Targets frequency response

[bbsailor]

The purpose of this exercise is to analyze the formation of specific frequencies for conducting nonferrous ground and metal objects. What is happening inside the sensing network when the target is represented by only one eddy current loop?. The eddy current in this loop is calculated by a differential equation of first order, which forms a time constant L/r. The simplified circuit diagram of sensing network is shown above in posting # 20. For spectral analysis and simulation, the above diagram is transformed to simplified equivalent network shown below in Fig. 11.
Note that in this diagram, the total inductance L of eddy current loop is formed by two windings in series: the secondary one of transformer K1 and the primary one of transformer K2. The forward transfer parameter Z21 of sensing network has dimension of impedance: the electromotive voltage E2 inducedin RX coil (port 2-2 without load), divided to TX coil current (port 1-1). Note that the equation in red frame is valid in frequency domain only.
In the time domain, this network is complicated since every transformer K represents differentiation. This increases the order of DE of the whole system. Therefore, the received voltage E2 is proportional to second derivative of TX current. The analysis in time domain can't show us how target should be excited. The action of sensing network is visible in frequency domain. To analyze how twice differentiation forms specific frequencies for target, we need an instrument NETWORK ANALYZERto plot in complex plane twoport parameter Z21. Search WEB for and download the mentioned above software "NI_Multisim_Analog_Devices_Edition_10_0_1.exe ".

Mike,

Add to your analysis the time constant (TC) of the coil turn off current (coil discharge TC slope) as governed by the coil inductance divided by the effective value of the damping resistor. The effective value of the damping resistor (Rd) in a mono coil is governed by the value of Rd which is in parallel with the input resistor (Rin) typically 1K ohm while the clamping diodes are conducting down to about 0.6V. After that, the value of Rd alone governs the coil discharge TC slope. This coil discharge TC slope along with the speed of the opamp coming out of saturation will govern the earliest possible sampling time.

The coil discharge slope occurs in three phases.
Phase 1. MOSFET clamping. Here, the flyback voltage is clamped by the MOSFET voltage rating. It is observed as a flat-topped flyback pulse at the same voltage amplitude as the MOSFET voltage rating.
Phase 2. The Combined parallel values of Rd and Rin down to 0.6V.
Phase 3. The value of Rd alone down until the amplifier comes out of saturation.

You can use the free program MiscEL to see the discharge curves of different coils, damping resistors and input resistors, along with the earliest sampling times possible by the combinations of those component values. Note that the value of Rd is determined by the following components: Coil inductance, coil capacitance, MOSFET COSS, coax cable capacitance, and the amplitude of the flyback pulse being damped by Rd.

To fully stimulate a particular target TC, the coil discharge TC should be 5 times faster than the target TC.

When you do your analysis, choose a particulat target TC and optimize the coil discharge TC characteristics for that target, then see what happens for targets with longer or shorter TCs.

You will find out that there are practical considerations in overall physical design, coil and circuit design that interact.
1. TX PPS rate
2. Coil current/TX pulse width
3. Flyback voltage
4. MOSFET voltage
5 Coil, Coax Cable and MOSFET capacitance
6. Rd value
7. Rin value
8. Opamp gain
9. Opamp speed and time to come out of saturation
10. Target TC
11. Coil discharge TC
12. Earliest sampling time (delay)
13. Soil reaction to TX pulse
14. Local radiated noise
15. Coil sweep speed
16. Coil diameter
17. Integration time and number of samples being integrated
18. Distance of desired target from coil
19. Ground balancing method
20. Battery voltage and battery life
21. Weight (coil, shaft, control box, battery)

The art of design is understanding the variables that you can change while recognizing which variables are already optimized, close to being optimized or fixed. I recommend that you identify and focus on a set of approximately three different target TCs so you can see the effect of optimizing a design for each one and then comparing the consequences of that design on the other target TCs.

bbsailor

[mikebg]

Exercise #1

Hi bbsailor,
You're right about everything to be done. I hope and your contribution and participation of all who can show in this forum how to design ultimate metal detector.

I started everything from scratch, why exercise is #1. The design of a metal detector should begin with studying, analyzing and measuring the spectral characteristics of the target, which term according to English jargon is called frequency response. Designer must understand how sensor "sees the color" of target and to know how to "illuminate" it, that is what must be the spectral characteristics of the TX coil current. After analyzing the sensing network, we will know what signals to produce sensor for further processing.
　
This is only an initial step in carrying out the first exercise, set more than one year ago. From this first step is understood that although the proposed equivalent circuit of the sensing network is quite simple,
it is still difficult for the designer to understand what's happening in the
system "Sensor - Target". The next two steps in this exercise should lead to
more simplified equivalent circuit of the system because they have to ignore the
very spectral characteristic of the sensor.
　
Having taken all steps of the first exercise, we will have enough knowledge to make a second exercise: "Measurement of spectral characteristics of the targets". Participants in this forum, which make these two exercises will have enough knowledge to participate in new threads, such as: "How should MD sensing network works?" , "How should MD TX works?" and "How should MD RX works?". After answering these questions, we will understand why today's metal detectors are not designed properly.
Do you think we can simply start direct a section in the forum "How should be designed the ultimate metal detector"?

[WM6]

Do you think we can simply start direct a section in the forum "How should be designed the ultimate metal detector"?

Why not. We all tend to some of new-age detector.

If we assume that the simplified approach to the construction of an alternate detection circuit in exercise (figure 11) is right (regarding from bbsailor given variables).

What about (RX sensor circuit) resonance drift in near of different soil, how to compensate this?

Very interesting postings from you, mikebg, thank you.

[mikebg]

Articles like in Wikipedia

Hi WM6 and all,
I believe that to design the ultimate metal detector, we must be able to write and edit articles in the same way as it does in Wikipedia.
I monitor the forums for metal detectors for some 10 years to figure out how to apply knowledge of people having hobby "QRP ham radio design". They create TXs and RXs designed to detect nanovolt signals buried in microvolt interference. This hobby is slowly but surely dying, so people who love him should be adapted to design TXs and RXs for MD.
It had passed8 years since the beginning of this forum, when Carl announced that it creates a "worldwide collaborative design group for the purpose of developing commercial detectors". Then I figured that I have neither sufficient knowledge of English or in slang English terminology peculiar to metal detectors, nor on the theory of EMI sensor, or processing of signals. Confer a lot of time with my friends on hobby, until we reached the conclusion that now is not we can be useful for the activities of collaborative design group.

Over the past two years I have gotten so much ability to customize and repare the machine translation in English that even Bruce^Crocodile can understand what I mean :-). I managed to unscramble the importance of a number of incorrect slang English terms and replacing them with the right international terms. Now, having observations of so many forums and knowledge of metal detectors,that I will afford to nominate proposals for many things that we the participants of this forum should make not only for our hobby and pleasure, but also for training of personnel who will create the future devices for MD and demining.
I do not think it is necessary to create a design group, because Carl has already done so two years ago. I think we need to create Open research group to study and overcome the principal drawbacks of EMI sensors and metal detectors. We need an online magazine "MD design", authors and editors. The articles in the magazine should be edited like in Wikipedia. If we have articles describing how to avoid or minimize the disadvantages of sensors and metal detectors, we will set up a perfect block diagram. The next two steps: the design of the circuit diagram and the design of hardware will not pose problems for the majority of participants in the MD forums.
Here are my brief suggestions:
A. To create anopen group for R & D on sensors and MD. Purpose of the group: the training of participants in the forum through research, revision, rediscovering and reinventing everything related to EMI sensor and metal detectors. I propose the name of the group is "REMI". The member of the group is every author or editor of article in online magazine "MD design".
B. Starting a project with the aim of creating the perfect block diagram of the EMI sensor and perfect block diagram of a metal detector. Propose project name: "GLEANER". Nominate a project manager: Joseph Rogowski (bbsailor).
C. Detailed explanations for the nomination and names of the stages for research and development, I will give in my next posting.

Meanwhile, in order to exploit the time while expecting other offers and while discussing them, I'll start a new thread in the section "Coils". We must begin by this section, because we choose as a perfect rule of action of EMI sensor, stay two steps to establishing a perfect block diagram of ultimate metal detector. Moreover, the man nominated to project manager, is an expert in the field of EMI sensors. The title of the thread will be "How should EMI sensors work". Discussions on Ultimate EMI Sensor will produce thinking as participants in this forum and my hobby comrades on "QRP ham radio design". But unfortunately the posting is not like an article in Wikipedia that anyone can edit and finish writing.

To be continued (after verifying that the Google machine will be able to translate this essay in Australian language :-).

　

[mikebg]

Simplification of sensing network

To understand what is happening inside the sensing network before first differentiation, let us simplify the above circuit, removing TX current and transformer K1. In the following equivalent network (Fig.12), they are replaced with a voltage source. It is negative in time domain (according to the Lenz's rule).
In this simplified network, the forward transfer parameter has no dimension - output voltage divided to input voltage (like an attenuator). In time domain, the induced electromotive voltage E2 is derivative of eddy current.
Differentiation in the time domain means quadrature, ie a rotation of 90 degrees in the frequency domain. To see the rotation of forward transfer parameter, let's simplify more the network in Fig. 12 and see for beginning the forward transfer parameter of eddy current loop. The equivalent circuit of eddy current loop is shown in Fig. 13.
In this network, the forward transfer parameter is Y21 because it has dimension admittance: eddy current, divided by its EMV. The next step is to connect this network to NETWORK ANALYZER. Search WEB for and download the software "NI_Multisim_Analog_Devices_Edition_10_0_1.exe ".

[mikebg]

Continuation of posting #109

Here is a detailed description of my suggestions given in posting #109:
A. I suggest the name of the project to be GLEANER. This name indicates that our machine will be significantly better than existing ones, so you may glean, that can detect targets even in places that have already been searched by other machines.
C. I suggest for project manager Joseph Rogowski. Joe is a retired U.S.Army strategic planner for an Army-led Department of Defense distributed computing system, former college faculty member teaching Audio/TV production and managing a college media department. He is an award winning TV Producer for the U.S. Army, and later became a technical writer to manage Technical Manuals for Army communication and electronic systems. He conceived and managed the Army’s first interactive videodisc technical manual released in 1989. He is a Workflow Management Coalition (WfMC) Fellow.
He sails Barnegat Bay, N.J. (bbsailor) in the spring and summer. Winter and fall finds him on N.J. barrier islands (Long Beach Island and Absecon Island) metal detecting. His first experience with coils came in his younger years from designing guitar pickups for N.J. custom guitar makers.

C. propose work on R & D of GLEANER to perform the following steps:
1. Stage One: To create a block diagram of signal processing, which is devoid of the shortcomings of the existing block diagrams of metal detectors. Steps to implement the first phase are:
1.1. Theoretically, the spectral characteristics of the study findings. Creating a skilled staging for waiver of the spectral characteristics.
1.2. Analysis to existing EMI sensors and identifying measures to reduce their handicaps.
1.3. Analysis of the TX and the shortcomings of previous study designs. Drawing a block diagram of the TX with a minimum of defects. Create a staging experimental measurement parameters of TX.
1.4. RH analysis and study weaknesses of previous designs. Drawing a block diagram of RX with a minimum of defects.
1.5. Composing general block diagram of metal detector GLEANER.
2. Second stage: Design principle schemes of individual blocks.
3. Third step: packaging system design and PCB assembly for an experimental model.
4. Stage Four: Creating a skilled staging for measuring parameters of metal detectors. Model experimentation and improvement schemes.
5. Fifth Stage: Final packaging system and design of printed circuit board.
D. I propose the name of the group to REMI, where R means: research, revision, rediscovering, reinventing. The EMI means Electromagnetic Induction.

Alternative proposals and expect a response from Joe that agrees to conduct such a master revolutionary project. I hope that in winter he will have more free time. It will have the support of a society whose hobby was now "QRP ham radio design". These people will reduce their pain by the fact that "Ham radio" died, if they applied in the field of metal detectors their knowledge in the construction of hypersensitive receivers.
　
　
　
　

[mikebg]

NETWORK ANALYZER

How NETWORK ANALYZER works? It calculates the 4 parameters of the connected twoport network .
You can learn in WIKIPEDIA for two-port network and its parameters. Then read Help in the software of NETWORK ANALZYER.
For us the most interesting is the Forward transfer parameter. It has as index the number 21 or the letter F. Remember the parameter H21 (or Hfe) for transistors type BJT and parameter Y21 or (Yfs) for transistors type FET.

[WM6]

Very pro and interesting approach and proposal, mikebg.
I hope that the Geotech experts involved.

Can only be beneficial even if achieved less than expected.

Do you think that, for example, the net analyzer can manipulate enough of the relevant parameters that can give us a realistic picture needed to make step from theory to working devices?

[mikebg]

To SPICE or not to SPICE?

WM6, For a professional designer, the NET ANALYZER is a very powerful tool for impedance matching. I am an amateur designer who is accustomed to the primitive method with sheet and pencil. I have created effective miliwatt TXs and sensitive nanovolt RXs for QRP ham radio without using SPICE simulator. For example, when I design an amplifier with transistors, I use only simple formulas containing parameter h21, neglect by the other three network parameters h11, h12 and h22. This is not correct. The SPICE and NET ANALYZER are using all 4 parameters, but they can not draw or block diagram, no circuit diagram.
When I started exploring metal detectors, I decided to SPICE simulate the attached equivalent circuit diagram. But it turned out that I do not need because I know what parameters of the diagram must have a minimum value, and which - maximum, what parameters should be stable and what parameters must be adjusted after being assembled device.
The SPICE simulator can not edit the circuit diagram of an electronic device. It can only show the shortcomings of the analyzed scheme and show for what values of the components these shortcomings are minor. The block diagram and circuit diagram are compiled by the designer.
In the Exercise #1, I will use NET ANALYZER to show that the sensors must have one additional coil, generating reference signal for synchronous demodulation.
In conclusion I can set an important exercise for MD designers. Let's design a block diagram of TX for metal detector with sine induction. The block diagram should provide maximum depth of detection and discrimination stability. After this exercise, we will design the circuit diagram of TX and test equipment for TX.
HINT: You need to analyze first how are modulated the parameters of the TX coil when it approaches the earth or salt water. Second, you should consider the harmful effects of the parametric modulation of the TX coil. Then you need to consider the advantages and disadvantages of existing TX circuits of metal detectors. Once you register all existing and possible measures for suppression of parasitic modulation, finally got to show what blocks must contain the perfect TX for sine induction.

[mikebg]

Forward transfer of eddy current loop

Let's start with Forward transfer parameter of an eddy current loop. Timeconstant of the shown loop is L / r = 159nH/1mohm = 159us.

[mikebg]

Polar Graph of above network

Admittance of an eddy current or forward transfer parameter Y11 in complex plane. Note that this plot is called "Polar Graph". The value of "Zo" is chosen equal to the resistance "r" to obtain testimony -3dB for frequency at which the phase lag is -45deg.

[mikebg]

Admittance expressed in polar coordinates

GLOSSARY:

Bode plot (the red linies) is approximation of Log-Log plot with asymptotes (stright linies). The error of this approximation is maximum -3dB and appears at cutoff frequency.
Cutoff frequency is the point where two asymptotes in Bode plot intersects. Synonimes are:
- f3dB or 3dB frequency,
- f45deg or 45 deg frequency,
- Corner frequency since Bode plot seems as a corner,
- Break frequency since Bode plot seems as a broken line,
- Characteristic frequency since this point characterizes boundary between regions:
LF region are frequencies below cutoff frequency
HF region are frequencies above cutoff frequency. Slope -20dB/dec = -6dB/oct is attributable for First order Low Pass Filter. This term is used in frequency domain. In time domain the RL network is Real integrator (in HF region only). An Ideal integrator has no resistance in series (capacitor or coil without ESR).

[mikebg]

Admittance expressed in rectangular coordinates

CONCLUSION:
The eddy current loop trasfers signal as an real integrator in its HF region. This allows us to differentiate signal once without loosing spectral information.
　
Admittance expressed in rectangular coordinates
SYNONIMES:
Re and Im (Real and Imaginery)
I and Q (Inphase and Quadrature)
R and X (Resistive and Reactive)

[mikebg]

Network for voltage transfer of an eddy current loop

Network for voltage transfer of an eddy current loop

As is known in the study of transistor amplifiers, the hybrid parameter H12 represents reverse voltage transfer. In common emiter network this is the parameter Hre. Since in principle both ports of two port network are equivalent (not defined input and output), we can flip horizontally Network Analyzer to make parameter H12 forward voltage transfer parameter G21. For a detailed explanation of G21, search WEB for "Two-port network" and read "Inverse hybrid parameters (g-parameters)" .

[mikebg]

Polar Graph of Voltage Trasfer

Voltage Trasfer of an Eddy current as Polar Graph
When Network Analyzer is inversed (flipped horizontally), instead hybride H-parameters, it represents G-parameters (inversed hybride parameters). Therefore, two readings on the Network analyzer's skin should be changed:
- The inscription "H-Parameters" should be "G-parametrers" and
- Inscription on button pressed H12 must be G21. Parameter G21 is nondimesional forward voltage transfer. This is inversion of H21 - the nondimesional forward current transfer parameter.
Home work

:-( for those who hate to work, but like to watch) -:
1. In time domain, the Voltage transfer by an eddy current loop is scaled derivative of its Transfer admittance. Compare the polar graph of Transfer admittance (shown in posting #116) with the polar graph of Voltage transfer shown here. Explain how differentiation in time domain amended complex spectral response in frequency domain.


2. In analyzing the transfer admittance, we parted frequency spectrum of the LF region and HF region as the boundary between them is the Cutoff frequency of target. Do the same analysis and Voltage transfer. Check with Network Analyzer that once differentiation signal in time domain amended Cutoff frequency.

3. The timeconstant of conductive ground depends on TX coil diameter. In frequency domain that means we can increase or decrease the width of LF region for ground signal. Analyze how we can use it?
NOTE: When we change TX coil diameter, the timeconstant (cutoff frequency) of conductive target remains unchanged only if its eddy diameter is smaller than TX coil diameter.