PhD-Level Ultrasonic Engineering • Medical • Manufacturing • Consumer
The Shock Show #2: Why is my resonance impedance not symmetric? P1
Have you ever tried to jam a square in a round hole? Do you say that you are too smart do do that? Well, have you ever applied the 3dB bandwidth to calculate the quality factor of a nonsymmetric resonance impedance response? I think you might have.
In this episode of THE SHOCK SHOW, we will dive into the first reason why resonance impedance is not symmetric. Read on here, or watch the show at the link:
Just because you aren't symmetric doesn't mean you are non-linear
We may jump to conclusions and say our non-symmetric resonance impedance "valley" is not symmetric because of nonlinearity. That can be true, but the reason for asymmetry that I will describe in this episode has nothing do with nonlinearity.
It has everything to do with low electromechanical coupling and low quality factor
If the coupling factor and the the quality factor are low, the parallel capacitor (think the BVD equivalent circuit) has non-negligible impact on the resonance response. A symmetric response, typical of a LCR circuit, shines from the rough when the LCR circuit's response is much larger than the parallel capacitor (coming from the static or intrinsic capacitance of your transducer/crystal.
If the coupling factor is low, than the ratio between capacitances in the BVD circuit is more drastic. AND, if the Q is low, the resonance current in the LCR circuit will also be smaller. As Q and k_eff get smaller and smaller, the response becomes more and more dominated by the parallel capacitor. THIS, causes non symmetric resonance impedance.
So where do we go from here!
Thankfully, because we are still linear despite the asymmetry, we can utilize different approaches for analysis. I go through a universal method of analysis in my impedance analysis course, but here is some information to get you started:
Instead of using absolute impedance for analysis, use real admittance for resonance frequency analysis and real impedance for antiresonance analysis. Q factor in this case is calculated from bandwidth 1/2 the max real admittance.