Microwave Oscillators and Detectors Based …
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rent, I mod . The phenomena is described as a non-resonant unlocking mechanism.
The mechanism responsible behind this phenomena can be explained by an analytic
model that shows the phase dynamics of the STNO under the effect of two competing processes—namely, parametric synchronization and modulation. The modulation
source changes the synchronized phase (φ 0 ), shifting it to a new value of φ 1 . At
the maximum modulating amplitude, φ 0 reaches φ max , at which the STNO cannot
lock anymore as φ 0 > π. A linear relationship thus exists between f unlock and the
modulation amplitude. The maximum phase difference can be calculated by [136,
137]:
f max = 2νν p − (p 0 )
I mod
I DC
1
2
4 2
p + f
2
mod
(18)
At the unlocking condition—that is, at f mod = f unlock , the experimental data for f unlock
versus modulation strength in Fig. 16c can be fitted with the above Eq. (18) by
assuming f max to be equal to the excitation bandwidth. Thus the unlocking observed
in Ref. [136] can be identified as the nonresonant mechanism [138].
Fig. 16 Modulation of a locked STNO. a Experimental and b simulated spectra of the synchronized
STNO versus f mod at a modulation current of I mod = 0.99 mA. c The relation between f unlock and
I mod /I DC shows an increase with I mod for both experiments and numerical macrospin simulations.
The solid lines are fits to the data according to Eq. (18). Reprinted from Dürrenfeld et al. [136],
with the permission of AIP Publishing
29
rent, I mod . The phenomena is described as a non-resonant unlocking mechanism.
The mechanism responsible behind this phenomena can be explained by an analytic
model that shows the phase dynamics of the STNO under the effect of two competing processes—namely, parametric synchronization and modulation. The modulation
source changes the synchronized phase (φ 0 ), shifting it to a new value of φ 1 . At
the maximum modulating amplitude, φ 0 reaches φ max , at which the STNO cannot
lock anymore as φ 0 > π. A linear relationship thus exists between f unlock and the
modulation amplitude. The maximum phase difference can be calculated by [136,
137]:
f max = 2νν p − (p 0 )
I mod
I DC
1
2
4 2
p + f
2
mod
(18)
At the unlocking condition—that is, at f mod = f unlock , the experimental data for f unlock
versus modulation strength in Fig. 16c can be fitted with the above Eq. (18) by
assuming f max to be equal to the excitation bandwidth. Thus the unlocking observed
in Ref. [136] can be identified as the nonresonant mechanism [138].
Fig. 16 Modulation of a locked STNO. a Experimental and b simulated spectra of the synchronized
STNO versus f mod at a modulation current of I mod = 0.99 mA. c The relation between f unlock and
I mod /I DC shows an increase with I mod for both experiments and numerical macrospin simulations.
The solid lines are fits to the data according to Eq. (18). Reprinted from Dürrenfeld et al. [136],
with the permission of AIP Publishing