I need help with modelling a 10 MHz Ultrasonic Transducer

Hi all,

I'm working on a project where I need to model a 10 MHz Ultrasonic transducer. After some research, I found out that using the Butterworth Van-Dyke (BVD) model would suffice for this.

The BVD consists of L,C,R in series, and one clamping C0 which is in parallel with those.

From the research papers I've read, they normally find these parameters via measuring an actual ultrasonic transducer with some network analyzer, reading off it's impedance and/or admittance, and highest resonance frequency.

I however, do not have any such physical transducer, nor VNA available.

As stated, I just need to get some numbers such that the simulated transducer operates around 10 MHz. Any ideas how I can come up with the parameters? Just plug in random numbers until I get a satisfactory response?

The transducer design is not the main part of my project(broadband impedance matching), so how "close" it is to a real one isn't that relevant.

If you have any other ideas, or recommendations, that would also be great! Thanks

Some reservations:

The LCRC model represents the transducer near it's resonance frequency, but not far from fundamental resonance frequency or e.g. overtone resonances. The "R" parameter respresents the sum of internal losses and external energy transfer, so it's supposed to change with the load conditions like interfacing the transducer with different media. The external medium can also detune the transducer.

If you don't have a real transducer, you must rely on datasheet specifications or general literature. Or derive the electrical parameters from a multiphysics simulation, based on piezoelectric material data.

A simplified high frequency transducer can be modelled as a piezo disc of λ/2 thickness, excited in longitudinal mode, one side backed with absorbing material, the other interfaced with a λ/4 transformer disc to the external medium.

dreamspace said:

I just need to get some numbers such that the simulated transducer operates around 10 MHz. Any ideas how I can come up with the parameters?

The transducer design is not the main part of my project(broadband impedance matching), so how "close" it is to a real one isn't that relevant.

Click to expand...

I guess you want the LC to resonate at 10 MHz? (I could be wrong.)

Using the formula for resonant frequency:

f = 1 / ( 2 Pi √(LC) )

You get 10 MHz with 16 nH and 16 nF. Impedance is in the vicinity of 1 ohm. However if you think transducer impedance is greater, then increase L, reduce C, by the same ratio.

For instance, suppose R = 100 ohms. Then try 1.6 uH and 160 pF.

Formula for reactive reactance: XL = 2 Pi f L

Formula for capacitive reactance: XC = 1 / ( 2 Pi f C )

To apply the formulas properly, you need to draw arrows at an angle which creates the shape of a parallelogram. However you can probably get by with ballpark values, since you say you do not need precise values.