# Frequency Response

1. Apr 22, 2008

### burnit

Hi All,

Firstly this is not homework etc but something i found on the internet that i need some help with. It is for the frequency response of subsurface metal targets. IE Metal Detectors etc.

My take on this as with some others that i have read is:
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The Eddy Currents which are confined to the Conductive zones, set up there own secondary magnetic fields having the SAME Frequency but not necessarily the same phase as the primary inducing field.
By inducing a ground Matrix or Target does not change the frequency of the target response signal. There are not to many things in Nature that can be induced with one Frequency & we have another Frequency come out of it.
I suppose that's why we Discriminate via Phase shift rather than Target Frequency.

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That was posted on a Forum & below is the response along with the PDF files i have attached.
I can't seem to see how these attachments show how the frequency response from a metal target changes the recieved frequency from the primary inducing field frequency?
I may not be looking at this the same way or misreading it???
If somebody could take the time to explain things i would appreciate it very much!

Below is the reply to the above.
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The only wrong thing in your posting is your term "Target frequency". Target may be identifyed by its characteristic frequency, and even by its resonance frequency (if metal is ferrous). It has no own frequency.
"I suppose that's why we Discriminate via Phase shift rather than Target Frequency", means that my "Lesson" and "Exercise" are written too briefly.
Because the rest of your posting is correct, I will explain it in great detail.

Fig. 2 in the "Lesson" is valid for both linear and nonlinear systems. If a network is linear, it responds with the same Frequency as excitation. Then the magnitude and phase of received signal can be represented by a point M in the impedance line shown in fig. 3. If we change TX frequency from zero to infinity, the point M moves on arc in fig. 3 from origin to point 100% and the phase of response changes from 0 to -90 deg. The arc represents in complex plane response of an eddy current for all frequencies.

What represents the straight lines OA and OB in fig. 1? The answer is - response for fundamental frequency. If the system is nonlinear, it also responds with the same frequency as TX, but adds harmonics. For example, if we excitate an ferrous object with transmit TX frequency 2kHz, we receive also this fundamental frequency 2kHz, but there is in output also remarcable magnitude of second harmonic 4kHz, and especially of third harmonic 6kHz because the third harmonic is attributable to magnetizm. The complex plane can,t represent correct response of nonlinear properties as magnetizm. The straight lines OA and OB in fig. 1 are only an approximation, which shows that phase of fundamental frequency not changes with change of TX frequency. We will use them in future exercises to analyse frequency response of ferrous conductivity.

For a linear system, we can plot a normalized transfer impedance with relative magnitude 100% as shown in fig. 3. For a nonlinear system, transfer impedance in complex plane may represent only the response for fundamental frequency. For example, if we increase TX ampereturns twice, this no means that the signal will increase twice moving point M in twice distance from origin on straight lines OA or OB. Hysteresis cycle shows, that magnetism has saturation and this limits the maximal possible magnetic signal. The point M shifts less than twice if the magnitude of TX field increases twice, but the oppsite happens when the magnitude of TX field decreases. Very important thing for a nonlinear system is BIAS. We will discuss this in future exercises.

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