Storing and dumping processes of energy in high quality factor resonant cavity
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摘要: 为了计算高品质因数谐振腔的储能过程和泄能过程，将高品质因数谐振腔的输入膜片和输出结构分别建模为一个二端口网络和一个三端口网络，根据高品质因数谐振腔的信号流图，提出了一种基于递推的数值计算方法。用该方法设计了一个工作在2.92 GHz附近的基于BJ32波导的高品质因数谐振腔，给出了谐振腔的储能过程和泄能过程。当输入膜片开口宽度取20 mm、输出膜片开口宽度取60 mm时，计算得出的谐振频率为2.9198 GHz，饱和储能时间为2.6 μs，输出脉冲宽度6.82 ns，输出峰值增益为129.6，能量效率为0.169。Abstract: In order to calculate the storing process and dumping process of energy in high quality factor resonant cavity, the input iris and the output coupling structure are modeled as a 2-port net and a 3-port net respectively, and an algorithm based on iteration is proposed according to the signal flow graph of the high quality factor resonant cavity. The algorithm is then used to design a high quality factor resonant cavity working around 2.92 GHz and based on rectangular waveguide of type BJ32. When the width of the input iris takes 20 mm and the width of the output iris takes 60 mm, the resonant frequency, the storing time, the pulse width of the output pulse, the peak output power gain and the energy efficiency are calculated to be 2.9198 GHz, 2.6 μs, 6.82 ns, 129.6 and 0.169, respectively.
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图 1 谐振腔的示意图及S参数计算模型
Figure 1. Schematic of the resonant cavity and the model for calculating S-parameters
图 2 谐振腔的S参数及z轴上电场计算结果
Figure 2. Calculated results of S-parameters and electric field intensity at axis z
图 4 经过2000步递推计算得出的输入端功率增益
${G_{2}}{\rm{(200}}0)$ Figure 4. Power gains
${G_{2}}{\rm{(200}}0)$ at the input port after 2000 iterations
图 5 储能过程中输入端功率增益
${G_{\rm{1}}}$ ,${G_{2}}$ 及输出端功率增益${G_{\rm{6}}}$ Figure 5. Power gains
${G_{\rm{1}}}$ ,${G_{2}}$ at the input port and power gains${G_{\rm{6}}}$ at the output port in storing process
图 6 泄能过程中输入端功率增益
${G_{\rm{1}}}$ 及输出端功率增益${G_{\rm{6}}}$ Figure 6. Power gain
${G_{\rm{1}}}$ at the input port and power gain${G_{\rm{6}}}$ at the output port in dumping process表 1
${w_{\rm{1}}}$ 取不同值时谐振腔参数计算结果Table 1. Calculated parameters of the resonant cavity when
${w_{\rm{1}}}$ takes different values${w_1}$/mm $\Delta \lambda $/mm ${f_0}$/GHz $\left| {{S_{11}}} \right|$/dB $\left| {{S_{{2}1}}} \right|$/dB ${P_ + }$/W ${G_ + }$ ${Q_0}$ ${Q_{\rm{e}}}$ 20 1.08 2.9194 −25.33 −5.86 26.8 53.6 18501 52019 22 1.08 2.9189 −16.39 −4.58 23.1 46.2 18488 31304 25 1.08 2.9179 −8.69 −3.52 15.1 30.2 18460 13376 
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表 2
${w_{2}}$ 取不同值时谐振腔参数计算结果Table 2. Calculated parameters of the resonant cavity when
${w_{2}}$ takes different values${w_{2}}$/mm $\Delta \lambda $/mm ${f_0}$/GHz $\left| {{S_{11}}} \right|$/dB $\left| {{S_{{2}1}}} \right|$/dB ${P_ + }$/W ${G_ + }$ ${Q_0}$ ${Q_{\rm{e}}}$ 60 1.08 2.9229 −26.1 −6.25 28.7 57.4 18502 58721 66 1.08 2.9213 −26.1 −6.01 27.5 55 18503 54612 72.14 1.08 2.9194 −25.33 −5.86 26.8 53.6 18501 52019
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表 3 输入膜片的S参数
Table 3. S-parameters of the input iris
${w_{\rm{1}}}$/mm Si11 Si12 20 −0.9881+0.0748j 0.0098+0.1290j 22 −0.9781+0.1180j 0.0201+0.1663j 25 −0.9499+0.1964j 0.0487+0.2355j
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表 4 输出结构的S参数
Table 4. S-parameters of the output structure
${w_{2}}$/mm So11 So12 So13 So33 60 −0.2319−0.0767j 0.7514−0.2568j 0.47+0.2962j −0.1047+0.6096j 66 −0.2428−0.0301j 0.7252−0.2794j 0.5105+0.2729j −0.0158+0.5731j 72.12 −0.2405+0.0165j 0.7040−0.3105j 0.5228+0.2556j 0.0294+0.5481j
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表 5 输出峰值增益
Table 5. Peak gain at the output port
${w_{2}}$/mm $\left| {{S_{{\rm{o}}13}}} \right|$ ${G_ + }$ ${G_{\rm{S}}}$ ${G_{6{\rm{p}}}}$ $\eta $ 60 0.5555 57.4 70.86 129.6 0.169 66 0.5555 55 67.90 77.34 0.101 72.12 0.5555 53.6 66.17 77.95 0.102
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