VDI-RODERICO

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to show that you can have a good approximation of the atan(x) with the log(x) the U206-C more or less adds and offset (vdi center) and some kind of log so at the end you might have something like log(log(x/y)+offset) at pin 8 and then you can compare both atan(x) and log(x) and see how different they are (attached figure), in principle, there is no clear advantage in implementing this over the atan(x) in software, however, IMO the advantage here is that you do not need a microcontroller and the hardware implementation is always faster than that of the software

Well that's close enough. So you're saying that adding an offset allows a compensation factor to be applied that would approximate the atan function. And I thought that was just to centre the needle above the zero start point of the scale. ( like when measuring ohms on an old analog meter.) Shows how much I know.

Well if you don't mind staring at a bouncing needle for hours, then I guess it's good, but still there are so many parts when you have to include the meter update logic circuitry etc. with a micro, the parts count is smaller I guess, but the power demands are greater.
VDI numbers are only advantageous if the resolution is good and the x and y sources are accurate and stable with low noise.

Perhaps processing a log amp output allows some saving of resources or a lower bit count. I don't know.

[roderico]

to show that you can have a good approximation of the atan(x) with the log(x) the U206-C more or less adds and offset (vdi center) and some kind of log so at the end you might have something like log(log(x/y)+offset) at pin 8 and then you can compare both atan(x) and log(x) and see how different they are (attached figure), in principle, there is no clear advantage in implementing this over the atan(x) in software, however, IMO the advantage here is that you do not need a microcontroller and the hardware implementation is always faster than that of the software

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Something is complicated here ... Maybe everything is easier? Here .. such an amplifier was used in the Russian forum ..[ATTACH]48928[/ATTACH]

That's just some sort of active pass filters and gain stages, for both X and Y. Nothing spectacular there. Are there any more parts of the circuit?

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when x and y have the same sign the ratio x/y is positive and the vdi can be projected into the 1st quadrant (0,90), however, when x and y have different sign, I guess the other part of the circuit somehow has to invert the sign for the log to work (i.e. x/y > 0) and move the needle in the opposite direction, waltr?s ltspice simulation would help to understand how this circuit works

I'm afraid my math skills go through low pass filter(they cut off at extremely low level)
I think that the outputs of both log amps are both negative voltages. Such that differencing them stills end up being negative (Log(X) being always larger negative than Log(y) ), only to be inverted by the final stage after the difference amp. So the resultant ratio is always algebraically positive.

[roderico]

Something is complicated here ... Maybe everything is easier? Here .. such an amplifier was used in the Russian forum ..[ATTACH]48928[/ATTACH]

this could be tested directly with the current firmware and it would be interesting to see how it compares with the current version

[roderico]

Atan2(x,y) gives the quadrature angle in radians, I can grasp this. But not sure of the Log transfer function. Maybe the analog meter just can only give rough "groupings" of VDI indications. In other words, there will be parts of the meter display where the needle will never settle.
A silver dollar causes the meter to deflect almost full scale. And gold shows up as gold. So the meter works good.

when x and y have the same sign the ratio x/y is positive and the vdi can be projected into the 1st quadrant (0,90), however, when x and y have different sign, I guess the other part of the circuit somehow has to invert the sign for the log to work (i.e. x/y > 0) and move the needle in the opposite direction, waltr?s ltspice simulation would help to understand how this circuit works

[SWL]

Something is complicated here ... Maybe everything is easier? Here .. such an amplifier was used in the Russian forum ..

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Atan2(x,y) gives the quadrature angle in radians, I can grasp this. But not sure of the Log transfer function. Maybe the analog meter just can only give rough "groupings" of VDI indications. In other words, there will be parts of the meter display where the needle will never settle.
A silver dollar causes the meter to deflect almost full scale. And gold shows up as gold. So the meter works good.

[roderico]

this looks to me a hardware implementation to extract a vdi, where log amps are used to transform multiplications and divisions to sums and differences, the pic extract a vdi basically as atan2(x/y) where x/y = tan(phi) and phi is the phase difference, I'm just guessing but up to pin 7 U206 we have log(x/y), a hardware implementation of atan2 might not be simple but log(x/y) can overlap atan function in some region of interest

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Log amps are interesting and can be kind of 'mind blowing' when digging into the math.
dbanner,
The simple schematic you posted is a good basic log amp circuit. The reason for the two amps is to correct for thermal variation in the bi-polar transistors and to be able to Set an input current (V to I) range.
Attached is a good article on how and why.
The White's circuit in the US4783630 patent is very interesting. The Meter seems to indicate VDI.
I have been looking at it and plan to run it in LTSpice.

I noticed that the transistors used in the whites patent are matched pair in single package. The meter does indeed display good VDI readings, but whether the (1mA) meter is acting as a log meter or lin meter is not clear to me. Another interesting aspect is the compressing of the signals in the log transfer function. This might supposedly give a better and more stable and accurate VDI readings (meter resolution) on the said meter. I assume this is not necessary if using a Micro.
The analog meter might be replaced by LM3914 or is it the LM3915 in single dot LED mode, one of those is a logarithmic display driver, can't remember which one. But perhaps you could drive one of these directly after the differencing amplifier. The math would determine the the correct implementation.

[waltr]

Log amps are interesting and can be kind of 'mind blowing' when digging into the math.
dbanner,
The simple schematic you posted is a good basic log amp circuit. The reason for the two amps is to correct for thermal variation in the bi-polar transistors and to be able to Set an input current (V to I) range.
Attached is a good article on how and why.

The White's circuit in the US4783630 patent is very interesting. The Meter seems to indicate VDI.
I have been looking at it and plan to run it in LTSpice.

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Well there is what appears to be an antilog amplifier?? after the differencing amp.(whites log amp and meter VDI circuit). So there is some math going on here all the way through. A series resistor at the inputs to the log amps (voltage input device) converts to a proportional current. These are current sinking (NPN) log amps.

[roderico]

all this can be done by software if we know the exact algorithm, the differential amplifier would compute the difference of the log amps, i.e. except from constants, log x - log y = log (x/y), do they use just log(x/y) as a vdi?

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Here is the exact same circuit topology I found in an article. Perhaps all the software needs is a good ratiometric table for referencing the signals. I know little on this topic, so please forgive the shallow explanations.

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You are correct. The output of the x and y log amps outputs (Vout1 and Vout2) are fed to a difference amplifier with a gain of 10. I am not expert here. But I assume one can replicate the mathematical functions in the software.
There is something referred to as logarithmic-ratiometric ("log-ratio"). Compressing the signals seems to offer some benefit in terms of precision. The DC log amp transfer function seems to be very good for this task(VDI measurements). There are even chips (max4206) which are dedicated to this purpose.