Internal inductance versus external inductance

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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Current distribution in the ground plane
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Magnetic Head Connector - 3
Fig. 6 Current distribution in the left and
right circular wire
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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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Measurement and Simulation Results
Self and mutual resistances, L11, L12 by
different methods Quasi-static error may exceed
300!!
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• 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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• For a two-loop system, V21
• Similarly,
• The total energy

(6.159)
(6.160)
(6.161)
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• Generalizing the result to a system of n loops
  carrying currents I1, I2, , In
• where

(6.162)
(6.166)
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• 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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• 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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• 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

b
a
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• Since coil 2 has N2 turns, we have the linkage
• The magnetic coupling coefficient
• The best coupling is k1 of no leakage flux (ab,
  l1l2)

(6-151)
(6-135)