Low-noise buffer for high-gain pedals

[Fancy Lime]

Hi everyone!

Motivation
In my everlasting quest to make my designs as low-noise as they can reasonably be, I decided to take a step back and try to learn how it's done properly instead of applying my otherwise favorite method of trying out unverified claims and suggestions from random forum posts and see if they work. One place where noise matters a lot is the input/gain stage of high gain fuzz/distortion/overdrive pedals. So I decided to try and tackle the noise on a Big Muff variant, which always bothered me a lot. I can get down the noise without changing the sound by changing a few components but I cannot get it "quiet quiet". While I am aware that there are limits to how quiet it can possibly and reasonably be (and how quiet it realistically have to be anyway), I am currently wondering where they are.

Idea
So my idea was to re-design the input gain stage using an MPSA18 with a proper source resistance to bring the noise figure to the lowest possible. Since the source resistance includes whatever comes before that stage (the pickup+guitar volume+cable... resistance if its first in line or almost nothing if it comes after a buffered pedal or whatever), a consistent performance would require a buffer on the input with a defined series resistance after it to get a more or less constant source resistance. Right so far? So my idea was to add such a buffer, which of course only makes sense if that buffer introduces (much) less noise under all realistic operating conditions, than the variable source resistance would under the worst conditions.

Question
Is that something to realistically hope for? Or would the extra noise from the buffer outweigh the benefits on the gain stage? Does a common collector amp suffer from the same source resistance dependence of the noise figure as the common emitter, in which case this discussion is kind of moot anyway. If it is worth it, what type of (reasonably simple) buffer performs well or not so well noise-wise? I was considering the "standard" Boss-style input buffer, its JFET-equipped cousin, or a Cornish-style buffer (for extra mojo-points). An op-amp buffer does not make much sense in this role because if I had to use an op-amp for lowest noise, I would more likely convert the whole first stage to a non-inverting op-amp stage (and the last stage too, hybrid op-amp/transistor Muff!). Still, would be good to know if an op-amp would perform better than the discrete options. If going discrete, any suggestions for transistor types?

Thanks and cheers,
Andy

[merlinb]

For lowest noise with a high impedance source (like a guitar) you need a JFET or JFET opamp, not a bipolar transistor. You also need the fet (or opamp) to provide some gain -enough to make its self noise swamp whatever comes after it, e.g. the rest of the big-muff circuit. A TL07x with a gain of just 2x or 3x might be enough. A unity gain buffer doesn't improve the signal to noise ratio (well, not unless you had some seriously bad current noise to start with, which the buffer eliminates. This is unlikely though).

Bipolar transistors deliver lowest noise when the source impedance is low. An opamp gain stage can provide this easily. A FET gain stage might not, but if it has enough gain so that its self noise STILL swamps the bipolar, then this it moot of course.

[antonis]

For BJT lovers, there's always the boot-strapped buffer option..

[Fancy Lime]

Hi Merlin,

huh... maybe I don't fully understand the datasheet. And I apparently explained things overly complicated. So: My idea was, to use a high impedance buffer to provide the following (preferably BJT) gain stage with a low impedance input because, as you pointed out, that should allow said gain stage to operate with the least amount of noise? Therefore the buffer itself would not actually improve the SNR but simply provide optimum conditions for the gain stage. Does that make sense?
If I understand Figure 5 in this datasheet: https://www.onsemi.com/pub/Collateral/MPSA18-D.PDF
correctly, then the noise produced by an MPSA18 should be minimal with a source resistance of, e.g. 10k for 100µA collector current or 50k for 10µA. My thinking was that if I have a buffer up front, which provides an output resistance of less than the desired source resistance of the gain stage, I could just add a series resistor between the two to get near the desired value of source resistance. Am I getting this right?
From your answer I take that, if my plan works at all, a JFET buffer would be the only thing that might help other than an op-amp, right? How about a impedance-bootstrapped BJT like in the Cornish LD-1? Does impedance bootstrapping help at all with moving the optimum impedance point of a BJT higher?


Hi Antonis,
yepp, that would be the Cornish LD-1.


Thanks,
Andy

[GibsonGM]

Why not try all 3 variants and see if you get less noise?   It would be faster than 'supposing' about it, I think.   

Ex: I could 'suppose' that the more stuff you put in the signal path, the more noise you're going to get...and that boosting the signal above the noise floor right away may be the best thing you'll find to make the circuit "as quiet as possible".  The benefits of trying to find some 'ideal impedance' thru buffering would, I believe, just add more noise or do nothing.   But I really AM supposing that, based on conventional wisdom and a lot of reading.    I accept noise in high gain circuits - it's always going to be there - and if it needs to be QUIET, I use a noise gate; that's just me, tho.

If you build it, you will know 

[merlinb]

If I understand Figure 5 in this datasheet: https://www.onsemi.com/pub/Collateral/MPSA18-D.PDF
correctly, then the noise produced by an MPSA18 should be minimal with a source resistance of, e.g. 10k for 100µA collector current or 50k for 10µA.

This is a common trap for young players. What that graph shows you in the noise figure, not the noise level. Noise figure is a way of saying how much worse the SNR is when it comes out compared to when it went in, including the self noise of the source resistance. It's a power ratio. If something comes out just as noisy as it went in then you have an amazing noise figure, but its tells you nothing about how noisy your circuit is in absolute terms.

Noise figure is a useful metric for radio engineering where you're dealing with signal power, not voltage. Noise figure is a trade off between voltage noise and current noise, and the minimum occurs when the two are equal. But in audio land we usually only care about voltages; we minimise current noise altogether by keeping the source resistance as small as possible.

Starting with a low source resistance gives you the best voltage SNR, period. 'Adding' some to make 10k adds a bit of voltage noise and a lot of current noise, so the ratio of output noise power to input noise power (i.e. the noise figure) looks better. But you're guitar voltage signal has just been made plain noisier. Which is bad.

[Fancy Lime]

Hi Mike,

normally I would agree, just playing with several variants that might work to see what indeed does work and what works best is how I usually do it. As most DIYers, I assume. However, noise of a input gain stage of a distortion pedal (or any circuit really, but it matters most in a high gain distortion because the noise gets amplified more than with other stuff) depends partly on interactions with the guitar or whatever other circuitry comes before the stage. So I would like to understand the theory so I don't have to buy dozens of guitars for testing purposes in order to build something that works well in general and not just in my particular setup. To me, designing stuff that is useful for others as well is part of the fun of the whole DIY thing. The stuff I make just for myself to play with (and might only work well with my particular setup) never gets posted here. I wouldn't bother writing a post about yet another marginally different Muff unless I found it to be an improvement that may benefit other people too. I learned most of what I know about electronics because many others do the same. I guess I just outgrew the "look what I made" phase of showing off stuff that does not really have meaning to others. Strange times, we live in, that make me feel I have to justify this instead of posting pictures of my breakfast on 5 different "social media" "services" that keep track of my caloric intake and tell my watch how much I have to run today. *rant off*

BTW, I don't mean to dismiss conventional wisdom, it often works. Nevertheless I like the (probably fake) quote attributed to, among others, Confucius: "Conventional wisdom is often the opposite of wisdom" 

Long story short: I would fee a bit less stupid if I knew what I was doing before I was doing it.


Cheers,
Andy

[Fancy Lime]

If I understand Figure 5 in this datasheet: https://www.onsemi.com/pub/Collateral/MPSA18-D.PDF
correctly, then the noise produced by an MPSA18 should be minimal with a source resistance of, e.g. 10k for 100µA collector current or 50k for 10µA.

This is a common trap for young players. What that graph shows you in the noise figure, not the noise level. Noise figure is a way of saying how much worse the SNR is when it comes out compared to when it went in, including the self noise of the source resistance. It's a power ratio. If something comes out just as noisy as it went in then you have an amazing noise figure, but its tells you nothing about how noisy your circuit is in absolute terms.

Noise figure is a useful metric for radio engineering where you're dealing with signal power, not voltage. Noise figure is a trade off between voltage noise and current noise, and the minimum occurs when the two are equal. But in audio land we usually only care about voltages; we minimise current noise altogether by keeping the source resistance as small as possible.

Starting with a low source resistance gives you the best voltage SNR, period. 'Adding' some to make 10k adds a bit of voltage noise and a lot of current noise, so the ratio of output noise power to input noise power (i.e. the noise figure) looks better. But you're guitar voltage signal has just been made plain noisier. Which is bad.

Hi Merlin,

ah, that is exactly the kind of info I need. I guess I should have looked up the definition of the noise figure instead of assuming it's relevance. So, Figure 6 is the more relevant one for us? But the question remains: Would (e.g.) a JFET buffer to bring the input resistance of the gain stage down add more noise (which is then amplified by the gain stage) than the "impedance optimization" saves in the gain stage? In other words, would the total circuit become quieter or noisier? Well, I guess I'll have to try. At least know I know a bit better how to proceed with the testing.

Thanks,
Andy

[Rob Strand]

If I understand Figure 5 in this datasheet: https://www.onsemi.com/pub/Collateral/MPSA18-D.PDF
correctly, then the noise produced by an MPSA18 should be minimal with a source resistance of, e.g. 10k for 100µA collector current or 50k for 10µA. My thinking was that if I have a buffer up front, which provides an output resistance of less than the desired source resistance of the gain stage, I could just add a series resistor between the two to get near the desired value of source resistance. Am I getting this right?

The first thing to know is minimizing noise figure is *not* minimizing noise.   Noise figure is the ratio of the input signal to noise to the output signal to noise.  When you add series resistors it makes the input signal to noise worse, which brings down the noise figure, but actual increases the output noise level!   Adding series resistances is a no no.  Adding dividers to the signal is also a no no.

See this app note,
http://www.electro.fisica.unlp.edu.ar/temas/pnolo/p1_AN-104.pdf

Optimizing the noise is done by choosing the correct current,
http://www.elenota.pl/datasheet_download/88791/AN-222

BJTs produce noise voltages and noise currents and this is why an optimum exists for a give source impedance.  A JFET however is often a better choice for high impedances because it does not have the noise current component.

One caveat is when you get to source 10k ohm impedances and above transistors produce more noise than the theory predicts (this comes about due to impurities and surface effects on the silicon).   The old "low noise" transistors are low noise because they reduce those effects  when using high impedances.   (They are in fact not low noise when you deal with low impedances because they have a large base series resistance, maybe 400ohm.  Modern low noise transistors are low noise for low impedances and might have a series resistance of 10 ohms.)

For opamps, it is well known that the inverting type amplifier has poorer signal to noise than the non-inverting case.    Intuitively the reason is it add a resistor in series with the source, which violates the above rule for low noise.
The big muff uses the non-inverting configuration.   The transistor equivalent of the non-inverting opamp circuit is,
http://www.electronics-tutorials.ws/amplifier/amplifier9.gif?x98918
However, it still inverts.   The difference is actually that it uses series feedback.

One option would be to replace the front end with a low-noise series feedback stage.  The trouble is there is enough gain in that first stage to clip, so replacing it could affect the sound- maybe not much.   Another option is to scale down the resistances of the first stage and optimize the bias current minimize the *output noise*.    Then add a JFET buffer.  You may want to make the input impedance 33k to get the same pickup loading - but it will ultimately increase the noise because if forms a divider with the pickup (note here it is not in series with signal).   I think this is more where you wanted to go.    You have to make sure you compare apples to apples as the buffer will add some noise.    Putting this into context there is a limit to how low you can get the noise because the guitar pickups themselves produces thermal noise.

[Edit1:  I found a file on my computer from June 2002 where I was trying to reduce the noise of the Big Muff front end.   I've got a transistors stage with the emitter feedback and no series resistor, like the example above.   It looks like I was just casually playing around with it since I only used a resistor for the source impedance.  Anyway, the s/n improvement was 3.8dB.  Probably do better with more work.
Edit2: I also notice I put a DC coupled buffer *after* the first stage.   And it says about 5.8dB s/n improvement with a buffer.    I'm presuming  the motivation for the buffer was to lower the output impedance since the o/p impedance of the BM type stages is lower than the collector resistor.  Maybe that allowed me to tune something.

Despite the details, it *is* possible to make considerable improvements.
]

[GibsonGM]

No disrespect for what you're doing intended,  Andy.  Making things quieter has been the holy grail for some for a long, long time...maybe you'll be the one to crack that nut open and get to "how" and "why"!   I'm certainly no guru, able to tell you with authority that it can or cannot, or should not, be done.

It is a much more noble undertaking than posting pics of your dinner on Facebook, yes   

[Rob Strand]

Configuration:
- Buffered front-end
- Scale entire first stage by a factor x.  This means reduce all resistors by x and increase all caps by x.
- Before scaling: Add 10k to 20k in series with 39k to crudely emulate pickup impedance. This keeps the same effective gain.  Then scale combination for final value in scaled circuit

Results:
x      s/n improvement
3     3.2dB
5     4.5dB
20   7.2dB     within 1dB of minimum  but operating current isn't practical

Using x=3 to 5 is certainly practical.

Could do better by changing the type of circuit used for the first stage as mentioned in previous post.

The s/n values are just based on nV/rtHz noise densities.   A better estimate would use a pick-up model and an a-weighted noise value however I suspect the relative improvements will turn out the same.

The whole motivation for scaling the circuit is to reduce the value of the input series resistance, which is the main contributor to noise.

[R.G.]

Good advice as noted above.

This is confusing because you can get both equivalent voltage noise and current noise sources from an input. Well, excess noise too, but today's devices make this pretty rare, at least at audio. Because both kinds of noise wind up causing audible noise on the output of whatever you 're building, you need to pick an input device that works best for minimizing what kinds of noise come from the source that's driving your input - which is of course, unknown. You may think it's a guitar, and that may be true for the first use, then the second use will be to put another pedal in front of it, with an unknown output source impedance that is quite different from the 4K-18K reistive plus 1H-4H inductive source impedance of a guitar pickup as mangled by the tone and volume controls on the guitar.

In general, you get the lowest noise from an input stage that uses bipolars for low to middlish source impedances, and FETs of one kind or another at quite high impedances. There is a very deep well of info on matching devices to source impedances in the electronics biz. The Japanese hifi companies even made special very-very-low rbb' transistors for acting as the input devices for moving-coil phono cartridges.

Not knowing what's connected to your input is a real problem. The best quick and dirty answer is to use a TL07x opamp, which is quite good in terms of not adding a lot of excess noise beyond what your inevitable biasing resistors will add, especially for the price. There are quieter opamps, but the price escalates quickly, and availability may or may not be a problem.

Another issue is gain structure or gain architecture. The general wisdom is that buffers on inputs contribute impedance conversion, but little or no gain, so for the very lowest, hang-the-cost, d@mn-the-torpedoes low noise performance, you want your first stage to have both low added noise over the bandwidth of interest, AND have a big, whacking gain to get the way up over the noise floor of the next stage. This is because whatever first stage you use, its noise is added to the signal noise and the biasing resistor noise, and is amplified by everything past the first stage. So a no- or low-gain first stage is a problem with noise by the very nature of it.

Another issue is bandwidth. You've no-doubt seen little references to bandwidth in noise specs, as in "nV/rootHz". Noise sums as the RMS of the noise contributions at each frequency that's being amplified. Want less noise? Cut the signal bandwidth. Many noise reduction schemes do exactly this. The dolby process used a selective boost of treble and a cut on reproduction to cut the noise of the reproduction medium. Companding cuts noise by first getting the input signal for a process to be as high as possible in passing through a noisy medium, then expanding the noise down with  the signal's quiet parts on exit. Noise gates, treble pre-boost, and many, many other things have been thrown at noise.

Knowing a little about this makes me have to suppress a guffaw down to a quite chuckle when I hear some amp builders or wannabees talking about carbon comp's magic tone and cursing their amps for being too noisy.

Best choice? Make your input stage not be a buffer, but instead make it the >>proper<< input impedance to match your (unknown) signal source impedance.  ooops, did I say that out loud???   

[PRR]

> a proper source resistance to bring the noise figure to the lowest possible. Since the source resistance includes whatever comes before that stage......, a consistent performance would require a buffer on the input with a defined series resistance after it to get a more or less constant source resistance. Right so far?

No. Never add series resistance. It adds hiss while reducing signal. Never decrease shunt resistance neither.

Much of the above is spot-on. You are really facing "a guitar" which is not a simple defined impedance. Nevertheless, TL072 can usually be lower hiss than the self-hiss of the guitar's internal resistances. You can get very near there with a BJT, but this is not simple, and you have to juggle bandwidth.

A recent paper from TI (Merlin is ref #2) touted the OPA1642. Hiss is 5nV/rtHz which is numerically less than TL072. And also probably less than the guitar's self-hiss. It is 10X the price of '072, and may be a just-audible difference in the right conditions.

This first stage should have more than enough gain to overwhelm the hiss of the next stage. There's too many "Muffs" for me to think on that tonight. If the first Muff stage is just gain, let the '072/1642 do that chore. If it is "color", more thought needed.

[PRR]

Input impedance of a 1971 Muff is about 75K. (33K, 100K, and Miller on 470K). This is a non-negligible load on guitar. It tone-sucks and level-sucks right off the bat. Not a lot, but if you "fix" that to follow low-hiss design, it will be "different".

The 33K input +adds+ to the self-hiss of the instrument. The 33K:100K divides the signal before you get to a transistor. The rich bias in the first stage is optimum for a low source impedance like 1K.

For infinitely small signal, Muff has gain of 200,000(!!). It's gonna hiss whatever you do.

The input stage biases near 3V DC and gain of 15 means it will start to clip the very highest guitar peaks. Is this essential? I dunno. I would experiment with a '072, biased off-center with 2Meg, with 4.7K and 330r gain-set resistors.

[antonis]

<partially off-topic, but..>

Tending to approach our ultimate goal we sometimes risk to deviate from some other desirable principles..
(e.g. focusing on R.G.'s 4th paragraph, we may obtain an ultra low noise buffer but with a remarkable non-linearity (distortion)..)

FETs are notorious (compare to BJTs) for their g_m variation with regard to Drain current and also for their higher output impedance (due to lower transconductane)..

On the other hand, BJTs suffer from relative low impedance (even the boot-strapped ones..)

A good compromise would be a Bi-Fet Op-Amp or it's simpler descrete form like below:



R acts as a "current sink" for (roughly) constant current for FET (V_BE/R) "stabilizing" its g_m value..
(it doesn't actually form an ideal current source due to V_BE variation with Collector current but its variation has much narrower margins than g_m's one - if I recall it right, V_BE varies according to natural logarithm of I_C whereas g_m varies according to suare root of I_D..)

Taking into account all the above well said about s/n ratio improvements & low value resistances you may obtain a "low-noise/high precision" buffer but it shouldn't be in the contrary to conventional wisdom.. 
(said from a lazy to breadboard/measure guy)..

[anotherjim]

There are 2 "buffer" stages in the BMP that happen to be inverting. Could they not be replaced by 2 non-inverting op-amp stages?

[Fancy Lime]

Hey guys,

thank you very much for the detailed information! I appreciate your time and effort a lot!

So, to sum up the results of this discussion: my original plan is not going to work. If I understood you all correctly, a well designed op-amp input stage seems most promising. And as Paul noted, the small signal gain of some (most?) Muff versions is bordering on the ridiculous. I can attest from my prior testing that raining that in to saner values (like e.g. in the clipping stages of some? Russian Muffs) makes a huge difference in noise without reducing the "perceived gain" or maximum distortion very much.

Interesting that you should mention the TL072 for this purpose. I more or less abandoned this particular crowd favorite after some a-b testing vs a NE5532AP in inverting and non-inverting amplifier stages and found the latter to be less noisy (although the difference was small and I did not measure anything, so I might have been mistaken) and to sound better (again marginal, possibly imaginary difference).

New plan: Replace the input gain stage and the output recovery stage with non-inverting op-amp stages, as Jim also suggested. Kind of like a transistor Muff in op-amps clothing (or something, gotta work on my metaphors). A FrankenPi's Muffster, if you will. And once we're at it, I'll also try replacing the transistor clipping stages with op-amp work-alikes (non-inverting maybe?) and with inverter stages like in the ROG 22/7. Anyone else having a radioactive mutated turducken for Christmas dinner? I hope I get this breadboarded over the weekend. Might be a nice base for a Multi-Muff with different types of clipping to switch in and out and to cascade just in case we want our beloved noise back

Cheers,
Andy

[PRR]

> TL072 ... a-b testing vs a NE5532

At what source impedance??

2K to 10K, the '5532 is nearly "perfect". Hiss voltage is lower than these source resistances.

20K up, the '072 is nearly "perfect". It has higher hiss voltage but nearly no hiss current.

[Fancy Lime]

Hi Paul,

thanks for the info. I tested the chips in a tube screamer-like two stage booster (no clipping diodes, no input or output buffers), paying no attention to impedances. I really should get my theory first before starting frantic random testing.

Cheers,
Andy

[Tuvalu]

Hello!
We are talking about the Big Muff, I understood correctly?
The element responsible for the increased noise level is the input resistor of 39 kOhm. Its thermal noise is 25 nV/sqrt_Hz. Compare with 18 nV for TL072, 1 nV for 2SK170. And this without taking into account the noise current of a bipolar transistor, under these conditions makes a considerable contribution to the overall noise.
Therefore, at the input, I put the bufer on the JFET* (2SK117, 163, 170, 209 ...), then the first stage of big muff, but with a serial resistor of 3.3 kOhm. Of course, the gain increases, but it can be reduced by the Sustain pot. The noise of this circuit is very low.

*The current noise of the JFETs is extremely low, which is important for high-Z sources, such as guitar pick-up.