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# # Electronic Circuits Lecture 7 Phasor

. 3 min read

Motivation: to solve the normal Sinusoidal Signal sources more efficiently

## 求解正弦输入的电路 (AC) Steady response

$$L\frac{di}{dt}+Ri = V_m cos(\omega t+\phi) \ i = \underbrace{\frac{-V_m}{\sqrt{R^2+\omega^2L^2}}cos(\phi-\theta)e^{(-R/L)t}}{\text{Transient response}}+\underbrace{\frac{-V_m}{\sqrt{R^2+\omega^2L^2}}cos(\omega t+\phi-\theta)}{\text{Steady state response}}$$

1. Steady state solution is sinusoidal稳态是正弦形式的
2. Response frequency = source frequency响应频率和输入频率相同
3. Magnitude & phase of response differs from that of source响应的幅度和相位与源的响应不同（相位不同）

LTI: Linear Time Invariant (LTI) circuit线性时不变

WHY?

natural phenomenon are sinusoidal.

very easy signal to generate and transmit.

very easy to handle mathematically.

EXAMPLE

1. 正弦
2. 单频
3. 稳态