Relationship of AM to PM noise in selected RF oscillators

We have studied the amplitude modulation (AM) and phase modulation (PM) noise in a number of 5 MHz and 100 MHz oscillators to provide a basis for developing models of the origin of AM noise. To adequately characterize the AM noise in high performance quartz oscillators, we found it necessary to use two-channel cross-correlation AM detection. In the quartz oscillators studied, the power spectral density (PSD) of the f/sup -1/ and f/sup 0/ regions of AM noise is closely related to that of the PM noise. The major difference between different oscillators of the same design depends on the flicker noise performance of the resonator. We therefore propose that the f/sup -1/ and f/sup 0/ regions of AM and PM noise arise from the same physical processes, probably originating in the sustaining amplifier.<<ETX>>


I. INTRODUCTION
T 0 OUR KNOWLEDGE there has been little quantitative work analyzing ,the relationship between AM and PM noise in oscillators. Most of the literature assumes that the AM noise is much smaller than the PM noise. Leeson, Parker, and others have described models of PM noise in oscillators [l]- [3]. We are not aware, however, of any theory for the spectral dependence of the AM noise close to the carrier. We have therefore undertaken a detailed study of PM and AM noise in several quartz oscillators at 5 and 100 MHz to provide a basis for developing models of the origin of AM noise.
To adequately characterize the AM noise in high performance quartz oscillators, we found it necessary to use two-channel cross-correlation AM detection. The signal is split by a reactive power splitter into two signals that are each AM detected. The resulting baseband signals are then amplified and the power spectral density (PSD) of the cross spectrum between the two channels is computed. This technique provides a noise floor of order -190 dBc/Hz for AM noise at 50 kHz and -160 dBc/Hz at 10 Hz for signals of approximately + l 3 dBm.
An improved three-comered-hat technique using crosscorrelation makes PM noise measurements more quickly and accurately than the traditional three-comered-hat measurement technique [4J, [ S ] . In this approach the noise contribution of both the two references and the measurement systems average down to zero as 1 where I\-is the number of measurnments taken. In our setup we were able to obtain a PM noise floor fl The relationship between the AM and PM noise can be exploited in many areas of analysis to assist in the design of new oscillators. It is tedious to determine the PM performance of a new oscillator design, especially one that exhibits performance superior to existing references. At the very minimum three oscillators of similar performance are required. (The requirements on the performance of the other oscillators can be relaxed considerably if the modified threecomered-hat approach is used [4], [5].) On the other hand the AM performance of a single superior oscillator can be more easily assessed using the two-channel cross-correlation AM detection techniques presented in this paper. Therefore, it can be beneficial to use the readily obtained AM performance to evaluate the noise more quickly.

MEASUREMENT TECHNIQUES
At the output of the spectrum analyzer we obtain S,(f)/2 for AM noise, or S+(f)/2 for PM noise measurements. These are the single-sideband spectral densities of our signal. The practical definition for the power spectral density of amplitude fluctuations is given by where k ( f ) is the change in amplitude measured at Fourier separation f from the carrier, V, is the average carrier voltage and BW is the noise bandwidth of the spectrum analyzer. For the measurement system shown in where the proportionality constant c11 = [ k U G ( f ) l 2 .
Subtracting the source noise from (3) and (4), respectively, we are able to obtain the noise in each channel [see (6) and (7)].

IV. AM AND PM NOISE FOR SELECTED OSCILLATORS
AM and PM noise measurements on various oscillators are described below. The mathematical models for their relationships are presented in the following section. Fig. 4 shows the AM and PM noise of a 5 MHz oscillator that uses an AT-cut resonator driven at low power. The AM noise was measured using the techniques described in the previous section. Calibration of the PM noise was done using a three-comered-hat technique outlined in [S]. The PM noise in the 0.3 to 3 Hz range shows flicker frequency (f-3) as expected with white PM noise at higher Fourier frequencies. The AM noise shows f -2 (white frequency) behavior as does the PM noise until 30 Hz and continues to follow the white PM noise to higher Fourier frequencies. The models for the AM and PM noise are both similar for the f P 2 and f o components of the noise. The 100 MHz oscillator in Fig. 8

VI. CONCLUSION
The model relationships between the various 5 MHz oscillators present strong evidence to suggest that there is a connection between the AM and PM noise for a specific oscillator. f-' and fo components in both the AM and PM noise seem to come from the same source. The 100 MHz oscillator relationships are inconclusive in this respect, although they maintain similar model relationships between the two SC-cut oscillators tested. We speculate that the difference in the model and the data in Fig. 8 could be due to compression in the output amplifier of our system. The fo component of the AM and PM noise for the 100 MHz oscillators, however, seems to be similar and should give some information about the thermal noise characteristics in our oscillators.