Communication systems rely on low-phase-noise signal sources such as tunable oscillators or phase-lock-loop (PLL) synthesizers for reliable voice communications and to ensure transmitted data integrity. Challenges still remain in achieving reasonable trade offs in low phase noise, low thermal drift, low power consumption, low cost, and potential for integration in integrated-circuit (IC) processes, however.^{1-38} With ever- increasing demands for high-speed data communications at rates in excess of 2 Gb/s,^{1-10} the phase-noise performance of the tunable signal source becomes critical in achieving acceptable system bit-error-rate (BER) performance.^{9} Fortunately, a design approach based on the use of selfinjection- locked compact coupled planar resonators (CCPRs) has been used to develop a line of high-performance, miniature RF/microwave signal sources that offer performance levels well suited to the demanding requirements of existing and emerging wireless communications systems.

Phase noise is a critical parameter for many electronic systems. For example, in short-distance radar systems, the capability to detect different targets as a function of time is dependent upon the phase-noise-performance of the system's VCO module. Such systems require a high-performance VCO with low phase noise and high DC-to-RF conversion efficiency, and VCO designers are constantly asked to make trade offs between phase noise, power consumption, tuning range, interference immunity, size, and cost considerations.^{6-12}

Constraints on high-quality factor (Q) resonator used in high-performance VCO circuits are particularly demanding, and a monolithic-microwave- integrated-circuit (MMIC) integrable solution has been the dream for decades.^{4} In general, a high Q resonator element is required to achieve low VCO phase-noise characteristics, but the realization of high Q resonator in planar form is difficult due to the higher loss characteristics of the resonator at high frequencies.

Dielectric resonators (DRs), for example, exhibit a high Q factor and have been used in high-spectral-purity signal sources at RF and microwave frequencies. Unfortunately, tunable oscillators based on DRs have been limited to narrow tuning ranges, are sensitive to vibration, high in cost, and not suited for current MMIC fabrication technologies.

An alternative, more cost-effective approach is to eliminate the DR and use a printed resonator, which is appropriate for use with current semiconductor manufacturing processes. Unfortunately, the phase-noise characteristics of VCOs based on printed resonators is inferior to VCOs using DRs since the Q of the DR is much higher than that of a printed resonator. ^{7-22} Planar resonators, such as ring, hairpin, spiral, and coupled resonators, can be easily implemented in a MMIC fabrication process, but with typically much larger size and lower Q than commercial DR-based oscillators. ^{2-10} The current work details research on a novel approach to improve the Q factor of a conventional printed resonator. The approach involves the use of a compact, modecoupling mechanism that is also well suited to MMIC processing.

Two available solutions are currently used for implementing highperformance VCOs. A DR-based VCO is usually the prime candidate for its high-Q performance at microwave frequencies. However, the DR requires precise machining for fabrication, and careful placement of the dielectric puck for optimal resonator coupling. This involves manual tuning of the DR for desired frequency operation. ^{7} The second approach involves fabricating an oscillator with MMIC techniques to produce a small, lowcost source, albeit with poor phase noise due to the low Q of printed resonators.1-10

Although dielectric-resonator-oscillator (DRO) circuits have been widely used as high-performance signal sources, designers have sought to replace DRs with printed resonators in order to reduce size and cost.^{1-18} To review, a DR is a piece of dielectric material usually manufactured in a circular shape like disk or a cylinder with high relative dielectric constant (e_{r} > 1) that acts as a resonant cavity by means of reflections at the dielectric/ air interface. *Figure 1* shows the typical DR in a polar coordinate for giving brief insights about the possible resonant condition for a given parameters (L, a, e_{r}). From ref. 8, it can be shown that by matching the tangential fields at the resonator interface (dielectric/air) at |*z*| =* L / 2* , one can derive the following

where L = the length of the DR, a = the radius, ε_{r} = the relative permittivity, and c = the speed of light.

From Eq. 6, the transcendental equation yields two possible solutions for resonant wavelength, λ, but only one of these is valid in yielding a deterministic solution within the dielectric (λ_{er}) and air (λ_{eo}).

*Figure 2* shows the typical high-performance DRO circuit using a DR in a push-push configuration. This design offers low phase noise but limited in tuning and poor subharmonic rejection.^{8} The exact placement of the DR disc between two parallel microstripline is critical, and slight variations can lead to higher harmonics and poor phase noise.

In addition to this, predicted DR resonant frequencies may differ from the measured results due to slight variations in temperature that cause problems during mass production and for integration of circuits. Such problems limit the usefulness of DRs. The frequency drift is not a straightforward function of temperature changes (due to different thermal expansion coefficients for cavity and dielectric pucks) and not easily corrected. The thermal sensitivity of a DRO can be reduced somewhat by the use of PLL circuitry and temperature control, although these are not integrable, cost-effective solutions.

Standard ICs are planar, so only those resonators having a planar structure are suitable for integration with such circuits.^{2-8} Unfortunately, integrable planar resonators are limited in Q and, therefore, in phase-noise performance. The poor phase-noise performance of a planar-resonatorbased VCO is due to the slow rate of change of phase and associated group delay characteristics of the resonator over the desire tuning range.

Recent publications explore the possibility to replace DR and techniques to improve the Q factor of the planar resonators for VCO applications, which have advantages for low cost, low phase hits, wide tuning range, and suited for on-chip realization.^{18-22} Resonators formed with lowtemperature- cofired-ceramic (LTCC) technology (*Fig. 3*) offer possible alternatives with high Q, and the technology can be adapted to MMIC processes, but it is difficult to integrate in a compact configuration.^{2 }Printed helical resonators are also a possibility for good high-Q performance in small size at microwave frequencies. *Figure 4* depicts the typical 3D layout of an inductively coupled helical resonator with two three-quarter-turn loops with via-hole connection.

*This concludes Part 1 of this three-part series. Next month, coupled resonators will aid -in VCO designs.*

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