диафрагмированные волноводные фильтры / eb914dcd-3e22-43e5-8e68-9b00aaebfd3c

Abstract—Whispering gallery mode resonator unit for low phase-noise oscillators was designed and tested at room and low temperatures. Use of the E-plane filter and optimization of the unit of coupling the resonator with microstrip transmission line allowed us to separate the operating EH 11 1 1 mode for the purpose of steady operation of the oscillator at 29.4 GHz. The obtained dependence of the resonator external Q-factor on the resonator height over a microstrip transmission line allows foretelling the transmission coefficient depending on the resonator height over a microstrip line that gives the chance to simplify process of the oscillator tuning, especially at low temperatures.

Keywords—whispering gallery modes; cavity resonators; microwave oscillators

I. INTRODUCTION

Low-noise oscillators are major components of modern microwave communication, radar and measuring systems. Such oscillators are created, as a rule, on the basis of high-Q resonant systems, which are connected into a loop of feedback of low-noise microwave amplifiers (LNA). The most suitable resonators in the microwave range of wavelengths are sapphire resonators with the whispering gallery modes (WGM) that is caused by extremely high values of Q-factor due to the very small losses in sapphire crystal. Using sapphire WGM resonators, for example, oscillators with the small level of phase noise were constructed at frequencies 10 GHz [1, 2] and 23 GHz [3]. However, in these works resonators were included into an oscillator feedback loop, using coaxial loopback antennas as coupling elements, which complicate control of balance of amplitude and a phase.

In this work the resonator module on the basis of sapphire disk WGM resonator, which is included into an oscillator feedback loop, is proposed and produced, using microstrip transmission lines. Such including of the resonator provides exact control of balance of wave amplitude by change of distance of the resonator over the transmission line and a phase by movement of the resonator along the line.

II. DESIGHN AND TESTING OFWGMRESONATOR UNIT

The resonator module was designed and produced for operation at a frequency of 29.4 GHz and consists of such basic elements: 1 - sapphire disk of a diameter of D=18.03mm

and thickness of L=3.02mm, 2 - microstrip transmission lines, 3 - waveguide and waveguide-to-microstrip line transitions, 4 - half-open case, 5 - band-pass filter (Fig. 1). In the photo it is possible to see the various constructive elements of fastening of the resonator, and also the elements allowing one to cool effectively the resonator module.

4

1

3 2

a)

5

4

3

1

2

b)

Fig. 1. CST microwave studio model (a) and photo (b) of whispering gallery mode resonator unit.

Frequency spectrum of the resonator module in the closed case is dense because the case modes are excited along with a disk WGMs, therefore the case is produced without sidewalls. Thus the frequency spectrum becomes almost identical to a spectrum of a single disk (Fig. 2).

Steady operation of the oscillator requires spectrum sparseness that is reached by use of the 3-pole E-plane bandpass filter [4]. The filter has a center frequency of

exhibits the insertion loss of approximately 0.5 dB, outside the passband reduction is more then 30 dB. Use of the filter allows us to achieve significant sparseness of the spectrum. Only HE12 1 1, EH11 1 1 and HE9 2 1 modes are excited in WGM resonator unit.

On the basis of efficiency of their excitation (Fig. 2) and electromagnetic fields distribution (Fig. 3), the EH11 1 1 mode was chosen as operating one. It is also important to choose such a position of the resonator relative to the microstrip transmission lines and also the resonator height so that the operating mode EH11 1 1 had the greatest difference of amplitudes with parasitic HE12 1 1 and HE9 2 1 modes.

For this purpose calculations of amplitudes of the operating and parasitic modes were carried out depending on distance on edge of the resonator to microstrip transmission line X (Fig. 4.) and also from the resonator thickness L. Fig. 4 shows that optimum position of the resonator is the X = -1mm that corresponds to difference of amplitudes more than 20 dB.

0

Frequency (GHz)

Fig. 2. Calculated spectrum of WGM resonator unit.

Fig. 3. Distribution of electromagnetic fields of EH11 1 1 mode.

Position, X (mm)

Fig. 4 Amplitudes of operating and parasitic modes depending on distance between an edge of the resonator and the microstrip lines at Z=2mm. Inset shows the resonator displacement relatively to the microstrip transmission lines.

It should be noted that at increase in thickness of the resonator, the amplitudes of both operating and parasitic modes decrease, but the amplitude of parasitic mode decreases quicker. The difference between these modes is 2 dB when thickness is 2 mm but this difference becomes 10 dB when thickness is 3 mm. Based on that F=29.4 GHz is the operating frequency, it is possible to consider L=3mm as optimum height of the resonator that corresponds to a wavelength in sapphire at this frequency.

One of important indicators at tuning the oscillator is the transmission coefficient. At a given position of edge of the resonator relatively to a microstrip transmission line X = -1mm the coefficient of transmission will depend on two parameters: distance between the resonator and microstrip transmission line and Q-factor of the resonator. Experimental dependences of the loaded Q-factor, resonant frequency and transmission coefficient are presented in Fig. 5 and Fig. 6.

The loaded Q-factor of the resonator can be expressed:

where T is temperature, L0 is losses in the coupling line, S13 is a transmission coefficient and Z is the distance between the resonator and the microstrip lines. On the basis of (1) and (2)

it is possible to find the Eigen Q-factor Qunload and the external Q-factor Qext (Fig. 7.).

At approach of the resonator to the microstrip lines, the losses conditioned by scattering of electromagnetic field of the resonator at a coupling element become essential. Therefore expression for the Eigen Q-factor can be written:

2

Distance, Z (mm)

Distance, Z (mm)

Fig. 5. Experimental dependences of the loaded Q-factor and resonant frequency on the distance of the resonator from the microstrip transmission line.

Distance, Z (mm)

Fig. 6. Experimental dependences of coefficients S12 and S13 on the distance of the resonator from the microstrip transmission line.

where Q0 and Qsc are Q-factors conditioned by losses in a single disk and scattering energy at the coupling elements accordingly. At the big values Z the losses due to scattering energy at the coupling elements become small in comparison with losses in sapphire, i.e. the Eigen Q-factor tends to Q0, and knowing Qunloaded, we can find Qsc on the basis of (3) (Fig. 7.).

Also it should be noted that at small Z values Qunloaded tend to Qsc because energy scattering at the coupling elements

increases and Q0 is independent on coupling of the resonator

with the line. At the same time Qloaded tends to the Qext. Coupling of the resonator doesn't depend on Q0, therefore,

knowing dependence of Qext on position of the resonator over a microstrip transmission line and neglecting the losses caused by the сoupling elements at big values of Z> 2mm, it is possible to predict a height Z for both the preset values of Q- factor of the resonator and the transmission coefficient. For example, taking in attention that Q-factor rise from 450000 to about 900000 when temperature of the resonator decrease from 120 K to 90 K, it is possible to obtain dependence of coefficient S13 on the distance Z at T=90 K (Fig. 8.). Dependence in Fig. 8 is conditioned by removal of degeneration of the whispering gallery modes at low temperatures.

Fig. 7. Q-factors Qloaded, Qunloaded, Qext and Qsc depending on the distance of the resonator from the microstrip transmission line

Distance, Z(mm)

Fig. 8. Dependence of transmission coefficient S13 on the distance Z of the resonator from the microstrip transmission line

On the basis of Fig. 8, the transmission coefficient S13 = -17 dB at Z = 4.15 mm, which correlates well with experimental value S13 = -18 dB.

Opportunity to predict the transmission coefficient at low temperatures is very important circumstance at tuning of the oscillator as it allows the tuning only by movement of the resonator along microstrip transmission lines, which allows adjusting in turn balance of phases.

III. CONCLUSION

The WGM sapphire resonator-based unit for low phasenoise oscillator was designed, made and investigated at room and cryogenic temperatures. In spite of the fact that the spectrum of the resonator unit is dense, it is possible, using the band-pass filter and also using optimization of the coupling unit of the resonator with a microstrip transmission line, to separate the operating EH11 1 1 mode rather easy. The resonator-based unit was optimized for operation at a frequency of 29.4 GHz, however can be rather simply modified for higher frequencies. Possibility of easy control of the transmission coefficient and also possibility of movement of the resonator along the microstrip transmission lines allow concluding that the developed device is the challenging one for low phase-noise oscillators, especially at low temperatures.

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REFERENCES

[1]Poseidon Sci. Instrum., Fremantle, W.A., Australia, Tech. data sheet, 2016.

[2]http://www.uliss-st.com, data sheet, 2016.

[3]S. A. Vitusevich, K. Schieber, I. S. Ghosh, N. Klein, and M. Spinnler, “Design and characterization of an all-cryogenic low phase-noise

sapphire K-band oscillator for satellite communications,” IEEE Trans. Microwave Theory and Techniques, vol.51, No.1.pp. 143169, 2003.

[4]R. Vahldieck, J. Bornemann, F. Arndt, and D. Grauerhoh, “Optimized Waveguide E-plane Metal Insert Filters for Millimeter Wave Applications," IEEE Trans. on MTT, Vol.MT"- 31, N0.1, 1983, pp.6569.