Optimum Source Impedance For Opamps (Regarding Noise...)

Something confused me when I was trying to calculate the optimum source impedance for for an opamp stage at the front-end of a mic preamp.

As I understand it, the optimum impedance is the opamp's voltage noise divided by its current noise.

This gives a reasonable value for an NE5534:

Vn = 4nV/Rt. Hz @1KHz
In = 0.6pA/Rt. Hz @1KHz

So, optimum source impedance = 6.7K

That seems reasonable, but when I apply this to the OPA604, I get a figure which seems a bit unbelievable to me... :

Vn = 11nV/Rt. Hz @1KHz
In = 4fA/Rt. Hz @1KHz

Femto amps?.....

So, optimum source impedance here = 2.75M....... MegaOhms?...



What have I got wrong?

You haven't got anything wrong. In practical terms, this means that FET-input opamps are essentially devices with only voltage noise, so the higher the input Z (at least up to 2.75M in the case of the OPA604) the less noise the opamp will add to the source's inherent noise. Same as tubes, in fact. That's why we use high-ratio trannies with FETs and tubes, and (sometimes) lower-ratio trannies with bipolar transistors.

In practical terms, an OPA604 has an equivalent input noise resistance of about 6k (ignoring any resistors in the feedback network). With any source impedance >= 24k, therefore, it will add <1dB of noise to the source's inherent noise.

Peace,
Paul

So, if I were to choose an appropriate inbput transformer for a FET input opamp, then what are the constraints on what ratio I choose, if I am aiming for maximum transformer gain? Would it just be the effect of the transformer itself (ie. more degradation / colour at higher ratios) which would limit how high a ratio one chose?

Cheers,

Roddy

Would it just be the effect of the transformer itself (ie. more degradation / colour at higher ratios) which would limit how high a ratio one chose?

Click to expand...

Yes, and perhaps the need for low gain settings. You might consider the noise figure of the transformer as well--it might happen that you get less noise with a transformer having low turns ratio as it probably has lower DC resistance as well.

Samuel

One comment about FET amp noise: an oft-neglected component that is just beginning to get important for audio is "induced gate noise", where the channel thermal noise capacitively couples into the gate circuit. It gets clearly noticeable around 100kHz for high source impedances, and it is one of the constraints to be considered when paralleling a bunch of FETs for lower voltage noise.

It also has a weak dependence on temperature (~square root T, since it is just coupling channel thermal noise) as opposed to the drain-gate leakage (which doubles for every 10-12 degrees Kelvin).

See some of the curves in the back of Motchenbacher's books for an indication---although these are old parts not much has changed.

So you say that cascoding would make them having lower noise?

Samuel

You already know about the pitfalls of high-ratio transformers -- frequency response problems, high DC resistance, etc.. There's another pitfall in dealing with FET-input circuits, including opamps: they generate distortion at high frequencies when fed hot signals from high impedances, due to nonlinear gate capacitance. (Bipolars do too, but considerably less.)As a result, it's a good idea to keep your transformer's turns ratio within reasonable limits; probably 1:10 is the maximum I'd recommend. With a 150-ohm mic that gives you an impedance feeding the 604 of about 13.5k (counting the tranny's loading resistor), which isn't quite to the 24k level required for lowest noist, but it's pretty close. Add in the DC resistance of the secondary and the (stepped-up) resistance of the primary, and you're close enough to the ballpark.

On the other hand, run the numbers for a 1:10 tranny and a 1:5, and you may still get less noise from the 1:5 if it has lower DC resistances.

Peace,
Paul

[quote author="Samuel Groner"]So you say that cascoding would make them having lower noise?

Samuel[/quote]

No, unfortunately---the bad news is internal to the given device. There might be ways to back out some of the noise depending on the correlation coefficient involved, and possibly some strategy involving a use of the device simultaneously as a varactor. These are deep waters. I used to think about this stuff a lot when I was making cooled preamps for astronomy. There are applications to condenser microphones though, clearly.

Super-low-Cdg devices have appeal, but most of the time have so many other problems, like snakes-on-a-plane hordes of low-frequency excess noise, that they make no sense for audio.

[quote author="pstamler"]... There's another pitfall in dealing with FET-input circuits, including opamps: they generate distortion at high frequencies when fed hot signals from high impedances, due to nonlinear gate capacitance. (Bipolars do too, but considerably less.)....
Peace,
Paul[/quote]

Always a good reminder Paul!

Here we can get help from the bootstrapped cascode, by effectively removing the signal's modulation of capacitance. Many advantages are conferred, with a few downsides (restriction of common-mode range for a given set of power supply rails, for one). I think I recall somewhere a monolithic part that did this, and there is also the approach of active drive of the rails to track the signal as shown in an AES paper years ago---I will try to find the reference. The authors stole that idea a few years before I had it and used it for a blameless buffer amp. Thanks to Mike Smedegaard for pointing out the prior art---too late to include in my own AES preprint of '97 though.

Note as well that it doesn't need to be nonlinear gate capacitance. Although it is nonlinear (like apparently everything else that exists in the physical universe, if we look closely enough!) a signal-driven linear variation is enough to produce the distortion.

Here we can get help from the bootstrapped cascode.

Click to expand...

I'd be very interested if you could post a schematic/reference to this stuff. I just started to do some work for my new high performance laboratory preamplifier and this could indeed be helpful--thanks!

Samuel

Thanks for all the great information.

Would anyone care to run through a simple noise comparison with me for a Jensen 990 opamp using two different ratios using one type of transformer?

If so, I'll start with the conditions:

Microphones: 200 Ohm

990 Opamp:

Vn = 1.13 nV/Rt.Hz
In = 1 pA/Rt.Hz

"Optimum" source impedance = 1.1K

Lundahl LL1538 Transformer:

Resistance Of Each Primary (2 of): 44 Ohms - (44 for 1:2.5, 88 for 1:5)
Secondary Resistance: 880 Ohms

Voltage gain at 1:2.5 = 8dB
Voltage gain at 1:5 = 14dB

Reflected impedance @1:2.5 = 1250 Ohms
Reflected impedance @1:5 = 5k Ohms



Now, I'm not really sure what effects the DC resistance of the coils in the transformer have.... I assume that their resistance is added to the reflected impedance at the secondary and this contributes to the noise? Does it have any other impacts?

I can start off by looking at the noise contributed by the opamp/reflected impedance (Zsource*In + Vn, etc.) , but I'm not sure where to go from there.....?

Cheers,

Roddy

> So, optimum source impedance here = 2.75M....... MegaOhms?...

Yes. For absolute-lowest noise, wind your secondary up until you either approach 2-3 Meg or hit some other snag.

In wideband audio (in most iron-core work), the snag is that stray inductance rises with primary inductance, but (for a given power level) the stray capacitance is fairly fixed, maybe 100-300pFd. So the upper resonance falls in frequency as design impedance rises, about as the square-root. Past 10K or 100K we can't get much past 15KHz response, even with permalloy (reduces physical size and thus capacitance) and interleaving.

Resistance can be a problem. Actually, for super-high-Z windings, resistance tends to be "too low". We can't hammer copper arbitrarily thin at commercial price, winding time rises faster than number of turns (fine wire breaks so you wind even slower), but OTOH some dead resistance helps damp the annoying top resonance.

You do not need to wind to the "optimum" to get respectably good noise.

Design a rafter for a house. An "optimum" beam will taper to the ends. Depending on load and span, it may be thick at the ends and slender in the middle, or fat in the middle and slender ended. It could even be fat in the center, slender toward the end, but bulge-out at the very end for nailing-space. But what would Joseph do? Toss a 2x8 up there and be done with it. The 5%-40% of wood that could "optimally" be saved is negligible in the overall job, while custom cutting would be expensive, for cutting and for hauling-off the odd scraps you "saved".

4nV/RtHz is about the noise of a 1K resistor. If you get the secondary above 1K, say a 1:3 step-up on a 200 ohm mike, mike self noise overwhelms amplifier noise. Yes, going from 2K to 2Meg gives 30 times more signal but 1dB-2dB lower output noise, and maybe 1KHz transformer bandwidth which may not be good.

> Jensen 990 opamp .... "Optimum" source impedance = 1.1K

Well, yeah, but 1.13nV/RtHz is nearly the noise of a 200 ohm resistor. You could run the mike right to the 990 and get a usable noise figure; all the tinkering in the world could not make it 3dB better.

And Deane's goal was "simple" (in retrospect). A 1:2 ratio to a 1.13nV/RtHz amp will give an excellent noise figure. The 600-800 ohm secondary naturally has an upper resonance far-far above 100KHz. AND the 150:600 transformer can be wound bi-filar, for an order of magnitude lower leakage inductance. And the lack of inter-winding fishpaper allows fatter wire and lower dead resistance.

You won't go wrong following Deane's path.

> Lundahl LL1538 Transformer:
Resistance Of Each Primary (2 of): 44 Ohms - (44 for 1:2.5, 88 for 1:5)
Secondary Resistance: 880 Ohms
Reflected impedance @1:2.5 = 1250 Ohms
Reflected impedance @1:5 = 5k Ohms

Lundahl's windings always confuse me.

But it looks like you have 880 ohms dead resistance added to 5K reflected impedance (a lot) or 880 added to 1,250 (a lot-lot).

By "a lot", I don't mean it sucks. A really terrific 150:600 winding might get below 40 ohms added to the 200 ohm source, and if you do the math you'll see we are in tenth-dB and not audible. What are the noise voltages of 200, 240, and 288 ohm resistors? Taking 200 ohms as our 0dB reference: 0dB, 0.8dB, 1.58dB. The 990 with the 1:2 tranny Deane (and others) designed for it is one of the few ways to get near 1dB NF. If you can hear the difference between 1dB NF and 1.6dB NF we should use you for a calibration standard.

.... some of these numbers are not making sense. Maybe it is late. I think I am not including all the winding resistances.

Assume that 1:2 "is" a good ratio for a common mike and the 990. Use Lundah's 1:2.5, close enuff. You have 44 ohms primary, and 880 ohms secondary, dead resistance. The secondary reflects to the mike as 880/2.5^2 = 141 ohms. Dead resistance referred to primary is 44+141= 185 ohms. Compared to a 150-200 ohm mike, it is a lot, and suggests a ~3dB NF.

Take 1:5. Now 88... no, something is wrong. Are you sure those primary resistances are right? Could it be 88 at 1:2.5 and 44 at 1:5?

IAC: He's got a lot of resistance there. These trannys better have astonishing bass response. And you should have more need for bass response than last-dB noise figure.

[quote author="rodabod"]Microphones: 200 Ohm

990 Opamp:

Vn = 1.13 nV/Rt.Hz
In = 1 pA/Rt.Hz

"Optimum" source impedance = 1.1K

Lundahl LL1538 Transformer:

Resistance Of Each Primary (2 of): 44 Ohms - (44 for 1:2.5, 88 for 1:5)
Secondary Resistance: 880 Ohms

Voltage gain at 1:2.5 = 8dB
Voltage gain at 1:5 = 14dB

Reflected impedance @1:2.5 = 1250 Ohms
Reflected impedance @1:5 = 5k Ohms[/quote]

Okay, let's look at the 1:2.5 case, which will probably be a better match to the Jensen anyway. Your primary resistance is 44 ohms, so your real reflected source resistance is (2.5^2) x (200 + 44), or 1525 at the secondary. Add 880 for the secondary resistance, and the secondary is presenting a 2405 ohm source impedance to the opamp. (Note that this is approximately 2x what it would be in a perfect transformer with no DC resistance, so your noise figure will already be compromised by about 3dB.) I haven't looked at the datasheet, but many Lundahl trannies are designed to be used with only a Zobel, no reqular terminating resistor, so we'll ignore the termination for the moment. We'll also assume the resistance of the opamp's feedback network is 95 ohms, just to pick a round number. So the total equivalent impedance is 2500 ohms. Assume 20kHz bandwidth

Now let's look at noise sources. First comes the Johnson noise of the transformer's secondary with all the stuff reflected to it. That'll be 0.91uV.

Johnson noise = sqrt(total resistance x 1.656e-20 x 20,000)

The equivalent input noise from e is .156uV.

Voltage noise = sqrt(e^2 x 20,000)

And the noise due to i will be .354uV.

Current noise = sqrt((i x total resistance)^2) x 20,000)

Add those up by the rms method and you get total noise of .989uV, or -117.9dBu. That's the equivalent at the transformer's primary of -125.9dBu. A 200 ohm resistor has an equivalent noise of -129.6dBu, so the noise figure is about 3.7dB. Most of the degradation comes from the transformer. Use the 1:5 hookup and the opamp will contribute more current noise, and the performance will be a bit worse.

Peace,
Paul

Sorry I wish I had more to add but Roddy - thanks for starting this thread and thanks to PRR, PaulS and Brad etc for all the info.

Its a fantastic thread!
:thumb:

Cheers Tom

Nice thread indeed. This link might be redundant now, but let's just add it:

Calculating Transformer Related Noise Figure (15KB PDF)

Regards,

Peter

[quote author="Samuel Groner"]

Here we can get help from the bootstrapped cascode.

Click to expand...

I'd be very interested if you could post a schematic/reference to this stuff. I just started to do some work for my new high performance laboratory preamplifier and this could indeed be helpful--thanks!

Samuel[/quote]

I've shown a couple of single-ended amps with bootstrapped cascodes in here a while ago (someone else hosted the images).

I did just run across the AES paper by the Victor Company of Japan people:

Funusaka and Kondou, Feedforward Floating Power Supply (High-Response-Speed Equalizer Circuit), JAES Vol. 30, No. 5, 1982 May, pp. 324-329.

I've shown a couple of single-ended amps with bootstrapped cascodes in here a while ago.

Click to expand...

Yep, I've got these somewhere on my HD, thanks for the reminder! I must have mixed up things pretty badly when writing my last post in this thread as I was thinking you were talking about bootstrapping the substrate of dual JFETs (2SK389, what else)--bootstrapped cascodes are more or less clear to me as there is a ton of ICs who do it.

Samuel

Driving the substrate is not a bad idea in some cases either.

Can you elaborate on the advantages and possible improvements? And what do you reference the substrate to?

Samuel

[quote author="Samuel Groner"]Can you elaborate on the advantages and possible improvements? And what do you reference the substrate to?

Samuel[/quote]

Well, take the SK389 for example. In a differential pair arrangement with plenty of loop gain, the substrate C is already being moved around by the feedback and is mostly bootstrapped out from being a load on the source at audio frequencies.

But suppose you are using the SK389 as a follower, with the upper source fed from a current source using the lower device. Then you might wish to drive the substrate from the follower output, so as to remove most of the capacitive loading of the source. For the 389 I've measured something around 20pF of loading when this is not done---small, probably negligible most of the time, but there it is.