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Phase noise
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Phase noise is the frequency domain representation of rapid, short-term, random
fluctuations in the phase of a wave, caused by time domain instabilities ("jitter"). Generally
speaking radio frequency engineers speak of the phase noise of an oscillator, whereas
digital system engineers work with the jitter of a clock.
An ideal oscillator would generate a pure sine wave. In the frequency domain, this would
be represented as a single pair of delta functions (positive and negative conjugates) at the
oscillator's frequency, i.e., all the signal's power is at a single frequency. All real oscillators
have phase modulated noise components. The phase noise components spread the power of
a signal to adjacent frequencies, resulting in sidebands. Oscillator phase noise often
includes low frequency flicker noise and may include white noise.
Phase noise (L(f)) is typically expressed in units of dBc/Hz at various offsets from the
carrier frequency. For example, a certain signal may have a phase noise of -80dBc/Hz at an
offset of 10kHz and -95dBc/Hz at an offset of 100 kHz. These are really phase noise
density values. Phase noise can be measured and expressed as single sideband or double
sideband values. Phase noise is sometimes also measured and expressed as a value
integrated over a certain range of offset frequencies. For example, the phase noise may be
-40dBc integrated over the range of 1kHz to 100kHz. This Integrated phase noise
(expressed in degrees) can be converted to jitter (expressed in seconds) using the following
formula.
Jitter(seconds) = PhaseError(degrees) / (360xFrequency(hertz))
Contents
[hide]
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1 Measurement
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2 Spectral purity
3 References
4 Further reading
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5 See also
6 External links
[edit] Measurement
Phase noise is often measured using a spectrum analyzer which can show the noise power
over many decades of frequency eg. 1Hz to 10MHz. There is often a base noise curve with
superimposed spikes at specific frequencies. The general slope in various frequency
regions hints at the source of the noise, eg. low frequency flicker noise decreasing at 30
dB/Hz per decade (=9 dB/Hz per octave). [1]
The Leeson equation includes noise decreasing at 6 dB/Hz per octave due to resonators.[2]
[edit] Spectral purity
Spectral purity is how close an oscillator's output frequency comes to an ideal line of zero
width. [3]
[edit] References
1. ^ http://rfdesign.com/mag/607RFDF2.pdf Low noise oscillators
2. ^ http://www.odyseus.nildram.co.uk/Systems_And_Devices_Files/PhaseNoise.pdf
3. ^ Wolaver, 1991, p.105
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Noise in mixers, oscillators, samplers, and logic: an introduction to cyclostationary
noise
National Institute of Standards and Technology Time and Frequency Metrology
Group
[edit] Further reading
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Wolaver, Dan H. 1991. Phase-Locked Loop Circuit Design, Prentice Hall, ISBN
0-13-662743-9
A. Hajimiri and T.H. Lee, "A general theory of phase noise in electrical
oscillators", IEEE Journal of Solid-State Circuits, Vol. 33, No 2, Feb. 1998
Pages:179 - 194, DOI 10.1109/4.658619
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A. Demir, A. Mehrotra and J. Roychowdhury, "Phase noise in oscillators: a
unifying theory and numerical methods for characterization", IEEE Trans. on
Circuits and Systems I: Fundamental Theory and Applications, Vol. 47, No 5, May
2000, Pages:655 - 674, DOI 10.1109/81.847872
A. Chorti and M. Brookes, "A spectral model for RF oscillators with power-law
phase noise", IEEE Trans. on Circuits and Systems I: Regular Papers, Vol. 53, No
9, Sept. 2006 Pages:1989 - 1999, DOI 10.1109/TCSI.2006.881182
[edit] See also
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Jitter
Spectral density
Noise spectral density
Flicker noise
[edit] External links
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A technical article about phase noise in signal sources due to phase modulation.
Phase-noise measurement software for various GPIB-equipped spectrum analyzers
(freeware, includes Win32 C++ source)
Clock (CLK) Jitter and Phase Noise Conversion
Phase noise and frequency synthesizers
Phase Noise measurement using the phase lock technique
Retrieved from "http://en.wikipedia.org/wiki/Phase_noise"
Categories: Oscillators | Telecommunications terms
Technique Trims VCXO Phase Noise
This patented circuit approach can improve the phase-noise performance and frequency stability
of even low-cost voltage-controlled crystal oscillators.
Ulrich L. Rohde, Ajay Kumar Poddar
|
ED Online ID #16332
|
August 2007
Frequency reference standards are essential to achieving frequency accuracy
and phase stability in electronic systems. Such sources require the chief
characteristics of low phase noise and good frequency stability.1-13 The best
oscillator performance can be expensive, however. Fortunately, a patented
approach has been developed to design and optimize the performance of
voltage-controlled crystal oscillators (VCXOs), even those with relative low
quality-factor (Q) resonators, to achieve excellent phase noise and frequency
stability.
A typical oscillator consists of a tuned circuit and an active device such as a
transistor. Ideally, the tuned circuit provides a high loaded Q, generally from
less than 100 for simple circuits to more than 1 million for
crystal-resonator-based circuits. Noise arises from the active device as well as
from resonator losses. Noise from a bipolar transistor, for example, stems from
base and collector contributions and from device parasitic elements, such as
the base-spreading resistor. The filtering effect of the resonator tends to
remove the device noise, with higher Qs delivering greater filtering effects. The
Leeson equation relates these noise effects.1 The formula was modified by
Rohde for use with VCOs.2
The equation is linear, with many unknowns. Among the more difficult
oscillator performance parameters to predict are output power, noise figure,
operating Q, and flicker corner frequency. The parameters can not be derived
for linear conditions but require large-signal (nonlinear) analysis.3 But by
combining Leeson's formula with the contributions of the tuning diode,2 Eq. 3
results, making it possible to calculate oscillator noise based on a linear
approach:
where:
£(fm) = the ratio of sideband power in a 1-Hz bandwidth to the total power (in
dB) at the frequency offset (fm);
f0 = the center frequency;
fc = the flicker frequency;
QL = the loaded quality factor (Q) of the tuned circuit;
F = the noise factor;
kT = 4.1 10–21 at 300°K (room temperature);
Psav = average power at oscillator output;
R = the equivalent noise resistance of tuning diode (typically 50 Ω to 10 kΩ);
and
Ko = the oscillator voltage gain.
Equation 1 is limited by the fact that loaded Q typically must be estimated; the
same applies to the noise factor. The following equations, based on this
equivalent circuit, are the exact values for Psav, QL, and F, which are required
for the Leeson equation. Figure 1 shows the typical simplified Colpitts oscillator
giving some insights into the novel noise calculation approach.4
From ref. 3, the noise factor can be calculated by:
After some small approximation,
Figure 2 (left) illustrates the dependency of the noise factor on feedback
capacitors C1 and C2. From Eq. 1, the phase noise of the oscillator circuit can
be enhanced by optimizing the noise factor terms as given in Eq. 3 with
respect to feedback capacitors C1 and C2.
Equation 4 can be found by substituting 1/re for Y21+ (+ sign denotes the
large-signal Y-parameter).
When an isolating amplifier is added, the noise of an LC oscillator is
determined by Eq. 5.
where:
G = the compressed power gain of the loop amplifier;
F = the noise factor of the loop amplifier;
k = Boltzmann's constant;
T = the temperature (in degrees K);
P0 = the carrier power level (in W) at the output of the loop amplifier;
F0 = the carrier frequency (in Hz); fm = carrier offset frequency (in Hz);
QL = (πF0τg) = the loaded Q of the resonator in the feedback loop; and a R and
aE = the flicker noise constants for the resonator and loop amplifier,
respectively.