Noise from active filters: An unwelcome surprise

RE: Noise from active filters: An unwelcome surprise

Liang Huang — Thu, 05 May 2022 11:50:17 GMT

Hi John

I have a question regarding noise bandwidth in noise calculation. The noise in table 1 is calculated with a bandwidth of 10kHz, but I noticed that noise gain beyond 10kHz is 0dB (as shown in Fig2) which means that noise beyond 10kHz is not zero. Therefore, I wonder why you don't consider noise beyond 10kHz in noise calculation. I think that noise is influential if GBW of the opamp is high. I don't know what is wrong.

Look forward to your reply. Thanks a lot.

RE: Noise from active filters: An unwelcome surprise

John Caldwell — Mon, 14 Apr 2014 17:25:12 GMT

Ahmet, noise gain is different than signal gain because it is always measured from the non-inverting input of the amplifier as I show in Figure 1. In these two circuits, the noise gain is measured from the point where I have inserted the voltage sources (VG1 in both circuits) however the signal gain would be measured from the filter input (where R2 and R4 are grounded).

RE: Noise from active filters: An unwelcome surprise

Kendall Castor-Perry — Sun, 13 Apr 2014 15:35:50 GMT

A quick comment on Stephen P's post below. If the values of the two resistors aren't the same, you can put them in either order and you'll get the same filter frequency response for sure. But the noise properties will be different - easily shown in simulation. There's a great paper by Peter Billam on optimizing for this - if you can't track it down, mail me at filterwizard@cypress.com and I'll try to dig out my own copy. Noise - and offset - in filters is a fascinating topic, I've covered some facets of it in my Filter Wizard columns.

RE: Noise from active filters: An unwelcome surprise

Ahmet Cetin — Thu, 10 Apr 2014 14:12:54 GMT

Thank you for given information. Higher Q cause higher noise output. If transfer function is the same effect to both signal and noise, Is S/N ratio change for higher Q? or is noise gain diffirent from signal gain? Regards.

RE: Noise from active filters: An unwelcome surprise

John Caldwell — Thu, 03 Apr 2014 16:03:27 GMT

Stephen,

You bring up really great points about the location of the passive components within the Sallen-Key filter circuit. I will have to do some investigating on how they affect the filter output with a step input (maybe a future blog post?).

b) My two articles listed in the Basic Rules section (rule 3, item 1) examine the effects of capacitor voltage coefficient on signal distortion, but not dielectric absorption. In his book The Design of Active Crossovers, Douglas Self confirms your recommendation for using a high quality capacitor to ground with a comparison of polyester and polypropylene capacitors. However, when I repeated this investigation using ceramic capacitors, the results with mixed dielectric types (C0G and X7R) were still unacceptable, so I avoid recommending that customers try it unless their signal levels are extremely low or they have no other option.

Thanks for reading my blog post and providing some high quality input! I hope you'll come back to the Precision Designs Hub in the future!

RE: Noise from active filters: An unwelcome surprise

Stephen Power — Tue, 01 Apr 2014 12:26:00 GMT

Of course I forgot the sqrt (n) bit in the Q formula, where n is the ratio of caps.

RE: Noise from active filters: An unwelcome surprise

Stephen Power — Tue, 01 Apr 2014 12:23:22 GMT

Hi John

I would like to add the following comments regarding the unity gain 2-pole low pass Sallen-Key topology.

(a) For the unity gain SK, with regard to fc and Q, I believe that it makes no difference which of the resistors is closest to the signal source since fo= 1/(2*pi*sqrt(R1*R2*C1*C2)) and Q = sqrt(R1*R2/(R1+R2). However, if a step input is applied to the filter then it is better to have the larger resistor closest to the signal source. I believe the reason is due to the increase in op amp output impedance with frequency. When a step signal is applied a spike appears at the output of the filter. By putting the larger resistor closest to the signal source the attenuation is higher and the spike is reduced. Note that this is only true for the unity-gain SK.

(b) Capacitor Dielectric Absorption (DA) is a problem with active filters. I believe that DA is voltage dependent, with the problem getting worse as the voltage across the capacitor increases. Looking at the unity gain SK, the capacitor to GND sees the full signal while the feedback capacitor has approximately 0V across it. Generally in SK filter design the caps are not equal with one value several times the other. For low frequencies the cap values might need to be quite large (perhaps several hundred nF) and it may be difficult to get the right cap types (NP0 or PPS for SMD, polypropylene for TH). Hence, I believe that if you have to choose then it is better to make the cap to GND the smaller value, higher quality, capacitor and the feedback capacitor the higher value lower quality part (Of course, best if both are of high quality).

regards

Steve

RE: Noise from active filters: An unwelcome surprise

Soufiane Bendaoud — Thu, 27 Mar 2014 06:38:53 GMT

Very nicely done and yes this is often overlooked. Thanks John