Coil resistance

[Sergey_P]

The RX resistance matters very little.

The electromagnetic characteristic that distinguishes one substance from another is phase. If the phase of the detector's receiver impedance is indistinguishable from the phase of the surrounding soil impedance, they have no effect on each other. To reduce phase noise in the detector's receiver when searching on the ground, it is necessary to approximate the phase of the detector's receiver impedance with the phase of the surrounding soil impedance. In this case, the coil resistance plays a significant role.

[Carl-NC]

The electromagnetic characteristic that distinguishes one substance from another is phase. If the phase of the detector's receiver impedance is indistinguishable from the phase of the surrounding soil impedance, they have no effect on each other. To reduce phase noise in the detector's receiver when searching on the ground, it is necessary to approximate the phase of the detector's receiver impedance with the phase of the surrounding soil impedance. In this case, the coil resistance plays a significant role.

You'll have to explain more because I don't understand. In a circuit where the RX coil is loaded by a simple resistor (say, 10k) then the phase shift of the RX coil is practically zero even with a coil resistance of, say, 100Ω. Even if you lowered the load resistance enough to create a phase error, it would still be reasonably constant and would simply be removed by the ground balance calibration, along with the phase shift of the preamp.

Ground permeability can cause a shift in the inductance value but it is typically a very slight change and, for a resistively loaded RX coil, still won't make any difference. The IDX RX coil is capacitively loaded but I assume it is set considerably off-resonance of the TX frequency precisely to avoid issues with the Q causing variations in the phase shift. In the end, I can see how the RX coil resistance can matter where the RX coil is resonated at the TX frequency, but otherwise not so much.

[Sergey_P]

Ground permeability can cause a shift in the inductance value but it is typically a very slight change and, for a resistively loaded RX coil, still won't make any difference.

The detector measures two parameters simultaneously: amplitude and phase. Changing the sensor's impedance in the presence of soil changes the measured values simply by changing the distance to the ground surface. This introduces additional noise, reducing target sensitivity.
To reduce noise in the presence of soil, the sensor's impedance must be phase- and impedance-matched to the ground.
The transmitter (TX) is phase-matched, and its active resistance is selected based on the required magnitude of the generated field. A non-resonant LR oscillator or a detuned LRC oscillator with external excitation is used (an extreme case is a low-Q oscillator).
The receiver (RX) is phase-matched, and its active resistance is selected based on the conductivity of the surrounding soil in the search field. (An example calculation for the sensor described above is shown in the image.)

[Carl-NC]

Sergey_P, I've moved this to a new topic because I'd like to discuss it more in-depth. What you are saying (especially in your last post) goes against everything I've understood about the effects of coil impedance. I'd like to start with the TX coil:

The transmitter (TX) is phase-matched, and its active resistance is selected based on the required magnitude of the generated field. A non-resonant LR oscillator or a detuned LRC oscillator with external excitation is used (an extreme case is a low-Q oscillator).

The best TX coil is an ideal inductor (R_TX = 0) such that the TX drive voltage and TX current are exactly 90° apart. That way the phase reference for the demod clocks has no error due to wire resistance that might change with temperature. It also minimizes power loss. The high Q may result in phase noise but if the demod phase rotators are reasonably fast then the demods will track the TX phase and it should not matter much.

But we never have R_TX = 0, there is always some wire resistance and the design trade-off is between the resistance and the weight of the coil. I have never seen anyone use TX resistance as a way to control the magnitude of the generated field -- that is done with the power supply. Intentionally adding resistance just wastes power.

The receiver (RX) is phase-matched, and its active resistance is selected based on the conductivity of the surrounding soil in the search field. (An example calculation for the sensor described above is shown in the image.)

On the RX side, I agree that RX coil resistance creates thermal noise which is detrimental. But 50Ω adds less than 1nV/rtHz which is lower than most of the preamps used in VLF designs. The effect of RX-R on the phase depends on whether the coil is loaded with a simple resistor, parallel resonated with a cap (either on-resonance or off-resonance), or is series resonated. As long as the self-resonant frequency of the coil is well above the operating frequency, the only situation I see where the series resistance makes any difference is for parallel on-resonance. Again, I've never heard of anyone designing the RX coil to match the ground's loss angle. Finally, the example calculation is for a series RLC circuit, so I don't understand the relationship.

[Sergey_P]

Hi Carl-NC
As the coil approaches the ground surface, additional losses occur due to ground conductivity, and the phase shift changes due to the introduction of additional resistance into the coil. To maintain phase stability, the coil's phase shift must be matched to the ground phase.
"A high Q value can lead to phase noise, but if the demodulator's phase rotators are fast enough, the demodulators will track the transmitter's phase, and this shouldn't be a significant problem."
...and we'll lose the target signal...
"The design tradeoff is between coil resistance and weight."
There are no tradeoffs. Coil parameters are determined based on the availability of an existing power supply, excitation method, required field strength, Q factor, frequency, and dimensions.
"Again, I've never heard of anyone designing a receive coil taking the ground loss angle into account."
...explained above...
"Finally, the calculation example is given for a series RLC circuit, so I don't understand the relationship."
We don't have a separate EMF source feeding the parallel oscillatory circuit through the source resistance. The EMF is generated within the oscillatory circuit, and the current flows sequentially through all the elements of the RLC circuit, meaning we have a classic series oscillatory circuit.

[moodz]

Sergey's claim, stated plainly: the ground presents a complex impedance with a particular loss angle; you should design the RX coil so its own impedance phase approximates that angle, and then ground effects on the coil are suppressed. Carl's position: coil series resistance has almost no effect on RX phase for a resistively-loaded or off-resonance coil, any fixed phase error is absorbed by ground balance anyway, and the only case where R_RX really bites is a coil resonated at the operating frequency.

Carl is right on the physics, but he dismisses the one sub-point where Sergey is correct, and Sergey is describing a real design constraint under a wrong mechanism.

The matching argument doesn't survive scrutiny

Two impedances sharing an argument does not decouple them. There's no theorem behind it — it's an analogy borrowed from transmission-line matching, where phase-matching means something specific and entirely different. The physical quantity that matters is the reflected impedance ΔZ that ground loading adds to the coil, roughly jωM²/Z_g for the conductive part plus the χ' − jχ'' viscous term that actually dominates at VLF. ΔZ is set by coil geometry, frequency and ground properties. It is not a function of the coil's own R_coil. You cannot make the ground's contribution smaller by changing your series resistance; you can only change how ΔZ maps into output voltage. That mapping is R-sensitive only when the coil sits in a high-Q resonance — which is exactly Carl's carve-out, and exactly the circuit Sergey's calculator depicts.

The deeper point Sergey misses: ground balance works precisely because the ground vector's phase is stable while its magnitude varies with height. Néel relaxation over a log-uniform barrier distribution gives a near-constant loss tangent across the VLF band, so the ground signal traces a fixed direction in the demodulated plane and can be nulled by rotation. Height changes move you along that vector, not off it. Residual "phase noise" on real ground comes from a second, differently-phased component — salt conductivity, mixed mineralogy, hot rocks — which is a two-vector problem requiring a second measurement, not a coil-resistance problem.

Where Sergey is right and Carl is too quick

Post #5's rebuttal on the series-versus-parallel objection is correct. When the EMF is induced in the winding itself rather than injected from an external source through a source impedance, the loop is a series RLC — L, R_coil and C carry the same current. The "parallel-resonant RX coil" is the same circuit seen from the capacitor terminals; the familiar result that terminal voltage equals Q times the induced EMF is derived from exactly the series analysis his calculator performs, with Q = (1/R)√(L/C). Carl's "it's a series circuit, I don't see the relationship" isn't a good objection — and it's slightly awkward given he'd already conceded parallel-on-resonance as the exception, which is the same case.

So both men agree that R matters at resonance and hardly anywhere else. They've argued past each other about why.

The TX exchange

Carl is right that R_TX = 0 is the ideal — clean 90° between drive voltage and current, no copper tempco walking the demod reference (0.39%/K on R, which is only a phase error to the extent R is comparable to ωL), and no wasted power. He's also right that there is a genuine trade between resistance and coil weight, and Sergey's "there are no trade-offs" is a dodge: once you fix supply, field strength, Q, frequency and diameter, wire gauge is precisely the remaining free variable, and copper mass versus loss is precisely the trade.

But Sergey's "R selected for required field magnitude" is coherent for one topology — a series-resonant TX driven from a fixed voltage, where at resonance the reactances cancel and I = V/R exactly. That's a standard way to set ampere-turns. The trouble is he explicitly specifies non-resonant LR or detuned LRC in the same sentence, where current is set by ωL and R does almost nothing. His statement is internally inconsistent rather than wrong.

Numbers

Carl's noise figure checks: √(4kTR) at 50 Ω, 293 K is 0.90 nV/√Hz, below any realistic VLF preamp. Worth adding that in a resonant RX, coil thermal noise is multiplied by Q alongside the signal, so raising Q improves SNR against preamp noise until coil noise dominates — R matters for noise only in relation to what follows it. And ground loss does add a real resistive component to the coil, which is thermal-noise-generating in the antenna-noise sense; at VLF conductivities it's negligible against copper R, but it's the one place Sergey's instinct about ground and resistance touches something real.

The test that would settle it

Sweep the coil on an impedance analyser at the operating frequency, at several heights over mineralised ground, and plot ΔZ in the complex plane. Then add a series resistor and repeat. If Sergey is right, the ΔZ locus should shrink or rotate toward the added-R condition. It won't — the locus is invariant, and only the operating point moves.

[Sergey_P]

Some MD4U forum members who have assembled coils using ground phase matching technology have reported quieter detector operation near the ground without loss of range, as well as a slight increase in range at a lower sensitivity threshold, which is, of course, subjective.
"Hot rocks" and phase shifts on buried objects in the direction of the ground phase are related to the method of ignoring the ground signal based on the phase at the outputs of correlation accumulators (demodulators) and are unrelated to the issue of detector stability near the ground surface. There are other methods for eliminating the ground signal...

[Carl-NC]

Good info, Paul. I'm not trying to argue for or against anything, I'm trying to figure out what Sergey is saying and to see if I've missed something here. I still don't understand his point.

On the TX side

The field generated by the TX current is the reference phase for the whole system; everything follows that, so there is nothing on the TX side to match to ground. The TX coil creates a magnetic field and the ground responds to that field; the ground response is a largely in-phase signal with a small (~0°-10°) loss angle. Again, you cannot compensate for this in the TX coil, it is what it is.

I agree that in a series-resonant coil driven with a low-R voltage signal the peak current is limited by the R_TX, but in VLF I cannot think of anyone who drives the TX coil this way. The only designs I can think of with a series-resonated TX coil is in the MXT/F75, but the series LC is part of a series-parallel boost circuit driven by a current source signal. Here, the R_TX makes less of a difference; for example, doubling the R_TX in the F75 cuts TX current by about 5%. I have used a voltage driven series-resonated TX coil in the half-sine work I did and, yes, in that case R_TX was much more critical for peak TX current. But even then, it doesn't change the phase relationship between the TX field and ground.

What can change in the TX-vs-ground equation is the proximity effect that soil permeability has on L_TX. As you lower the coil, L_TX increases slightly (but R_TX stays the same) and alters the phase of the TX voltage which is commonly used to drive the demod clocks. This can increase ground noise as you vary the height of the coil over ground. The solution is always to minimize R_TX towards zero. No value is better than zero.

On the RX side

This is more complicated, because of the myriad ways people load the RX coil. You have

1. High impedance (just opamp capacitance)
2. Parallel resistor (plus parasitic capacitance)
3. Parallel capacitor, off-resonant
4. Parallel capacitor, on-resonant
5. Series capacitor, off-resonant
6. Series capacitor, on-resonant

The first three are common and #5 shows up in some Dave Johnson designs. In all cases the R_RX creates thermal noise so that is always a consideration. We typically model the RX coil like this:

which seems to be a series RLC but in reality that is only true for case #1 above; in the other cases it is a series-parallel circuit like this:

And for case #1, assuming we are running well below the SRF of the RX coil, the R_RX makes almost no difference in either amplitude or phase because the Z(C_RX) is so high, typically >100k.

Case #2 is about as easy; with, say, a 10k load resistor the R_RX can be quite large and still not affect phase, although it does start to attenuate the RX signal. Still assuming SRF >> f_TX.

The other cases vary depending on how far from resonance it is, but generally the R_RX affects Q and can cause phase shifting and attenuation. The Dave Johnson series off-resonant designs (F75/T2/etc) include a series 5k resistor so it is already de-Q'd and just about any RX_R will work the same way. In all cases, the phase shift has a static component and a temperature-dependent drift; the static part is removed by the ground balance circuit while the drift can be a problem unless you have ground tracking. This brings up a thought...

Ground Balance

The R_TX causes a slight increase in the TX voltage phase. It is possible to design the RX coil circuitry (including the R_RX) so that it has an identical phase shift such that a perfect ferrite (phase = 0) is balanced. But real ground usually has a slightly higher loss angle, so I'm now wondering if the detectors that use this "coil-ground matching" technique are those with a fixed ground balance, and the coil resistances are being manipulated to effectively ground balance the detector.

[pito]

[QUOTE=Carl-NC;
a small (~0°-10°) loss angle.[/QUOTE]

[pito]

magmitude

[getsa]

Something more practical:

2 cases - same result (supposedly)...
- 58-turn coil + 220nf cap= 8kHz
- 45-turn coil + 330 nf cap= 8kHz.

Which variant would be more effective/efficient, and why?

Greetings

[Smirnov-Arta]

Something more practical:
...

Forget about the number of turns. There is only the final inductance—nothing else! Those 45 or 58 turns will yield different inductance values depending on the diameter. Even with the same number of turns (say, 45) on the same diameter, the winding method alone can result in a significant difference in inductance. So, I repeat: forget about the turns. Things will become much clearer to you then. And that is without even touching upon the circuit's Q-factor.

[Sergey_P]

a perfect ferrite (phase = 0)

Ferrite is a virtually ideal inductor L with a phase of approximately 90°.
The phase component of soil is approximately 84–87°. Depending on the moisture content, the resistivity varies from 10 to 150 ohms/m, causing a phase shift.
A thin, shorted wire ring is used as a reference for measuring the zero phase, as is done by geophysicists.

[Carl-NC]

Ferrite is a virtually ideal inductor L with a phase of approximately 90°.
The phase component of soil is approximately 84–87°. Depending on the moisture content, the resistivity varies from 10 to 150 ohms/m, causing a phase shift.
A thin, shorted wire ring is used as a reference for measuring the zero phase, as is done by geophysicists.

If you are looking at the magnetic fields, then perfect ferrite is 0°; the B-H curve has no gap so it distorts the magnetic field but causes no delay. If you are looking at the induced voltage on the RX coil, then ferrite is -90°.
A thin shorted ring produces a 90° magnetic phase shift, or a 0° phase shift in the induced RX coil voltage.
Heavy pure silver (Atocha bar) produces a 180° magnetic phase shift, or a 90° phase shift in the induced RX coil voltage.

Here is how to look at it using the TX magnetic field as the reference:

Here it is when using the TX drive voltage as the reference:

[Carl-NC]

Something more practical:

2 cases - same result (supposedly)...
- 58-turn coil + 220nf cap= 8kHz
- 45-turn coil + 330 nf cap= 8kHz.

Which variant would be more effective/efficient, and why?

Forget about the number of turns. There is only the final inductance—nothing else!

If you are designing a new metal detector and do not have to be compatible with an existing coil, then this is a valid question. I assume this is for the TX coil; in one case you have 1.2mH and the other is 1.8mH. Probably you won't see much difference, but for a constant voltage drive the lower inductance will produce a slightly higher ampere-turns, which is what really matters on the TX side.