# Coupled Antennas

by JPBenowitz
Tags: antennas, coupled
 P: 127 Can anyone provide some literature on antennas spaced apart such that the spacing distance is much less than the wavelength? I am specifically interested in the mutually coupling behaviour as a function of small separation distances.
 Sci Advisor Thanks P: 1,906 They would not be considered as individual antennas if they were that close. They would be analysed as a single antenna. This is a numerical job for the NEC style of antenna simulators. http://en.wikipedia.org/wiki/Numeric...magnetics_Code You will need to better identify their structure before an analysis of the specific case can be referenced.
PF Gold
P: 2,627
 Quote by JPBenowitz Can anyone provide some literature on antennas spaced apart such that the spacing distance is much less than the wavelength? I am specifically interested in the mutually coupling behaviour as a function of small separation distances.
you really need to give a bit more info on what you have in mind
1) are the 2 antennas on the same freq?
2) do you want them as a phased array ?
3) what sort of antennas ? .... dipoles, yagis?

any closer than that and the interaction between the 2 arrays destroys radiation patterns which will result in loss of gain.

cheers
Dave

P: 127
Coupled Antennas

 Quote by davenn you really need to give a bit more info on what you have in mind 1) are the 2 antennas on the same freq? 2) do you want them as a phased array ? 3) what sort of antennas ? .... dipoles, yagis? for phased yagis, to get the best gain and radiation pattern, the optimum distance apart for a phased array is one wavelength any closer than that and the interaction between the 2 arrays destroys radiation patterns which will result in loss of gain. cheers Dave
I am modeling neuronal axons as Collinear Coaxial Cables that are separated on the magnitude of nanometers to micrometers where the wavelength is on the magnitude of millimeters.
 Sci Advisor Thanks P: 1,906 I believe you might treat parallel axons as close directionally coupled coaxial cables. If I remember correctly, like a coaxial cable has an insulated external conductive screen, an axon has a myelin sheath. If the chemical charge balance remains within that myelin sheath structure, then there should be little electrostatic imbalance. If the longitudinal charge transfer is balanced then there should be little external magnetic field. That would suggest that axons should not cross-couple. They are natural coaxial cables. So what have I missed? What false assumptions have I made?
P: 127
 Quote by Baluncore I believe you might treat parallel axons as close directionally coupled coaxial cables. If I remember correctly, like a coaxial cable has an insulated external conductive screen, an axon has a myelin sheath. If the chemical charge balance remains within that myelin sheath structure, then there should be little electrostatic imbalance. If the longitudinal charge transfer is balanced then there should be little external magnetic field. That would suggest that axons should not cross-couple. They are natural coaxial cables. So what have I missed? What false assumptions have I made?
There are myelin gaps every 2mm along the axon with a high density of ion channels. When the channels are active there is both an influx and efflux of ions across the membrane. So we have ions from the electric double layer (the effective outer conductor) diffusing through the unmyelinated membrane into the cytoplasm (the effective inner conductor) and ions diffusing from the cytoplasm through the unmyelinated membrane to the electric double layer. I've have been modeling this as a Collinear Coaxial Cable where at each myelin gap the inner conductor is connected to the outer conductor.
 Sci Advisor Thanks P: 1,906 A large magnetic impulses can cause significant currents in an electrolyte, which may trigger an electrical response. But I don't see how an axon can generate sufficient magnetic field to influence a neighbour. I think an electrical model that ignores magnetic fields may be quite realistic. The myelin sheath can be seen as the common black insulation on a coaxial cable. I suspect the diffusion channels at the nodes are used to balance the electrolyte levels within the axon. So consider a model where there is a matrix of resistors at each node. That matrix represents the ion flows across the node, between layers and with the external ion reservoir. That external ion reservoir can probably be modelled as an electrical ground. If the gaps in the myelin sheaths of parallel axons line up with each other, then there may be some slight coupling or modulation between nodes by ground potential differences, due to ground currents. But I expect the “internal” signals are sufficiently “digital” to not be significantly effected. If we think of a node as a resistive “T” or “Pi” attenuator, then there must be sufficient gain in the chemical transmission line, (axon), to regenerate the pulse after attenuation through a node. I guess diffusion at the node must also provide the chemical energy to power that gain. What would the resistive matrix modelling a node look like? What ions are flowing? The more I think about the model, the less I see it as coupled antennas, and the more I see it as a network of currents.
P: 127
 Quote by Baluncore A large magnetic impulses can cause significant currents in an electrolyte, which may trigger an electrical response. But I don't see how an axon can generate sufficient magnetic field to influence a neighbour. I think an electrical model that ignores magnetic fields may be quite realistic. The myelin sheath can be seen as the common black insulation on a coaxial cable. I suspect the diffusion channels at the nodes are used to balance the electrolyte levels within the axon. So consider a model where there is a matrix of resistors at each node. That matrix represents the ion flows across the node, between layers and with the external ion reservoir. That external ion reservoir can probably be modelled as an electrical ground. If the gaps in the myelin sheaths of parallel axons line up with each other, then there may be some slight coupling or modulation between nodes by ground potential differences, due to ground currents. But I expect the “internal” signals are sufficiently “digital” to not be significantly effected. If we think of a node as a resistive “T” or “Pi” attenuator, then there must be sufficient gain in the chemical transmission line, (axon), to regenerate the pulse after attenuation through a node. I guess diffusion at the node must also provide the chemical energy to power that gain. What would the resistive matrix modelling a node look like? What ions are flowing? The more I think about the model, the less I see it as coupled antennas, and the more I see it as a network of currents.
That's the contemporary model utilizing Linear Cable Theory and its assumptions. The only problem is that is has been observed that neurons can synchronize their action potentials when they are close (See Ephaptic Coupling of the drosophila fruit fly). Furthermore, it has been most recently observed that separate parts of the brain can oscillate at the same frequency and is independent of electrochemical signals, in other words the endogenous electric field in the extracellular medium is assisting in information processing.

To start things off I do not model the axon as an equivalent circuit; this is an idealization that I believe has missed a fundamental property of the neuron. Instead I begin with the electrodiffusion equation and the poisson equation in cylindrical coordinates. This is a system of nonlinear 2nd order spatiotemporal partial differential equations. Conceptually the problem is easy. There is initially a boltzmann distribution of ions on the surface of the myelin sheath (dielectric) and a boltzmann distribution of ions on the inner membrane surface. Keep in mind the ionic species and surface charges are not the same. When we run the system in time there is active diffusion across the membrane perturbing the distribution of ionic species on both sides of the axon producing a time changing potential. The magnetic field has been measured and it is negligible but my hypothesis is that the far-field plays some role in neuronal oscillations.

Since there is a high density of ion channels and pumps at the myelin gaps and a sufficiently large potential difference across the membrane, when these channels open the ions will accelerate and thus radiate.