# Measuring Frequency Shift

A previous question on doppler shift velocity sensor make me ask this question. @Chris_stattron provided an insight but I was too curious to leave it at that comment hence the question.

Assume, I am trying to build a device that works at 40Khz and I am trying to understand doppler shift to measure the displacement of the object in concern. The movement of the object creates some doppler shift and everything static doesn't.

Now, my initial, software driven approach was to sample this at say 100Khz and look at the shift digitally but Chis suggested an analog cancellation approach using a receiving mixer. Essentially, what he said was that the local oscillator frequency is used for the receiving mixer and the signal, so that the return signal could easily be sampled with a simple ADC as opposed to expensive ADCs.

Mixing outgoing and returned signals and taking the difference as an indication of relative velocity is by far the easiest way of calculating velocity from Doppler shift.

As often, a useful place to look for the general principles is Wikipedias article on Doppler shift and I don't need to duplicate much of this.

The most important aspect is how to determine velocity, given by

• f_remote = f_transmitted x (Vsound + Vremote) / (Vsound + Vtransmitter)

Diagram from wikipedia.

Vsound is the velocity of sound in the medium and Vremote and Vtransmitter are the velocities of remote object and transmitter relative to the medium (here air). If the transmitter is still you can eliminate that factor. (Or if remote is still and transmitter moving you get a similar result.)

Rearranging gives Fdoppler

   = Ftx - Frx = F_transmitted x (Vsound + Vremote) / (Vsound)


Put simply, doppler frequency is transmit frequency multiplied by the speed of the remote object as a fraction of the speed of sound. If you move tx and hold rx steady the term ends up on the bottom line but the result is close enough to the same.

NOW you can meaure Ftx and Frx and calculate the difference, but the opportunities for error are significant. Instead, just heterodyning the two in a mixer and low pass filtering to extract just the difference frequency gives you what you want automagically.

Here is a complete "simple" medical Doppler ultrasound unit. I've included the lot rather than just the mixer you asked about as it shows several useful things. At the top is the Tx (transmitter) and at the bottom the Rx (receiver). In the middle is an unnecessary (for your purposes) extra part but it shows the principle of mixing a second time. If you connect pin 1 of the two AD633's and remove the middle block you get basic Doppler RADAR unit. The transmit signal on pin 1 and received signal on pin 3 are combined to produce sum and difference frequencies. The AD633 is a 4 quadrant analog multiplier AD633 Datasheet. Circuit diagram from here

There are a range of ways of mixing signals and this is certainly not the cheapest but is a good starting point due to the "worked example". The AD633 in the block removed from the middle does exactly the same as the bottom one except that it mixes a local signal that offsets the transmit signal so that the output Doppler signal is in a more convenient range for the application - just ignore it is this is confusing.

Diode mixer

About the simplest and cheapest mixer available is a "diode mixer" which uses the non linear characteristics of a diode to mix two signals. There are simpler versions than this

but this is a bit more explanatory visually than the simplest possibilities. Circuit diagram from here

See here for a few dozen more diode mixer circuits - that's just a Google images search on diode mixer.

"REAL WORLD" EXAMPLE - MIT Coffee Can RADAR:

MIT Coffee Can RADAR - looks good. Doppler / Ranging / Synthetic Aperture

Uses "Mini Circuits" modules so semi discrete / block construction.

Manual - excellent

Block diagram - uses separate TX/RX Cantennas with LNA on RF rx.

• great.. Could you perhaps enhance the answer with some simple circuit.. I am interested in that mixer part. thx – Frank Aug 5 '11 at 7:19
• See updated answer - 4 quadrant multiplier mixers and diode mixers. – Russell McMahon Aug 5 '11 at 9:18
• I tried to implement this, found that the carrier is very strong relative to doppler modulation (mostly leakage). I am afraid that the multiplier cannot handle this dynamic range. What do you think? – Ilan lewin Jun 6 '16 at 14:42
• @Ilanlewin You need to reduce the oscillator level (no surprise there :-) ). You could shield the oscillator and screen the oscillator to mixer direct path. In the door-opener/person detection commercial units they have a signal path from oscillator to mixer via a cavity (aka hole) that is significantly smaller than the wavelength of the oscillator. I assume that coupling is via "higher order modes". A look at some applications indicates that RF in is often amplified pre-mixer. | Fig 3.2 p45 .... – Russell McMahon Jun 7 '16 at 7:25
• Is there a mixing solution other than a multiplier which will allow for a larger dynamic range? Because I am worried that even if I reduce the leakage, still my surrounding environment (room) reflects the carrier at a level much greater than the level of the doppler shift from my (small) target – Ilan lewin Jun 7 '16 at 7:28