Frequency Deviation In LCOscillators Using IC Amplifiers 
Jochen Bauer
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While integrated circuit (IC) amplifiers are mostly used with RC and crystal oscillators, they can also be used as a feedback device for LC oscillators. However, two basic problems of practical LC oscillators, the development of parasitic oscillations with frequencies above the intended oscillation frequency range under certain conditions and a deviation of the actual oscillation frequency from the natural frequency
of the LC tank often become more pronounced when using integrated circuit amplifiers instead of one single active component. This is mostly because integrated circuit amplifiers often exhibit an appreciable delay between input and output signal even at relatively low frequencies. In the attached PDF document an extensive investigation of both, parasitic oscillations and frequency deviation, using a generic nonideal differential amplifier LCoscillator can be found. In the remainder of this post I would like to give a summary for the reader less interested in the math ematical details: We shall base our analysis on a generic LC oscillator using a differential voltage amplifier as shown in The LC tank is modeled by an ideal inductor L, an ideal capacitor C and a parallel loss resistance R_{P} that subsumes the losses occurring in the inductor and the capacitor. The feedback device "FB" is a In the ideal case, such a differential amplifier exhibits neither a delay time between input and output nor is it's amplification behavior frequency dependent. However, integrated circuit amplifiers, due to the A basic understanding of the behavior of the oscillator with phase shifted feedback can be obtained by going below the oscillation threshold and analyzing the response of the feedback device when driven externally by a small sinusoidal input voltage using complex phasors. From this linear analysis, we obtain the phase shift regions where the feedback device delivers positive feedback into the LC tank causing oscillations if the amplification factor of the feedback device is sufficiently high. Those phase shift regions are: 0°<φ<90°, 270°<φ<450°, 630°<φ<810° and so on... Oscillations occurring for phase shifts of 270° and above are typically undesired parasitic oscillations Introducing a nonlinear feedback device model with delay and gain rolloff at higher frequencies we are able to do a time domain analysis using differential equations. The model in use has a phase shift and gain frequency dependency that is shown in the following diagram. Here, a_{0} is the small signal DC gain (ω=0). Note that the parameters of the model have been chosen such that the above phase shift behavior re sembles the phase shift behavior of an LM311 voltage comperator. We shall now focus on the occur rence of parasitic oscillations above the primary (intended) oscillation frequency range for different values of the DC gain a_{0}. In the following diagram, the oscillation amplitude (if oscillations occur) has been plotted over the natural frequency ω_{0} of the LC tank for different values of a_{0}. (Note that a_{0}=200000 is the typical DC gain of a LM311 voltage comperator). Obviously, for a high gain of a_{0}=200000 (red curve) the circuit will oscillate not only when the natural This unfavorable behavior persists even down to a_{0}=10 (green curve) although the amplitude of the The reader may have noticed that for a_{0}=200000 even in the frequency range around 3MHz where the linear analysis predicts no oscillations at all, the amplitude curve indicates some residual oscillations. A deeper investigation reveals nonsinusoidal oscillations with frequencies jittering between the primary and parasitic oscillation frequency range. This is clearly a nonlinear phenomenon of the circuit. We shall now turn our attention to the deviation of the oscillation frequency ω_{osc} from the natural
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This article was edited 24.Mar.16 21:13 by Jochen Bauer . 