Presentation is loading. Please wait.

Presentation is loading. Please wait.

Lecture 211 Phasor Diagrams and Impedance. Lecture 212 Set Phasors on Stun 1.Sinusoids-amplitude, frequency and phase (Section 8.1) 2.Phasors-amplitude.

Similar presentations


Presentation on theme: "Lecture 211 Phasor Diagrams and Impedance. Lecture 212 Set Phasors on Stun 1.Sinusoids-amplitude, frequency and phase (Section 8.1) 2.Phasors-amplitude."— Presentation transcript:

1 Lecture 211 Phasor Diagrams and Impedance

2 Lecture 212 Set Phasors on Stun 1.Sinusoids-amplitude, frequency and phase (Section 8.1) 2.Phasors-amplitude and phase (Section 8.3 [sort of]) 2a. Complex numbers (Appendix B).

3 Lecture 213 Set Phasors on Kill 3.Complex exponentials-amplitude and phase 4.Relationship between phasors, complex exponentials, and sinusoids 5.Phasor relationships for circuit elements (Section 8.4) 5a. Arithmetic with complex numbers (Appendix B).

4 Lecture 214 Set Phasors on Vaporize 6.Fundamentals of impedance and admittance (some of Section 8.5) 7.Phasor diagrams (some of Section 8.6)

5 Lecture 215 Phasor Diagrams A phasor diagram is just a graph of several phasors on the complex plane (using real and imaginary axes). A phasor diagram helps to visualize the relationships between currents and voltages.

6 Lecture 216 An Example - 1F1F VCVC + - 2mA  40  1k  VRVR V

7 Lecture 217 An Example (cont.) I = 2mA  40  V R = 2V  40  V C = 5.31V  -50  V = 5.67V  

8 Lecture 218 Phasor Diagram Real Axis Imaginary Axis VRVR VCVC V

9 Lecture 219 Impedance AC steady-state analysis using phasors allows us to express the relationship between current and voltage using a formula that looks likes Ohm’s law: V = I Z Z is called impedance.

10 Lecture 2110 Impedance Resistor: –The impedance is R Inductor: –The impedance is j  L

11 Lecture 2111 Impedance Capacitor: –The impedance is 1/j  L

12 Lecture 2112 Some Thoughts on Impedance Impedance depends on the frequency . Impedance is (often) a complex number. Impedance is not a phasor (why?). Impedance allows us to use the same solution techniques for AC steady state as we use for DC steady state.

13 Lecture 2113 Impedance Example: Single Loop Circuit 20k  + - 1F1F10V  0  VCVC + -  = 377 Find V C

14 Lecture 2114 Impedance Example How do we find V C ? First compute impedances for resistor and capacitor: Z R = 20k  = 20k  0  Z C = 1/j (377 1  F) = 2.65k  -90 

15 Lecture 2115 Impedance Example 20k  0  k  -90  10V  0  VCVC + -

16 Lecture 2116 Impedance Example Now use the voltage divider to find V C :

17 Lecture 2117 What happens when  changes? 20k  + - 1F1F10V  0  VCVC + -  = 10 Find V C

18 Lecture 2118 Low Pass Filter: A Single Node-pair Circuit Find v(t) for  =2  k  0.1  F 5mA  0  + - V

19 Lecture 2119 Find Impedances 1k  -j530k  5mA  0  + - V

20 Lecture 2120 Find the Equivalent Impedance 5mA  0  + - VZ eq

21 Lecture 2121 Parallel Impedances

22 Lecture 2122 Computing V

23 Lecture 2123 Change the Frequency Find v(t) for  =2  k  0.1  F 5mA  0  + - V

24 Lecture 2124 Find Impedances 1k  -j3.5  5mA  0  + - V

25 Lecture 2125 Find an Equivalent Impedance 5mA  0  + - VZ eq

26 Lecture 2126 Parallel Impedances

27 Lecture 2127 Computing V


Download ppt "Lecture 211 Phasor Diagrams and Impedance. Lecture 212 Set Phasors on Stun 1.Sinusoids-amplitude, frequency and phase (Section 8.1) 2.Phasors-amplitude."

Similar presentations


Ads by Google