active filter quickie

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jeth

Well-known member
Joined
Jan 26, 2006
Messages
124
Location
Uk/Mexico
Any one know if there are any disadvantages using an equal C, equal R circuit for the sallen and key HP/LP filter sections..as opposed to the equal R circuit?
 
Equal C equal R requires some gain to realize typical filter shapes. If you want that gain in the passband then it's convenient. If you don't it's less so.

When you say "as opposed to the equal R circuit" I assume you mean an equal R lowpass?
 
The equal C, equal R schematics i've seen were claimed to be unity gain. The equal R circuits had different values for C, but were shown for high AND low pass..

I'd put the schematics here but they're in an excel file and i can't extract them.
 
You need gain for the popular Butterworth a.k.a. maximally-flat frequency response, Q = 0.707. In that case the gain is about 1.585. If you extract the signal from the inverting input of the opamp you will have unity gain in the passband but a ~high output impedance unless your gain-setting divider network is very low-Z (which may be hard for the opamp to drive). If you buffer the input(s) with a follower you can get the low Z but at the cost of another opamp.

See this for examples of SK filters with equal R equal C:

http://www.engr.uky.edu/~gedney/courses/ee221/project/Active_Filter_Summary.pdf

That ref. points out that Q = 0.5 is the lower limit for equal R equal C, which does correspond to unity gain in the passband.

With equal R and unequal C's you can do Sallen-Key unity gain lowpass; with equal C's and unequal R's, Sallen-Key unity-gain highpass. There are other topologies with more opamps but Sallen-Key is cheap and easy.
 
I reviewed some other schematics and you're right, it's the unequal circuits for unity gain. I did some calculations on these before and found generally that R1= 2xR2 in the equal C highpass, and C1=2xC2 in the equal R lowpass, so the values aren't too tricky to work out.
 
[quote author="jeth"]So, if i want to avoid the high z output, and keep unity gain, those are the best option?[/quote]

Yes. Another advantage is the unity-gain circuits don't generally oscillate with an open input, although the noise goes up, whereas the >1 gain ones do oscillate. I learned this the hard way when a few powered speakers (out of a bunch) began to howl when the wipers on the crappy potentiometers feeding the >1 gain SK highpass filters got intermittent and open-circuited :oops: . Hanging a resistance at the input to ground will fix it---and thinking about it now I realize I never did determine what the value required is relative to the other circuit values.

To Crusty2's conjecture/experience: both of the topologies do load the source in a frequency-dependent way, so if the source Z is not very low you may see some significant deviations from the expected response. In fact, this loading effect is used to make boost-cut EQ circuits, as the input of a Sallen-Key highpass looks like a grounded series R-L-C circuit with an additional R across the L.
 

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