Tunable Magnetoacoustic Oscillator with Low Phase Noise

A frequency-tunable low-phase-noise magnetoacoustic resonator is developed on the base of a parallel-plate straight-edge bilayer consisting of an yttrium-iron-garnet (YIG) layer grown on a substrate of a gallium gadolinium garnet (GGG). When a YIG-GGG sample forms an ideal parallel plate, it supports a series of high-quality-factor acoustic modes standing along the plate thickness. Due to the magnetostriction of the YIG layer the ferromagnetic resonance (FMR) mode of the YIG layer can strongly interact with the acoustic thickness modes of the YIG-GGG structure, when the modes’ frequencies match. A particular acoustic thickness mode used for the resonance excitations of the hybrid magnetoacoustic oscillations in a YIG-GGG bilayer is chosen by the YIG-layer FMR frequency, which can be tuned by the variation of the external bias magnetic field. A composite scheme of a magnetoacoustic oscillator, which includes a FMR-based resonance preselector, is developed to guarantee satisfaction of the Barkhausen criteria for a single-acoustic-mode oscillation regime. The developed low-phase-noise composite magnetoacoustic oscillator can be tuned from 0.84 to 1 GHz with an increment of about 4.773 MHz (frequency distance between the adjacent acoustic thickness modes in a YIG-GGG parallel plate), and demonstrates the phase noise of $-116$ dBc/Hz at the offset frequency of 10 kHz.

Figure 1

(a) Scheme of a simple one-port reflection-based MAR, which is experimentally characterized using a vector network analyzer (VNA); (b) thickness distributions of the magnetic FMR mode and standing acoustic modes in the YIG-GGG bilayer sample; (c) $S_{11}$ parameters of the one-port MAR at different values of the perpendicular-to-plane magnetic bias field.

Figure 2

Coupling coefficients in the MAR as functions of the excitation frequency and the excited acoustic mode number $\lambda$: (a) theoretically calculated coupling coefficient between the FMR mode of the YIG resonator and the thickness acoustic modes of the YIG-GGG structure; (b) experimentally measured coupling coefficients: ${\sigma }_{\mathrm{YIG}}$ between the strip-line line and the FMR mode of the YIG resonator (blue squares); $\sigma$ between the FMR mode of the YIG resonator and the acoustic thickness modes of the YIG-GGG structure (red circles), ${\sigma }_{\mathrm{MAR}}$ overall coupling between the strip-line and the acoustic thickness modes (green triangles). The region highlighted in yellow indicates the frequency band where the overall coupling coefficient is suitable for the operation of the oscillator scheme. Note, that the FMR frequency of the YIG resonator is adjusted for a particular acoustic mode by changing the bias magnetic field $H_0$. In the frame (c), the experimental $S_{11}$ parameter at the magnetic field $H_0=215.3$ mT and in the frequency band $869\pm 15$ MHz is plotted on the Smith charts. The main loop with a diameter $\mathrm{\Delta }$ corresponds to the FMR mode, while inner loops correspond to acoustic modes. The central inner loop with a diameter $\delta$ corresponds to the acoustic mode with which the FMR frequency is aligned. The values of $\mathrm{\Delta },\delta$ are used to calculate the experimental values of ${\sigma }_{\mathrm{YIG}}$, ${\sigma }_{\mathrm{MAR}}$, $\sigma$, while the frequencies $f_0,f_1,f_2,f_{11},f_{22}$ are used to calculate the $Q$ factors $Q_{\mathrm{YIG}},Q_{\mathrm{MAR}}$, as described in Appendix pp2. At the frequencies where the coupling coefficient $\delta$ is close to zero, the inner acoustic loops disappear from the MAR $S_{11}$ parameter diagram.

Figure 3

$S$ parameters of the one-port (see Fig. 1) and two-port composite (Fig. 4) MARs: black line, $S_{11}$ parameter of the one-port MAR and $S_{21}\mathrm{parameter}$ of a two-port MAR; blue line, $S_{21}$ parameter of the FMR-based preselector; red line, $S_{21}$ parameter of the composite two-port MAR. The mode numbers of a corresponding acoustic thickness modes in the YIG-GGG parallel plate are given in brackets. Points A, B, and C are where the Barkhausen criterion for stable auto-oscillations is satisfied.

Figure 4

Scheme of a MAO based on a composite two-port MAR consisting of a one-port YIG-GGG MAR (left part of a YIG layer) connected to a YIG-FMR-based preselector filter (right part of the YIG layer). The left part in connection with a circulator forms a two-port MAR, which is connected to the purely magnetic YIG-FMR-based preselector filter formed by the right part of the YIG layer, where the acoustic modes are eliminated by scratching the bottom surface of the GGG substrate.

Figure 5

Experimentally measured phase-noise figures for auto-oscillators based on a purely magnetic YIG-FMR resonator (blue line) and on a composite two-port magnetoacoustic YIG-GGG resonator (red line). Dotted black line shows the estimation of the phase noise obtained from Leeson’s formula, Eq. (1), for a FMR-based magnetic preselector resonator ($Q_{\mathrm{YIG}}=365$), while the dashed black line shows a similar estimation of a phase noise for the composite two-port MAR (Fig. 4) having the $Q$ factor $Q_{\mathrm{MAR}}=2497$.