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

Click For Summary

Discussion Overview

The discussion revolves around the sensitivity of the quality factor Q in a circuit analysis, particularly in the context of a low-pass filter design. Participants explore how variations in circuit components, such as resistors and capacitors, may affect the value of Q.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether Q can be insensitive to the value of capacitance C, noting that their calculations yield Q = 1, which seems implausible.
  • Another participant suggests that using dissimilar resistors and capacitors could allow for a wider range of Q values, indicating that Q is sensitive to component values.
  • A different participant argues that the circuit's sensitivity to Ra and Rb is significant at interesting Q values, emphasizing the need for individual component values due to drift and tolerance issues.
  • One participant expresses uncertainty about the control of Q, stating that it is influenced by the ratio of Ra and Rb, and warns against values too close to 2 due to potential oscillations.
  • Another participant notes that for low-pass filters, there is typically no requirement for Q to exceed 1, suggesting that the circuit design can be straightforward for many applications.
  • A later reply indicates that with Q < 1, the use of Ra and Rb may not be necessary, proposing that different capacitors could suffice, while also highlighting the sensitivity of Q to these resistors in more complex filter designs.

Areas of Agreement / Disagreement

Participants express differing views on the sensitivity of Q to circuit components, with some suggesting that it can be controlled through component variation, while others highlight significant sensitivity issues that arise in practical applications. The discussion remains unresolved regarding the implications of these sensitivities on circuit design.

Contextual Notes

Participants mention the importance of individual component values and the potential for oscillations in the circuit, indicating that assumptions about component matching may not hold in practice.

FOIWATER
Gold Member
Messages
434
Reaction score
12
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)
 

Attachments

  • Untitled.jpg
    Untitled.jpg
    27.4 KB · Views: 500
Engineering news on Phys.org
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.
 
This cell does NOT work because at any interesting 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.
 
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.
 
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.
 
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.
 

Similar threads

Explicit Calculation of Q Factor of Loaded Tuned Circuits
  • · Replies 9 ·
Replies
9
Views
3K
Q of R+LC Circuit: Understanding Q & Phasor Analysis
  • · Replies 6 ·
Replies
6
Views
3K
Types of circuits that have a nonlinear response to R
  • · Replies 29 ·
Replies
29
Views
2K
Circuit analysis via polyhedron
  • · Replies 5 ·
Replies
5
Views
2K
How is KVL used in the node method KCL equations?
  • · Replies 3 ·
Replies
3
Views
2K
Theory question about neutrals in circuits
  • · Replies 32 ·
2
Replies
32
Views
4K
Solving Power Delivery Issues in a 5V Series Circuit with a 1.5V Rated Relay
  • · Replies 12 ·
Replies
12
Views
3K
Need help with an ultrasonic sensor interface circuit to ev3
  • · Replies 1 ·
Replies
1
Views
2K
I don't understand transistors in combinations .... Or maybe basics ....
  • · Replies 68 ·
3
Replies
68
Views
7K
Second order ODE for RLC circuit
  • · Replies 2 ·
Replies
2
Views
1K