Q-factor question

1. Mar 30, 2014

EE4life

Hi all,

Given the impedance spectrum of a resonance circuit, I know that in order to calculate the Q factor we find the 3db bandwidth and then we use the following equation

Q = f_r/f_3dbbandwidth,

to find Q.

My question is how can I use, for example, the 1db bandwidth to calculate the Q factor. There should be some multiplication factor in there somewhere for this case.

Thank you

Last edited: Mar 30, 2014
2. Mar 30, 2014

Staff: Mentor

That depends on the order of the circuit, no?

3. Mar 30, 2014

EE4life

I'm not sure. Basically, I am interested Q-factor measurement of piezoelectric resonance. See the link for the resonance circuit(lowest impedance in resonance).

Because impedance should behave in a predictable way, I think we should be able to determine the Q-factor based on any given impedance data close to the resonance point, be it 3db or lets say 1db. I just dont know how to go about the derivation of Q-factor in terms of a 1db bandwidth.

4. Mar 30, 2014

meBigGuy

Q is defined as the ratio of the center frequency to the bandwidth which contains half the power. I don't know how, from just the 1db bandwidth, to determine what the 3 db (half power) bandwidth is. It would depend on the Q, which is what you are trying to determine.

5. Mar 30, 2014

Staff: Mentor

Do you have a SPICE model for the piezo? That can give you the order of the frequency response...

6. Mar 31, 2014

meBigGuy

The simple question is:
Given a simple series RLC circuit, calculate the Q from the measurement of the 1dB bandwidth and center frequency.

This paper goes through the detailed steps to calculate the 50% power frequencies (V = .707). Do the same for the 12.6% power frequencies (solve for w1). Knowing w1 for both cases, determine how to convert. What I don't know is whether there is a single answer that is not based on the relative values of R, L, and C. I doubt that they just fall out. But, I have not proven it either way.

http://ocw.mit.edu/courses/electric...pring-2006/lecture-notes/resonance_qfactr.pdf

For more on resonators:
http://www.ee.olemiss.edu/darko/rfqmeas2b.pdf may help.

7. Mar 31, 2014

EE4life

No spice model. For the time being, I will be happy to solve this problem for a simple oscillator equivalent system.

The basic definition of Q has nothing to do with the 3db bandwidth:
Q=2 pi (energy stored per cycle)/(energy lost per cycle).

I hypothesize that the 3db bandwidth is used to characterize Q because the equation for Q ends up being simple with no multiplication factors. I forgot to mention that I also measure the phase.

My problem is that at times real piezo resonance impedance spectrum does not match the ideal resonator spectrum because RLC parameters can change slightly, changing the Q as a slight function of frequency. Therefore, it is better to take the "average" Q value by using several calculation of Q using different bandwidths including 3db exactly (of course adjusted with the correct Q equation accordingly).

This is my best solution to the problem so far: Given any impedance data point with its phase (eg 23degrees), we can calculate what the resonance impedance (0 degrees) outta be (using phase triangle). Then after that, we can calculate the 3db impedance, and then find the frequency giving that impedance. Assuming we measuring the actual resonance frequency, we can find the bandwidth to the calculated 3db frequency. Using this method we can calculate several Q factors (which would be the same in a an ideal resonator) and average them to find the 'average' Q I was speaking about.

8. Mar 31, 2014

f95toli

Yes, it can be done, but the problem is that the 1 dB value is not goig to be as accurate which is why it is rarely used.
It is also a bit ambigious in mos real world situations if the resosonance is somewhat assymetric (and they always are); at least with a 3dB fit people will know what you mean.

If you really have a resonance so weak that you need the 1dB value you are better off just fitting the whole curve. It is much, much more accurate.

There are litteraly books about how to extract Q values (I have a copy of one somewhere) and you can also find plenty of review articles.

9. Mar 31, 2014

EE4life

I would like to use the more of the curve than the 3db point to get a more accurate and repeatable value for Q. For example, I would calculate the Q on the 1, 1.5, 2, 2.5, 3 db and then average it to get a more accurate and repeatable value. This is sort of analogous to a curve fit.

Did the suggestion I make in the last post make sense? I would appreciate if you could direct toward a reference where a curve fit method is demonstrated and for the other than 3db bandwidth is used to calculate Q. I have only seen the curve fit program on an impedance analyzer (I am not using an IA for my data because I use higher voltage), but I wish to do the calculations on my computer.

10. Mar 31, 2014

The Electrician

Would it suffice for your purpose to determine the values in the model found at:

https://www.efunda.com/materials/piezo/electronics/elec_equiv_circuit.cfm

I have a piezo disc from a computer which I measured with an impedance analyzer. I get the following result (impedance magnitude Z in green, real part of the impedance Rs in yellow). The measurement was made over a frequency range including the first major resonance:

I measured Cp at 100 Hz and using the equations given in the reference, solved for L and C. I took R to just be its measured value at the series resonance, 184.8 ohms. Then I plotted Z and Rs using the expression for the impedance of the model:

The calculated plot is similar to the measured impedance, but the shape of the Rs curve is a little different, indicating that the simple model doesn't include some non-idealities.

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11. Mar 31, 2014

EE4life

Although you can calculate the Q using an equivalent circuit approach, what I want to do is use several more points than the simple method suggests.
My goal is to include several points to calculate Q, thereby getting a more accurate and repeatable measurements.