Concept Flashcards#
What domain do we use to analyze RLC circuits in sinusoidal steady state?
The frequency domain.Why do we move from the time domain to the frequency domain in RLC analysis?
To replace differential equations with algebraic equations using complex numbers.What is impedance?
Impedance, Z, is the complex opposition to current in AC circuits and is measured in Ohms.What is the impedance of a resistor in the frequency domain?
\( Z_{R} = R \)
Purely real.
What is the impedance of a capacitor?
\( Z_{C} = \frac{1}{j\omega C} = -\frac{j}{\omega C} \)
Purely imaginary.
What is the impedance of an inductor?
\( Z_{L} = j\omega L \)
Purely imaginary.
How do we convert frequency to angular frequency?
\( \omega = 2\pi f \)
What is a phasor representation of a sinusoidal voltage?
Time domain:\( V\cos(360^\circ f t + \phi) \)
Phasor form:
\( V_{\text{RMS}}\angle \phi \)
What value is used as the magnitude of a phasor?
The RMS value of the sinusoidal signal.How do we combine impedances in series?
Add them directly:\( Z_{eq} = Z_{1} + Z_{2} + \dots \)
How do we combine impedances in parallel?
\( Z_{eq} = \left( \frac{1}{Z_{1}} + \frac{1}{Z_{2}} + \dots \right)^{-1} \)
How is Ohm’s Law written in the frequency domain?
\( \widetilde{I} = \frac{\widetilde{V}}{Z} \)
How do we convert a phasor current back to time domain form?
If\( \widetilde{I} = I_{\text{RMS}}\angle \phi \)
then
\( i(t) = (I_{\text{RMS}}\sqrt{2})\cos(360^\circ f t + \phi) \)
What assumption do we make in sinusoidal steady state?
All transient behavior has decayed and the system operates in a steady, repeating sinusoidal pattern.How do we write a voltage divider in the frequency domain?
\( \widetilde{V}_{out} = \widetilde{V}_{in}\left(\frac{Z_{component}}{Z_{total}}\right) \)