How to choose speaker impedance for a VERY specific application?

Question

Ok, so this may be a long post. I want to preface by saying I have very limited electrical engineering knowledge, so thank you in advance :-)

I'm working on a medical device for a college project. Because of COVID-19, we aren't able to actually prototype and test our device but we want to design it as best we can virtually. The device application requires that a constant sound source be sent up a nostril. The signal generated should be < 10 V pp, 7 kHz, 100 dB > (based off of a clinical study).

The study we based our values off of uses a 50 ohm speaker, but our device needs to be powered by a smartphone audio jack.

What impedance speaker can I use to accommodate the signal inputs? It's also important that the speaker is no bigger than 1-3 cm. Will we need an amplifier as well? Is this even possible?

Answer 1

The result depends on exact details and precision of the transducers you must have, i.e. how "medical grade" you want it to be. For example how much you allow for tolerance of acoustic reproduction, is it +/- 1dB or +/- 0.1dB for a given voltage or power signal.

And your parameter about sound pressure is a bit unclear, but assuming you need 100dB SPL at the transducer, not at some other distance like at 1 meter, then I have a solution.

Cheapest possible in-ear headphones can easily reach sensitivity of 100 dB per milliwatt. They are also powered by a standard smartphone audio jack, and fits into nose. Actual impedance may be irrelevant in this application as long as the phone can push enough power into that impedance, and the transducer is sensitive enough to provide you over 100dB SPL with that, but the headphones I have are rated at 16 ohms at 1kHz which is quite typical value. They also can typically take 100mW before getting damage so it will be impossible to break them e.g. by setting smartphone volume to maximum.

Many in-ear headphones also come with multiple sizes of silicone tips for adjusting how tight it fits into the nose - I mean ear.

Downside of this makeshift solution is of course repeatability and calibration, as there is no way to know which volume level is correct for 100dB output, as it depends on the combination of the smartphone and headphones.

Answer 2

The signal generated should be < 10V pp, 7 kHz, 100 dB > (based off of a clinical study).

I'm assuming < 10Vpp is for safety reasons? So what you are really saying is that you need a 7 kHz transducer with a sensitivity of 80dB/V? Make sure your reference and the datasheets you are looking at are measuring the same way, as probably the datasheet is not considering transducers in someone's nose. Assuming measuring in some sensible way, that isn't very high, cheap headphones can do much higher than that.

The study we based our values off of uses a 50 ohm speaker, but our device needs to be powered by a smartphone audio jack.

Headphone jacks will usually power anything above about 10-15 ohms. Lower and you might trigger short circuit protection. I would pick whatever transducer you can find that meets your sensitivity requirements and then look at impedance next.

Will we need an amplifier as well?

Headphone output is usually less than 1Vpp, so using an amplifier will get you an extra 10-15 dB before you bump into your specified 10Vpp limit. It will also let you use impedances below 10-15 ohms which the integrated amp on a smartphone may not like.

Is this even possible?

You'll need to look at what transducers are available and see if you can find one that meets your spec. However, since you've said that someone else already did this, my guess is at least one such transducer exists.