A positive feedback system oscillating under self-sustained mode is shown to have an extremely high gain. Modeled as one port, the expected Q is much higher than the loaded Q-factor of the resonator. With just thermal noise present, random phase/frequency deviation is linear. Centered about the oscillator frequency omega/(0), noise frequency on both sides is more amplified with decreasing separation distance. Ultimately, frequency pulling may result in synchronous locking with hysteresis, which occurs because a real oscillator displays a truncated limiting curve. Once locked onto a signal, smaller levels are ignored. A new approach to the design and characterization of a simple tuned oscillator is offered: According to the phenomenon of injection locking, there exists an expected quality factor relating the shape of the truncated limiting curve to an ideal curve. In this paper, synthesis and innovative analytical methods of academic interest are revealed: 1) application of the transducer loss method is revised to establish a new method for oscillator characterization; 2) a transparent method of normalizing a two-port network in the presence of white noise is developed; and 3) in quartz crystal controlled oscillators, characterization of the noise originating from an equivalent noise-resistance determined from parameter of the quartz crystal is proposed. It is shown that the two-port model can also be approximated on a one-port basis. In conclusion, a sample of closed-form estimation of expected Q-factor order of magnitude of piezoelectric resonator oscillators is calculated.
This paper presents the effects of calcination time and sintering temperature on the properties of CaCu(3)Ti(4)O(12). Electroceramic material of CaCu(3)Ti(4)O(12) was prepared using a modified mechanical alloying technique that covers several processes, which are preparation of raw material, mixing and ball milling for 5 hours, calcination, pellet forming and, sintering. The objective of this modified technique is to enable the calcination and sintering processes to be carried out at a shorter time and lower temperature. The x-ray diffraction (XRD) analysis result shows that a single-phase of CaCu(3)Ti(4)O(12) was completely formed by calcination at 750 degrees C for 12 hours. Meanwhile, the grain size of a sample sintered at 1050 degrees C for 24 hours is extremely large, in the range of 20-50 mum obtained from field emission scanning electron microscopy (FESEM) images. The dielectric constant value of 14,635 was obtained at 10 kHz by impedance (LCR) meter in the sintered sample at 1050 degrees C. However, the dielectric constant value of samples sintered at 900 and 950 degrees C is quite low, in the range of 52-119.