Design a Third Order Sallen-Key with Gain  - Page 1
Forum section: electronics / projects

author: Yansi
author_rank: Super Contributor
timestamp: September 05, 2018, 09:43:17 am
content: Hi!I am designing a third-order Sallen-Key low pass filter. The cutoff frequency should be 1Hz. That is fine, I came for example with this:But to optimize the circuit and as the filter will be working with rather small voltages in the region of interest, I would like to add some gain to it.It would either help me to have a gain of about 7 or 40. I think that it should be possible to do. From what I have read so far, the only component that has to be changed after adding gain is the feedback capacitor. Its value has to be decreased. But I do not understand or find by how much do I have to reduce its value.If I take a simple 2nd order Sallen-Key low pass, such as this:and add gain to it, for example 7.8 (6k8 and 1k feedback resistors) and reduce the value of C1 by 7.8, I get 128nF. If I then plot the response, the system becomes unstable and oscillates as there is to much peaking. Why?To my biggest surprise, if I do the same, but increase the gain to 40 and reduce C1 by 40 to 25nF, the response looks correct and system is stable. What the hell?! //EDIT: It seems this is in fact unstable too//I do not understand what the hell is going on or how to apply gain to the third order one, but guessing the rule will be the same for both. Question is, if I can find the ruleThanks,Yan

author: Benta
author_rank: Super Contributor
timestamp: September 05, 2018, 10:33:43 am
content: That's far too much gain for a Sallen-Key. Your frequency response will be all over the place.Go for an MFB filter instead.Here's a good app note:www.ti.com/lit/an/sloa049b/sloa049b.pdf

author: Yansi
author_rank: Super Contributor
timestamp: September 05, 2018, 11:06:44 am
content: Well thank you for hint, never heard of the MFB filter.I have tried calculating one, unfortunately with sensible capacitor size <1uF it requires resistances well above 10Mohm even for a -unity gain. Which is a double no for my application, where I need lowest possible offset voltage. Having high resistances also means no leakage in the capacitors is allowed, hence only foil types (and small capacitances) allowed.For a gain of -40 resistor values become one would say ... a bit offensive.So I probably should re-think the concept all over again.By the way, what defines the "way too high gain" for the filter?

author: Benta
author_rank: Super Contributor
timestamp: September 05, 2018, 11:45:16 am
content: Quote from: Yansi on September 05, 2018, 11:06:44 am1 Hz is very low, and you'll have to get used to using caps significatnly larger than 1 uF, there's no way around it.Concerning gain and Sallen-Key, the topology exhibits rather high component sensitivities (always >1 even at gain=1) and it gets much worse as the gain is increased.Component sensitivity means how much filter parameters change with component tolerance. For instance, at higher gain using 1% resistors, cutoff frequency might change by 15%.The MFB filter is harder to calculate, butmuchbetter in this regard. With careful design, sensitivities of 1 and lower can be achieved.

author: Zero999
author_rank: Super Contributor
timestamp: September 05, 2018, 12:13:02 pm
content: How about using two stages: one amplifier, perhaps with only a basic single order RC filter, followed by a Salen-Key filter with unity gain?

author: IDEngineer
author_rank: Super Contributor
timestamp: September 05, 2018, 01:36:37 pm
content: Quote from: Hero999 on September 05, 2018, 12:13:02 pmThis is the correct answer, even if you use something other than a Sallen-Key filter. Gain block first (with the first layer of filtering), followed by a second opamp implementing additional filtering.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: September 05, 2018, 02:00:52 pm
content: Also, if you want a steeper filter, you can add an RC in front to get a 3rd order. The values of the filter all change (because it's not a constant resistance source anymore), for which you need either a calculator, or a simulator and a bit of poking around.Tim

author: Yansi
author_rank: Super Contributor
timestamp: September 05, 2018, 02:13:09 pm
content: The component sensitivity does not matter, as far as it does not invite stability issues. I do not care exactly about 1Hz, I just need a DC signal filtered out of an AC signal, that may be one or two orders of magnitude higher, than the DC component. Hence I can not use a gain stage first, I would reach the saturation limit very fast with not much gain.I first apply the steep low pass filter to get rid of the AC component, then I add a gain stage. It still would be possible to do so with a low Voffs opamp. I can also calibrate the offset automatically by shorting the input. This was actually in my first prototype, that worked even with a cheap-ass TL062 amp with rather moderate offset (that was then cancelled by software). I thought I could get away with a single precision OPamp and without the offset calibration.The reason why I did want to use a low pass with gain was so I could utilize a low cost auto-zero amplifier like MAX4238. Unfortunately that one is only single per package and the size constraints of my application limits me in how many packages I can put there. (While I not want to go to silly component sizes below 0603 and SOT23/SO8)Still I am getting issues with high resistance in the opamp inputs though, but around 2Mohm is still manageable for me with a low bias current opamp. (Of course I have both inputs see the same DC resistance to ground).QuoteExactly, that is how the 3rd order Sallen Key works. Unfortunately I am not that familiar mathematically with MFB filters. Found none calculators for a 3rd order one and while having issues with offensively high resistances in the MFB filter (2nd order one), I chose to stick what I wanted to do originally, as described above.

author: Benta
author_rank: Super Contributor
timestamp: September 05, 2018, 02:33:28 pm
content: TI filter design tool:http://www.ti.com/design-tools/signal-chain-design/webench-filters.html

author: Zero999
author_rank: Super Contributor
timestamp: September 05, 2018, 02:49:14 pm
content: Quote from: IDEngineer on September 05, 2018, 01:36:37 pmQuote from: T3sl4co1l on September 05, 2018, 02:00:52 pmI was thinking of a basic non-inverting amplifier, with an RC before the input and a capacitor across RF, followed by the Sallen-Key filter, which can then be designed in isolation.

author: ogden
author_rank: Super Contributor
timestamp: September 05, 2018, 03:14:33 pm
content: Quote from: Benta on September 05, 2018, 10:33:43 amQuote from: Benta on September 05, 2018, 02:33:28 pmVery good filter wizard:http://www.analog.com/designtools/en/filterwizard/

author: T3sl4co1l
author_rank: Super Contributor
timestamp: September 05, 2018, 03:57:30 pm
content: Quote from: Hero999 on September 05, 2018, 02:49:14 pmFYI, the cap across Rf doesn't help -- it just effectively reduces the GBW of the amp, making it a poorer amp/buffer.Anyway, yeah but, if you're going to that length, you probably:1. Can get a much steeper filter (up to 5th order with a standard response, 6th order if you don't mind it's slightly sloppier than a standard one) for the same gain, or2. Can use a single amp with more GBW to do the gain and filtering at once.Regarding MFP, relevant:http://sim.okawa-denshi.jp/en/MultipleFB3Lowkeisan.htmTim

author: Yansi
author_rank: Super Contributor
timestamp: September 06, 2018, 04:56:34 pm
content: Thank you guys for all suggestion. I've learnt at least something new here (the MFB).The PCB is currently almost finished, waiting for some other dimensional specs to be finished.