Designing an Integrator circuit

[moodz]

Transfer Function: The Laplace transform of an integrator is given by 1/s.
A typical low-pass filter (e.g., an RC filter) has a transfer function of 1/(1 + sRC), where R is the resistance and C is the capacitance.

DC Behavior:
An ideal integrator has infinite gain at DC (s=0), meaning a constant input signal results in a linearly increasing output.
Integrators have infinite DC gain, while low-pass filters typically have a gain of 1 at DC.

Low-pass filters have a flat response at low frequencies, unlike integrators which have increasing gain at low frequencies.


IMHO you cant beat an ADC and digital precision ...

in code :

begin
if INTEGRATION_TIME < INTEGRATION_PERIOD then
SIGMA = SIGMA + ADC_SAMPLE
INTEGRATION_TIME = INTEGRATION_TIME + 1
else
SIGMA = ADC_SAMPLE
INTEGRATION_TIME = 0
end if
loop


There is a simpler way even ...

[cristiano.sar]

Is it a good idea to have a switch to immediately discharge an integrator capacitor after the sampling time (ex.: a 10uS sample width)? Does this make any difference in performance or is not useful at all?

[green]

A test. Target, three layers 1x1inch aluminum foil swinging from a pendulum 10 inches above coil. Varied swing distance to see the effect speed had on signal strength. 200mm coil. Target is glued to center of a 200mm disk to cover photo cell(centered over coil about .4inches below disk) when the target is over the coil. Sweep speed, meters/sec=.2meters/cover time(sec). Target at edge, signal about half target centered.

[Qiaozhi]

When I joined this site to learn about detectors I had a problem with the circuit being called an integrator. For me integration had a time function, integrate velocity you get distance. Output continues to change if input isn't zero. DeBoo integrator looks like a true integrator to me. The ones we are using with our detectors look like low pass filters(they average). bbsailor calls it a lock in amplifier. Could someone explain why we call it an integrator.

Any dc offset at the input will cause the output of an ideal integrator to increase until eventually it hits the power rail and gets stuck. In a practical integrator (like the one's we use in our PI detectors) there is a resistor placed across the feedback capacitor to prevent integration of the dc input. This works because the impedance of the capacitor is extremely high at dc, and the feedback resistor is dominant. The reverse is true at high frequencies.

[green]

Do not forget about the DeBoo single supply, non-inverting integrator.

https://www.maximintegrated.com/en/a...ex.mvp/id/1155

When I joined this site to learn about detectors I had a problem with the circuit being called an integrator. For me integration had a time function, integrate velocity you get distance. Output continues to change if input isn't zero. DeBoo integrator looks like a true integrator to me. The ones we are using with our detectors look like low pass filters(they average). bbsailor calls it a lock in amplifier. Could someone explain why we call it an integrator.

[Teleno]

Do not forget about the DeBoo single supply, non-inverting integrator.

https://www.maximintegrated.com/en/a...ex.mvp/id/1155

[green]

Hello Green,

Thank you for your tips!

Yes, I have solved the problem But none the wiser

I do routinely put in ceramic decoupling caps where they should be.
I removed C7, no change.
Removed C6, no change.
Removed R16 ... Bingo ... Oscillation gone.

R16 was "jumpy" when measuring the resistance.

Put in a new one. It now works. Dunno what was going on inside that somehow defective resistor.

Thanks. Don't have a guess why R16 could cause the problem. Maybe someone that knows could enlighten us.

[Polymer]

Hi polymer
Wondering if you solved the oscillation on pin 7 of the LM358. Couple things to try, add a .1uf ceramic on the power pins 4 and 8 to common, remove the 1uf capacitor on the output to see if the oscillation changes. Haven't played with a Surf PI, just curious why the oscillation.

Hello Green,

Thank you for your tips!

Yes, I have solved the problem But none the wiser

I do routinely put in ceramic decoupling caps where they should be.
I removed C7, no change.
Removed C6, no change.
Removed R16 ... Bingo ... Oscillation gone.

R16 was "jumpy" when measuring the resistance.

Put in a new one. It now works. Dunno what was going on inside that somehow defective resistor.

[green]

Hi polymer
Wondering if you solved the oscillation on pin 7 of the LM358. Couple things to try, add a .1uf ceramic on the power pins 4 and 8 to common, remove the 1uf capacitor on the output to see if the oscillation changes. Haven't played with a Surf PI, just curious why the oscillation.

[green]

Joseph, thank you very much for your reply.

I have read a lot about lock in amplifiers since your post. My head is still spinning ...
Some time will be needed to catch up and make experiences hands on.

I ran into a problem with just that - experimenting.
Hope this is the right place to post this.

I replaced the 1M resistor at the front end (5534) with a 100k resistor.
So far so good. Less sensitivity, but much less noise.
Changed the resistor at the output stage U3A LM359 from 100k to 330k
and the capacitor from 100nF to 33nF.

I cannot adjust threshhold anymore and have substituted the 33nF with 22nF, 47nF.
Nothing changes.
Something seems amiss further upstream looking at Pin 7 of LM358.
The inputs/outputs of 4093 & 4066 appear to be working fine.
I have substituted all IC's and I still have the same problem.

Here is the oscilloscope picture (Pin7 LM358, Pin2 4066, Pin4 LM358 and Pin6 5534 as reference)
[ATTACH]40662[/ATTACH]

I will later be getting back to the following you so kindly mention:

"For or those interested, you can easily see low lock in amplifier theory can be applied to pulse induction integration but pay attention to:
1. Full stimulation of your target based on its time constant.
2. Lowest delay you can achieve.
3. Optimum coil size for target.
4. Sweep speed to optimize the number of RX samples being integrate.
5. Maximum PPS rate you can operate at for your desired targets while fully stimulating them.

I hope this adds a new perspective on integration."

OH YES IT DOES - it's filtering through my synapses ... with not too much discrimination I hope ...

With kind regards, Polymer

I think you shouldn't see the oscillation on pin 7 of the LM358. Trying to drive a capacitance load can cause an OP amp to oscillate. Don't see one on the schematic. Driving a length of coax can be enough capacitance.

[Polymer]

Joseph, thank you very much for your reply.

I have read a lot about lock in amplifiers since your post. My head is still spinning ...
Some time will be needed to catch up and make experiences hands on.

I ran into a problem with just that - experimenting.
Hope this is the right place to post this.

I replaced the 1M resistor at the front end (5534) with a 100k resistor.
So far so good. Less sensitivity, but much less noise.
Changed the resistor at the output stage U3A LM359 from 100k to 330k
and the capacitor from 100nF to 33nF.

I cannot adjust threshhold anymore and have substituted the 33nF with 22nF, 47nF.
Nothing changes.
Something seems amiss further upstream looking at Pin 7 of LM358.
The inputs/outputs of 4093 & 4066 appear to be working fine.
I have substituted all IC's and I still have the same problem.

Here is the oscilloscope picture (Pin7 LM358, Pin2 4066, Pin4 LM358 and Pin6 5534 as reference)


I will later be getting back to the following you so kindly mention:

"For or those interested, you can easily see low lock in amplifier theory can be applied to pulse induction integration but pay attention to:
1. Full stimulation of your target based on its time constant.
2. Lowest delay you can achieve.
3. Optimum coil size for target.
4. Sweep speed to optimize the number of RX samples being integrate.
5. Maximum PPS rate you can operate at for your desired targets while fully stimulating them.

I hope this adds a new perspective on integration."

OH YES IT DOES - it's filtering through my synapses ... with not too much discrimination I hope ...

With kind regards, Polymer

[bbsailor]

Well, I suggested you post this question and then I forgot to answer!

The purpose of the integrator is to constructively add successive positive samples (resulting from a target) while averaging out everything else. That is, random noise (which is both positive and negative) will average to zero. So the integrator needs to have a charge rate that is fast enough (compared to the sample rate) to build up a signal, and a discharge rate that will get rid of the signal fairly quickly one the target is gone, so you don't get an audio response long past the target.

So let's make up some numbers. Sample rate is 1kHz, so sample period is 1ms. Sample width is 10us or 1%. Let's say a weak target signal from the preamp is 10mV. A single sweep of the coil takes 1 second.

We get 1000 pulses per swing, so as we go over a target we might get 10-20 positive samples. Let's say exactly 10. Without an integrator, this would result in 10 samples that are 10mV high with a 1% duty cycle.
This is a time-averaged signal of 100uV and probably will never trigger the audio.

Let's say we use a single-ended integrator shown below; R1=1k, R2=100k, C1=0.1uF. When the switch is closed vin (=10mV) is converted to a 10uA current (i1) by R1 and charges the cap. dv/dt = i/C1 which gives 10uA/0.1uF = 100V/s, so in 10us the cap charges up by a whopping 1mV. Wow, a whole millivolt? Yup.

When the switch opens the integrator is left with R2 discharging C1, at a time constant τ = R2*C1 = 10ms. We have 990us of discharge time (sample switch open) so the signal drops to e^(-990us/10ms) = 90% of whatever the sampled value is. So when the switch is closed, the cap charges by 1mV, and when the switch is open the cap discharges by 10%.

We assumed a 10mV signal for 10 samples, so at the end of each of the 10 samples we have:

1: 1.00mV
2: 1.90mV
3: 2.71mV
4: 3.44mV
5: 4.10mV
6: 4.68mV
7: 5.22mV
8: 5.69mV
9: 6.12mV
10: 6.51mV

6.5mV doesn't sound like much, but it's 65 times better than the average 100uV without the integrator. And the integrator is usually followed by a gain stage so if it has a gain of 100 (e.g., HH) then the final voltage applied to the audio is 650mV. That's much better.

Finally, when there is no more target signal, the integrator cap will discharge in about 3τ (95%) so a time constant of 10ms means the integrator output dies off in about 30ms.

- Carl

If anyone wants to learn more about pulse induction RX signal integration, look up the following phrase "lock in amplifier theory".You should see links to many PDF files from equipment manufactures and universities explaining how lock in amplifiers extract signals buried in noise. What Carl has explained above gets into the theory about how a lock-in amplifier works and how similar it is to what happens when you can integrate many RX signals when searching for very small or very deep targets.

The key number is how many samples are being integrated while the targe in within the coil area. This translates into coil size, sweep speed and the pulse rate of the TX pulse. Eric Foster would integrate many signals in his 3000PPS PI machines and integrate from 500 to 1500 RX signals to improve the RX sensitivity rather than putting more power into the TX signal.

Short TX pulses are optimum for small low TC targets and allows earlier sampling to detect at 10 us or earlier on small gold targets. By integrating many samples target signals can be extracted from the noise.

For or those interested, you can easily see low lock in amplifier theory can be applied to pulse induction integration but pay attention to:
1. Full stimulation of your target based on its time constant.
2. Lowest delay you can achieve.
3. Optimum coil size for target.
4. Sweep speed to optimize the number of RX samples being integrate.
5. Maximum PPS rate you can operate at for your desired targets while fully stimulating them.

I hope this adds a new perspective on integration.

Joseph J. Rogowski

[Polymer]

I have been playing with the Surf Pi shifting high gains from the 5534 to the back
and running into problems with the integrators.
Thought I could find a formula for calculating matching R's & C's. Didn't happen.

Finally found this thread.

The replies here have made my day!

I have a good picture in my minds eye now of how they work.
My soldering iron is firing up ...

A BIG Thank you!

Cheers

[Alexismex]

Hello Carl,
you are a very good teacher, thank you for this best and precise explanation ,
also the quality of the condo is very important
sludos
alexis

[1843]

Thank you!

Hi Carl,
Thank you very much! Your explanation is excellent!
Best Regards