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Optimization Method of Amplitude Loss Caused by Digital CR-(RC)n Forming on Rise Time
DOI: 10.12677/nst.2024.122011, PDF, HTML, XML, 下载: 122  浏览: 243  科研立项经费支持

Abstract: The pulse rise time causes amplitude loss for CR-(RC)n pulse forming based on z transform. In this paper, based on the basis of deducing the recursion algorithm of real-time operation of CR-(RC)n filter in digital nuclear spectrometer system, the CR-(RC)n filter forming simulation with rise time is carried out for step signal, and the amplitude loss of the output pulse is proportional to the rise time or the order of the filter. In this algorithm, b is the main parameter affecting the output result. The algorithm is optimized by eliminating the influence of order n in the output pulse peak time (nτ). The simulation results of the optimized algorithm show that the value of parameter b decreases with the decrease of the amplitude loss of the output pulse, and the output amplitude loss caused by the rise time can be compensated by adjusting the size of b.

1. 引言

Nakhostin采用z变换推导出了不同n值时的CR-(RC)n电路的数字迭代算法 [11] 。杨小艳等通过改变阶跃信号的上升时间，模拟经过数字CR-(RC)n成形的输出，发现输出脉冲的幅度损失与其达峰时间成正比 [12] 。本文将以数字CR-RC滤波为基础，仿真不同上升时间的阶跃信号作为输入信号时，其输出脉冲在幅度上各有差异，与无上升时间阶跃信号经过数字CR-RC滤波成形的输出脉冲相比，在输出幅度上均存在不同损失。通过优化算法发现，调节其中的参数可以有效补偿幅值上的损失。

2. CR-(RC)n数字化滤波递归算法

CR-(RC)n滤波器由一个CR微分器和几个RC积分器实现。理论上，当使用无穷多个积分阶段时，可以很好地实现类高斯脉冲成形。滤波器经过z变换的传递函数可以表示为：

$H\left(z\right)=\frac{Y\left(z\right)}{X\left(z\right)}$ (1)

$X\left(z\right)=\frac{z}{z-1}$ (2)

${V}_{semi}\left(t\right)=\frac{1}{n!}\cdot {\left(\frac{t}{\tau }\right)}^{n}\cdot {\text{e}}^{-\frac{t}{\tau }}$ (3)

$Y\left(z\right)=H\left(z\right)X\left(z\right)$ (4)

Figure 1. CR-(RC)n filter digital recursion algorithm derivation flow

Table 1. Digital recursion algorithm of CR-(RC)n filter of orders 1~4

Figure 2. CR-(RC)n filter forming with different orders n

3. 仿真实验

3.1. 幅度损失

Figure 3. CR-RC forming with step signals of different rise times

Figure 4. CR-(RC)n forming output amplitude loss comparison

3.2. 改进算法

Table 2. Digital recursion algorithm of orders 1~4 for CR-(RC)n filter with uniform τ value

3.3. 解决效果

Figure 5. CR-RC filter forming with different b values

Figure 6. Amplitude loss of CR-RC filter output with different b values

4. 结论

1) 输出信号在相同达峰时间的条件下，输出幅度随着阶数的减小而增大，即CR-(RC)4滤波成形的幅度最小，CR-RC滤波成形的幅度最大；

2) 输入信号在相同上升时间的条件下，CR-(RC)n滤波成形输出的幅度损失随着阶数n的增大而增大，CR-RC滤波成形的幅度损失最小，而且随着输入的阶跃信号上升时间的增大，其输出的幅度损失也会逐渐增大；

3) 通过实验发现，调整参数b的大小可以补偿上升时间带来的幅度损失，幅度损失的影响也会随着b值变小而变小。

NOTES

*通讯作者。

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