A study of injection locking and pulling in oscillators

Razavi, Behzad

doi:10.1109/jssc.2004.831608

Cited by 1,030 publications

(383 citation statements)

References 16 publications

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“…The phase noise of the optomechanical oscillation under injection was also investigated, and as expected 9 the presence of the locking signal improves the optomechanical oscillation phase noise. Figure 5 is the measured phase noise spectral density of the detected optical power for two frequency ranges ͑a͒ 0.01-10 kHz and ͑b͒ 10-1000 kHz.…”

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“…At a given ratio between modulation amplitude of the input signal and amplitude of the optomechanical oscillation imposed on the optical output ͑A inj / A OMO ͒, locking occurs within a limited bandwidth around f OMO ͑known as lock range͒. Similar to an electronic oscillator, for tuning slightly above and below the edge of lock range, the oscillator is quasilocked 9 and the rf spectrum consists of a series of closely spaced decaying beat frequencies in the vicinity of f OMO ͓Fig. 2͑c͔͒.…”

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“…2͑c͔͒. Based on the theoretical prediction using the general theory of injection locking for self-sustained oscillators, 9 the lock range can be written as a͒ Electronic mail: mhz@chtm.unm.edu. …”

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Observation of injection locking in an optomechanical RF oscillator

Hossein‐Zadeh

Vahala

2008

LEOS 2008 - 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society

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Injection locking of a radiation-pressure optomechanical oscillator is demonstrated through external modulation of the optical pump power near the optomechanical oscillation frequency. It is shown that the frequency and phase of a microtoroidal optomechanical oscillator can be locked to those of an electronic oscillator ͑or any other signal͒ that can modulate the optical input power and whose frequency is within the lock range. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.3028024͔Injection locking is a well-known effect in both selfsustained electronic and photonic oscillators ͑lasers͒. When a periodic signal with a frequency close to the oscillation frequency and large enough amplitude is injected into a selfsustained oscillator, the phase and frequency of the oscillator can be locked to that of the injected signal.1 Here this phenomenon is investigated in an optomechanical oscillator ͑OMO͒.2-4 OMOs are driven by radiation pressure and rely upon "dynamic back action" created when a continuouswave ͑cw͒ optical pump is blue-detuned relative to a resonance of an optical resonator that also features high-Q mechanical modes. 5 The OMOs of this study are based on high-Q silica microtoroids.2-4 The high optical Q factor and the unique geometry of toroid resonator ͑that enables efficient coupling between optical and mechanical degrees of freedom through radiation pressure͒ lead to self-sustained rf mechanical oscillations of the microtoroid structure 2-4 ͑even to gigahertz frequencies 6 ͒. Characterization of the phase noise and oscillation frequency have confirmed that the microtoroid OMO is potentially important in certain rf-photonic systems.7, 8 We demonstrate that partial amplitude modulation of the optical input power can lock both frequency and phase of the optomechanical oscillation to that of the external oscillator ͑used to modulate the input optical power͒. Preliminary experimental results confirm that injection locking in an OMO exhibits the characteristics of injection locking in electronic oscillators. Figure 1 shows the experimental arrangement used to study injection locking in the microtoroid OMO. The optical power from a tunable laser passes through a Mach-Zehnder ͑MZ͒ modulator and is coupled into and out of the microtoroid optical resonator using a fiber-taper coupler. The amplitude of the optical input power ͑P in ͒ is partially modulated by a single tone rf signal from a tunable rf synthesizer applied on the MZ modulator. The modulation index is thereby used to control the strength of the weaker injection-locking signal ͑modulated fraction of P in ͒ in comparison to the pump ͑cw fraction of P in ͒. The spectrum of optical power that is coupled out of the microtoroid is then analyzed in a rf spectrum analyzer. Also, the phase of the output signal is compared to that of the electronic input signal ͑injected signal͒ using a lock-in amplifier. When the amplitude of the injected signal is large enough and its frequency ͑f inj ͒ is close to optomechanical oscillation frequency ͑f OMO ͒, we obse...

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Observation of injection locking in an optomechanical RF oscillator

Hossein‐Zadeh

Vahala

2008

LEOS 2008 - 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society

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“…This mean value is also supposed to be unbiased thanks to the measurement protocol. This is the case if and only if we do not take into account the instrument uncertainties and a possible FOG nonlinearity, e.g., injection locking or pulling effects (Razavi, 2004). For this last, Eq.…”

Section: Interpolated Four-position Methodsmentioning

confidence: 99%

Fog-based automatic true north detection for absolute magnetic declination measurement

Gonsette

Rasson

Bracke

et al. 2017

Geosci. Instrum. Method. Data Syst.

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Abstract. Absolute magnetic measurements are of great importance in magnetic observatories. They allow not only instrument calibration but also data quality checking. They require the vertical and the geographic or true north as reference directions, usually determined by means of a level and by pointing an azimuth mark, respectively. We present here a novel system able to measure the direction of the magnetic field and of the vertical and true north. A design of a north seeker is proposed taking into account sensor bias as well as misalignment errors. Different methods are derived from this model and measurement results are presented. A measurement test at high latitude is also shown.

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“…If the amplitude and frequency of I inj are chosen properly, the circuit oscillates at ω inj rather than at ω 0 , and injection locking occurs [9]. Fig.…”

Section: B Orthogonal Injection Lockedmentioning

confidence: 99%

A CMOS Quadrature VCO With Subharmonic and Injection-Locked Techniques

Lee

Wang

Lin

2010

IEEE Trans. Circuits Syst. II

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A 1-V quadrature voltage-controlled oscillator (QVCO) using subharmonic and injection-locked techniques (SHIL-QVCO) is presented. Instead of using the traditional transformer-coupling LC tank with a large area to implement the quadrature output, we use a frequency-doubled differential pair with an injection-locked method. The proposed QVCO is implemented with a TSMC 0.18-µm 1P6M CMOS process having a 1.4 × 0.67 mm 2 chip area. This QVCO has the advantages of low phase noise and low power consumption. Experimental results show that the QVCO has a phase noise of −126 dBc/Hz at an offset frequency of 1 MHz and a power consumption of 4.9 mW to achieve a 186 figure of merit. Moreover, a tuning frequency between 2.17 and 2.52 GHz can be obtained with a tuning voltage range of 0-1 V for the IEEE 802.15.4.Index Terms-Frequency doubled, injection locked, oscillator, quadrature, radio-frequency complementary metal-oxidesemiconductor (RF CMOS), subharmonic, voltage-controlled oscillator (VCO).

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A study of injection locking and pulling in oscillators

Cited by 1,030 publications

References 16 publications

Observation of injection locking in an optomechanical RF oscillator

Observation of injection locking in an optomechanical RF oscillator

Fog-based automatic true north detection for absolute magnetic declination measurement

A CMOS Quadrature VCO With Subharmonic and Injection-Locked Techniques

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