[hpsdr] Somethings on noise

[KA2WEU at aol.com]

_[Components]_ (http://www.mwrf.com/Topics/TopicID/717/717.html) 
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,_ (http://www.mwrf.com/Authors/AuthorID/1399/1399.html) 
_Ajay Kumar  Poddar_ (http://www.mwrf.com/Authors/AuthorID/1659/1659.html)   
|  ED Online ID  #16332 |  _August 2007_ 
(http://www.mwrf.com/Issues/IssueID/602/602.html)  


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_ 
(http://www.mwrf.com/Files/30/16332/Figure_01.gif)  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_ (http://www.mwrf.com/Files/30/16332/Figure_02.gif)  (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 aR 
and aE = the flicker noise constants for the  resonator and loop amplifier, 
respectively.


<-- prev.  page     [1] _2_ 
(http://www.mwrf.com/Articles/Index.cfm?ArticleID=16332&pg=2)  _3_ 
(http://www.mwrf.com/Articles/Index.cfm?ArticleID=16332&pg=3)  _4_ (http://www.mwrf.com/Articles/Index.cfm?ArticleID=16332&pg=4)      
_next page  -->_ (http://www.mwrf.com/Articles/Index.cfm?ArticleID=16332&pg=2)  



************************************** Get a sneak peek of the all-new AOL at 
http://discover.aol.com/memed/aolcom30tour
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.openhpsdr.org/pipermail/hpsdr-openhpsdr.org/attachments/20070825/e78ef136/attachment-0003.htm>