# الدوائر الكهربية رباعية الأقطاب

الدوائر الكهربية رباعية الأقطاب هي عبارة عن دوائر كهربائية تحتوي على مدخل و مخرج، أي تحتوي على أربعة أقطاب.

## العلاقة بين المتغيرات

| | $\mathbf {[z]}$ | $\mathbf {[y]}$ | $\mathbf {[h]}$ | $\mathbf {[g]}$ | $\mathbf {[a]}$ | $\mathbf {[b]}$ |
| $\mathbf {[z]}$ | ${\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {y_{22}}{\Delta \mathbf {[y]} }}&{\dfrac {-y_{12}}{\Delta \mathbf {[y]} }}\\{\dfrac {-y_{21}}{\Delta \mathbf {[y]} }}&{\dfrac {y_{11}}{\Delta \mathbf {[y]} }}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {\Delta \mathbf {[h]} }{h_{22}}}&{\dfrac {h_{12}}{h_{22}}}\\{\dfrac {-h_{21}}{h_{22}}}&{\dfrac {1}{h_{22}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {1}{g_{11}}}&{\dfrac {-g_{12}}{g_{11}}}\\{\dfrac {g_{21}}{g_{11}}}&{\dfrac {\Delta \mathbf {[g]} }{g_{11}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {a_{11}}{a_{21}}}&{\dfrac {\Delta \mathbf {[a]} }{a_{21}}}\\{\dfrac {1}{a_{21}}}&{\dfrac {a_{22}}{a_{21}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {-b_{22}}{b_{21}}}&{\dfrac {-1}{b_{21}}}\\{\dfrac {-\Delta \mathbf {[b]} }{b_{21}}}&{\dfrac {-b_{11}}{b_{21}}}\end{bmatrix}}$ |
| $\mathbf {[y]}$ | ${\begin{bmatrix}{\dfrac {z_{22}}{\Delta \mathbf {[z]} }}&{\dfrac {-z_{12}}{\Delta \mathbf {[z]} }}\\{\dfrac {-z_{21}}{\Delta \mathbf {[z]} }}&{\dfrac {z_{11}}{\Delta \mathbf {[z]} }}\end{bmatrix}}$ | ${\begin{bmatrix}y_{11}&y_{12}\\y_{21}&y_{22}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {1}{h_{11}}}&{\dfrac {-h_{12}}{h_{11}}}\\{\dfrac {h_{21}}{h_{11}}}&{\dfrac {\Delta \mathbf {[h]} }{h_{11}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {\Delta \mathbf {[g]} }{g_{22}}}&{\dfrac {g_{12}}{g_{22}}}\\{\dfrac {-g_{21}}{g_{22}}}&{\dfrac {1}{g_{22}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {a_{22}}{a_{12}}}&{\dfrac {-\Delta \mathbf {[a]} }{a_{12}}}\\{\dfrac {-1}{a_{12}}}&{\dfrac {a_{11}}{a_{12}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {-b_{11}}{b_{12}}}&{\dfrac {1}{b_{12}}}\\{\dfrac {\Delta \mathbf {[b]} }{b_{12}}}&{\dfrac {-b_{22}}{b_{12}}}\end{bmatrix}}$ |
| $\mathbf {[h]}$ | ${\begin{bmatrix}{\dfrac {\Delta \mathbf {[z]} }{z_{22}}}&{\dfrac {z_{12}}{z_{22}}}\\{\dfrac {-z_{21}}{z_{22}}}&{\dfrac {1}{z_{22}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {1}{y_{11}}}&{\dfrac {-y_{12}}{Y_{11}}}\\{\dfrac {y_{21}}{y_{11}}}&{\dfrac {\Delta \mathbf {[y]} }{y_{11}}}\end{bmatrix}}$ | ${\begin{bmatrix}h_{11}&h_{12}\\h_{21}&h_{22}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {g_{22}}{\Delta \mathbf {[g]} }}&{\dfrac {-g_{12}}{\Delta \mathbf {[g]} }}\\{\dfrac {-g_{21}}{\Delta \mathbf {[g]} }}&{\dfrac {g_{11}}{\Delta \mathbf {[g]} }}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {a_{12}}{a_{22}}}&{\dfrac {\Delta \mathbf {[a]} }{a_{22}}}\\{\dfrac {-1}{a_{22}}}&{\dfrac {a_{21}}{a_{22}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {-b_{12}}{b_{11}}}&{\dfrac {1}{b_{11}}}\\{\dfrac {-\Delta \mathbf {[b]} }{b_{11}}}&{\dfrac {-b_{21}}{b_{11}}}\end{bmatrix}}$ |
| $\mathbf {[g]}$ | ${\begin{bmatrix}{\dfrac {1}{z_{11}}}&{\dfrac {-z_{12}}{z_{11}}}\\{\dfrac {z_{21}}{z_{11}}}&{\dfrac {\Delta \mathbf {[z]} }{z_{11}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {\Delta \mathbf {[y]} }{y_{22}}}&{\dfrac {y_{12}}{y_{22}}}\\{\dfrac {-y_{21}}{y_{22}}}&{\dfrac {1}{y_{22}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {h_{22}}{\Delta \mathbf {[h]} }}&{\dfrac {-h_{12}}{\Delta \mathbf {[h]} }}\\{\dfrac {-h_{21}}{\Delta \mathbf {[h]} }}&{\dfrac {h_{11}}{\Delta \mathbf {[h]} }}\end{bmatrix}}$ | ${\begin{bmatrix}g_{11}&g_{12}\\g_{21}&g_{22}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {a_{21}}{a_{11}}}&{\dfrac {-\Delta \mathbf {[a]} }{a_{11}}}\\{\dfrac {1}{a_{11}}}&{\dfrac {a_{12}}{a_{11}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {-b_{21}}{b_{22}}}&{\dfrac {-1}{b_{22}}}\\{\dfrac {\Delta \mathbf {[b]} }{b_{22}}}&{\dfrac {-b_{12}}{b_{22}}}\end{bmatrix}}$ |
| $\mathbf {[a]}$ | ${\begin{bmatrix}{\dfrac {z_{11}}{z_{21}}}&{\dfrac {\Delta \mathbf {[z]} }{z_{21}}}\\{\dfrac {1}{z_{21}}}&{\dfrac {z_{22}}{z_{21}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {-y_{22}}{y_{21}}}&{\dfrac {-1}{y_{21}}}\\{\dfrac {-\Delta \mathbf {[y]} }{y_{21}}}&{\dfrac {-y_{11}}{y_{21}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {-\Delta \mathbf {[h]} }{h_{21}}}&{\dfrac {-h_{11}}{h_{21}}}\\{\dfrac {-h_{22}}{h_{21}}}&{\dfrac {-1}{h_{21}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {1}{g_{21}}}&{\dfrac {g_{22}}{g_{21}}}\\{\dfrac {g_{11}}{g_{21}}}&{\dfrac {\Delta \mathbf {[g]} }{g_{21}}}\end{bmatrix}}$ | ${\begin{bmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {b_{22}}{\Delta \mathbf {[b]} }}&{\dfrac {-b_{12}}{\Delta \mathbf {[b]} }}\\{\dfrac {-b_{21}}{\Delta \mathbf {[b]} }}&{\dfrac {b_{11}}{\Delta \mathbf {[b]} }}\end{bmatrix}}$ |
| $\mathbf {[b]}$ | ${\begin{bmatrix}{\dfrac {z_{22}}{z_{12}}}&{\dfrac {-\Delta \mathbf {[z]} }{z_{12}}}\\{\dfrac {-1}{z_{12}}}&{\dfrac {z_{11}}{z_{12}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {-y_{11}}{y_{12}}}&{\dfrac {1}{y_{12}}}\\{\dfrac {\Delta \mathbf {[y]} }{y_{12}}}&{\dfrac {-y_{22}}{y_{12}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {1}{h_{12}}}&{\dfrac {-h_{11}}{h_{12}}}\\{\dfrac {-h_{22}}{h_{12}}}&{\dfrac {\Delta \mathbf {[h]} }{h_{12}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {-\Delta \mathbf {[g]} }{g_{12}}}&{\dfrac {g_{22}}{g_{12}}}\\{\dfrac {g_{11}}{g_{12}}}&{\dfrac {-1}{g_{12}}}\end{bmatrix}}$ | ${\begin{bmatrix}{\dfrac {a_{22}}{\Delta \mathbf {[a]} }}&{\dfrac {-a_{12}}{\Delta \mathbf {[a]} }}\\{\dfrac {-a_{21}}{\Delta \mathbf {[a]} }}&{\dfrac {a_{11}}{\Delta \mathbf {[a]} }}\end{bmatrix}}$ | ${\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{bmatrix}}$ |

## مراجع

* ↑ Portal, EEP-Electrical Engineering; Edvard (31 Oct 2012). "Application of 4-pole Switchgear Devices". EEP - Electrical Engineering Portal (بالإنجليزية). Archived from the original on 2022-05-29. Retrieved 2022-12-06.
* بوابة الفيزياء
* هذه بذرة مقالة عن موضوع يتعلق بالكهرباء بحاجة للتوسيع. فضلًا شارك في تحريرها.