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Figure 1 shows a typical differential transmission-line-loaded, SRR-based metamaterial resonator oscillator. For a differential (push-pull) oscillator, the incident wave energy injected by the cross-coupled inverters propagates in forward waves along the transmission line towards the circuit’s short point; the energy is reflected at the SRR load, and the reverse wave has a superposition of the incident wave and leads to a resonance when in phase. Stronger wave reflection means less loss and higher resonator Q.20

Approach Drops SMD DRO Phase Noise, Fig. 1

When working with artificial composite materials, the negative permeability response can be manipulated by including electrically small resonant shapes, such as split rings. Figure 2 depicts a typical SRR structure for the realization of tunable μ(μ < 0) and ε(ε < 0) characteristics for applications in tunable oscillator circuits.17,18

Approach Drops SMD DRO Phase Noise, Fig. 2a

Approach Drops SMD DRO Phase Noise, Fig. 2b

Möbius strips offer unique characteristics, including self-phase-injection properties along the mutually coupled surface of the strips, enabling enhanced Q for a given size of printed transmission-line resonator. The oscillator’s loaded Q, QL, is described by Eqs. 5 and 6:

Approach Drops SMD DRO Phase Noise, Eq. 5

Approach Drops SMD DRO Phase Noise, Eq. 6

where:

φ(ω) = the phase of the oscillator’s open-loop transfer function at steady state and

τd = the group delay of the metamaterial Möbius strip resonator.

Approach Drops SMD DRO Phase Noise, Fig. 3

Figure 3 shows a typical metamaterial-based, Möbius-strip resonator and its equivalent lumped-element model circuits. From Eqs. 5 and 6, by introducing mode injection into metamaterial Möbius strips, phase-dispersion, loss, and group delay can be optimized.

Approach Drops SMD DRO Phase Noise, Fig. 4For applications requiring compact size DROs, surface-mount-device (SMD) DROs have been developed in housings measuring just 0.75 × 0.75 in. and also available on printed metamaterial Möbius strips in 0.5 × 0.5 in. and 0.3 × 0.3 in. square packages for low-cost signal-source applications. These oscillators can be extended to any number of fixed frequencies, typically from 3 to 18 GHz, without long lead times required to produce the sources. Figure 4 shows a typical layout of a 10-GHz DRO in a 0.75 × 0.75 in. housing (a model DRO 100-8 from Synergy Microwave Corp.) while Fig. 5 shows measured phase noise, at better than -108 dBc/Hz offset 10 kHz from the carrier.

Approach Drops SMD DRO Phase Noise, Fig. 5These oscillators should be powered by a clean DC bias voltage, otherwise an external regulator should be employed to minimize variations in supply voltage. A DRO factory set for an output frequency of 10 GHz, for example, can be mechanically adjusted by about ±50 MHz.

An electrical tuning port provides an adjustment range of ±1 MHz with tuning voltages of +1 to +15 VDC to compensate for frequency drift in phase-locked systems. The supply-current is typically 30 mA and the temperature range is specified from -25 to +70°C.

Dr. Ajay K. Poddar, Chief Scientist

Dr. Ulrich L. Rohde, Chairman

Synergy Microwave Corp., 201 McLean Blvd., Paterson, NJ 07504; (973) 881-8000, FAX: (973) 881-8361

Editor's Note: Ulrich L. Rohde was recently named the recipient of the 2014 C.B. Sawyer Award.

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