Lecture 17: Analysis with Sinusoidal Sources, Transformers Nilsson ENG17 : Circuits I Spring May 26, 2015

Impedance and Reactance 2

Review 3 Find v o (t)

Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 4

Impedances in Series 5

Impedances in Parallel 6

Delta-to-Wye 7

Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 8

Source Transformations 9 Same as before, but now with impedances

Thevenin-Norton Equivalents 10

Example 11 Find using source transformation

Example 12 Find Thevenin Equivalent

Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 13

Node-Voltage Example 14 Find I a, I b, I c

Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 15

Mesh-Current Example 16 Find V a, V b, V c

Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 17

Phasor Diagrams 18

Example 19 Use phasor diagram to find R that will cause resistor current (i R ) to lag the source current (i S ) by 45° when ω = 5 krad / s.

Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 20

Transformer Circuit 21

Frequency Domain Circuit 22

Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 23

Ideal Transformer 24

Sign Convention 25

Impedance Matching 26

Example 27

Recap Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 28