摘要
在频率控制领域中,常用最小二乘法来进行数学逼近,但所需的是频率偏差最小而不是它的平方和最小。为此,在频率控制领域首次引入了最佳逼近算法,它能给出频率偏差的最小-最大解。该文不仅给出了最佳逼近算法用于晶体谐振器频率温度特性曲线拟合的方法和例子,并将该算法与最小二乘法作比较;从中看出该算法与最小二乘法比较具有优势。而且给出了它用于单电容温补晶振(TCXO)设计的方法和例子,并且在这个基础上制作了一个TCXO样品,经过补偿后该TCXO的频偏小于±1×1-0 6。结果表明:在频率控制领域最佳逼近算法比最小二乘法更有效。该算法对曲线拟合和工作温度范围在晶体谐振器两个零温度系数点之间的TCXO有实际意义。
In the frequency control domain,the least square approximation is the most universal mathematics approximation method. However we want to get the least value of frequency deviation ,not the least quadratic sum of it. So the best approximation algorithm in this domain, which can draw the mini-max solution of the frequency deviation,is introduced in this paper. We demonstrate the best approximation algorithm method and its application to the frequency-temperature curve fit of the crystal resonator. A comparison between these two methods is made. The result shows that the best approximation has an advantage over the least square approximation. Then ,its application to the single capacitor TCXO design is presented. Base on this method,we make a sample TCXO whose frequency deviation is less than 4-1 X 10-s after compensation. We consider that the best approximation is more effective than the least square approximation in frequency control domain. This algorithm has utility value for curve fit and the TCXO whose operation temperature range is between the two zero-temperature-coefficlent points of the crystal resonator.
出处
《压电与声光》
CSCD
北大核心
2005年第4期452-454,共3页
Piezoelectrics & Acoustooptics
