1. Internal inductance versus external inductance
Example. Magnetic-Head Connector (MHC)
Configuration of high speed magnetic head connector.
Simulation only demonstrates current distribution in ground
plane and in the two circular wires at 1 GHz.
Courteously performed under financial support of W.L. Gore
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2. Current distribution in the ground plane
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3. Magnetic Head Connector - 3
Fig. 6: Current distribution in the left and right circular wire
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4. Measurement and simulation Results for MHC
Measurements from 1 MHz to 1 GHz
Fig. 9: Self and mutual resistances, R11, R12 by different methods
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5. Measurement and Simulation Results
Self and mutual resistances, L11, L12 by different methods
Quasi-static error may exceed 300%!!
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6. The work done by the field (to establish magnetic fields) is
6-12: Magnetic Energy
Consider a single closed loop of inductance L1 without initial current.
The work done by the field (to establish magnetic fields) is
W1 is the stored magnetic energy.
(6.157)
(6.158)
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7. For a two-loop system, V21 Similarly, The total energy (6.159) (6.160)
(6.161)
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8. Generalizing the result to a system of n loops carrying currents I1, I2, …, In
where
(6.162)
(6.166)
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9. 6-12.1: Magnetic energy in terms of fields
Using
The magnetic energy (6.166) becomes
where As
(6.167)
(6.169)
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10. From vector identities, we can obtain
where the integrand is magnetic energy density,
From the stored magnetic energy one can evaluate the
Inductance of a system/circuit:
(6-172)
(6-174)
(6-175)
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11. Example 6-18 Mutual inductance. Two coils of N1 and N2
terns are wound on a cylinder core of radius a and
permeability The windings are of lengths
Find the mutual inductance.
Solution.
The magnetic flux l2 l1 b a
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12. Since coil 2 has N2 turns, we have the linkage
The magnetic coupling coefficient
The best coupling is k=1 of no leakage flux (a=b, l1=l2)
(6-151)
(6-135)
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