P1246341511eHVbr

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Multiresonant Coreless Inductors and Transformers
LEES
Joshua W. Phinney David J. Perreault Jeffrey
H. Lang Massachusetts Institute of Technology,
Laboratory for Electromagnetic and Electronic
Systems
Abstract Inductors wound on magnetic cores cannot
be miniaturized as effectively as other
power-system components at high switching
frequencies a relatively large core is necessary
to lower AC flux density and to raise inductor Q.
A coreless winding tapped with capacitors so as
to introduce harmonically related resonances,
however, can develop large impedances without
large inductance. Such multi-resonant devices
block switching-harmonic currents with large
resistive impedances, and can be miniaturized for
high-frequency operation with no core-loss
penalty. In this project, tapped toroidal
inductors and transformers are fabricated in a
two-layer copper electroplating process, in which
winding turns are plated into epoxy molds
patterned over a copper seed layer.
Capacitor taps
Wells (dark rectangles) are formed in a 0.5mm
layer of photosensitive epoxy covering substrate
copper. Epoxy not hardened by ultraviolet
exposure is removed in a development step,
leaving molds to shape subsequent layers of
electroplated copper.
The lowest layer of 10?m copper (light regions)
is patterned to connect turns of the magnetic
structure, and acts as an electroplating seed
layer for the growth of high-build copper posts
and crossbars.
capacitors and the complete set of radial taps
omitted for clarity

• Applications
• A direct converter (such as the boost converter
  above left) blocks odd-harmonic switching
  currents, and is therefore most effective around
  50 duty ratio.
• A multi-resonant device in a voltage-fed
  push-pull converter (right) eliminates one
  primary-side switch at 50 duty ratio.
  Transformer impedance maxima occur at odd
  harmonics of a principle resonance. By aligning
  the switching frequency with this resonance at
  50 duty ratio, the magnetic structure only
  supports half-wave symmetric voltage waveforms
  across its primary winding. During switch-off
  half-cycles, the multi-resonant structure rings
  the primary voltage in a reverse-polarity copy of
  the applied waveform with the switch on, exactly
  as the eliminated switch would do.

• Harmonically-related Impedance Maxima
• A transmission line (a) transforms a terminating
  impedance RL to its reciprocal, seen as ZLINE at
  the source, for every odd quarter-wavelength of
  line.
• A lumped transmission-line model (b) is similar
  to capacitively tapped inductor (c), apart from
  the stage-to-stage coupling. Coupling limits the
  high-frequency phase through the network, but
  results in a similar pattern of odd-harmonic
  impedance maxima. The network fundamental
  frequency is at n/?LC for an untapped inductance
  L loaded at n taps with a total capacitance C.
• A toroidal winding tapped uniformly about its
  periphery with no detailed knowledge of its
  n-port inductance matrix, yields impedance maxima
  at odd-harmonic frequencies to a good
  approximation. More taps increases the quality
  of this approximation, at the expense of a higher
  fundamental frequency.

Computed Impedance Magnitude Zin
(a)
RL
Zline
(b)
Measured Impedance Magnitude Zin
1.7k? maximum
(c)
RL
Zin
1st
3rd
5th
harmonics