Why are TX and RX coils in many VLF IB designs not tuned to the same frequency?

[searchbear]

There is a fundamental question that I haven't been able to answer so far: Why are there so many designs in which the TX coild and RX coil aren't tuned to the same frequency? For example Tesoro double D: TX: 14.5 kHz RX: 16.1 kHz. Why is that? The phase shift created by metal objects could be detected by a coil with the same frequency as long as the Q-factor isn't too high (which it won't, ever). Is the idea to create an intentional directional phase pre-shift?

[waltr]

Very good question.
I just went back over chapters 9 & 10 in the ITMD 2nd edition and this question is not answered.
Carl is working on the 4th edition so hope he addresses this.

My take from building a TGSL and several coils is this difference is resonance controls what the amplitude changes and direction of phase shift when a target passes under the coil. This is to obtain both GEB and Discrimination. It also seems to increase the sensitivity to targets.

A good experiment for you is build a coil which the TX & RX resonance the same. You could simply change the cap across the RX coil to resonant at the same frequency as the TX coil.
Can you adjust GEB to eliminate ground (ferrite)?
Does the Discrimination still work properly?
How is the sensitivity?

[Carl-NC]

Adding a parallel cap to the RX coil makes it into a bandpass filter and at the resonant frequency the phase shift rolls from +90 to -90 degrees at a rate that depends on the Q. Suppose the RX coil is 1mH and has a series resistance of 10Ω and we are running the TX at 10kHz. The required cap value for resonating the RX coil at 10kHz is 253.3nF and the Q is 6.28. The resulting phase response looks like this:



This is normalized so that '1' means 10kHz. At exactly 10kHz the phase slope is very steep so any phase noise on the TX or phase modulation due to targets will result in a wildly varying phase error. So instead the RX resonance is offset (preferably below the TX frequency) to get it to a lower phase slope.

[searchbear]

I see! That makes a lot of sense! So for multi frequency the Q-factor has to be dropped, I guess, and then the exact values don't matter that much anymore?

[Carl-NC]

You would not resonate the RX coil at all in a multifrequency design. It needs to be wideband.

[searchbear]

Totally wideband? Why not super low Q to get better rejection against slow changes? Does it hurt sensitivity too much?

[Carl-NC]

All MF designs currently on the market use a square-wave drive on the TX so the RX is looking at exponentials. For this, you want a wideband RX to preserve the harmonic content.

I suppose you could try a low-Q resonance on the RX coil, I've never looked into it for MF. As a thought exercise, suppose your MF design uses 5kHz & 25kHz. The obvious choice to resonate the RX coil would be 11.2kHz, the geometric mean of the frequencies. The 5kHz signal would have its 3rd harmonic boosted a bit while the 25kHz signal would have all its harmonics reduced. Not sure what that does to fidelity, I suppose whatever it does could be dealt with in DSP.