Q: What is the best way to measure the phase difference between two signals with an accuracy approaching 0.01 degrees?

Application: I'm using a 40 kHz ultrasonic transducer to measure distance (and later vibrations). The transducer is operated in continuous wave mode and the distance measurement, corresponding to ultrasonic signal phase, manifests itself as a transducer impedance variation. I want to measure 1um displacement, so in terms of 40kHz ultrasonic (in air) this corresponds to 0.05 degrees of phase.

Measurement: Using an impedance bridge with a reference, as close as possible to the transducers mean impedance together with an op-amp I am able to generate a signal proportional to +/-180 phase shift. My VNA measurements indicate a relationship of about 0.02 degrees of phase per 1um in my region of operation. With a little headroom, I would like to target a phase measurement capability of 0.01 degrees.

Method 1: I've looked at quadrature mixing (output signal with the reference, & reference -90 degrees : sine and cosine). Low pass filtering the results and dividing to get the tan of the phase angle. It seems like the long way around with the need for mixers/dividers/multipliers. Also I'm not quite sure how to generate the cosine signal. I don’t fully trust an op-amp integrator. Is there a way to generate perfectly quadrature signals? I realise my measurement accuracy will depend on the accuracy of generated mixing signals.

Method 2: Next I’ve been looking at finding mixing parts which can integrate what’s mentioned in 1. The problem is that an overwhelming majority of these types of devices (perhaps all?) are designed for high frequency RF applications. I did find the AD8339 DC to 50 MHz, Quad I/Q Demodulator and Phase Shifter which looks very suitable. Still I’m not given much in the datasheet about the phase measurement accuracy.

Method 3: I've looked briefly at a PLL solution. Again these PLL parts seem to all be targeting RF applications. At first glance it seems like I would only use the phase detector element, which seems never to have accuracy specified. I guess (not a PLL guru by any means) that the accuracy if the PLL is by virtue of the feedback rather than the highly accurate phase detector. Is there a clever way of putting my transducer inside the loop to generate an accurate phase measurement?

Method 4: Go digital, convert signals to square waves using a zero crossing detector and EXOR them and use a high frequency digital clock to count the pulse width.

Four alleys to explore then. I'm wondering if someone has the experience to advise me which one has the most potential. I don’t have the resources to explore all four, but my feeling is to keep it analogue, and I have no experience with PLLs. Is there another solution I have not considered.

Thanks

 

I've actually designed some ultrasonic ranging products, and worked on other devices there too. All the products were based on crystals that resonated at either 1MHz or 3MHz.

For distance we used a 1MHz crystal along with method 4: transmit side would ping and time how long for the echo to arrive (or a single crystal would do both jobs). The system would resolve to 0.1" between 18" and 10 feet.

Do note this is not a continuous wave, it pings a few cycles, waits for the echo, then repeats.

Your accuracy is much tighter then mine ever was.

 

Is this for a production instrument or a one off?

The Tellurometer used phase measurements in your fashion, perhaps you could look at their methods and transpose them from microwave to ultrasonics?

 

I've used a variation on your method 4 with pretty high accuracy.

1. convert both signals to squarewaves (try to get duty close to 50%).
2. feed both squarewaves into 2 microcontroller digital input pins.
3. sample BOTH inputs together, over time either randomly or at a beat frequency (does not matter as long as there are enough samples).
4. Mathematically sum "earlier" or "later" events.

An "earlier" event is if waveA went / edge before waveB went / edge, OR if waveA went \ edge before waveB went \ edge.

This can get you some REALLY high resolution readings of phase, and tolerates imperfect duty cycle, but it needs some time to collect enough sample data (depending how high your resolution needs to be).

If you sample both inputs at say 1MHz you can get a lot of phase data accumulated by the time you have been measuring for a second or two.

 

Is this for a production instrument or a one off?The Tellurometer used phase measurements...

I'll have a look at the Tellurometer. Right now its just a POC in the lab but ultimately should develop into a production instrument

it pings a few cycles, waits for the echo, then repeats.
Your accuracy is much tighter then mine ever was.

Yea, I looked at pulsed but ruled it out because of the accuracy requirements. Pulsed Doppler however might have some potential but its another level of complexity and I'm not sure yet if the vibration will be enough

I've used a variation on your method 4 with pretty high accuracy....If you sample both inputs at say 1MHz you can get a lot of phase data accumulated by the time you have been measuring for a second or two.

Nice idea, I'll look int it. Do you remember what kind of accuracy you achieved, although i understand it also limited by the transducer

Any one with experience of Methods 1 & 2 who could give some insight?