but in an augmented loudspeaker system that includes a powered woofer from an internal class-D amplifier, problems arise. For example, if an external power amplifier drives the loudspeaker, the load impedance the external power amplifier sees will not be flat, as the impedance rises to near infinity at ultra-low frequencies and reaches infinity at DC.

A rising low-frequency impedance is seldom a big deal for a solid-state or OTL power amplifier, but it can be a big one for a transformer-coupled, tube-based one. Here is a partial workaround:

We use a 100-ohm power resistor for R1, the external power amplifier has more to bite on at low-frequencies. If we used an inductor and resistor, we would have to use a huge and expensive power resistor. A better and more interesting workaround would be to use two woofers, with one firing rearwards from the back of the enclosure.

Click on schematic to see enlargement

A front and back set of woofers overcome the low-frequency cabinet diffraction loss and cancels the back-and-forth cabinet motion, as both woofers work in phase but in opposite directions. (As that pesky Newton's Third Law of Motion informs us, for every action there is an opposite reaction.) The rear-firing woofer experiences a 1st-order low-pass filter, while the front-firing woofer sees a 3rd-order low-pass filter. This means the rear woofer's phase departs from the front woofer's at higher frequencies. But as the woofers become more directional as the frequencies climb upwards, it should not prove to be a big problem. In fact, it might prove to be a feature.

Now for something different, many times have I shown power-augmented loudspeaker designs, which hold an internal power amplifier to augment the external power amplifier's output. The obvious choice for the internal power amplifier is a class-D amplifier, as it is small, cheap, and low-heat.

There's a lot going here, so fasten your mental seatbelts. First, I don't know of any unity-gain stable class-D power amplifier, so the 1k resistor was added the negative-feedback loop to attenuate the class-D amplifier's input signal, which the amplifier will then amplify back to unity-gain. Second, the black dots denote PCB edits, wherein the class-D amplifier's preexisting output shunting capacitor no longer terminates into ground but into the positive input terminal on the loudspeaker. Why the change? Having the two woofers shunted by this capacitor helps the woofers not see high-frequencies, thereby furthering the implicit low-pass filtering. (Yes, I know that if you haven't read my previous posts, this will make little sense. On the other hand, those in the know will let out a, "Well, duh.")

One potential problem we face is that most class-D power-amplifier modules are now of the bridge-tied load (BTL) topology, not the "single-ended" (SE) topology I have shown here. The BTL type uses two class-D amplifiers in a balanced configuration with the load in between the two outputs.

Image from Texas Instrument SLOA 290

Click on schematic to see enlargement

Since monopolar power supplies are less of a hassle, class-D amplifiers are usually designed to operate with them, which means that their output sits at half the B+ voltage, which explains why the "single-ended" topology sports output coupling capacitors. In contrast, the BTL and PBTL topologies obviate the need for these huge coupling capacitors and improve the amplifier's PSRR, which is great, except that they don't work in my designs.

By the way, rather than further muddy the already muddy waters of audio nomenclature, the "single-ended" class-D topology should have been labeled LGT topology, which stands for Load Ground-Terminated. Or, we could have had GTL, Ground–Terminated Load—anything but "single-ended." Imagine the glee from the advertising department when they saw the label "single-ended" in the IC class-D data-sheet.

Free-Lunch Aikido Line-Stage Amplifier
I like to keep my channels separate, independent power B+ voltage supplies, signal grounds, and heater power supplies. Hell, I have even used separate enclosures in a stereo line-stage amplifier, i.e. absolute dual mono. Reasons are not hard to find, less crosstalk, less power-supply interaction between channels, and potentially a more sane grounding arrangement. Moreover, absolute dual mono works best with dual mono power amplifiers.

Sadly, the house-ground nightmare remains, but can be remedied with two House-Ground circuits, one per channel.

(Don't ask; I am sold out of the kits, alas.)

In fact, I wonder if a dual-channel phono preamp could be built in two enclosures, with the turntable-ground going to the house ground.

I also like to give the vacuum tubes DC-regulated heater power supplies. Why? No hum, longer life due to a slower turn on, that is if you design wisely. (A well-designed low voltage regulator will slowly ramp up to its target output voltage, which can be done with a large-valued capacitor across the voltage-setting resistor.) After several readers told me that separate heater power supplies for each channel sounded better, I decided to test this assertion. They were right, as a better sonic image resulted with greater clarity. Not a huge upgrade, but nonetheless a worthwhile one.

Okay, how do we get all this and how do we do it effortlessly? Here is my hybrid solution, a power buffer also provides the heater current:

Click on schematic to see enlargement

Note the single B+ voltage and no heater power supplies. What see here is a relatively low voltage Aikido gain stage followed by a MOSFET-based source follower, which is constant-current source loaded. This unity-gain follower idles at the required heater current (150mA), which is set by the constant-current source. The top 12AU7's heater element rides along with the output signal, thereby establishing a fixed voltage relationship between the top 12AU7's cathodes and their heater. The bottom 12AU7's heater sees a steady voltage drop due to the 1kµF shunting capacitor.

The P-channel MOSFET will get hot, as it dissipates 6.15W, so a heatsink will be needed for it. Although my assumption here is that each channel gets its own high-voltage power supply, a single power supply could be used. Note we cannot use different tubes in this configuration, as unlike the usual Aikido arrangement with its dedicated input and output tube, here the bottom triode holds an input tube and an output triode. The MOSFET can be replaced by an IRF9520 or something more modern. I would avoid replacing it with a PNP transistor, however, as the distortion went up in SPICE simulations. The MOSFET's idle current flow of 150mA is certainly hot for line-stage amplifier. On the other hand, the source-follower can burn through yards and yards of the most capacitance-laden interconnect. In addition, it shields the Aikido cathode follower output stage, which runs on woefully low idle current due to the very low B+ voltage, from tough external loads. Here is the SPICE-generated Fourier graph for 1Vpk at 1kHz into a 20k load resistance.

The MOSFET's idle current flow of 150mA makes it suitable for a single-ended headphone amplifier. Headphones from 32 ohms to 300 ohms could be easily driven to screaming SPLs. For example, 150mA into a 32-ohm load equals peak voltage swings of 4.8V, which is 4.8 times greater than your phone can deliver, and as voltage squared determines output power, it delivers 23 times more power. The peak output swing into 300-ohms headphones is staggering. With a 33 µF capacitor output coupling capacitor and 300-ohm load, the same SPICE simulation produces a nearly identical set of harmonics plotline as with the 20k load. Here is the graph for the circuit with a 470 µF capacitor coupling capacitor and 32-ohm load.

This is about as good as it gets. Why? Look at the 3rd harmonic. The third harmonic sounds like constrained, canned, fake, compressed music—because that is precisely what it is, i.e. compression.

Next, note the relatively strong 2nd harmonic, nature's harmonic and the single-ended signature harmonic. By the way, as each channel gets its own Free-Lunch Aikido, with separate grounds, balanced headphones would be the way to go. Failing that, the two grounds must be tied together at the ground terminal of the three-section headphone jack.

The relatively high current and big potential voltage swings raises the possibility of a parafeed (i.e. parallel feed) power amplifier with a coupling capacitor and output transformer—a transformer without an airgap.

The first thing we do is replace the 12AU7s with 12DW7/ ECC832/7247 tubes, which are according to the tube manual:

The 7025 is the fancy version of the 12AX7. The input stage creates the needed gain, while the 12AU7-based Aikido cathode follower output stage delivers a low output impedance and enough current to drive the MOSFET's gate. For example, let's say that we wish to build a small single-ended amplifier to drive 4-ohm computer loudspeakers. The constant-current source displaces 33.8V at idle, which limits us to a potential output voltage swing of ± 30Vpk. We divide 30V by 0.15A to find the optimal load impedance and get 200 ohms. Next, we divide 200 by 4 and get 50, which we take the square-root of ( √ 50) to get the winding ratio, about 7 to 1.

Click on schematic to see enlargement

By the way, we can also work out, on the back of an envelope, the maximum power output, by multiplying the idle current against the peak output voltage swing, 0.15A x 30V = 2.25W. This may not seem like a lot, but remember that the loudspeakers sit less than a yard from your ears. Besides, they sell $$$ 1W 300B-based OTL amplifiers, so you will have some bragging rights with your mighty two-watt single-ended amplifier. In addition, perhaps you have heard of a speaker company named Klipsch. For an 8-ohm loudspeaker, the winding ratio equals 5:1, while the primary impedance remains at 200 ohms. Where does one find an output transformer with a primary impedance of 200 ohms? How about a PA matching transformer. Here is Gemini to the rescue:

AI Overview

A Public Address (PA) constant-voltage audio matching transformer allows amplifiers to drive multiple speakers over long distances without signal loss. Also known as a line-matching transformer, it steps up the voltage at the amplifier (usually to 70V or 100V) and uses step-down transformers at each speaker to convert it back to a standard impedance (e.g., 8 Ω or 4 Ω). [ 1 , 2 , 3 , 4 , 5 ]

How Constant-Voltage Systems Work
Constant-voltage (commonly 70.7V in North America or 100V globally) systems are designed for Public Address (PA) and background music setups found in schools, office buildings, and warehouses. [ 1 , 2 ]

• The Problem: Running standard, low-impedance speakers (4 Ω to 16 Ω) over long distances causes severe power loss and signal degradation over thin wires.

• The Solution: The transformer at the amplifier steps the output up to a high voltage. Because the voltage is high, the current is correspondingly lower, allowing you to run very long cables with negligible power loss. [ 1 , 2 , 3 , 4 ]

Parts Express sells a 15W constant-voltage audio transformer for $8.40, model 300-039; use the 5W primary tap. On the other hand, we could divide 115 by 7 and get 16.4. Why? We could find a 25VA 15Vac toroid power transformer, which might actually work better than the PA transformer. Wouldn't a 16Vac be better? Maybe. Maybe not, as the power transformer's output voltage is often quoted at peak power output with both the wire and core losses included. In other words, the 15Vac transformer might actually deliver 16.4Vac with an unloaded secondary. No doubt, some adventurous readers are thinking: why stop at a B+ voltage of only 100Vdc, why not use 300Vdc instead, so a 15W parafeed single-ended power amplifier could be made? Well, as I love to point out, topology is indifferent to scale.

With a B+ voltage of 300Vdc, we could reasonably get 133V peak voltage swings, which against the 150mA idle current equals 10W of average (RMS) output power. Of course, a much bigger P-channel MOSFET will be needed (if not two in parallel), which will require running the Aikido cathode follower stage at a much higher idle current, say 10mA to cut through all the capacitance presented by the more powerful P-channel MOSFET. (An emitter-follower driver stage might be needed.) It's certainly doable, as we do not run into the usual limitation of maximum heater-to-cathode voltage limits. Or, we could build a dual-use Aikido, one that can drive either a power amplifier or 32-ohm headphones with it two outputs, giving us a pure-tube line-stage amplifier and a hybrid headphone amplifier.

Click on schematic to see enlargement

Of course, the 470µF output capacitor can be bypassed by a high-quality film capacitor. (Here the low-voltage B+ voltage works majorly in our favor, as nonpolarized electrolytic capacitors stop at about a 100V voltage rating and low-voltage polypropylene film capacitors are much cheaper than high-voltage ones. As for the power supply, here is one possibility.

I would use a 100VA toroid. The rectifiers can be HER108 or MUR420 or 600V FRED rectifiers; the latter are screaming fast, such as the VS-HFA04TB60-M3, which offers a reverse-recovery time of 28 nanoseconds. If we replace the RC filters with LC filter (choke and capacitor), the raw B+ voltage before the choke can be a low 105Vdc. Okay, if absolute dual-mono isn't your cup of tea, we can realize some big savings in cost and heat dissipation. Here is how:

Click on schematic to see enlargement

One power supply feeds it all—tubes, MOSFETs, constant-current sources, and heaters. Each P-channel MOSFET now draws half the idle current, only 75mA. The MOSFET dissipation drops to only 2.13W per channel, which translates to smaller heatsinks; in fact, we could probably get away with wimpy clip heatsinks. The 75mA constant-current source can be made from an LM317-HV and 16.5 current-setting resistor. In fact, a P-channel MOSFET and an LM317-HV can share the same heatsink. Moreover, if you are driving a stereo power amplifier, the dual mono construction offers little.

See my Post 537 for an explanation of what is going wrong here and what is going right below:

Note how the return current remain within their channels.

Music Recommendation: Agnes Obel, Aventine
I listened to this album (as a CD) over a decade ago. I found it interesting, but not an audiophile-dream album. Yet, I have seen its cover in audio magazines and ads, but this was not enough to compel a re-listening. What did prompt me? Deutsche Grammophon released an album titled, The Echoes of Women - International Women's Day 2024, which runs over two and a half hours and holds mix of classical and contemporary music.

Moreover, the album was curated by Agnes Obel, with one track of her music. Okay, that got my attention. Amazon Music streaming service offers a few of her albums in higher resolution than CD, which is welcome, as they are certainly audiophile grade.

//JRB

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AI Summary
Adobe's AI's report on this post:

Reasoning and Approach
To summarize the key points of the document, I focused on extracting the main technical concepts, design recommendations, and notable observations from the text. The document covers advanced crossover design for class-D amplifiers, practical loudspeaker system configurations, and a hybrid tube/MOSFET line-stage amplifier. I have organized the summary into thematic sections for clarity and included examples where relevant.

Key Points Summary

1. Crossover Design for Class-D Amplifiers

• Class-D Compatibility: The document discusses crossover designs tailored for class-D amplifiers, which can handle low-impedance loads (e.g., dips to 2.66 ohms at high frequencies) that would challenge class-A or class-AB amplifiers.

• Dual-Voicecoil (DVC) Drivers: A DVC driver's voicecoils are wired with one in opposite phase to the other (especially the one in parallel with the tweeter). This configuration acts as a free low-pass filter, canceling high-frequency signals and simplifying crossover requirements.

• Zobel Networks: Recommends adding Zobel networks (capacitor and resistor) across DVC voicecoils and tweeters to counteract inductance effects, but not across woofers.

• Crossover Implementation: Describes a two-way crossover using a 2nd-order Linkwitz-Riley high-pass filter for the tweeter and a lumpy 1st-order low-pass filter for the DVC woofer, resulting in flat-phase, transient-perfect crossovers with 2nd-order protection for the tweeter.

• Application Example: Suggests pairing a 5-inch fullrange driver with a 6-8 inch DVC subwoofer in a divided enclosure for improved bass and clarity.

2. Class-D Output Filtering and System Integration

• Output Filter Design: Cites International Rectifier's recommendations for output LC filters in class-D amplifiers, targeting 40 dB attenuation at the switching frequency (typically 400 kHz), and discusses filter types (Butterworth for flatness, Bessel for phase linearity).

• Passive Crossover Integration: Proposes using high-quality inductors and capacitors in the passive crossover to replace standard class-D output filters, moving the low-pass filter cutoff from 40 kHz down to the audio crossover frequency (e.g., 400 Hz).

• Impedance Considerations: Notes that certain configurations can cause rising low-frequency impedance, which may be problematic for transformer-coupled tube amplifiers. Offers workarounds such as using a power resistor or dual woofers (front and rear firing) to address cabinet motion and diffraction loss.

• Amplifier Topologies: Discusses the limitations of bridge-tied load (BTL) class-D modules for these designs and clarifies terminology around 'single-ended' vs. 'load ground-terminated' topologies.

3. Free-Lunch Aikido Line-Stage Amplifier

• Dual Mono Construction: Advocates for separate power supplies, grounds, and even enclosures for each channel to reduce crosstalk and improve sound quality.
• Heater Power Supplies: Recommends DC-regulated heater supplies for vacuum tubes to reduce hum and extend tube life. Separate heater supplies for each channel can improve sonic imaging.

• Hybrid Solution: Presents a hybrid Aikido gain stage followed by a MOSFET source follower, which also supplies heater current. This design allows for high current and voltage swings, making it suitable for both line-stage and headphone amplifier applications.

• Performance: SPICE simulations show low distortion and strong 2nd harmonic content (desirable for single-ended designs), with the ability to drive headphones from 32 to 300 ohms.

• Parafeed Power Amplifier: Explores using the circuit as a parafeed (parallel feed) power amplifier with a coupling capacitor and output transformer, including calculations for optimal load and transformer winding ratios.

• Power Supply Options: Details options for dual mono and single power supply configurations, with considerations for heat dissipation and component selection.

4. Music Recommendation

• Recommends the album "Aventine" by Agnes Obel, noting its improved audiophile quality in recent high-resolution streaming releases.

Example Implementation

• Crossover Example: For a 300 Hz crossover, use a 2nd-order Linkwitz-Riley high-pass filter for the tweeter and leverage the DVC woofer's out-of-phase voicecoil for a 1st-order low-pass effect.

• Amplifier Example: For a single-ended headphone amplifier, use a MOSFET source follower idling at 150 mA, capable of driving both low- and high-impedance headphones with low distortion.

This summary captures the document's main technical insights, practical recommendations, and notable observations for advanced audio system designers.

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