differential amplifier filter derivation - Page 1
Forum section: electronics / projects

author: Morgoroth
author_rank: Regular Contributor
timestamp: March 13, 2016, 05:56:43 am
content: I'm trying to figure the derivation of a differential amplifier filter, I have a differential signal I want to filter and when I have the equations for it, I can't find any derivation and my attempts to get it by myself has been unsuccessful.The filter I want to implement is this:http://electronicdesign.com/analog/improve-noise-immunity-rtd-ratiometric-measurementsIf any one have knowledge of a book talking about this kind of designs I'll be very greatful.Thanks in advance.JP

author: bson
author_rank: Unknown
timestamp: March 14, 2016, 05:52:12 am
content: I think it's a greatly simplified formula to approximate the response based on Cdiff being at least 10 times Ccm.It's not that hard to derive a more exact response. If the two input voltages are V1 and V2 you're looking for the response across Cdiff; this is your Vout. The network forms a loop between V1 and V2, consisting of an RC divider, Cdiff, and a second RC divider. The impedance Z is the series sum of these impedances. The easiest is to calculate the current across Cdiff and multiply by its impedance (1/jwCdiff) to get Vout. Start with V1 by grounding V2. The current is i1=V1/Z. Then repeat for V2: i2=-V1/Z. The net current is i1-i2. Note that if V1=V2 the currents match and the net current is 0, leading to Vout=0; this is the common-mode rejection. Anything common to V1,V2 will be canceled. Then you get Vout=(i1-i2)/jwCdiff. H(s) = Vout/(V1+V2) = (i1-i2)/sCdiff. (i1,i2 will also be functions of s.) Expand and solve for s=0.707 (-3dB, the half-power point). Note that if R1=R2, i2=-i1 and i1-i2=2*i1.I quickly ran ran it with sympy and got:>>> wc=S.solve(S.Eq(H,0.707),s)>>> wc[0.414427157001414*(C1 + R1)*(C1 + R2)/(C1*Cdiff*(2.0*C1 + R1 + R2))]To get fc you obviously need to add 2*pi to the denominator. My best guess is the constant in the nominator is 0.707*2-1.Hopefully this is ballpark enough to get you started. Maybe verify with a spice simulation.

author: Morgoroth
author_rank: Regular Contributor
timestamp: March 14, 2016, 02:12:30 pm
content: TY very much, that help me a lot, now I have more questions about filters for differential amplifiers but I think I'm going to ask in another threat for it, could be helpful for others.thanks again.

author: uncle_bob
author_rank: Unknown
timestamp: March 14, 2016, 02:16:23 pm
content: HiIf you take this off to another thread, it's probably a good idea to tag that thread in this one. If you don't people wind up finding a bunch of fragmented information that goes nowhere.Bob

author: T3sl4co1l
author_rank: Super Contributor
timestamp: March 14, 2016, 07:40:02 pm
content: Why wouldn't you simply filter everything at the same level, i.e., use only Ccm, no Cdiff? You're only reducing the interference further...In fact, having less CM noise is probably much more beneficial. Most ADCs can deal with their normal signals being a little funny, i.e., the differential being noisy. High performance ones (like >20Msps, for SDR and whatnot) are notorious for having crappy common mode response that they don't tell you about. I don't know how well that applies to S-D types. (SAR types vary; if they have a true differential input, they should be okay, but if they're doing it the really crappy way by interleaved sampling of the +/- channels via mux, they'll be the worst possible...)Also, just throwing in caps can sometimes be dangerous; I wouldn't trust a hard wired input to not be carrying nasty RF. A little CLC filtering action, at least with a ferrite bead in there, will go a long way to keeping things happy in nasty (e.g. industrial) environments! (Or if the ADC can handle the resistance, using resistors over 1k will do better than any ferrite bead.)Tim

author: uncle_bob
author_rank: Unknown
timestamp: March 14, 2016, 07:55:20 pm
content: Quote from: T3sl4co1l on March 14, 2016, 07:40:02 pmHiI think the OP has headed off to another thread so we may not be talking to him at all anymore.Bob