مكونات متوافقة الطور ومتعامدة

رسم بياني يوضح تشكيل الطور[(φ (t] وهي دالة غير خطية تتزايد من 0 إلى π / 2 خلال الفترة (t) ما بين 0 و 16 . ويعرف المكونان المؤلفان من تشكيل السعة باسم مكون متوافق الطور (I ، الخط الرفيع الأزرق، دالة تناقصية) ومكون تربيعي أو عامودي (Q ،الخط الرفيع الأحمر، دالة تزيادية).

في الهندسة الكهربائية ، يمكن تفكيك أو توليف الدالة الجيبية [ ${\displaystyle \sin(x)}$] ذات تشكيل زاوي (angle modulation) من دالتين جيبية مشكّلة بالسعة (amplitude-modulated) التي يتم تعويضها في الطور بربع دورة (π / 2 راديان). جميع الدوال الثلاث لها نفس التردد. تعرف الدوال الجيبية المشكلة بالسعة بالموجات العامودية متوافقة الطور. في بعض السياقات يكون من الملائم أكثر الإشارة إلى تشكيل السعة (القاعدي) فقط بهذه الشروط.[1]

عندما يتم تطبيق جهد جيبي إما على مكثف بسيط أو ملف كهربائي ، فإن التيار الناتج الذي يتدفق يتعامد "عامودي" مع الجهد.

نموذج الإشارة ذات النطاق الضيق

في تطبيقات تشكيل الزاوية، مع تردد الموجة الحاملة f, φ هي أيضاً دالة متغير الزمن،[2] :

*يحتاج تعديل هذا القسم*

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$[3]

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mn>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mn><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mn>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mn><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

mi><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo></mrow><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo></munder></mrow><mrow class="MJX-TeXAtom-ORD"><mtext>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mtext></mrow></munder><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mrow><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mrow><mn>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mn><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mn>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mn></mfrac></mrow></mrow><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo></mrow></mrow><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo></mover></mrow><mrow class="MJX-TeXAtom-ORD"><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mn>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mn><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo></mrow></mover><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mi>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mi><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo><mo stretchy="false">

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo></mrow><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo></munder></mrow><mrow class="MJX-TeXAtom-ORD"><mtext>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mtext></mrow></munder><mo>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

</mo></mrow>

${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$

${\displaystyle }$${\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}$[4]

</img>

مراجع

1. Gast, (2005). 802.11 wireless networks : the definitive guide (ط. 2nd ed). Sebastopol, CA: O'Reilly. ISBN:0596100523. OCLC:58828461. مؤرشف من الأصل في 2019-12-12. {{استشهاد بكتاب}}: |طبعة= يحتوي على نص زائد (مساعدة)
2. Wade, J. G. (John Graham), (1994). Signal coding and processing (ط. 2nd ed). Cambridge: Cambridge University Press. ISBN:0521412307. OCLC:28927715. مؤرشف من الأصل في 2019-12-12. {{استشهاد بكتاب}}: |طبعة= يحتوي على نص زائد (مساعدة)
3. Karimi-Ghartemani، M.؛ Karimi، H.؛ Iravani، M. R. (2004-4). "A magnitude/phase-locked loop system based on estimation of frequency and in-phase/quadrature-phase amplitudes". IEEE Transactions on Industrial Electronics. ج. 51 ع. 2: 511–517. DOI:10.1109/TIE.2004.825282. ISSN:0278-0046. مؤرشف من الأصل في 2019-04-01.
4. Naidu, Prabhakar (2003). Modern digital signal processing : an introduction. Pangbourne: Alpha Science. ISBN:1842651331. OCLC:50876694. مؤرشف من الأصل في 2019-12-12.

انظر أيضا

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