调制域信号数字式差动放大电路研究

A Digital differential Signal Amplifier in Modulation Domain

通过研究不满足Shanon采样定理的采样, 发现当以低于Nyquist频率的采样频率对正弦周期信号采样时,能获得频率为该正弦周期信号频率与n倍采样信号频率之差的正弦周期信号的采样样本，在一定条件下能够实现采样频率变化的差动放大。本文从频谱混叠的角度解释角调制信号差动放大的原理, 给出了调制域中的差动公式和信号放大公式，并给出了适用于载波为方波的角调制信号的数字式差频放大电路的电路图，推导了该电路的误差和Allan方差公式， 在文中给出了实验值 。

By analyzing a sampling procedure that is not consistent with the Shanon sampling theorem，it is found that if a sine wave is sampled by a periodic signal which frequency is lower than the Nyquist frequency， a sample can be obtained with its frequency equal to the difference of the frequency of the sine wave itself and the n times of the sampling frequency. Under certain conditions, the variation of sampling signal can be amplified differentially. This paper explains the principle of differentially amplifying angular modulated signals based on the analysis of spectrum alias and derives the formula of differential amplification for the modulated signals. A typical digital differential amplifier is given for such signals, for which the carrier is rectangular waves. Error function and the Allan variance for this amplifier is also presented. The usefulness of proposed amplifier is proved by the data of experiment results.