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<!DOCTYPE html>
<html>
<head>
<title>EE281-Electric Circuits</title>
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class: center, middle
# EE-281 ELECTRIC CIRCUITS
## Ozan Keysan
[ozan.keysan.me](http://ozan.keysan.me)
Office: C-113 <span class="meta">•</span> Tel: 210 7586
---
# Review
## Ohm's Law (Resistivity, Conductivity)
--
## Kirchhoff's Current Law
--
## Kirchhoff's Voltage Law
--
## Node, Branch, Loop, Mesh
---
# Analysis Methods
## Scalability?
<img src="http://www.k8iqy.com/qrprigs/2n26/2n26txrevcd.gif" alt="Drawing" style="width: 600px;"/>
---
# Analysis Methods
## 1-Nodal Analysis
### Unknown: Node Voltages
### Uses Kirchhoff's Current Law
--
## 2-Mesh Analysis
### Unknown: Mesh Currents
### Uses Kirchhoff's Voltage Law
---
# Steps for Nodal Analysis
## 1-Choose a reference node (ground).
## 2-Label node voltages.
## 3-Write KCL equations for each node.
## 4-Solve the equations.
---
# Choosing Reference Node
- ### Node that interconnects the most branches.
--
- ### Usually at the bottom of circuit.
--
- ### Label ground with one of the symbols below:
---
# Label each node voltage:
## Except the ground node!
---
# Write KCL for each node
## Incoming Currents + Outgoing Currents = 0
--
## The most practical way:
### Use \\(-\\) sign for incoming currents.
### Use \\(+\\) sign for outgoing currents.
---
# Example-1:
## Calculate node voltages:
---
# Example-1: Label nodes
---
# Example-1:
### Answer: \\(V_1 = 40/3 V \quad V_2 = 20 V \\)
---
# Example-2:
---
# Example-2:
### Answer: \\(V_1 = -6 V \quad V_2 = -42 V \\)
---
# Dependent Sources
## Dependent Voltage Source
## Shown with a square sign
## Its value is dependent on another variable
---
# Dependent Sources
## Dependent Current Source
## Shown with a square sign
## Its value is dependent on another variable
---
# Dependent Sources
## Dependent Current Source
---
# Example-3:
---
# Example-3:
### Answer: \\(V_1 = 4.8 V \quad V_2 = 2.4 V \quad V_2 = -2.4 V \\)
---
#Example:
## Obtain resistance matrix for:
---
#Example:
## Obtain resistance matrix for:
---
# Example:
## Resistance Matrix:
$$
\begin{bmatrix}
\frac{1}{R_1}+\frac{1}{R_2} & -\frac{1}{R_2} & 0 \\\
-\frac{1}{R_2} & \frac{1}{R_2}+ \frac{1}{R_3}+\frac{1}{R_4} & -\frac{1}{R_4} \\\
0 & -\frac{1}{R_4} & \frac{1}{R_4}\\\
\end{bmatrix}
\begin{bmatrix}
V_a \\\
V_b \\\
V_c \\\
\end{bmatrix}
=
\begin{bmatrix}
I_1 \\\
0 \\\
-I_2 \\\
\end{bmatrix}
$$
---
# Example:
## Remember!
## Conductance = 1/ Resistance
## $$G = \frac{1}{R}$$
---
#Conductance Matrix:
## (Sometimes it is more convenient)
$$\begin{bmatrix} G_1+G_2 & -G_2 & 0 \\\ -G_2 & G_2+ G_3+G_4 & -G_4 \\\
0 & -G_4 & G_4 \end{bmatrix}
\begin{bmatrix}
V_a \\\
V_b \\\
V_c
\end{bmatrix}
=
\begin{bmatrix}
I_1 \\\
0 \\\
-I_2
\end{bmatrix}
$$
---
# No Escape from Linear Algebra!
# $$Ax=b $$
--
# $$x=A^{-1}b $$
---
# Any questions?
## You can download this presentation from: [keysan.me/ee281](http://keysan.me/ee281)
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