Algorithm Challenge

[Carl-NC]

OK, here is a mini-challenge. Let's say you design a mixed analog/digital detector. You read in the X & R signals to the micro, and at some point you want to calculate the magnitude and phase. Mathematically, they are:





However, these can be slow calculations in a micro. The challenge is this: Come up with magnitude and phase calculations which seek to minimize both execution time and memory requirement, and produce acceptably accurate results. "Acceptably accurate" is up to you to define, and to explain and rationalize if necessary.

I have possible solutions but will wait to see what others come up with.

[pito]

Just use X + R and R/X , the numbers remain dependent on the amplitude and phase shift. Instead 10 degrees you have 35 fox ( a new unit with any name )

[moodz]

Thats strange. I was just working on this.

By taking the log of the input signals ( ref and sig ) all the trig math is dispensed with.

Vmag = K log ( Va / Vb ) + c ..... K and c are trivial constants.
Vphase = S ( Qa - Qb ) ...... S is the Phase slope ( eg millivolts per degree ) and Qa and Qb are the phases of Va and Vb respectively

conceptually it looks like this. PD is the phase detector.



the whole thing can be done in real circuits or partial or fully digital ... same result ( depending on your ADCs etc ).

In the real world my workbench circuit is recovering the amplitude and phase of a 50 millivolt signal in 10 volts pp noise with around 1% of phase and magnitude error @ 40 Khz.

[Carl-NC]

Just use X + R and R/X , the numbers remain dependent on the amplitude and phase shift. Instead 10 degrees you have 35 fox ( a new unit with any name )

I should have pointed out that this needs to work for the entire 180° of target space. I like to draw polar plots with 0° on the left and 180° on the right, opposite from normal trig, because that's how detector meters operate.



So, for example, R/X goes to infinity for small foil. And X+R is negative for ferrous targets.

[Carl-NC]

Thats strange. I was just working on this.
...

Your attachments didn't come through.

[pito]

1. So, for example, R/X goes to infinity for small foil.
2. And X+R is negative for ferrous targets
.

1. so put limit ( threshold ) if value is higher we know that is a foil.
2. use abs( X+R ),
√(x² + y²) it is some kind of abs

[pito]

1% of phase and magnitude error

In my opinion VDI is about + /-10% accurate

[moodz]

Your attachments didn't come through.

I only embedded a graphic. Didnt attach anything.

To get 180 degrees just need the right sort of phase detector ... eg ( dual D Flip flop type or reciprocal counting etc ).

[moodz]

In my opinion VDI is about + /-10% accurate

You are right but I am using a signal recovery technique before I measure the VDI .. in most detectors they just amplify / filter the RX signal then measure the VDI.
The signal recovery technique allows for phase and amplitude recovery without the distortion ( phase due to filtering and amplitude due to non linearity in amplification ).

[pito]

I think you are talking about: lock - in amplifier, which is not so good for metal detectors applications.

[moodz]

I think you are talking about: lock - in amplifier, which is not so good for metal detectors applications.

Can you explain your reasoning ? ( its not a lockin amplifier though )

[moodz]

another solution ...
fast artan calculation using vector rotation.

[pito]

Can you explain your reasoning ? ( its not a lockin amplifier though )

to big

[moodz]

hmm .. there are smaller ones on ebay etc ..

[moodz]

They are pricey ... or you can roll your own sig recovery and get results like this ...