TGS synhronous detector. Math

[habitbraker]

Hello! Hope you will understand my english style.

I am trying to understand how TGS(L) works. And Im stuck in the SD part.
I simulated SD in ltspice(added .asc file below). I know that I am not simulating all the noise and exact amplitudes - just the perfect case - in theoretical level an just one chan.
Simulation went pretty perfect - I got output voltage exactly like this formula predicts - Uout= A*(2/pi)*cos(phi).
(you can change freq, phi, amplitude-Umax).
I got this formula from here http://www.advancedlab.org/mediawiki...In%29_Detector
The Problem is that method in link uses all period - integrate first T/2, then inverts and integrate second T/2. I kindof understand derivation of formula in link above (actually I dont understand where 1/RC is lost and from where factor 1/T comes from. I could use explanation there too ).

But could enyone show me derivation for TGS SD output voltage?
I got this far : http://www.wolframalpha.com/input/?i...t%3D0+to+T%2F2
But its far from what I need to get (A*(2/pi)*cos(phi)).

[habitbraker]

OK I figured myself this far: It integrates or averages value of input voltage between t and (t+T/2) [T=period of working frequency]

And average value is area of signal form divided by Time interval. In this case - Area formed by half period of sine and X axis divided by half period.

Result is exactly what output voltage is.
http://www.wolframalpha.com/input/?i...t%3D0+to+T%2F2

But One thing I still dont understand - where 1/RC is lost???

[simonbaker]

OK I figured myself this far: It integrates or averages value of input voltage between t and (t+T/2) [T=period of working frequency]

And average value is area of signal form divided by Time interval. In this case - Area formed by half period of sine and X axis divided by half period.

Result is exactly what output voltage is.
http://www.wolframalpha.com/input/?i...t%3D0+to+T%2F2

But One thing I still dont understand - where 1/RC is lost???

I think the 1/RC is "lost" because your analysis is focusing on the steady-state DC output assuming a constant amplitude and phase shift of the input signal, because you are analyzing one cycle and extending that to all cycles. If the input signal phase and amplitude don't change, then any R and C values will produce the same steady-state voltage in the long run.

In reality, the input signal phase and amplitude is a function of time, and for each cycle, the SD will integrate a different voltage.

That varying voltage is a function of time and will have a spectrum. In effect it is the signal that is applied to the RC circuit part the SD. The RC circuit will filter the signal as a first order low-pass filter, which is what we want for a metal detector, because our target signal is very slow, based on how fast we sweep the coil. We want higher frequency noise signals to be filtered out.

We basically assume that our target signal has a constant phase but varies in amplitude at a very low frequency (our sweep frequency). Noise however varies a lot in phase, frequency, and amplitude. We hope the amount of noise that has the same frequency and phase bandwidth as our target signal is very small -- if so, then the SD will average out most of the noise to near zero if our RC constant is long enough.

That's the idea, I wish I could make it more mathematical for you.

BTW: The TGS circuit has additional filtering during the amplification stages also.

Regards,

-SB

[habitbraker]

Thanks! You took me one step closer!
So Input signal is some kind of Amplitude modulated - at law of how fast you move coil over the target, how far is traget, resisitivity of target...
If I understand correct, in perfect world phase shift introduces only magnetic materials - those witch contains Fe.

Supose I am regulated ref (gate voltages) siganals with disc/ground phase shifters exactly at 0 and 90 degrees with respect to RX signal so that Vout from SD1 is proportional to Acos(phi) and SD2 to Asin(phi) (2/pi is not important - its Const)

In other words:
SD1=Acos(phi)
SD2=Asin(phi)

So if if Vin=0 (in perfect world ) both SD Vout would be zero.
If Vin>0 and phi=0 then SD1>0 and SD2=0 - MD response = negative(or positive?)
If Vin>0 and phi>0 then SD1>0 and SD2>0 - MD response = positive
If Vin>0 and phi<0 then SD1>0 and SD2<0 - MD response = negative

Am I correct?

[simonbaker]

Thanks! You took me one step closer!
So Input signal is some kind of Amplitude modulated - at law of how fast you move coil over the target, how far is traget, resisitivity of target...
If I understand correct, in perfect world phase shift introduces only magnetic materials - those witch contains Fe.

Supose I am regulated ref (gate voltages) siganals with disc/ground phase shifters exactly at 0 and 90 degrees with respect to RX signal so that Vout from SD1 is proportional to Acos(phi) and SD2 to Asin(phi) (2/pi is not important - its Const)

In other words:
SD1=Acos(phi)
SD2=Asin(phi)

So if if Vin=0 (in perfect world ) both SD Vout would be zero.
If Vin>0 and phi=0 then SD1>0 and SD2=0 - MD response = negative(or positive?)
If Vin>0 and phi>0 then SD1>0 and SD2>0 - MD response = positive
If Vin>0 and phi<0 then SD1>0 and SD2<0 - MD response = negative

Am I correct?

Yes, I think you understand it.

In terms of the physics of targets, I think conductive materials introduce phase shift to the RX signal, while purely magnetic materials (e.g. ferrite) will change amplitude of RX signal, but not the phase.

Our two synchronous detectors are not exactly 90 deg apart since we have the DISC pot and GB pot to modify them slightly for our purposes. Generally, we set the DISC pot so that targets with phase shift above a certain level will make a positive output and phase shift below that level make a negative output in that channel (SD1). Only positive output can make an audio beep.

We also set the GB pot so that all conductive targets will make a positive signal in that channel (SD2), but pure magnetic material will make a zero signal (or negative, but zero is ideal). Because pure magnetic materal "amplitude-modulates" the residual RX signal (we call it the "null" signal), the GB pot setting depends on the phase of the residual RX signal. But it is tricky, because there are some capacitive components to the residual RX signal that probably are not affected by magnetic material and so you can't just believe your scope. We use actual ferrite to test the GB pot setting.

So the settings are not exactly like the "classical" synchronous detector you read about, where the two SDs are 90 deg apart and calculations are use to derive the phase and amplitude of the original signal.

This scheme makes the detector immune to magnetic ground variations when no targets are present. However, when targets are present, pure magnetic materials can combine with the target signal (modulate it) and so are not eliminated entirely. For example, if there is a layer of "black sand" (ferrite") and a hole where it is absent, and also a piece of gold in the hole, it may be possible that while the gold increases the detected signal, the dropout of the ferrite simultaneously down-modulates it and maybe cancels the signal. Just a hypothetical.

As you indicated, the detector will only make an audio beep if both SD1 and SD2 have positive outputs at the same time -- that is the logic.

Regards,

-SB

[habitbraker]

Thanks! Such explanations are very rare in internet, trust me

All this time I thought that magnetic materials introduce phase shift and conducive (eddy curr) introduce A changes. Guess I need to learn how exactly materials affect coil coupling. Could it be thougt like transformer?

About SD: So we dont set Disc Phase shifter exactly at zero and 90 degrees wih respect to RX siganal.
Instead of that for examle: lets Supose that RX quiscent phase shift is 0 deg(I know it isnt) with respect to TX. So if we set Disc at 10 deg with respect to TX, every shift which is below those 10 deg will make output negative. If more than 10 - positive

But isnt it mean that there need to bee some quiscent Amplitude otherwise purely resistive materials couldnt make any signal?

[simonbaker]

Thanks! Such explanations are very rare in internet, trust me

All this time I thought that magnetic materials introduce phase shift and conducive (eddy curr) introduce A changes. Guess I need to learn how exactly materials affect coil coupling. Could it be thougt like transformer?

About SD: So we dont set Disc Phase shifter exactly at zero and 90 degrees wih respect to RX siganal.
Instead of that for examle: lets Supose that RX quiscent phase shift is 0 deg(I know it isnt) with respect to TX. So if we set Disc at 10 deg with respect to TX, every shift which is below those 10 deg will make output negative. If more than 10 - positive

But isnt it mean that there need to bee some quiscent Amplitude otherwise purely resistive materials couldnt make any signal?

Yes, I think a transformer is a good model to start with. Imagine a transformer with a conductive core vs. a ferrite core. You can probably find some good explanations on this site of how different targets react to the magnetic field and how they interact with the search coils in terms of phase shift, etc.

Yes, I think you are understanding how the Disc setting works. You are also correct that signals of a certain phase will not make any signal in a particular SD channel. But generally our target signal phases are not near the quiescent signal phase, so we use the DISC control to select which targets we want, and we use the GB control to suppress modulation of the quiescent signal by magnetic materials in the ground.

Terminology: I think of a purely resistive material as the same as purely conductive material -- in other words, no "magnetic" properties. And all conductive materials (I think) will create a signal that has some phase shift relative to the "quiescent" signal.

Maybe you meant purely magnetic material, like ferrite, requires some quiescent amplitude to be detected. You are basically correct there I think. Because ferrite "amplitude modulates" any coupling between the TX and RX coils, you would need some signal there to be modulated by the ferrite for detection. Now generally, there always is some quiescent signal because we cannot perfectly "balance" the coils to eliminate it. But since we do not want to detect ferrite anyway (unless in all metal mode maybe), we try to adjust the GB pot so that even if we have some quiescent signal, we set the GB control pulse phase at 90 degrees to the quiescent signal to ignore it (or make it go negative).

If the GB pot is adjusted to "zero out" the quiescent signal, then conductive targets will be detected because they will have a phase different from the quiescent signal and such that the output is positive. This also means that we want to choose our quiescent signal phase so that it is not in the range of normal targets, but this seems to happen easily by nature.

I'm not giving a very good explanation here, but I think you have a pretty good idea of it. I would search this site for more explanations and maybe read some of the patents you see referred to.

Regards,

-SB