Can the value Q not be sensitive to the circuit components?

In summary, The speaker is discussing a circuit they have attached and are trying to analyze. They have solved for the transfer function and found it to be plausible, but when solving for Q, they get a value of 1 which they find unlikely. They also mention that they have confirmed the values for Ra and Rb and that Q is controlled by their ratio. They suggest using different values for m and n to achieve a wider range of Q values. The speaker also mentions that the circuit is not suitable for multiple biquads and that using identical components can result in oscillation. They believe that this cell, along with other circuits that try to compensate for limited bandwidth, do not work well.
  • #1
FOIWATER
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I have attached a circuit I am trying to analyze,

Is it possible that Q is not sensitive to the value of C?

I solved my transfer function Vo/Vi, and I get (2/c^2R^2)/(S^2 + S(1/RC) + 1/(R^2C^2))

Which looks plausible at the present time, however when I solve for Q, get 1 here? It is not sensitive to any circuit parameters... I'm sure that couldn't be possible.?

Thanks for looking.

(Just confirming, because Ra = Rb, K = 2 correct)
 

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  • #2
If you were to re-analyze the circuit, but using dis-similar resistors (e.g., R and m.R instead of both equal to R), and (similarly) capacitors of C and n.C, I expect you'll find that you can set Q to a wide range of values.

m and n being fractions.
 
  • #3
This cell does NOT work because at any intersting Q it is exceedingly sensitive to Ra and Rb.

By the way, when analyzing the sensitivity of a filter cell or any design, you can't keep R=R. You have to give an individual value to each component, because the drifts and tolerances don't match an other.
 
  • #4
I am not the expert of filter. I thought Q is control by ratio of Ra and Rb. k=2 is cutting a little close, I saw oscillation around this number. I usually try to keep it no more than 1.5.
 
  • #5
With this being a low-pass filter, there generally is no requirement for Q>1. As an easy straight-forward design, the circuit should suit many applications.
 
  • #6
With Q<1 you don't need RA and RB at all. Just use different capacitors.

If the filter has several biquads then the needed Q climbs and immediately, this cell gets unusable, because a finite RA/RB gives an infinite Q (the cell oscillates) and before that, Q is ridiculously sensitive to RA/RB.

I know that so many books and courses recommend this cell, but they didn't try it by themselves.

It's just like the biquadratic cells that pretend to compensate the limited bandwidth of the op amps by inserting one more identical op amp in the feedback: all these cells oscillate.
 

1. Can the value Q be adjusted to be less sensitive to circuit components?

Yes, the value Q can be adjusted by changing the circuit components such as resistors, capacitors, and inductors. By selecting components with lower values, the sensitivity of Q can be reduced.

2. What causes the value Q to be sensitive to circuit components?

The value Q is sensitive to circuit components due to the inherent properties of the components such as resistance, capacitance, and inductance. These properties affect the overall performance and stability of the circuit, thus impacting the value Q.

3. Is there a way to calculate the sensitivity of Q to circuit components?

Yes, the sensitivity of Q to circuit components can be calculated using mathematical formulas and equations. This can help in selecting the appropriate components to achieve a desired value of Q.

4. Can the sensitivity of Q to circuit components be reduced to zero?

No, it is not possible to completely eliminate the sensitivity of Q to circuit components. However, it can be minimized by careful selection and optimization of the components used in the circuit.

5. How does the sensitivity of Q to circuit components affect the overall performance of a circuit?

The sensitivity of Q to circuit components directly impacts the stability and accuracy of the circuit. A higher sensitivity can lead to fluctuations and distortions in the output signal, while a lower sensitivity can result in a more precise and stable circuit.

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