IEEE Circuits and Systems Magazine - Q2 2018 - 33

t6
Expt.
Expt. Avg.
Ideal Model

-0.6 t4

t5
0
iFM (mA)
(a)

-1

t3

0

t2

-0.8

t1

t6

0.0
νFM (V)
(b)
t2

t3

t4

0.8

-0.5

0.0
φFM (mV.s)

t2

-0.5

t4

-1.0

t5

-0.5

PLL

t1

t6

2
Time (ms)
(e)

(d)

0.5

t2

t3

t4

t5

2
Time (ms)
(f)

4

t6

0.2
0.0

EFML
ED
ELL

-0.2
0

0.0
φFM (mV.s)

0.4

0

0.5

t3

(c)

-1

0

t5

0.0

PFML
PD
P (mW)

(diFM /dt)/vFM (A /V.s)

1

5

t5
t4

0.5

-70

1

Ideal Model
Expt. (Raw)
Expt. (Smoothed)

t1

dφFM /dt (V)

t3

t1

t6

70

E (µJ)

0.0

t1
di FM /dt (A /s)

φ FM (mV.s)

1.0

t2

0.6

0

4

sEcOnd quartEr 2018

Expt
T Model

(diFM /dt)/vFM (A /V.s)

temperature variations, it is possible to use two extreme values of
p ^ T h that represent dissipation
and storage of energy in the FML
to approximate the dynamical behavior. Using a negative value of
p ^ T h = - 4.5 that indicates minimal energy dissipation, we were
able to reproduce the pronounced
minima found in the two branches of the experimenta l plot of
L -FM1 ^z FM h vs. z FM for the case with
a parallel LL in the circuit, while
using positive or smaller magnitude negative values of p ^T h , we
were able to fit to the rest of the
curves (for both the circuits with
and without the LL), as shown in
Fig. 5. This relationship introduces

(diFM /dt)/vFM (A /V.s)

Figure 4. fml with parallel ll characterization. (a) plot of z FM against i FM from experimental data (red curves 'Expt.'), from calculation of the restoring function (green curve 'Expt. avg.'), and the same model as in fig. 2(a) (gray curve 'Ideal model'). 't1'-'t6'
are temporal markers. (b) plot of di FM dt against v FM, exhibiting a pinched hysteresis loop. (c) plot of d z FM dt against z FM . (d)
1
plot of ^di FM dt h v FM (or L -FM
) against z FM for experimental data (raw and smoothed). Ideal model corresponds to Equation 4.
(e)-(f) plots of powers and energies vs. time, for the restoring function or reversible stored flux ('fml'), the dissipative component
('d') that causes the ferromagnetic switching, and for the 27 mh parallel linear inductor ('ll'). the small but noticeable net gain
in E FML and loss in E LL are calculation artifacts attributed to small changes in the resistances by a few Ohms, which can be time
and temperature dependent.

No LL

5

0
-0.5

0.0
φFM (mV.s)
(a)

0.5

With LL

5

0
-0.5

0.0
φFM (mV.s)

0.5

(b)

Figure 5. flux and temperature dependent inverse differential inductance for the fml.
1
plots of ^di FM dt h v FM (or L -FM
) against z FM . Experimental data ('Expt.', pink circles)
1
^z FM, T h
and the generic non-linear (-1,0) element inverse differential inductance L -FM
('t model') corresponding to Equation 6. (a) case with no ll. set of p ^T h used was
(+1,-2) for the two component curves displayed. (b) case with a ll. set of p ^T h used
was (+3,-4.5) for the two component curves displayed.

IEEE cIrcuIts and systEms magazInE

33
Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q2 2018
