During the last decades, several theoretical models describing phase noise of oscillator signals have been established.
Verification of these models has mainly been done by computer simulations. However, what is still missing is a rigorous
experimental validation of diverse aspects of these models. This is not an easy job, since internal noise sources of the
measurement equipment superimpose the effects to be measured. Therefore, a novel measurement method is introduced.
Relatively strong, additional noise-sources are deliberately included into oscillator circuits. Controlling the power and
the spectrum of these sources allows to clearly identifying the effects of these sources to the spectrum of the oscillator's
output signal. This paper shows typical measurement results and their interpretations. It turns out that at least for the
oscillator under test, modeling with simple additive noise might not be sufficient. Rather, multiplicative noise must also
be taken into account. The consequence is that the output of oscillators might not only be affected by phase noise but
also by amplitude noise. Under these circumstances, models that explicitly exclude amplitude noise in oscillators might
need completion.
KEYWORDS: Oscillators, Digital video recorders, Amplifiers, Resonators, Interference (communication), Signal generators, Differential equations, Voltage controlled current source, Detection theory, Mathematics
A novel approach to the theory of phase-noise in resonator-oscillators will be given that is based on a combination of a large-signal-small-signal method, harmonic balance, and a modified Rice-model of signals plus noise. The method will be explained using a simple example. Since the type of oscillator under consideration not only de-attenuates eigen-oscillations but also noise in the spectral vicinity of the eigen-frequency, a signal is generated that is quasi-harmonic, and that might be described by means of a pseudo-Fourier-series expansion. Due to the specific description of the internal noise-sources, it is possible to use a time-domain description that at the same time reveals information about the spectral components of the signal. By comparison of these components, the spectrum of the oscillation might be determined. Relations between the spectrum of internal noise sources and the generated oscillator-signal will be recognized. The novel method will thus enable the designer to predict the phase-noise behavior of a specific oscillator-design.
The established description of linear, noise-generating systems in electronics uses mathematical techniques which were originally designed for linear, time-invariant systems. Noise spectra are often extracted from model descriptions in the time-domain by application of the Fourier-transform to the autocorrelation function of the output signal. Recently, it was pointed out that this description might be incomplete, since the parameters of noise-generating systems fluctuate, i.e. they vary with time. Therefore, the theory of linear time-variant systems (LTV-systems) should be applied rather than the theory of time-invariant systems. This was done for a very simple linear two-pole system. It turned out that even in this simple system novel, unexpected parts of the spectrum appeared in the output signal. In the submitted paper, this theory is expanded to linear, noise-generating four-poles and other n-ports. The mathematics of LTV-systems are well known since the fifties. It appears, however, as if their application to fluctuating noise-generating systems were limited to the analysis of narrow-band noise in the transmission channels of radio-links. The theory will, therefore, be adapted to electronic circuits which are fed by noise, and which have inner noise sources. It will be applied to a simple model of an integrated ohmic resistor in order to show the (so far unexpected) effect of the time-variance of parameters to the noise spectrum.
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