There is cylindrical ferrite rod antenna in free space. Ferrite Mu is about 1000. Rod diameter is much smaller then length. Is there a closed form expression (or approximation) for magnetic field power captured by such ferrite rod depending on length and diameter? (Low frequency operation; static EM field conditions apply)
Vladimir Vassilevsky DSP and Mixed Signal Designs
Assuming FAR FIELD Two ways to go:
If you haven't worked with femm let me know it's a simple model.
I have an article by J.S. Belrose that probably has what you're asking for, but the math is beyond my comprehension. My address is good, if you send me an email I'll send back a pdf of the article. I have a second article discussing thermal noise to signal ratio in tuned ferrite loop antennas, which may or may not be contained in the first article. I'll send both if you like. Mikek
Would you send both to me, too?
Hmm (maybe silly) but can you just use reciprocity and calculate the field generated by the coil?
George H.
Usually not much advantage after the rod is longer than 10 times diameter, or is that 100? Asymptotically approaches a limit.
Neglected to add [you knew this already, but for the lurkers] the effect of the rod is two fold. It effectively lowers the resistance of the coil by making it smaller diameter than it would otherwise have to be. The rod also moves the resonance into more physically available component range.
There is another effect. If the original coil were air core, large diameter with very small cross section; the voltage generated in the coil from the external field would follow a cosine function with the tilt of the coil's angle. However, add a rod and the function becomes a 'squashed' cosine function, whose 'squashing' becomes a function of the length of the rod. Envision the coil with a very long rod tilted in a field. The lines come down to the ends of the rod, then preferentially transfer down along the rod, energizing the coil, if the mu is high enough; there is little difference between in line with the field and tilted 45 degrees!
It should be in your email. Mikek
Could you please send me those two articles? vlv{@}abvolt{.}com
Vladimir Vassilevsky DSP and Mixed Signal Designs
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I heard a theory that ferrite rods actually suck electromagnetic energy int o the ends of the rod since the energy follows the path of least resistance . The lines of field bend to allow the energy to pass through the rod more easily than an air core coil. Any truth to that idea?
-Bill
If you can imagine the "bar magnet" field of the rod as an electromagnet (i.e., what the field looks like when the coil is energized), the pattern of the external field will be complementary to it. That is, instead of being concentrated in the center (around the coil), it's concentrated around the ends; and instead of making sort-of-semicircular loops from and to symmetrical points along the rod (leakage flux leaves the core somewhere in the middle, perpendicular to the core, travels through space, and arcs back to a symmetrical point on the core), makes a pinching sort of shape to the external field lines. Lines that don't enter the core will be sort of cinched in (like tightening a corset?) as they pass alongside the core; lines that enter will be shunted through. Lines nearly on axis will enter and exit at the ends (fringing from the corners, mostly), while lines somewhat off axis will be sucked in midway. Lines further away are deformed but not connected. All the flux lines which enter the core (rather than squeeze near it), and only them, count towards area of the coil.
The amount of "waisting" that occurs will be on par with core reluctance; a very thin (wire-like) core can be very long, but will have high reluctance (a large MMF drop), and so field lines won't be very attracted to it (you may consider a single mu-metal ribbon instead of an expensive, bulky ferrite core though!). A very squat core does very little, because it isn't long enough to short-circuit a sizable length of field lines.
I should think the core area can be approximately mu times smaller than the equivalent cross sectional area, and the length similar to the diameter of the circle enclosing that area.
Be interesting to see how simulations (or analysis, if possible) match up to this intuition.
Tim
-- Seven Transistor Labs Electrical Engineering Consultation Website: http://seventransistorlabs.com
Got them,thank you.
True, not a bad 'allegory'
Magnetic fields are more 'easily' obtained in a ferrite rod than in the air. All these cores for that matter. Since the fields are more easily made in the core material, there is almost NO energy stored in the metal...it's all in the air gap.
As a simple learning tool, nothing beats free femm 4.2 and its user's group is helpful for questions 24/7
I see your point, interesting to consider how the tips of the core must extend into the field so that as it distorts the field lines it can still 'scoop' the equivalent of mu times the rod 's area. that at least should get you the 67%, usually takes 3 diameters to get to 99%
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