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# WEBENCH® Tools/OPA859: Why is the Gain Bandwidth required in the Filter Design Tool Always so high?

Part Number: OPA859

Tool/software: WEBENCH® Design Tools

I'm trying to design to a a bandpass filter  with the filter design tool and I'm struggling to understand a few things from the design. The design parameteres required is a filter with a:

Bandwidth: 60KHz

Centre Frequency: 130 kHz

Gain: 40dB

I also wanted an amplifier that goes with Vmin of 0V and VMax of 3.3V so I entered  these values in the design section as well. The tool suggested the OPA859 and the following circuit was suggested:

But looking at the summary, the minimum gain bandwidth required  at each stage just looks absurdly large to me:

Filter stage 1 is given as:

Cutoff Frequency 110.357 kHz

Min GBW Reqd 490.91 MHz

Stage Gain 14.035 V/V

Stage Q 3.075 Stage

Topology Multiple Feedback

Stage 2 is given as:

Cutoff Frequency 152.59 kHz

Min GBW Reqd 682.279 MHz

Stage Gain 14.358 V/V

Stage Q 3.111

Stage Topology Multiple Feedback

Additionally, it's not quite clear where I bias the circuit. If I want a midpoint of 1.65V, Shouldn't I simply connect 3.3V to Vcc, 0 to Vee, then 1.65V to both positive inputs of the op-amp and the R3_S1/R3_S2 ? I appreciate any clarification,

thanks.

• Hi Daniel,

daniel_opa859.TSC

Kai

• Hi Daniel again,

you are right, the minimum required bandwidth is a bit arbitrary. It depends on how much gain reserve (loop gain) you want to have at the resonance frequency. In the literature other bandwidth requirements are given. Don Lancaster, for instance, states a minimum open-loop gain of OPAmp at the resonance frequency of 20 x Q^2, for a multiple feedback bandpass providing a gain of - 2 x Q^2. So, his gain reserve (loop gain) is only factor of 10.

Applied to your example this results in an unity-gain bandwidth of first OPAmp of about 20MHz which is much lower than 491MHz, obviously.

But make no mistake, a factor of 10 at the resonance frequency is the absolute minimum requirement to make a bandpass just only "work" as a bandpass. But it will not yield the best results. Why?

Assume an OPAmp having a typical open-loop nonlinearity of let's say 5%, then the closed loop harmonic distortion can only be brought down to 5% / 10 = 0.5% by the help of negative feedback loop. And this only at the resonance frequency, although the signal bandwidth of interest might be higher than the resonance frequency. So, for proper operation we need a much higher gain resreve. Multiply the gain reserve of factor 10 by another factor of 10 for getting low distortion even at a frequencey 10 times the resonance frequency. This will give 200MHz and you are not far away from the TI's minimum bandwidth requirement of 491MHz.

Of course, there are many other parameters which also suffer from a too small gain reserve, like - very important - closed loop output impedance.

So, the TI's minimum bandwidth requirement isn't as absurd as it might appear at the first sight :-)

Kai

• Yes Daniel, what comes out of the TI tool is oddly high, and yes Kai, it is actually absurdly high,

This is coming from FilterPro code done by BurrBrown folks circa 1989 - at that time, no one could imagine doing >20 kHz audio filters so just putting in a crazy high margin calculation was not to restrictive. There is an old app note that shows these simple guesses.

http://www.ti.com/lit/an/slyt113/slyt113.pdf?ts=1587905509300

I don't have the BP GBP margin calculation, but I did step through it (and why) in this article for the MFB LP, to start, you need the true gain bandwidth product, another slippery issue covered in Insight #12

https://www.planetanalog.com/use-true-gain-bandwidth-product-to-estimate-required-margin-in-active-filters-insight-13/

• So Daniel,

Not having the equations is no issue, here I ran the first stage for its LG, right around the Fo we always see a local minimum, that 40dB here is pretty generous - if, for instance, you were ok with 20dB, you could cut your target GBP by 10X. Cutting that by 5X would leave you 26dB min LG and so on.

Also, looking at the LG=0dB xover phase margin shows a very good 64deg. And then the file below,

1st stage LG.TSC

• Thank you Michael, insights #12 and #13 were very helpful and cleared up a lot of things for me.

• Hi kai,

any Idea why I'm seeing clipping at the output when I increase the amplitude of the signal? With a signal of amplitude 20m, I'm seeing clipping at 2.4V. I would have expected a peak of 2.65V.

• Hi Daniel,

the simulation follows the datasheet:

Kai