PI: negative capacitor instead of critical damping

[Teleno]

PI cols are usually designed as a compromise between inductcance and self-capacitance. Larger inductance (more turns) means increased sensitivity and depth. The drawback is increased self-capacitance which causes a longer damping decay hindering the detection of targets with faster time constants.


Imagine we could we just could pull a negative capacitance out of our toolbox and connect it in parallel with our Rx coil ... the self-capacitance of the coil would get cancelled and we would get a nearly ideal coil. Well, it's not science-fiction! a class of circuits called "Negative Impedance converters" (NIC) comes to our rescue.


The circuit I'm going to share today is one of those NICs. It only takes 8 generic transistors, two resistors and one capacitor that can be chosen to cancel the capacitance of our Rx coil.


This is the response of an underdamped 1200uH coil (blue) to a 5us target decay (red):




and this the response of the same coil connected to the negative capacitance (green):




The LTSpice simulation is attached.




Now you can relax those "fast" coil standards and increase number of turns at you hart's content to get at the deepest targets.

If someone cares to build it and test it please share your experience. I wish I had the time.

[Davor]

I'll see about your circuit later, but at the moment please note that the principle is already described in a lapsed patent US4443882 (so you may basically do whatever you like with negative capacitance), and - no surprise - an eye Candy - WO2013131133.

While it most certainly does as advertised, I'd check the noise as well, as the circuit - if applied to a monocoil - is an inexhaustible source of quality noise.

[Teleno]

I'll see about your circuit later, but at the moment please note that the principle is already described in a lapsed patent US4443882 (so you may basically do whatever you like with negative capacitance), and - no surprise - an eye Candy - WO2013131133.

While it most certainly does as advertised, I'd check the noise as well, as the circuit - if applied to a monocoil - is an inexhaustible source of quality noise.

I knew about the patent, however no practical circuit is provided so I had to dig my own.

The idea is to use it on a balanced Rx coil. Here's my simulation of noise, how bad is it?

[Davor]

I don't know. Relevant information is V(inoise) which you obtain by right clicking the plot window, chose "Add trace", and pick V(inoise). It is calculated as V(onoise)/gain per frequency.
In balanced Rx configuration it will not be affected by noise.

[Teleno]

Replacing Q3-Q8 by low signal MOSFET (2N7002 and Si1013) nd Q1, Q2 by 2N2369 the noise is one order of magnitude less.




Rx coil is 1,200uH - 560pF

Red: target voltage (1us tau).
Green: Rx coil voltage (negative C).
Blue: Rx coil voltage (critically damped).

[Davor]

Try V(inoise) instead. Or just add "gain" plot.

[Teleno]

Try V(inoise) instead. Or just add "gain" plot.

The cirtuit is not an amplifier, it just cancels the coil's capacitance. The smulation provides the noise level caused by the circuit at the ends of the coil. This noise will be imput to the eventual preamplifier (omitted). Unfortunately, this noise is the combination of the noises of the 6 bipolar transistors.

Is there a reason why a bipolar current mirror is so noisy? The contribution at the collectors of the BC547s or BC557s is a whoping 270nV/square(Hz) at 1MHz ... !

It seems MOSFETs cause less noise when used as current sources, so this might be the solution to the noise problem.

[Davor]

Because the signal source in Rx coil is induction voltage, you may always put a voltage source in series with a coil and see what happens with such signal afterwards. In this case you need to know what is the noise on the very coil, so I labelled the node "coil" to indicate it. You may observe the excess noise rising from about 10kHz exponentially. Reason for such phenomenon is positive feedback, and since there is no negative impedance without positive feedback - every such device is very noisy. Current sources are a minor problem.

Consequently the Candy patent turned bitter. Not every piece of patented junk ever gets real life embodiment.

This may work in induction balanced configuration where this noise is severely attenuated in Rx.

[Teleno]

Thanks for the comments, Davor.

If I click on the "coil" node, LT plots the noise there as "onoise". Isn't this the noise level at that node? I mean, if I plug this node into an amplifier, will that be the amplifier's inpout noise or not?

The MOSFET version looks much better:

[Davor]

At the node "coil" the signal gets attenuated with frequency due to inductance, and therefore it is not representative of the system noise. You may limit the frequency range to 100kHz or 300kHz in the plot window, as that would be a practical limit for PI, and see what is going on in more detail.
Now, if you consider 1nV/sqrt(Hz) to be a noise of a ~60 ohm resistor, and your coil's resistance is 12 ohm (0,4nV/sqrt(Hz)), it is clear that this circuit is very noisy. You might get a bit faster flyback, but at a cost of noise. One step forward, two steps back.

The way to obtain faster flyback with PI technology is by going low on coil inductance, or change technology altogether. Step voltage has no flyback.

[Teleno]

I'm using step voltage at the Tx coil, so flyback is not an issue. The Tx coil is always at a low impedance (self capacitance is short-circuited) and does not ring.

The issue is at the balanced Rx coil. In order to measure the Rx voltage it cannot be at low impedance, therefore it needs damping or else it would ring. Damping causes the Rx coil to decay on top of the target's signal, so you must wat till this decay is over before sampling. The delay cancels the advantage of the step voltage, because you can't sample as early as the Tx waveform theoretically would allow.

Another approach I'm trying is balanced Rx coil at low impedance. The target's signal is measured as a current rather than a voltage. Since the capacitance of the Rx coil is shorted, ringing does not occur and sampling can take place immediately. The problem is a slight imblalance between the Tx and Rx coils will shift the baseline of the signal, kind of a variably floating signal you need to chase. Something like this:

Tx: 150uH, 150pF
Rx: 1200uH, 560pF
Blue: Tx current.
Green: Rx current.

Balanced Rx coil:



Mismatch 1% :



Mismatch 10% :

[Davor]

For that particular reason you have EF to steer reference back to normal. In effect PI with EF is an auto-zero configuration, and that's only one of the advances lacking in VLF today.

Your reasoning is half correct. While you may expect ringing and you need to load Rx coil to prevent this, the extent of phenomenon is not nearly as pronounced as with monocoil. It goes like this:

Monocoil
- flyback jumps to ~400V and decays exponentially as determined by coil L / damping R
- it takes ~4us to reach levels below 100mV
- it takes another ~2us for op amp to regain consciousness
- earliest you can sample is ~7us

Induction balanced coil
- coils are balanced, and coupling factor is ~.001
- Tx goes to flyback and goes up to ~400V, but voltage at Rx reaches ~0.4V
- op amp is ready to deliver voltage for sampling almost immediately
- although Tx voltage is greatly reduced (together with Tx noise), the targets' voltage is received with basically the same voltage as with monocoil
- you may even use a significantly slower Rx coil (say, 4x Tx inductance) and still start sampling sooner than with a monocoil.

[Teleno]

Clear enough except for "EF", what does it stand for?

[Teleno]

Clear enough except for "EF", what does it stand for?

Ok I think it's "earth filed". Late samples can indeed used as the baseline. In the case of a shorted Rx the baseline is a decaying exponential with tau given by the coil's inductance ad resistance, so it's not constant as in EF.

[Davor]

It is not the only function of EF, but many people believe it is used only to compensate for voltages induced due to the Earth magnetic field, and vigorous swinging of the coil. In reality it also compensates any offsets from any other source, including 1/f noise. It therefore enables meaningful non-motion use. Again - no such thing in VLF.