Minimum Gain Bandwidth product for 2 pole active low pass

[Digital Larry]

I'm venturing out of my zone of comfort recently and actually designed a PCB!   

Lots of stuff to pack into a 1590BB and so I went with an SOT-23(5) aka SOT-25 single unit low voltage rail to rail op amp from Linear.  As I was reviewing the specs, I noticed GBW on the part I'd picked is only 200 kHz, which strikes me as REALLY low.  Looking through app notes for the part, it is being used in voltage regulators and other low frequency servo stuff.  This made me uneasy so I whipped open the part selector and found a different part, also from Linear, which has a 40 MHz GBW and says it is suitable for "active filters" which is pretty vague, but I threw caution to the wind and designed it in.

I realize that most of the time, any old op-amp laying around has plenty of GBW to spare and one doesn't think too much about it.  But 200 kHz GBW would mean that at 10 kHz the gain is only 20, and I started thinking about folding down the Bode plot but my innate sense for that really only applied to multi-stage transistor amps where the goal was an overall flat response.

I know I should ask a question here but I'll settle for observations/comments from anyone with a better feel for this stuff.

Thanks and best wishes to all in path of hurricanes or currently on fire.  I live in California and we've had fires in the local area in past years... knock on wood, it doesn't take much to set one off.

[R.G.]

As you're guessing, it depends on what the filter frequency is. You need "plenty" of gain at frequencies well above the actual turnover frequency of the filter to do a nominally good job. Also good guess about GBW and the gain at the highest frequency, etc.

The 200kHz one is fine for very low frequency filters, which is what DC regulators usually are.

I recommend you getting a copy of "The Active Filter Cookbook". You'll like it.

[Digital Larry]

Thanks RG, for reference I am just trying to make a simple 2-pole LPF at roughly 12 kHz.

[R.G.]

The 12kHz number runs you into much higher bandwidth needs, as you suspected. Go for something much higher than the 200kHz. My gut feel without doing some calculations is that 1MHz isn't enough. but 3-12MHz is simple and cheap these days.

[jonnyeye]

What kind of low-pass filter are you using? A Sallen-Key filter needs a gain of 90Q² at resonance/fc, while a MFB only needs a gain of 20Q². If you're doing a typical 12kHz Butterworth filter, you can probably ju-u-ust squeak by with the 200kHz GBW op-amp if using an MFB topology, but the Sallen-Key is a no-go.  Designing MFB filters is harder, but now that Mathematica/Wolfram Alpha exists solving the equations is pretty easy.

Here are a couple of free resources to keep you occupied until you can get the Lancaster book:

https://www.maximintegrated.com/en/app-notes/index.mvp/id/1762
http://www.ti.com/analog/docs/litabsmultiplefilelist.tsp?literatureNumber=sloa049b&docCategoryId=1&familyId=72

[Rob Strand]

There is a technique called pre-distortion which allows you to compensate for the opamp poles and finite bandwidth.   I think TI have some notes.

The problem with the classical Sallen and Key circuit with a low band-width opamp is the maximum attenuation at high frequencies is quite limited - it can be quite bad.   This has more to do with the output impedance of the opamp at high frequencies than anything else - basically a divider is formed with the filter feedback cap and the output impedance allowing the signal to bypass the opamp.  I believe TI also have a note in this.

The (inverting) MFB filter does not suffer from this issue nearly as much.

One thing that helps is to keep the size of the feedback cap small.  The resistances will the increase so you need to be careful of noise.   Desperate measures would be to load the output of the opamp with a resistor!

You can easily get a good approximation with the equations for a pre-distorted design then tweak it with SPICE.  However the circuit will only represent reality if both bandwidth the HF output impedance is modeled correctly in the simulation.

[Edit:  Another trick to keep HF attenuation is to use a one-opamp 3rd order filter.]

[PRR]

I agree: 200KHz is way-low for audio, even guitar.

However 16:1 gain in a unity-gain high-cut S-K filter smells like small error, not a don't-work problem.

Idiot Assistant says so too. Bottom plan is with SPICE's ideal infinite GBW GAIN block. Top is the same except the R-C on the output makes GBW 200KHz (check my RC math!). The error at the corner is invisible (<0.3dB @ 12KHz). Error increases (in a good way!) by 50KHz, and it goes the wrong way past 200KHz. But this is all 40dB down, which is plenty of rejection for audio crap (not enough if you play under a submarine transmitter).



Edit: Rob predicted this shape. And indeed the Zout matters, which is why I wild-pitched 100 Ohms. This may not be valid >100KHz.

[PRR]

GBW is one thing. '741's 1MHz GBW predicts 20KHz response even at gain of 10 or 20. But if you do this with complex audio at higher levels, it sounds trashy.

You need more-than 0.5V/uSec Slew Rate per V of peak signal for clean 20KHz hi-fi. For +/-15V supplies this suggests over 10V/uSec. Indeed TL072 (13V/uSec) is a great improvement in some early '741 (1V/uSec) studio gear.

You are single-9V supply? And obviously not looking for 20KHz. I'd say you can get by with 0.3V/uSec per peak Volt, 4V peak, 1.2V/uSec Slew Rate.

As you neglected to say *which* Linear brand chip you got, I can't say if it will suck on this score.

[Digital Larry]

Actually this is a single rail 3.3 volt circuit.  The chip I picked out of a haystack seems to be: LT6233CS6, AND it also looks like the filter topology I picked was Sallen-Key.  It is intended as an anti-aliasing filter for an FV-1 circuit.  In the current application (I am not taking FV-1 analog output back into the input) it is questionable whether any of this is even necessary.  However, supposing that I really did want to do that (e.g. in a delay or reverb application) we are talking about a 2 pole filter's ability to filter stuff above 12 kHz with a Nyquist frequency at 16 kHz, and I acknowledge that this would not be super-effective.

I need a buffer at the input so even if it is not set up for filtering I'll still need that.  I could also go JFET source follower.  See, this is reminding me why I prefer DSP programming... you don't have to pick components for every little thing!

I've gotten a little ahead of myself with this design but after a few months of analysis paralysis I decided to just make some PCBs and see whether they work or not!

This LT6233CS6 op-amp is a wee bit on the expensive side.  I don't mind building a few protos this way but wouldn't mind finding something under a buck in onesie-twosies.

For example, ST Micro TSV911ILT.  This has GBP = 8 MHz.  Digi-Key has them at $0.68 in unit qty.

Thanks!!!

DL