Calculating integrator gain

[Carl-NC]

Calculating the total gain of a PI (or any circuit containing demods) is a little tricky due to the sampling integrator stage. Ferinstance, Hammerhead has a preamp gain of 1000, followed by the sampling integrator, followed by a final gain stage of 100. If you take the integrator stage at face value it seems to have a gain of 100, which would give an overall system gain of 10 million.

But the integrator samples and for most of the time it's 'off'. When the switch is turned on the cap charges with a first time constant (tau1) due to the input R and the feedback cap. When the switch is turned off the cap discharges with a second time constant (tau2) due to the feedback R and the feedback cap. The effective gain of this stage is (with a lot of hand-waving) therefore



where ton is the turn-on time and T is the overall period. As ton --> 0 the gain approaches 0, which is expected. As ton --> T the gain approaches R2/R1.

Example:

Let tau1=470us, tau2=47ms, T=1.67ms, and ton=10us. The effective gain is 0.6.

[bklein]

So is that good, or does it matter much?
Does increasing the gain here make the detector more sensitive or just take longer to get out of saturation on big hits.

[Carl-NC]

The actual gain of the sampling integrator is not very important. What matters is the integration response, which correlates real (target) signals and cancels random (noise) signals. I recently saw a YouTube video of a PI test where the integrator was obviously too slow, resulting in horrible response lags.

[bklein]

I'm not sure what is happening with some detectors I've tried (various technologies) where you hit a hot target or mineralized area and the detector's sensitivity is then greatly reduced for a noticable period of time. Problem is, you often don't realize it right away and could sweep right over a good target and miss it because the audio doesn't change. It's almost like we need a visual indicator of this base threshold amplitude and perhaps a quick reset button of some sort. Is this what you are describing seen in the video?

[hdphilip]

that's insteresting Carl,

I've been thinking about that, more so in using a adc chip.

correct me if I'm wrong, having an integrator with a high speed adc chip is important, what the trick would be is to figure the correct time constant. so it doesn't overlap each conversation cycle, but yet long enough to help cancel out out some noise.

too long of a time constant, no point in having a fast adc, too short, and you missing out on the noise reduction, true?


Philip

[mikebg]

200 years mankind has a powerful tool for analysis and design, which is called "Frequency domain". According to this tool, the Hammerhead is wideband metal detector.

According to the frequency domain, the title of this thread should be:
HOW TO DESIGN RX FOR WIDE BAND METAL DETECTOR.
The designer of Hammerhead accidentally discovered a preamp, which frequency response is matched to frequency spectrum of TX and to frequency responses of most targets.This is made by the capacitor C1 which "wrong" value is shown below. However the value is not wrong.
The amplification of this preamp is a frequency dependent function having cutoff frequency fc. The gain below fc is a constant depending on resistor values only. This LF region of amplifier is not important for our targets. The important frequency information for targets is above fc of preamp. The "wrong" value of C1 makes the system more effective. The efficiency of system TX-TGT-RX can help us to find answer of above question, but the question is not correct. The correct question in frequency domain is
HOW TO DESIGN A WIDE BAND METAL DETECTOR?

To find the answer, we should know frequency responses of different targets and of environment. I know the correct design procedure:
THE DESIGN OF A WIDE BAND METAL DETECTOR SHOULD START WITH TX, NOT WITH RX.

Let we start to revise and redesign TX of Hammerhead. Why RX should receive step-down response of a target?

[Carl-NC]

that's insteresting Carl,

I've been thinking about that, more so in using a adc chip.

correct me if I'm wrong, having an integrator with a high speed adc chip is important, what the trick would be is to figure the correct time constant. so it doesn't overlap each conversation cycle, but yet long enough to help cancel out out some noise.

too long of a time constant, no point in having a fast adc, too short, and you missing out on the noise reduction, true?

Philip

A sampling integrator effectively does a frequency translation, and the output is only a few Hz regardless of the pulse rate. So you can use a slow ADC for this. A fast ADC is needed if you want to direct-sample the preamp without the integrator, and do the integration in software. You get better control of the taus in software.

[Tepco]

where ton is the turn-on time and T is the overall period. As ton --> 0 the gain approaches 0, which is expected. As ton --> T the gain approaches R2/R1.

Example:

Let tau1=470us, tau2=47ms, T=1.67ms, and ton=10us. The effective gain is 0.6.

Exactly, making another advantage in detector design using short TX pulse and high repetition rate, reducing t on/T ratio and effectively increasing integrator gain, without any component value change. Plus few more:

Long TX period is not needed, anything above desired target response time (say 20-30uS) is just a waste of power. Coil peak current will vary proportionally to pulse width, but energy stored in coil will vary whit square, then 3 times shorter TX is 9 times less energy, detector can run on 9 times higher freq. keeping same current consumption, effectively achieving x3 more system gain.

Less energy, easier to get rid of it, smaller flyback pulse now can be below switch avalanche voltage, avoiding avalanche phase and speeding up coil response (recovery time). Also, less peak current means smaller, lower capacitance transistor can be used, speeding up things even more.

Whit detector running at say 5kHz or more, and input amp blanked all the time except for sampling so no saturation will occur, it can be AC coupled and high pass filtered to detector operating frequency to attenuate LF interference, etc. Just few useless ideas…Best regard

[Tinkerer]

Fast target response

The actual gain of the sampling integrator is not very important. What matters is the integration response, which correlates real (target) signals and cancels random (noise) signals. I recently saw a YouTube video of a PI test where the integrator was obviously too slow, resulting in horrible response lags.

Fast target response or slow target response.
Could we set some "thump rules" for that?

A good part of it depends on the sweep speed. If the sweep speed is the standard 1m/s, and the coil is 12" in diameter, then a response time of 100ms will show the target with a lag of about 4". This is still under the coil but offset quite a bit from the center.
Cris-crossing a few times helps us defining the exact location to dig.

If we use a 40" coil, this same target response time would seem quite good. However, we will not swing the 40" coil at 1m/s either, so the 4" lag in target response would be more like 2", very good for a coil of this size.

So I think we could use as a rule of thumb, a percentage of the coil diameter, let's say 10%-good, to 30%-bad, for the lag in distance.

Tinkerer

[Jose]

Hi Forum
Very interesting all the discussion.
Referring to the statement made by Tepco, test in some PI increasing rate, noting a decrease in sensitivity unless the pulse width is kept TX 100 usec. or more.
This translates into increased power consumption, I've tried in the Delta Pulse and the GS4 I'm finishing.
I would like to work for example in the GS4 with a repetition rate of 3000 Hz and keep consumption low, without sacrificing sensitivity, but the evidence suggests that this is not possible, please correct me if I'm wrong.
Another question I have is whether to modify the integration time, increasing the TX frequency.
I appreciate any clarification to my question.
thanks
Jose

[Tepco]

Some clarification is obviously needed for this “short pulse” trick. Just increasing operating frequency, keeping pulse width unchanged will increase sensitivity (more samples integrated) but current consumption will rise proportionally, so compromise is needed at some point. Short TX pulse is one, good for surf-like and similar detectors, intended for small targets, coin sized or smaller, jewelry, small gold etc. Anyway, short decay targets, so short TX is enough to excite them. On larger detectors, like delta etc, whit larger coils, intended to find larger objects (longer decay), too short pulses are ineffective and you will lose range (actually, short pulse detectors are less sensitive to larger objects, end range to large metal sheet or sensitivity to cola can is smaller compared to unmodified classic detector, just not intended for such targets). Even whit delta, some limit exist, in most cases anything above 150-200uS is waste of power too, except for barrel drum hunting and 1m loop. Best compromise is to keep not too excessive pulse width and increase freq. until power consumption is still reasonable.
I never modified GS4, but GS5 is already at 3.7kHz and unchanged, 100uS long pulse.

Integrator time constant define detector response time, no need to change it if you change frequency.

So, short pulse (20-30uS) high freq. as i described before works best for some target types, not good for some other, but in general, shortest pulse for given target and highest freq. limited by power consumption is the best compromise. (also, in any detector whit N type transistor, you can try something better than IRF740, for example Toshiba 2SK2611 is relatively cheap and available)

[Jose]

Tepco thank you very much for your extensive clarification.
Jose

[Altra]

Nice explanation Carl. Maybe you could do a similar analysis of the SD type
single capacitor integrator.

Tepco, as always you make some good points. But, I don't think you can just compare TX pulse widths without stating the switching voltage and coil inductance.

For instance an Eric Foster design, Tx 120us @ 12volts or a SD type running a TX of 240us at 6v? Then add the coil L/R to the equation?

Regards

[Davor]

According to the frequency domain, the title of this thread should be:
HOW TO DESIGN RX FOR WIDE BAND METAL DETECTOR

More or less. Target frequency responses (taus) are very finite, so bandwidth is not THAT excessive. At Tx you do have a short pulse which spreads nicely over a wide frequency spectrum, but by virtue of synchronised SAH-style Rx samples, you observe quite narrow band phenomena. Just like modern digital oscilloscopes do.
The only component here that is exposed to the full wrath of wideband signal is a preamp, and IMHO it must be optimised for gain bandwidth product, and not so much for noise.

[Tepco]

Tepco, as always you make some good points. But, I don't think you can just compare TX pulse widths without stating the switching voltage and coil inductance.

For instance an Eric Foster design, Tx 120us @ 12volts or a SD type running a TX of 240us at 6v? Then add the coil L/R to the equation?

Regards

Specifying just pulse width is not enough, coil inductance and voltage applied over pulse period define peak coil current and energy stored in coil magnetic field, number of turns define field straight and target induced voltage.

However, target response time relative to pulse width is fixed, no matter what type of coil or voltage is used. To fully excite target, minimal pulse width comparable to decay time is needed. Small and conductive “fast” target will have fast decay curve, but short pulse will excite it fully, longer pulse is now waste of power. Larger and\or less conductive target will have longer decay, but longer time is needed for excitation (eddy current to reach certain value, L/R ratio), short pulse now will be waste of range! Just good compromise is needed for given situation.