Appendix J: Comparison — series resonance and parallel resonance

Loss

Hirose (1) considered the loss (Q) of a single piezoelectric ceramic that was driven longitudinally in the 31 mode. He discusses the causes of ceramic loss (section 3) and shows that (theoretically) antiresonant operation (parallel resonance) should have lower loss than resonant operation (series resonance). The experimental results in section¬†5 agree with this conclusion. In figure¬†2, the quality factor \( Q_B \) for antiresonance is higher than \( Q_A \) for resonance, while the temperature rise (due to loss) for antiresonance is lower than for resonance. Note that the results are for a single ceramic whose length is resonant. Presumably, the results are still valid for a non-resonant ceramic that is part of a complete transducer.

Graph - Q and temperature  rise for series resonance and parallel resonance
Figure J1. Q and temperature rise
for series resonance ("A" curves") and parallel resonance ("B" curves")

Prokic (1) conducted power loading tests on Branson 20 kHz transducers. The power was measured in air with an attached bell horn and then as the bell horn was progressively immersed in water. The transducer amplitude was maintained at 20 microns peak-to-peak.

Both in air and up to moderate loading, these tests showed that parallel resonance has lower loss than series resonance. (It should be noted that Branson's transducers are designed to operate at parallel resonance so the ceramic thickness and number of ceramics may not have been optimized for series resonance. For example, since series resonance requires lower drive voltage, fewer but thicker ceramics can be used without concern of electrical arcing.)

Power supply considerations

Compared to series resonance, parallel resonance has a very high impedance so that the current is low for a given power output.

Parallel resonance --> high voltage ==>

  • Ceramic thickness is limited by max allowed field strength
  • Arcing -