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It's interesting, after staring at the schematics for a bit, you realize that the structure is surprisingly simple. It just sums a weighted input with the the output of the adder, its first integral and its second integral (pretty obvious in hindsight). The response is:
H(s)=sum( g*vin + a*x...
I set R4 = R8 = R, and C2 = C3 = C (both integrators have same values), and simplify and get:
Gain: -R6/R1
Wn: sqrt(R2/R3) / (R*C)
Q = sqrt(R3/R2) * (1 + R6/R1) * (1 / (1 + R3 / R2) )
The values in the circuit are:
R1 = 100
R6 = 10M
R2 = 100k
R3 = 10k
R = 470k
C = 0.33p
With the above, I...
That sounds very insightful. Can you please elaborate on how adding a fourth OpAmp (I assume without adding another pole) helps the degrees of freedom?
@FvM, thanks. At this point, I am able to derive the 2nd order H(s) for the filter much like you did.
By writing H(s) as: (alpha * s)/(s^2 + beta * s + gamma), where alpha, beta and gamma are functions of the R's and C's, the Bode plot of H(s) in Octave agrees with Spice sim of the circuit...
First off, I really appreciate the obviously great amount of effort you've all put into this question. Thank you!
V- refers to the negative supply voltage, which should be connected to ground, which I hoped to clarify by the 'Single Supply' comment. I'm not sure, though, of the benefits of...
What you are noting as Vin1(t) is just Vcc, used to bring up the DC to Vcc/2 through the 100k dividers. I should probably have been more explicit than just marking it with 5V in my original schematic. I was also negligent in not pointing out that V- is connected to ground, as we are operating...
I am having a hard time understanding the operation of this bandpass filter - i.e. the qualitative operation of the feedback which would allow me to determine what sets F0, Q and gain. I think the two lower opamps operate as integrators centered around Vcc/2, but the rest of the loop has me...
An ideal mixer is a classic example of a time varying linear system - from the input port to the output port, not the LO port. If you mix a signal A with the LO and get out signal X and you mix a signal B and get out Y, then mixing A+B will give you X+Y (in an ideal mixer). This establishes...
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