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 [ $\sin (x)$] ذات تشكيل زاوي (angle modulation) من دالتين جيبية مشكّلة بالسعة (amplitude-modulated) التي يتم تعويضها في الطور بربع دورة (قالب:Pi / 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.

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 قالب:Mvar φ هي أيضاً دالة متغير الزمن، :

*يحتاج تعديل هذا القسم*

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mn>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mn><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mn>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mn><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

mi><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo></mrow><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mrow><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mrow><mn>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mn><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mn>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mn>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mn><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mi><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo><mi>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo></mrow><mo>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

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

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</mo></mrow>

$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

${\displaystyle }$$\sin [2\pi ft+\varphi (t)]=\underset{\text{in-phase}}{\underbrace{\sin (2\pi ft)\cdot \cos [\varphi (t)]}}+\underset{\text{quadrature}}{\underbrace{\stackrel{\cos (2\pi ft)}{\overbrace{\sin (2\pi ft+\frac{\pi }{2})}}\cdot \sin [\varphi (t)]}}.$

</img>

انظر أيضا

• Phasor
• Quadrature amplitude modulation
• Single-sideband modulation

وصلات خارجية

• I/Q Data for Dummies