Mulling over Slew

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featherpillow

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I did some searching about this subject, and found several informative posts, but nothing covering this subject exactly.

I'm reading a little about slew rate.

To calculate slew rate, the formula is V/S = I/C. That's volts per second equals current over capacitance. Slew rate is expressed as volts per microsecond; so the result is divided by 10^6 (10 to the 6 power). Is the current in the calculation the current produced by the source?

For example, if the current is 3mA, and the capacitance is 100pF, the slew rate is (I/C) 3x10^-3 / 100x10^-12 / 10^6 = 30V/µS...

Does this sound correct, or is my source material off?
 
It's the basic differential form of the terminal equations for an ideal capacitor: C*dV(t)/dt = i(t). That's pretty general; for constant current and constant C it becomes, rearranged, I/C = dV/dt = a constant, where the units are current in amps, capacitance in farads, and volts per second, as you have it.
 
[quote author="featherpillow"]What happens in the event of no C in the stage?[/quote]

As Brad says C is never zero. Decent vendors publish intrinsic capacitance figures for solid state discrete devices in their datasheets. In theory, if C were zero then the I/C method would be invalid because we cannot divide by zero. In practice, if C were infinitely small the slew rate would be infinitely large.
 
Nice work if you can get it!
Ha ha! I forgot about that! :grin:
At first, I figured this included Mr Miller and his parasitic friends, but how quickly I forgot about them!

So, if no C in the circuit, we use the intrinsic C of the device in the equation? Shouldn't we use the intrinsic C no matter what?
 
Often the external C at that node will be quite a bit larger than the other intrinsic ones, but for best accuracy they should all be included in the model.

Also, if the next stage is the output buffer, and there is capacitive loading on the output, this C reflects back to the node in question as well.



Just had the first power outage of the season, which was happily short. Time to turn the a/c back on and keep the fingers crossed.
 
What about instances of emitter-degenerated resistance for slew enhancement? I'm guessing that we use emitter R's to increase the overall I, thereby increasing slew (gm/I, right?) of something like an input stage (a bipolar stage)...

The tradeoff in a situation like that is the potential for voltage drift and degraded noise performance?

correction-I realized last night in my sleep that this is wrong--we don't use emitter R's to increase current, rather, we use the emitter R's to reduce transconductance (gm), right? It's the exact same reason that a FET transistor is faster than a bipolar in terms of response--lower transconductance!
 
[quote author="featherpillow"]we don't use emitter R's to increase current, rather, we use the emitter R's to reduce transconductance (gm), right? [/quote]

This side of the river we use emitter resistances in input pairs to improve matching. As you know this is comes through reducing gm. Larger emitter resistances can be used to reduce gain substantially to move a pole and increase the stability of an opamp. Of couse, there is the penalty of noise doing so.

[quote author="featherpillow"]It's the exact same reason that a FET transistor is faster than a bipolar in terms of response--lower transconductance![/quote]

I am not shure that is right. I thought speed of a device was defined mainly by its intrinsic capacitances.
 
It's the exact same reason that a FET transistor is faster than a bipolar in terms of response--lower transconductance!
I am not shure that is right. I thought speed of a device was defined mainly by its intrinsic capacitances.
I think featherpillow wanted to say that an opamp with FET input is usually faster (higher slew rate) than one with bipolar input. I'd say that this is true as a first-order approximation because of the reason given by him.

Samuel
 
> emitter-degenerated resistance for slew enhancement? I'm guessing that we use emitter R's to increase the overall I, thereby increasing slew (gm/I, right?) of something like an input stage (a bipolar stage)...

> correction-I realized last night in my sleep that this is wrong--we don't use emitter R's to increase current, rather, we use the emitter R's to reduce transconductance (gm), right?

How big is your "C"?

Two cases: "1: as small as possible" and "2: whatever it takes to make it stable under feedback".

For high-gain amps that can be fed-back to low closed-loop gains, we are always in situation 2.

The usual limit is that we need a 1-pole response to allow setting closed-loop gain to any value, but we have three stages and one of them is fat slow output devices.

Rarely, we can gimmick the input stage to very wide band. More often we put a capacitor around the first and second stages so their combined response is 1-pole, and make the output stage gain low for best bandwidth. Problem with that is: when the output stage does finally crap-out, the total amp goes 2-pole.

Assume a general-purpose op-amp, meaning the closed-loop gain can be as low as unity. The open-loop gain must fall no faster than 1 pole until it reaches unity (then it can fall as fast as it wants).

So we start with all fast stages. Usually the output stage is the hard one, so we run it emitter-follower. Even so, in many cases it will droop by 1mHz. That means open-loop gain of the first two stages must fall to unity at 1mHz.

How do we do that? We pick a compensation cap that will equal the input stage emitter resistances (including 1/Gm) at 1MHz.

If your input transistors are any darn good, adding emitter resistance will worsen their DC and noise performance. We don't want to do that.

So the compensation cap equals 1/Gm at 1mHz.

We can change input stage current, but that changes Gm, and that requires a change in the compensation cap to keep the 1MHz unity-gain frequency.

So for the naked BJT input, the relation between GBW and Slew is FIXED. If you have to get down to unity gain at 1mHz, your slew will be 1V/uS or less. 741 performance. No matter what current you run in the input devices.

An improved output stage, like the 5532 uses (on nearly the same process as 741) may let you compensate for a 10MHz unity-gain point, allowing a smaller compensation cap for the same input current, and thus a higher slew number.

The other way to go is to add some dead resistance under the Gm, reducing effective Gm, allowing a smaller compensation cap for the same unity gain frequency. There are several opamps made this way, sometimes in a choice of "decompensated" versions that are lower noise and better DC (less dead resistance) but not unity-gain stable.

So that is what you are doing with resistors. Reducing Gm, which allows a smaller compensation cap for the same stability, and keeping the same current but with a smaller cap that makes more slew.

While Gm/Ie is the same for any BJT device, FETs have lower Gm/Is. In effect they come with some dead resistance built in.

The TL072 uses both effects: the limit on classic IC output stages is a lame PNP, the 072 replaces it with a fast FET and an NPN booster, and uses low-Gm FET inputs too. You can't beat its slew-rate any simple way.

If they made an externally-compensated BiFET, and if you never needed unity closed-loop gain, you could (in theory) reduce the compensation cap in proportion to your lowest gain. We in fact did this with 741: the 301 is a 741 without its 30pFd compensation cap. For unity gain, the 301 needs a 30pFd cap, but for gain of 10 or more you can use a 3pFd cap. You get 10 times the GBW and 10 times the slew. At higher gains, the 301 is a fairly respectable audio amp even in high-level work.
 
I've finally gotten to the point where I think I've figured some of this out--thanks so much for the explanation, PRR. It took me a couple of months of reading it to get a better understanding of it.

So, for the sake of simplicity, when we're driving into the Miller C, is it the collector current (as Leach says) that's the determining current here? That seems to explain the reason why, as Self points out, a current mirror on the collector would roughly double slew without the problems typically associated with emitter degeneration.

However, I was reviewing some stuff that Luns (UC Berkley?) wrote, that seems to suggest that it's actually TOTAL current in the differential that we want to consider here. Am I unnecessarily confused by this?

Also, for the life of me, I can't seem to find the formula to determine the value of our compensation C. I know the items involved here that determine this--1/Gm, bandwidth, emitter resistance, etc. I would guess it would be some type of 1/distance thing involving bandwidth, right? Something tells me there was a 5534 datasheet of yore that had that forumula in it.

I also can't seem to get my head around the manner used to determine where to split the poles--everything I read seems to discuss it as some vague notional thing (IIRC the exact value wanders a bit anyway, right?) but I've never read any specifics. Or maybe I am reading specifics, but it's not gelling in my tiny mind :roll:
 
[quote author="featherpillow"]I've finally gotten to the point where I think I've figured some of this out--thanks so much for the explanation, PRR. It took me a couple of months of reading it to get a better understanding of it.

So, for the sake of simplicity, when we're driving into the Miller C, is it the collector current (as Leach says) that's the determining current here? That seems to explain the reason why, as Self points out, a current mirror on the collector would roughly double slew without the problems typically associated with emitter degeneration.

However, I was reviewing some stuff that Luns (UC Berklee?) wrote, that seems to suggest that it's actually TOTAL current in the differential that we want to consider here. Am I unnecessarily confused by this?

Also, for the life of me, I can't seem to find the formula to determine the value of our compensation C. I know the items involved here that determine this--1/Gm, bandwidth, emitter resistance, etc. I would guess it would be some type of 1/distance thing involving bandwidth, right? Something tells me there was a 5534 datasheet of yore that had that forumula in it.

I also can't seem to get my head around the manner used to determine where to split the poles--everything I read seems to discuss it as some vague notional thing (IIRC the exact value wanders a bit anyway, right?) but I've never read any specifics. Or maybe I am reading specifics, but it's not gelling in my tiny mind :roll:[/quote]

The current mirror also doubles the small-signal gain I believe, as well as adding its own phase shifts and noise. It does have the advantages that come with inherent balance at low-moderate frequencies compared to a simple load resistor, so that the precise value of the emitters' current is unimportant.

The slew rate, assuming the standard diff input + mirror circuit with second-stage feedback integrator, is just I/C where I is the total emitter current. We are hard-switching the input stage and steering all the emitter current or its inversion through the mirror to the integrator input, which responds with a voltage ramp at the output.

There are many discussions in greater detail, including more quantitative ones, of compensation. An old reference by Burr-Br*wn folks and their AZ pals at the time has the basics. Feucht has a brisk and much more general discussion in his Handbook of Analog Circuit Design and its CD-ROM expanded/revised version.

Like most things, the simple first-order approaches will get you a long way but the subtleties can fill volumes. There is no simple single formula though---you must know what the parasitics are, like the output stage behavior as outlined by PRR, before you can figure out what you need. You also need to know what the total system configuration is---feedback network, output load, etc.

No matter how well the open-loop gain of an op amp follows a single-pole response, it is always possible to get it to oscillate given the "right" feedback network :razz: Conversly, you can usually take an amp with a nonideal open-loop response and have a stable circuit with the proper choice of external feedback components. Feucht's material is particularly good on the latter.
 
> it's actually TOTAL current in the differential

Well, that's an absolute limit. You never want to get to that point, any more than you want your car hitting the walls of a tunnel. And the difference, Ie or 2*Ie, isn't really huge in audio terms.

> the value of our compensation C.

Find all your poles. Make them all as high as you can. Then clobber one so it rolls-off the total gain to unity before you hit the next higher pole.

Read National Semiconductor paper AN-A: The Monolithic Operational Amplifier: A Tutorial Study

The pages on thermal feedback are of little importance in discrete design.

The small signal frequency response and slew-rate sections are critical to designing a general-purpose feedback amplifier. Their way is not the only way, but it is sweet for its simplicity.
 
> An old reference by Burr-Br*wn folks and their AZ pals at the time

"Sorry, searches expire an hour after they're run"

Nothing in the URL you gave says what your search terms were.

Give us another clue: title, author, date, ISBN, something.
 
[quote author="PRR"]> An old reference by Burr-Br*wn folks and their AZ pals at the time

"Sorry, searches expire an hour after they're run"

Nothing in the URL you gave says what your search terms were.

Give us another clue: title, author, date, ISBN, something.[/quote]

Damn, forgot about bookfinder.com's ways.

Tobey, G. E.; Graeme, Jerald G.; Huelsman, Lawrence P.

Operational Amplifiers: Design and Applications

New York, McGraw Hill, 1971

ISBN: 0070649170

(some sellers add an "X" at the end of the ISBN stated)
 
Operational amplifier circuits: Design and application
Englewood Cliffs, NJ: Prentice-Hall, 1982 {also 1971}.
ISBN: 0-13-637447-6 (1982)
ISBN: 0-07-064917-0 (1971)
ISBN: 0-07-085845-4 (1974, Europe)

"This book," the authors write, "may be used as a text for a beginning course on op-amp circuits for which the student would need only a background in elementary algebra. Even a knowledge of circuit theory is unnecessary since its essential features are given in a self-contained chapter. By ignoring the practice exercises and the end-of-chapter problems, one may also use the book as an op-amp handbook, since it contains thorough descriptions of the op amp, its terminal connections, its practical limitations, and many of its applications." The chapter headings are: Operational Amplifiers, Introductory Circuit Theory; Op-amp Circuits with Resistors; Op-amp Circuits with Capacitors; Low-pass Filters; Other Types of Filters; Analog Circuit Design; Diodes and Transistors; Op-amp Circuit Cookbook; and Practical Guidelines. Ten chapters, 285 pages, with half-tones, figures, schematics, four Appendixes, Answers to Odd-numbered Problems, and Index; plus Contents and Preface; Practice Exercises throughout book, Problems at the end of many chapters, Further Reading at the end of Chapter 9.

Search libraries:
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$14 used

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