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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:

enter image description here

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.

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  • \$\begingroup\$ 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? \$\endgroup\$ – Linkyyy Dec 9 '18 at 20:10
  • \$\begingroup\$ Why not re-characterize at 1KHz steps, and also capture the 45 degree phase shift? \$\endgroup\$ – analogsystemsrf Dec 9 '18 at 20:12
  • \$\begingroup\$ 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? \$\endgroup\$ – Sunnyskyguy EE75 Dec 9 '18 at 21:27
  • \$\begingroup\$ @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. \$\endgroup\$ – Tibbe Dec 10 '18 at 8:10
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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.

Short Answer:

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.

How will YOU define your requirements?

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