Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| learn:courses:real-analog-chapter-10:start [2017/05/05 17:57] – [Example 10.19] Martha | learn:courses:real-analog-chapter-10:start [2022/10/04 11:38] (current) – external edit 127.0.0.1 | ||
|---|---|---|---|
| Line 1: | Line 1: | ||
| ====== Real Analog: Chapter 10 ====== | ====== Real Analog: Chapter 10 ====== | ||
| - | --> | + | [[{}/ |
| - | * {{ : | + | --> |
| + | | ||
| + | | ||
| + | * {{ : | ||
| + | * {{ : | ||
| + | * {{ : | ||
| + | * [[http:// | ||
| + | * [[http:// | ||
| + | * [[http:// | ||
| + | * [[http:// | ||
| + | * Chapter 10 Videos: | ||
| + | * [[http:// | ||
| + | * [[http:// | ||
| + | * {{ : | ||
| * {{ : | * {{ : | ||
| - | * {{ : | + | * {{ : |
| * {{ : | * {{ : | ||
| - | * {{ : | + | * {{ : |
| * {{ : | * {{ : | ||
| - | * {{ : | + | * {{ : |
| * {{ : | * {{ : | ||
| - | * {{ : | + | * {{ : |
| * {{ : | * {{ : | ||
| - | * {{ : | + | * {{ : |
| * {{ : | * {{ : | ||
| * {{ : | * {{ : | ||
| Line 587: | Line 599: | ||
| {{ : | {{ : | ||
| - | In [[https:// | + | In [[/ |
| $$\frac{d^2v(t)}{dt^2} + \frac{R}{L} \frac{dv(t)}{dt} + \frac{1}{LC} v(t) = \frac{1}{LC} v_S(t) (Eq. 10.53)$$ | $$\frac{d^2v(t)}{dt^2} + \frac{R}{L} \frac{dv(t)}{dt} + \frac{1}{LC} v(t) = \frac{1}{LC} v_S(t) (Eq. 10.53)$$ | ||
| Line 1375: | Line 1387: | ||
| $$|V_{out}| = |V_{in}| \cdot |H(j2)| = 3 \cdot \frac{1}{\sqrt{2}} = \frac{3}{\sqrt{2}}$$ | $$|V_{out}| = |V_{in}| \cdot |H(j2)| = 3 \cdot \frac{1}{\sqrt{2}} = \frac{3}{\sqrt{2}}$$ | ||
| - | $$\angle V_{out} = \angle V_{in} + \angle H(j2) = 20^{\circ} + 9-45^{\circ}) = -25^{\circ}$$ | + | $$\angle V_{out} = \angle V_{in} + \angle H(j2) = 20^{\circ} + (-45^{\circ}) = -25^{\circ}$$ |
| And the time-domain output voltage is: | And the time-domain output voltage is: | ||
| Line 1381: | Line 1393: | ||
| $$v_{out}(t) = \frac{3}{\sqrt{3}} \cos(2t-25^{\circ})$$ | $$v_{out}(t) = \frac{3}{\sqrt{3}} \cos(2t-25^{\circ})$$ | ||
| - | When $v_{in} = 7 \cos(4t-60^{\circ}$, | + | When $v_{in} = 7 \cos(4t-60^{\circ})$, $\omega = 4$ rad/sec, $|V_{in}|=7$ and $\angle V_{in} = -60^{\circ}$. For this value of $\omega$, and the given values of R and C, the magnitude and phase of the frequency response function are: |
| $$|H(j4)|= \frac{1}{\sqrt{1+(\omega RC)^2}}=\frac{1}{\sqrt{5}}$$ | $$|H(j4)|= \frac{1}{\sqrt{1+(\omega RC)^2}}=\frac{1}{\sqrt{5}}$$ | ||
| Line 1448: | Line 1460: | ||
| {{ : | {{ : | ||
| + | |||
| + | |||
| + | [[{}/ | ||
| + | [[{}/ | ||