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Technical Discussions
Kyle Reed
Kyle Reed
05:26 Oct-26-1999
Phase angle detection of resonance


I'm wanting to use a piezoelectric element in resonance as a transducer and I need precise determination of resonant frequency.

I've reviewed a number of patents that describe a way of determining resonant frequency through phase angle detection.

The excitation signal to a piezoelectric element is also fed into a lock-in amplifier as the reference signal. The response
signal from the piezo element is also passed to the lock-in amplifier and resonance is determined by sweeping frequency on the excitation source and determining where the phase between the reference and piezo signal is zero.

As resonant frequency changes, the lock-in amplifier allows a way of tracking the shift in frequency by determining if the phase=0 condition is met. A high precision frequency counter can be used to obtain precise determination of resonant frequency by monitoring the excitation signal source as it is adjusted to maintain the resonant condition.

Is this the most precise way to measure resonant frequency? Are there other schemes which could yield as precise a determination which do not require all the hardware I've described?

-stable excitation source (frequency adjustable via an intelligent interface (GPIP/RS232) or voltage control)

-lock-in amplifier with a phase output signal

-high resolution counter

-computer to read the phase angle, frequency, and adjust the excitation frequecy to track changes in resonant frequency.

One possible scheme I've considered is a pulse excitation source and a high speed A/D determination of the response from the piezoelectric element. I could do a FFT on the decay of the response from the transducer to determine resonant frequency; however, I doubt this would give me as high a precision as the system I've described above.

Also, is there alternative to using a phase measurement to determine the resonant condition? What other electrical measurement could be performed that would be sensitive to the resonant condition? Resistance, capacitance, or impedance of the circuit driving the piezo element???

Finally, if I'm wanting to use a raw piezoelectric ceramic or crystal element to design a transducer for such a system, would I have to have 4 electrodes on the element? Two for excitation, and two for response?

Any comments greatly appreciated. Any hardware recommendations for the descibed set-up or alternatives?

Kyle Reed
Microcoating Technologies, Inc.
Atlanta, GA

Wieslaw Bicz
PBP Optel sp. z o.o., Poland, Joined Feb 2009, 264

Wieslaw Bicz

PBP Optel sp. z o.o.,
Joined Feb 2009
01:53 Oct-26-1999
Re: Phase angle detection of resonance

2. If you use a pulse generator, you must make the same measurements and you will need to make FFT. The problem, you will have will be: the measurements with pulse doesn't produce the same results with almost all transducers as the measurements with bursts with one frequency.
The results depends also on the amplitude of the pulse.

3. The results of measurements, described under 1 and 2 depends on the position of the receiver in the field of the transducer.


I. The transfer function of an acoustic transducer is very complicatet, depends on the kind of electrical excitation (it is not possible to consider an transducer as a standing alone device - it is necessary to involve the sender (and receiver) in the consideration. The transfer function depends also on the position in the field.
II. The electrical resonance could be measured in an easy way using network analyser or together with the exiting cuircuit (maximum of power emitted or used).

You will also find out, that the resonance frequency depends on the temperature and the kind, how your transducer is coupled to the medium, and on the medium you use.

Wieslaw Bicz

Optel (http://www.optel.com.pl)


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