A study of injection locking and pulling in oscillators

Injection locking characteristics of oscillators are derived and a graphical analysis is presented that describes injection pulling in time and frequency domains. An identity obtained from phase and envelope equations is used to express the requisite oscillator nonlinearity and interpret phase noise reduction. The behavior of phase-locked oscillators under injection pulling is also formulated.     

Injection locking of microwave solid-state oscillators

Injection locking of microwave solid-state oscillators is discussed, based on the familiar theorem that the total impedance times the current is equal to the applied voltage. Both quasi-static and dynamic analyses of the locking range, large-signal injection, locking stability, and AM and FM noise are given, and recent experimental work is reviewed briefly. No applications of injection locking are discussed in detail.     

Resonant frequency and Q factor of axisymmetric composite microwave cavities

Resonant frequency and unloaded Q factor of composite microwave cavities are computed using surface integral equations for axisymmetric objects. The equivalence principle is used to formulate the problem so that the unbounded space Green's function can be utilized. The numerical results are verified experimentally for many samples of conducting cavities and dielectric resonators inside conducting cavities. Also, cases with a sector of the rotational cavity are considered by introducing a conducting corner. The method allows the computation of the stored energy in each dielectric region and the unloaded Q factor.     

Phase noise measurement of free-running microwave oscillators at 5.8 GHz using 1/3-subharmonic injection locking

An innovative method using subharmonic injection locking technique for the phase noise measurement of free-running microwave oscillators is presented. To reduce the system cost, a two-tier injection locking approach is used and an effective 1/3-subharmonic injection is established. Measurement on a 1.8-V 5.85-GHz voltage controlled oscillator demonstrates that the measurement system is promising.     

Injection locking of oscillators

An oscillator can be locked in frequency by an external signal which is injected into the oscillator. In the oscillator model developed by Adler [1], the mechanism of the locking process depends upon the following. 1) The initial frequency difference between the oscillator and external signals. 2) The relative amplitude between the injected and the oscillator signals. 3) The circuit parameters. There are cases when the time required for locking must be known, particularly when an oscillator is being locked to a pulsed signal. In this paper, the work of Adler is extended to develop an equation which is useful for higher levels of locking signal, a case often encountered when an oscillator is being injection locked by a pulsed signal. Because the solution of this equation is unwieldy and difficult to understand intuitively, except in very special cases, curves describing the locking mechanism were obtained using a digital computer. These curves enable a designer to construct oscillators which will provide a desired performance. The curves were checked experimentally and showed a close agreement between predicted and measured results. The experimental data indicates that the theory describes the locking time remarkably well even at high levels of locking signal.     

Linewidth and offset frequency locking of external cavity GaAlAslasers

Stable external cavity GaAlAs lasers operated with full-width-at-half-maximum (FWHM) linewidths of less than 3 kHz are discussed. Offset frequency locking has been demonstrated over long periods to within the 10-Hz resolution bandwidth of the experiment. The spectral characteristics of these devices are presented graphically     

Phase-noise measurement using two inter-injection-locked microwave oscillators

Phase noise in two mutually coupled oscillators is analyzed by the describing function method, and the after-lock phase noise of the oscillators is calculated in terms of their free-running phase noise. A new phase-noise measurement technique based on inter-injection locking of two similar oscillators is proposed. Experimental results are presented, which confirm the theory. It is shown that in the case of zero phase of coupling coefficient, the system is in the optimum state where the only required parameter for the measurement is the locking bandwidth. In this optimum state, as far as the locking bandwidth is measured correctly, imperfections such as the frequency drift, parameters discrepancy, and nonlinear susceptance of the oscillators have no serious effect on the measurement accuracy. The proposed method is compared to the conventional ones.     

Above cutoff frequency circuit principles for microwave tunnel diode oscillators

The principle of possible operation of a tunnel diode above its classically accepted resistive cutoff frequency is presented. This principle requires a new interpretation of the tunnel diode mounting and equivalent circuit. The theoretical analysis indicates that, if the tunnel diode is operated in the series circuit mode, the diode cannot be operated above its classical resistive cutoff frequency; but, if the same diode is operated in the parallel circuit mode, the diode can be operated far above its classical resistive cutoff frequency. Millimeter-wave operation of a microwave tunnel diode is given as an example. When the tunnel diode is operated in the parallel circuit mode, a new cutoff frequency appears. This is the conductive lower cutoff frequency. Below the conductive lower cutoff frequency and within certain forbidden frequency bands, the tunnel diode is in-operative in the parallel circuit mode. A method of operating the tunnel diode in the parallel circuit mode is given. Equations for the new cutoff frequency and the forbidden frequency bands are derived. The tunnel diode can be operated in the parallel circuit mode at an extremely high frequency and can be operated in the series circuit mode at a relatively low frequency.     

Nonlinear analysis of microwave FET oscillators using Volterraseries

A novel approach for determining the amplitude and frequency of nonlinear FET oscillators is presented. The nonlinear elements of the active device are modeled by the Volterra series method. The frequency and amplitude of oscillation are then calculated by solving two algebraic equations. Experimental results obtained from a constructed oscillator confirm the validity of the theory, the discrepancy between measured and calculated frequency and amplitude values being less than 10%     

PHASE AND FREQUENCY LOCKING OF MICROWAVE AND MILLIMETER WAVE POWER COMBINING

The phase and frequency locking of microwave, millimeter wave power combining were analysed and summarized in an all-round way. The master/slave phase locking of cavity oscillators, the peer phase locking of mutually coupled oscillators, and the peer phase locking of ring-connected multiple oscillators were investigated. The results of numerical calculations, and the relations of phase to phase locking model and oscillator parameters were given. And the cavity and space power combining aspects for microwave and millimeter wave were presented.     

Network analysis of microwave oscillators using microstrip transmission lines

A network and computer-aided-design approach is discussed which is useful in designing microstrip oscillators to operate between 10 and 20 GHz. The analysis is applied to GaAs m.e.s.f.e.t. active devices.     

Injection locking of punched-through-injection transit-time oscillators

Injection-locking experiments have been conducted with the punched-through-diode oscillator, and the results have agreed well with theory. This confirms the nature of oscillations to be of a negative-resistance type and not of a relaxation type.     

Optical injection locking of impatt oscillators

A method for locking impatt oscillators by illuminating the impatt diode with a low-power laser beam, amplitude modulated at microwave frequency, is described. A large-signal theory of impatt operation, including the effects of finite reverse saturation currents and their modulation by the laser beam, is presented and predicts locking ranges of several tens of MHz with laser powers of a few mW     

Initial observations of optical injection locking of oscillators using heterojunction bipolar transistors

For the first time, optical phase control of a hybrid heterojunction bipolar transistor (HBT) oscillator has been achieved. The results strongly indicate that the HBT is a suitable device for optically controlled oscillators. At a frequency of oscillation of 500 MHz a locking range of more than 15 MHz was measured ( Delta f/f equivalent to 3%). The optical tuning range of the oscillator exceed 25 MHz.<>     

A study of locking phenomena in oscillators

Impression of an external signal upon an oscillator of similar fundamental frequency affects both the instantaneous amplitude and instantaneous frequency. Using the assumption that time constants in the oscillator circuit are small compared to the length of one beat cycle, a differential equation is derived which gives the oscillator phase as a function of time. With the aid of this equation, the transient process of "pull-in" as well as the production of a distorted beat note are described in detail. It is shown that the same equation serves to describe the motion of a pendulum suspended in a viscous fluid inside a rotating container. The whole range of locking phenomena is illustrated with the aid of this simple mechanical model.     

Design of cavity-stabilised microwave oscillators

A comparison is made between transmission reaction and reflection cavity-stabilised oscillators. Their essential features such as maximum loaded Q factor and tunuble frequency range are shown to differ markedly. Based on these considerations, outlines are given for designing highly stable microwave oscillators.     

Four-channel frequency locking using back-reflection dips of afibre-fed Fabry-Perot filter

A 4-channel frequency locking system has been demonstrated using a fibre-fed Fabry-Perot (FFP) filter with a free spectral range (FSR) of 100 GHz. A back-reflection curve from the FFP was used for the extraction of an error signal in such a way as to overcome the limitation in the number of accommodatable channels due to the saturation in a photodetector. The frequency stability and locking range of each channel were within 15 MHz and over 12 GHz, respectively