## Origin of linewidth broadening? Frequency fluctuations!

Why is the linewidth broadened ? Phasenoise is the parameter that any engineer will ask you to provide in order to evaluate the performance and to define possible applications for an oscillator. From theory [Kim, Slavin], phase noise is a major contribution to linewidth broadening and linewidth is thus a good first indicator for phase noise performance. The phase φ and frequency ƒare directly related by 2πƒ=dφ/dt, so phase and frequency noise are as well. Hence, if the frequency of the oscillator fluctuates, evidently the linewidth will be enlarged.
How to measure frequency fluctuations ? A first approach to understand the origin of linewidth broadening and of phase noise is to demonstrate that the frequency is not constant, but fluctuates in time. This can already be seen when studying the emission peak on a spectrum analyzer and reducing the number of averages and the scan time [1]. Subsequent registrations of the signal will show that the centre frequency changes from one scan to the next. How can we better demonstrate this ? Fluctuations are stochastic processes and thus require time resolved experiments. So, instead of using a spectrum analyzer we need a fast single shot oscilloscope of sufficient vertical resolution [1, 2].
Evidence of frequency fluctuations in Magnetic Tunnel Junction Oscillators (Hitachi) :

• A typical scan of the time domain signal (total length 1-20µs), registered on a single shot oscilloscope is given in Fig. 1b (zoom of 4ns), where the voltage oscillations can clearly be seen. In Fig. 1(a) a larger part of 200ns is shown where the oscillations cannot be distinguished, but the envelope is outlined by the black trace. Taking the Fourier Transform of the total trace will provide the emission peak (Fig. 1(c)), as also obtained using a spectrum analyzer. So this does not provide any additional information. Taking however instead the Fourier Transform over a smaller window of 10 to 100 ns, and then gliding the window along the trace (yellow frame in Fig. 1(a)), will provide some idea of the ‘instantaneous’ frequency and its evolution in time, as given in the frequency-time spectrogram in Fig. 1(d). The spectrogram clearly shows that the frequency fluctuates in time. This experiment has been the first direct experimental visualisation of frequency fluctuations of STOs [2] and initiated a number of time domain studies in this direction.
fig1
• The spectrogram method has also been used to demonstrate that when two peaks are present in the frequency domain spectra see Fig. 2(a), the corresponding modes are not excited simultaneously, but are switched on and off alternatively, see Fig. 2(b). [1]

fig2

Timescale of frequency fluctuations

From the spectrogram one would estimate a fluctuation time of a few tens of nanoseconds. However this timescale is related to the analysis technique. In fact frequency fluctuations exist on all timescales (ms to ns) and are indeed better described by a white noise. This has been demonstrated in further experiments by our group [3] when extracting phase and amplitude noise (see the corresponding section on Phase and Amplitude Noise).
SPINTEC Publications

[1] D. Houssemeddine, PhD Thesis September 2009, http://tel.archives-ouvertes.fr

[2] Phys. Rev. Lett. 102, 257202 (2009), D. Houssameddine et al.

[3] Appl. Phys. Lett. 97, 182507 (2010), M. Quinsat et al.
Main contributors:

• Dimitri Houssameddine, PhD microwave characterization
• Michael Quinsat, PhD microwave characterization
• Jean-Phillipe Michel, RF instrumentation
• Alex Zeltser, Danielo Mauri, Jordan Katine, Hitachi GST, San José (MTJ development and nanofabrication)
• Marie-Claire Cyrille
• Ursula Ebels

References

[Kim] Phys. Rev. Lett. 100, 017207 (2008), J.-V. Kim et al;

[Slavin] IEEE Trans. Magn. 45, 1875 (2009), A. N. Slavin et al;