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TGSL Spice Simulation
The following is the approach that I've taken with regard to simulating the coupling between Tx-Rx coils.
Much of this (text) is from Wikipedia.
Starting with inductance:
The quantitative definition of the (self-) inductance of a wire loop in SI units (webers per ampere, known as henries) is
L= N\Phi*i
where L is the inductance, Φ denotes the magnetic flux through the area spanned by the loop, N is the number of wire turns, and i is the current in amperes. The flux linkage thus is
N\Phi = Li
N d(Phi)/dt=v.
A 2 coil search head can be modeled as a transformer with the following equations which describe transformer action:
V1 = L1*di1/dt - M*di2/dt
V2 = L2*di2/dt - M*di1/dt
The mutual inductance also has a relationship with the coupling coefficient. The coupling coefficient is always between 1 and 0, and is a convenient way to specify the relationship between a certain orientation of inductor with arbitrary inductance:
M = k sqrt{L1 L2}
where
k is the coupling coefficient and 0 ≤ k ≤ 1,
L1 is the inductance of the first coil, and
L2 is the inductance of the second coil.
Once the mutual inductance, M, is determined from this factor, it can be used to predict the behavior of a circuit.
The magnetic flux linked to both the primary winding and the secondary winding is said to be the main flux, (φ12 or φ21). The magnetic flux which interlinks only with the primary winding, and does not interlink with the secondary winding, is said to be the primary leakage flux, φσ1. The magnetic flux which interlinks with the secondary winding, and does not interlink with the primary winding is said to be the secondary leakage flux, φσ2. The primary side leakage flux becomes the primary side leakage inductance, and the secondary side leakage flux becomes the secondary side leakage inductance. Defining k to be the coupling coefficient, and denoting the leakage inductances of the primary side and the secondary side as Le1 and Le2 respectively, it follows that:
Le1 = (1-k)L1,
Le2 = (1-k)L2
In the case of a IB search head such as the TGSL, we want essentially zero mutual inductance, N*d(Phi)/dt=0, i.e. k=0.
Which then leads to:
Le1 = (1-0)L1 = L1
Le2 = (1-0)L2 = L2
So instead of a search head being modeled schematically as:
We have:
To simulate the presence of ground, metal or other objects I use the following schematic/configuration.
L3 is driven such that it is synchronized to Tx but contains driving circuitry for wave shaping (phase and amplitude) to simulate effects of ground and or metal.
K adjsts the coupling between the simulated response to Tx and the Rx coil.
I have used this configuration in recent simulations and it appears to work quite well. Of course other lumped parameters such as distributed capacitance, resistance, etc. can be added to the model.
Hope this is of help if not for anything else to stimulate conversation.
Much of this (text) is from Wikipedia.
Starting with inductance:
The quantitative definition of the (self-) inductance of a wire loop in SI units (webers per ampere, known as henries) is
L= N\Phi*i
where L is the inductance, Φ denotes the magnetic flux through the area spanned by the loop, N is the number of wire turns, and i is the current in amperes. The flux linkage thus is
N\Phi = Li
N d(Phi)/dt=v.
A 2 coil search head can be modeled as a transformer with the following equations which describe transformer action:
V1 = L1*di1/dt - M*di2/dt
V2 = L2*di2/dt - M*di1/dt
The mutual inductance also has a relationship with the coupling coefficient. The coupling coefficient is always between 1 and 0, and is a convenient way to specify the relationship between a certain orientation of inductor with arbitrary inductance:
M = k sqrt{L1 L2}
where
k is the coupling coefficient and 0 ≤ k ≤ 1,
L1 is the inductance of the first coil, and
L2 is the inductance of the second coil.
Once the mutual inductance, M, is determined from this factor, it can be used to predict the behavior of a circuit.
The magnetic flux linked to both the primary winding and the secondary winding is said to be the main flux, (φ12 or φ21). The magnetic flux which interlinks only with the primary winding, and does not interlink with the secondary winding, is said to be the primary leakage flux, φσ1. The magnetic flux which interlinks with the secondary winding, and does not interlink with the primary winding is said to be the secondary leakage flux, φσ2. The primary side leakage flux becomes the primary side leakage inductance, and the secondary side leakage flux becomes the secondary side leakage inductance. Defining k to be the coupling coefficient, and denoting the leakage inductances of the primary side and the secondary side as Le1 and Le2 respectively, it follows that:
Le1 = (1-k)L1,
Le2 = (1-k)L2
In the case of a IB search head such as the TGSL, we want essentially zero mutual inductance, N*d(Phi)/dt=0, i.e. k=0.
Which then leads to:
Le1 = (1-0)L1 = L1
Le2 = (1-0)L2 = L2
So instead of a search head being modeled schematically as:
We have:
To simulate the presence of ground, metal or other objects I use the following schematic/configuration.
L3 is driven such that it is synchronized to Tx but contains driving circuitry for wave shaping (phase and amplitude) to simulate effects of ground and or metal.
K adjsts the coupling between the simulated response to Tx and the Rx coil.
I have used this configuration in recent simulations and it appears to work quite well. Of course other lumped parameters such as distributed capacitance, resistance, etc. can be added to the model.
Hope this is of help if not for anything else to stimulate conversation.
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