Electronics > Projects, Designs, and Technical Stuff
2nd Order low pass filter - Why a topology?
Jay_Diddy_B:
Hi,
Here is a set of models to illustrate the difference.
There is loading in the RCRC filter that modify the response from a true double pole filter.
Because the second RC is 10x higher impedance than the first RC, the loading is minimal and the deviation from the true double response is about 0.5dB. This is probably acceptable in most applications.
I have attached the model
I used 'E' which is a voltage-controlled voltage source, an ideal buffer.
Regards,
Jay_Diddy_B
BartK:
Because I only want to filter out noise on my DC signal, I have taken a cornerfrequency of 1Hz. The frequency response of the filter is therefore not very important to me, but the step response is. For this reason I probably go for a Bessel response, so I would choose Sallen-Key compared to the passive filter + opamp.
Improving the Q is not relevant for the application in which this filter is to be used. However, I now understand why the Sallen-Key has certain advantages, certainly when a different response is required.
Due to its capabilities and possible configurations, the Sallen-Key topology is superior.
--- Quote from: T3sl4co1l on May 07, 2019, 05:05:00 pm ---The maximum Q factor for an RC network is 0.5 -- this limits how sharp the filter transitions from pass to cutoff. A higher Q is possible with passive LC or active RLC filters, giving sharper cutoffs (maximally flat (Butterworth), peaked (Chebychev), etc.), or more precise profiles (Bessel is very gentle, but just not quite as soft as an RC response, and most significantly so for high-order filters).
MFB is generally preferred for lower sensitivity to component variations. There are some other topologies which are preferred for high-Q filters, but this is only important in high-order and narrow band-pass/stop filters.
Incidentally, you do get one order almost for free -- the fact that the named filter profiles have poles positioned evenly around an ellipse, means that odd-order filters always have one real pole (and the rest as complex conjugate pairs). RC filters make real poles (this is the abstract mathematical reason why LC or gain is required to make a sharp filter), so you can solve for the pairs with active stages and throw in a single RC to finish it up.
The topology for that case can be found here (with calculators!):
http://sim.okawa-denshi.jp/en/Fkeisan.htm
Simply, it's another RC put in front of the usual RCRC filter. The values affect each other, so a different formula applies.
Tim
--- End quote ---
Since I do not use amplification, an MFB has a noice amplification of A+1=2 instead of A=1.
--- Quote from: Jay_Diddy_B on May 07, 2019, 05:18:41 pm ---Hi,
Here is a set of models to illustrate the difference.
There is loading in the RCRC filter that modify the response from a true double pole filter.
Because the second RC is 10x higher impedance than the first RC, the loading is minimal and the deviation from the true double response is about 0.5dB. This is probably acceptable in most applications.
---
I have attached the model
I used 'E' which is a voltage-controlled voltage source, an ideal buffer.
Regards,
Jay_Diddy_B
--- End quote ---
Thank you for your clear explanation!
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