# Ultrasonic transducer actual bandwidth for filtering

I have a pair of ultrasonic transducers with a "Thick Resonant frequency" of 975 kHz ±30kHz according to the data sheet. I did a frequency sweep test where I could see that they performed best at a frequency of 1 MHz (peak) as shown in the picture below:

I wonder what the actual bandwidth of the transducer model is:

• 975 kHz ±30kHz

or

• 1000 kHz ±30kHz ?

I am asking this because I am designing a bandpass filter where I need to define the bandwidth of it, and I am not sure what frequencies to choose as the transducers performs better at a forced frequency.

• Not sure what your question is. If the datasheet says that the frequency is 975 kHz ±30kHz, and you measure your unit to be 1000 kHz, which is whitin its boundaries, why would you redefine its spec? Dec 9, 2018 at 20:10
• Why not re-characterize at 1KHz steps, and also capture the 45 degree phase shift? Dec 9, 2018 at 20:12
• Have you been working on this since Feb?? from your previous unanswered question then on echo flow amplitudes in pipes. What is flow rate and % Doppler Shift? Dec 9, 2018 at 21:27
• @Linkyyy the question is if the bw moves with its peak frequency or not? Its a known fenomena that they perform better at a forced higher frequency. Dec 10, 2018 at 8:10

If total BW is defined as the 0.707 amplitude threshold ( -3dB) and on the lower half BW averages to -35kHz at 965 KHz, we might approximate it as a BW of 70kHz with a Q= 1000/70= 14 or inversely 1/Q=7.1%

Given a 10% 90% rise time,T = 0.35/f(-3dB) we expect a burst envelope rise time of 0.35/70kHz = 5 us or approximately 5 cycles at center f.

The center f tolerance is 30kHz @ 975kHz or 3%. The actual error is 25kHz or +2.5%

The effective rise time will not change significantly when a pulsed carrier is within the 3% tolerance spec. The load impedance and steady-state power load will be very frequency sensitive off actual center, yet not during the risetime of the pulse.

BW is not the same as Tolerance and is always expected to be greater otherwise it must be manually tuned.

## Other ( for the advanced user)

e.g. a Crystal with a natural 100 ppm tolerance is expect to have a BW of at least 100 to 200 ppm while MFG's with better process controls can achieve 25 to 50 ppm tolerance at 25'C although the BW will likely be the same.

Again %Tolerance must always be less than %BW.
However in a "good" part, the %error tolerance on the %BW relative to centre f or Tolerance error of Q will always be much less than the center frequency error .

Special 10MHz SC cut Xtals with <0.00001 ppm (1e-11) error at some ovenized temp, will still have a phase noise BW greater than 1e-11. These are used for extremely stable OCXO's and Stratum Level clocks.

A very high Q LC filter with a % BW of 0.5 or a Q of 200 but has a tolerance error of 1% is not very practical as the Q is greater than its centre tolerance with poor results. Since this is more difficult to produce low tolerance in LC components than crystals, LC BW's < 1% are difficult unless manually tuned and then must be temperature compensated.