The Journey of DIY No-Feedback Class D Amplifier (1) Subtitle: The Motivation and Story Behind It

What type of capacitor are you using?
Hi!

Just this type, regular polyester.

I can't recall the source, some are from Farnell and some are from eBay but they all seem to work Ok and have much bigger voltage ratings than they see.

I know the chip types can have weird non-linearities - varying capacitance with voltage IIRC.
The air coils I like because the 10uH are pretty easy to wind on a plastic sewing bobbin, look cute soldered in, and I know they will always be linear. Well, as linear as I can think of, under any and all conditions.

I prefer them in speaker crossovers too.
One day I'll experiment with speakers with two active coils, but one coil, probably the field coil, needs to have a rectified audio, so it would probably need some tweaking for the low level signals 😀

Anyway, on class D I found it was something quite easy to try, I haven't noticed any RFI/EMC/EMI etc. noise from them, but they do rise a few degrees in temperature. I did point them in different directions, but it didn't seem to matter.

I did have a thread here when I wound them, I'll see if I can find it..
.. ah, here:

As I remember there was huge consternation about melting coils and RF transmissions, but perhaps as it's just magnetic, not electromagnetic, I didn't have any trouble with them and I found the sound very sweet.
 

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If it is encased in aluminum, eddy currents in the aluminum will be shorting out the air coils, heating the case and reducing filtering effect. This is one benefit of shielded inductors, minimal interaction with nearby metal.
Worse I think would be an earth plane of the PCB, as iyt's copper and right next to the coils 😀

I didn't have the luxury of a new PCB, so mine stood up like trees, so the fields were on the plane of the board.
Between the two coils of each amp I'd look at the most favourable coupling / isolation.

If laying out a new PCB, I'd want holes in the PCB and the coils firing up and down, and then use 25mm standoffs do give them 25mm space above and below, and of course great cooling.

In my testing I just popped them back into the chinese case, they got slightly warm to touch, I'd reckon 10C above ambient perhaps. I did it to more then one amplifier and each time I liked the sound, and with a custom PCB I wouldn't consider ferrite, simply due to the shortcomings.
 
Just ran across this thread.
The sigma-delta Class D amplifier operates in a self-oscillating mode, where the feedback loop (R3) is set up to induce oscillation, essentially functioning as positive feedback. The integrator introduces a 90-degree phase shift, and together with the Schmitt comparator and subsequent MOSFET drivers, it accumulates around 360 degrees of phase shift, forming a positive feedback loop to generate oscillation. However, typical audio feedback refers to negative feedback for the audio signal, where a 180-degree phase shift (with some phase margin) is required. Can R3 in this feedback loop serve both as positive feedback for the pulse signal and negative feedback for the audio signal? Clearly, it cannot.
Why not? A resistor doesn't care what the phase or polarity of a signal passing through it is, it just determines the ratio of the voltage across itself to the current through it, with unchanged relative polarity of either. And a feedback circuit working through the resistor can be both positive and negative for different frequency bands. That's what frequency compensation of an amplifier deals with -- keeping the level of positive feedback at high frequency low enough to not oscillate, while providing enough negative feedback level in the lower frequency band to control gain and lower distortion. An ideal pulse has infinite bandwidth, the audio bandwidth isn't infinite. Phase shift of the HF part of the pulse bandwidth makes feedback there go positive.

IMO, the issue whether R3 is also providing global negative audio band feedback should be simple to determine -- if, in the simulation or build, you raise the value of R3 slightly (by, say, a factor of X times with X on the order of 1.05), does the midband gain of the amplifier go up by 20log(X)? If so, that's negative feedback in the audio band.

Not proof of anything, but an anecdote:
Some years ago I had a similar idea to yours. I'd read so many testimonials about things like reduced use of global feedback, class A, and single-endedness of circuitry having better or different sound than high-feedback class AB or class D (other than because of the usual known effects of distortion, noise and frequency response). To look into that (and to keep my newly-retired brain at some kind of work activity), I designed and built a series of power amplifiers meeting the related buzzwords: zero global feedback (though, lots of local feedback), single ended class A, even a big inductor in the circuit. But with very low noise, very low output impedance, and -70dB-ish harmonic distortion. Exhibiting a 2nd order-dominant distortion profile, with products dropping with increasing order. Fun project, but finally, to my perception it seemed (maybe due to negative expectation bias?) that the better the circuit performance got, the more the amps sounded like the ICEpower and UCD amps I'd been using in my system. I gave the amps away when I moved, their only advantage was in the wintertime in my cold basement.
 
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@bwaslo thanks for your comments and experiences sharing!
does the midband gain of the amplifier go up by 20log(X)? If so, that's negative feedback in the audio band.
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the gain of the AMP follows the ratio of R3/R1 with certain voltage of supply power for the power stage, which given by 20*log10(R3/R1), interestingly, quite similar with op amp. please see my derivation below:

Assuming the Vin is positive, within a sample period, the Vin is close to a constant. Then,

T(low) = a * C/ (Vdd/R3 - Vin/R1) and T(high) = a * C/(Vdd/R3 + Vin/R1), where a is a coefficient according to the integrate circuit configuration, C is the capacity of integrator, Vdd is the absolute number of the power supply of power stage, T(low) and T(high) are the time duration of the negative and positive modulation pulse. And Vdd/R3 - Vin/R1, in this case, should larger than 0, otherwise the capacitor won’t discharged and the there is no oscillation.

The V(out) is proportion to the duty cycle, then,
V(out) = (negative duty cycle – 0.5) * Vdd (use negative duty cycle is due to the amp output is inversed)

the Gain = V(out)/Vin

Gain = Vdd* (T(low) / (T(low) + T(high)) – 0.5 )/Vin = ((R3/R1) * (Vin/VDD) /2)*Vdd/Vin = 0.5 * R3/R1

if the Vin is negative, the derivation should be the same.


As for whether it is an audio negative feedback scheme, this is indeed a rather controversial topic, these are some further explanations following the thread you quoted. please refer to it if you are interested.

I did extensive discussion this topic with my previous and current colleague who are interested. the general consensus is:

The traditional audio negative feedback is a typical infinity impulse response system despite its non-linear correction, whereas the DIYed AMP is feedback sample-by-sample, meaning the feedback will not propagate to next sample from its previous one. this is similar to the digitize processing of SAR DAC.

Please correct me if any mistake, and any further discussion and comments are welcome!
 
Isn't the integrator a memory element, affecting infinite succeeding HF pulses? I don't see where it is ever 'reset' by shorting the caps, and I assume it maintains linear operation.

Also, am I missing something, or is there a polarity inversion not shown (maybe inside the gate driver block)? Otherwise it appears that the oscillator would just lock up -- a rising input will cause the integrator output to slope negative and make the p-channel output FET to turn on and stay on, never getting turned off.

Can you show a Bode plot of output vs input?
 
thanks! @bwaslo

(maybe inside the gate driver block)
I think so, should have an invert stage before the power stage. the diagram is cited from a paper with minor modification (might be my mistake).
Isn't the integrator a memory element, affecting infinite succeeding HF pulses? I don't see where it is ever 'reset' by shorting the caps, and I assume it maintains linear operation.
in each PWM cycle, the triangle wave will cross the zero twice, if remove the hysteresis feedback resistor (for easy analysis, will not impact the analysis result), the voltage over cap of integrator is 0 when the output is crossing zero. I think this is the so-called 'reset'. The integrator is a linear circuit; however, it works in nonlinear state because of input of non-linear digital signal.

assuming that the Vin is a discrete signal aligned with the PWM cycle. when triangle wave cross zero (0 voltage over CAP), a new cycle start, and a new discrete Vin[n] come in. I don't think, at this moment, anything can remember what Vin(n-1) is. the power stage will output a new PWM cycle with its duty cycle represent the input of Vin[n-1].

Can you show a Bode plot of output vs input?
what you want to show, analog output vs analog input? if yes, it is very time-consuming, I am not sure I can complete it in a short term.

Thank you once again for your very interesting discussion! It has been a great help in giving me deeper insights into the circuits. appreciate!!!
 
6. Subjective Listening Impressions of DIY headphone

The process of DIY a no-audio-feedback amplifier has been mostly covered, and now it’s the time for a summary. It spent a long time to collect/discuss/understand the feedback from my friends. To conduct the listening tests, I invited a diverse group of friends. Some are long-time audiophiles who’ve experienced a wide range of audio equipment, while others are friends from a band. I’d like to appreciate all of them here.

First, let me clarify something to avoid unnecessary misunderstandings or potential disputes with other amplifier brands. In the comparison tests, I won’t mention specific brands or models of other amplifiers. Instead, I’ll only provide their market prices for reference.

Second, while the subjective performance has been shown in previous thread, this thread focuses only on the objective listening experience.

A key aspect of the evaluation is the amplifier’s noise floor. No matter how good the sound quality is, excessive noise can ruin the listening experience. My basic method of testing was through direct listening. Using Shure SE535 in-ear headphone (Figure 1) in a very quiet, enclosed room. I could hear nothing except the sound of blood pumping through my ears. This suggests the amplifier’s noise level is extremely low.
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Figure 1,earphone for noise-floor test​

In the subsequent sound tests, I used several different headphones to evaluate the amplifier's performance. These included the Beyerdynamic T5 3rd Edition (closed-back, 32 Ohms) and Amiron Home (open-back, 250 Ohms), as well as the Sennheiser HD660S (open-back, 150 Ohms) and HD800 (open-back, 300 Ohms).


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Figure 2, test headphones
Without comparing the DIY amplifier directly to other headphone amplifiers, simply listening with different headphones reveals their distinct characteristics. Below are the subjective impressions of how each headphone performed when connected to the DIY amplifier. These evaluations are a result of cross-verification between several friends and me.

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Note:
Interestingly, opinions on soundstage width and height varied significantly among the friends. Some felt the soundstage was wider than shoulder distance, while others perceived greater height differences. This variance is likely due to individual subjective differences. The descriptions in the table primarily reflect my personal impressions.

Although each pair of headphones has its own unique sound characteristics, they all demonstrate excellent overall sound quality when paired with this amplifier. The common characteristic observed is the outstanding high-frequency and detail reproduction.

During listening tests comparing this DIY amplifier to several headphone amplifiers my friends and I had on hand, and based on feedback from music-loving friends, the following conclusions were drawn:

  1. Comparison with ~$500 Headphone Amplifiers:
    When compared to commercially available headphone amplifiers in the ~$500 range (including those with parallel op-amp outputs and discrete Class A designs), the DIY Class D amplifier demonstrated an overwhelmingly superior sound quality almost across all aspects.
  2. Comparison with ~$1000 Headphone Amplifiers:
    In the ~$1000 range, this DIY amplifier showed a significant advantage in high-frequency reproduction and detail resolution.
  3. Comparison with ~$2000 Desktop Amplifiers:
    When compared to desktop amplifiers priced around $2000, the DIY amplifier excelled in high-frequency clarity and transient response (which might not be due to these factors, but rather others), delivering more pronounced detail in vocals and string instruments. It also appears to capture more of the emotion and movement from both the player and the singer.
Some friends particularly enjoy using this DIY headphone amplifier to listen to violin pieces, while others prefer classical guitar or vocal performances. Their highlight feedback on various types of music is as follows:
  1. Violin:
    The pauses between musical phrases feel naturally connected, like a delicate balance of continuity and separation. This allows one to feel the performer's meticulous expression and unique emotional conveyance through subtle nuances in their playing.
  2. Guitar:
    Exceptional tonal clarity and texture make the plucking sounds remarkably lifelike, as if the performer is playing right in front of the listener.
  3. Vocals:
    The level of detail is astonishing, making it easy to discern the singer’s resonance techniques and vocal control.
I personally have little experience in audio equipment reviews, so some of the comments above may be inaccurate. From the perspective of pure music enjoyment, I find the DIY amplifier paired with the T5 3rd Edition and HD660S particularly enjoyable for long listening sessions.

If I were to differentiate between the two, I feel the HD660S excels in delivering captivating and expressive female vocals, while the T5 3rd Edition shines in its unique charm when reproducing symphonies and instrumental performances.

These observations are the result of a collective evaluation conducted over a period of listening tests by myself and my friends. We’ve aimed to provide as objective an assessment as possible of these subjective experiences. However, since none of us are professional reviewers, please forgive any inaccuracies in the descriptions.