headphone amp: hiss as a sign of oscillation or just a "natural" noise?

I have built a headphone amp according to the schematic in the attachment (C5s are common to both channels). It is based on a PRR's drawing from headwize (the site is now down, sorry). All seems quite well and working. There is just one small issue: with sensitive ear buds there is a noticeable hiss. Practically, it is not a problem, it is inaudible with Grado and I have no plans nor needs to use the amp with those buds. On the other hand, it is sometimes mentioned that hiss could be a sign of oscillations. Unfortunately, the only tool I have is a voltmeter, which does not seem to indicate any misbehavior of the circuit. The level of my experience is not nearly good enough to make an educated guess for the origin of the hiss. I would say it does not come from the power supply, I tried several and the hiss is unchanged (CRC filtered as one, linear regulated walwart as another, even just a bridge rectifier directly into those 2350uF C5s on amp PCB - surprisingly no hum).

Finally, I am getting to my question: Is it likely that the higher level of hiss is inherent to this type of circuit (too high resistor values, noisy constant current source or what not), or should any hiss be inaudible in well functioning circuit, meaning that the observed hiss hints to some kind of misbehavior? I guess that clear answer is impossible with the little information provided from my side, but it is pretty much all I have at the moment.

Thank you very much for opinions.

Ehhh.  You might have just enough noise from a properly functioning circuit to hear it in earbuds.

If you suspect oscillations, listen and touch various circuit nodes and note if it changes.  There will be injection of hum and other noise, and you will have to account for that.

Looks like the dominant noise, absent any in the source, is resistor thermal from R3.  That amounts to about 93nV/sq root Hz if the noise is white, at the output, which in a 10kHz BW is 9.3uV rms.  That's mightly low to hear in any big city even with earbuds.

DMOS is notorious for oscillating, but those 100 ohm gate stoppers should typically be enough, unless the wires are rather long.

> It is based on a PRR's drawing from headwize

He probably did not think it to death. May have been a suggested alternate path for someone else's thinking.

> there is a noticeable hiss.

What stands out is the signal gain R2:R1 47K:22K about 2, and the noise-gain R2R1||R3) or about 13. Seems like noise winds up 6 times higher than it "could" be. However schemes like these traditionally "work" at the end of an audio path, because Q1 self-noise is not high, and the full audio path (from microphone-amp first transistor) has gain of 10 or 100, overwhelming Q1 noise.

I'm grateful to bcarso for the analysis. Huh, R3 thermal may exceed Q1 noise times noise-gain.

Still, why did PRR do such a silly excess noise-gain? Ah, the 47K:4K2 levers the output node DC to about 14 times Q1 Vbe, which happens to be near-half of the 15V used. Lazy git. I bet he did the same thing, in mike preamps, and got paid for it. For decades. Not the lowest-noise mike-amps ever made, but nobody ever noticed.

Oscillation is possible. What bcarso suggested: poke it and stuff changes. I found a gitar-amp squeal just waving a pencil-tip around the tone-control wires. The squeal changed pitch, got a little better and a lot worse. I noted the worst position for the pencil tip, between two wires, pushed them further apart, and squeal stopped completely. I don't understand how that amp could squeal; but sometimes success is the best analysis.

> surprisingly no hum

That PRR... either he's lucky or not as dumb as he sometimes feels. No-hum comes from not having any good way for crap to get in. Q3 drain impedance is nearly infinite, and overall ground-referenced NFB holds its gate quite still: no hum getting in there. R4-R5 could let in a lot of crap, except C3 diverts a lot of it to the output which is again held-steady by overall NFB. That's just a byproduct of trying to find some output swing with 4V MOSFET devices under a mere 15V rail, but hey it works. It actually goes back to using Q1 Vbe as "DC reference". Better amps use a fraction of the power voltage to set the output DC point. But "fraction of power voltage" is always "fraction of power crap". Q1 Vbe drifts with temperature, and is not immune to rail-crap coming down R4-R5, but is more filtering per penny than a large cap.

Here's an ugly test-bed hack. Put a 120VAC power transformer winding in series with R3. The DCR will be too low to affect DC bias. The AC impedance rises above 4K by 100Hz, and will kill noise-gain in the "hiss" frequency range. If hiss drops dramatically, then we suspect poor choice of noise gain. If not, then maybe something else is going on. (However, the large inductance around all those caps "could" throw it into massive audio oscillation.... be careful of your ears!)

OR-- taking bcarso's word that R3 is to blame, and assuming you have a strong source, reduce R1 R2 R3 by a factor of say 10. (Better make C1 over 10uFd to keep full bass.) (Rpot will sag badly at mid-point with 2K2 load.) That gives 3 times lower noise voltage, enough to notice.

Or, if you come up with a convenient negative quiet voltage (a 9V battery maybe), move R3's ground return to it and make its value proportionately larger, or just adjust upward to center the output voltage at half of the positive supply.  Right now it's pulling about 0.65V/4.02kohm = 162uA.  With a fresh 9V (about 9.3V or so) the new value would be about 10V/162uA = 62kohm or so.

The easiest analysis takes R3's noise current and multiplies it by the feedback 47k to get its contribution to output noise.  That's 2pA/sq rt Hz, times 47k is 95 nV/sq rt Hz.  The next contribution of note is the noise voltage of the 2SC1815, which wiggles the input summing node and mostly causes current in R3.  That term is a good deal smaller than the first, since the 1815 has rbb' around 50 ohms and a half-thermal noise at 1.5mA Ic from r sub e of a roughly 9 ohm resistor.  So the input voltage noise should be about a nanovolt per square root Hz, and the noise gain of about 15 will make the noise at the output due to that about 15nV/sq rt Hz.

Making R3 larger helps both.

PRR> He probably did not think it to death. May have been a suggested alternate path for someone else's thinking.

Sure, I am fully aware of that. It was just a sketch from one of those threads "does anyone have a simple gain stage for Szekeres?". I took it, modified to what I thought was my liking and now I learn. Not a bad deal at all.

PRR> Still, why did PRR do such a silly excess noise-gain?

Oops, the imbalance between the noise and signal gains is a result of my modifications, the original plan said R1=15k, R2=100k and R3=10k.

Thanks a lot to both of you for the intro into noise analysis. I tried to put R2=2k2 and R3=200R in one channel and the noise is gone. It is not a very useful amp with those values but it seems confirmed now that the hiss was not caused by oscillations but by resistor thermal noise. I would not guess that 4k2 could be an issue.

All is well then. No oscillations, no noticeable hiss in Grado phones with my original values. I can safely put the original resistors back and listen to some music...

> original plan said R1=15k, R2=100k and R3=10k.

Same difference: need to lever-up the 0.6V Vbe more than we need to lever-up the audio.

Better, in that 47K is a bit lower noise-voltage than the 100K.

I'm still surprised the noise could be "audible" in a hi-fi earphone.

I'd also be surprised if it were audible with -any- source connected and playing "silence". Sure, the all-zeros of a truly blank digital recording may not swamp amp-hiss (though the D/A is never dead-quiet); I mean the "air" in a studio or concert hall when mikes are open at nominal gain but the bow has not yet hit the string. Commercial recordings often have that trimmed-off; I happen to have hours of "silence" in live-concert archives.

> negative quiet voltage (a 9V battery maybe), move R3's ground return to it

Brilliant. I was thinking: Q1 can pull to 1V, Q4 gate never needs to go much below 4V, stand two AAA-cells under Q1 emitter and re-bias. Factor of 5 improvement in noise-gain and thermal drift. The inverse 9V gives even more improvement.

PRR> I'm still surprised the noise could be "audible" in a hi-fi earphone.

Hi-fi... I don't remember what was written on the box, but the phones themselves say only "Sennheiser MX 550". They measure approx. 16ohm DC resistance.

PRR> I'd also be surprised if it were audible with -any- source connected and playing "silence".

I am afraid I don't have enough of this silence/ambience material to play with. But with the ear-buds the noise is really hard to miss. I have a couple of much quieter headphone jacks around here. As as wrote before, with Grado the situation is quite a bit different. Some noise can be detected by plugging/unplugging the phones while wearing them (if one tries really hard), but any program will hide it.

PRR> Factor of 5 improvement in noise-gain and thermal drift. The inverse 9V gives even more improvement.

Summarizing for myself: if I understand what has been written here so far, the output noise contribution from feedback divider / bias network is as follows: noise from R1||R3 multiplied by gain R2 / (R1||R3) plus noise from R2 itself. If I work it out adding squares of noise voltage amplitudes I finally get

    sqrt[ 4 k T Df R2 ( 1 + R2/R1 + R2/R3 ) ]

where Df is bandwidth. The best thing would be to reduce R2, but if I want gain 2 and input impedance no less than 10k I cannot get much there. Now I also see the somewhat counterintuitive suggestion to find a way of increasing R3. It is probably enough to go up to R3=R2 as it is not dominant any more then. That either means the extra negative rail or raise base of Q1 to 1/4 of positive supply. As PRR noted, there is enough room to do that. Gate of Q3 cannot go below Vbe+Vgs. Perhaps just a resistor at the Q1 emitter could do it, bypassed by a capacitor so that we don't lose open-loop gain. Although then the circuit really looks like there is as many capacitors as could fit - people just love such thoroughly AC coupled plans these days.

On the second thought, how much can we gain even if the R3 is sent to infinity? In the case the above equation is correct, the ratio of noise amplitudes without and with the R3 term is

sqrt[ ( 1 + 2 ) / ( 1 + 2 +11 ) ] = 0.46

Is it worth it at all?