# 短截线

1938年的真空管背包UHF收发器中的谐振短截线槽电路。大约长1/8 波长：（左面）200 MHz短截线为19 cm，（右面）300 MHz短截线为12.5 cm
1947年的10 kW的FM广播发射机展示了四分之一波长的谐振短截线板极振荡电路

## 短路短截线

${\displaystyle Z_{\mathrm {SC} }=jZ_{0}\tan(\beta l)\,\!}$

${\displaystyle l={\frac {1}{\beta }}\left[(n+1)\pi -\arctan \left({\frac {1}{\omega CZ_{0}}}\right)\right]}$

${\displaystyle l={\frac {1}{\beta }}\left[n\pi +\arctan \left({\frac {\omega L}{Z_{0}}}\right)\right]}$

## 开路短截线

${\displaystyle Z_{\mathrm {OC} }=-jZ_{0}\cot(\beta l)\,\!}$

${\displaystyle l={\frac {1}{\beta }}\left[(n+1)\pi -\operatorname {arccot} \left({\frac {\omega L}{Z_{0}}}\right)\right]}$

${\displaystyle l={\frac {1}{\beta }}\left[n\pi +\operatorname {arccot} \left({\frac {1}{\omega CZ_{0}}}\right)\right]}$

## 谐振短截线

${\displaystyle \beta ={\omega \over v}}$

${\displaystyle \omega _{0}={\frac {\pi v}{2l}}}$

## 参考文献

1. Shuart, George W. New high impedance lines replace coils (PDF). Short Wave Craft (New York: Popular Book Corp.). October 1934, 5 (6): 332–333 [March 24, 2015].
2. Ganesh Prasad Srivastava, Vijay Laxmi Gupta, Microwave Devices and Circuit Design, pp.29-31, PHI Learning, 2006 ISBN 81-203-2195-2.
3. ^ F.R. Connor, Wave Transmission, pp.32-34, Edward Arnold Ltd., 1972 ISBN 0-7131-3278-7.
4. ^ Matthaei, G.; Young, L.; Jones, E. M. T., Microwave Filters, Impedance-Matching Networks, and Coupling Structures, pp.681-713, McGraw-Hill 1964.