Nodal vs. Mesh
In nodal analysis, circuit variables are node voltages Nodal analysis applies KCL to find unknown voltages
Mesh Analysis
In mesh analysis, circuit variables are mesh currents Mesh analysis applies KVL to find unknown currents Bo
Circuit Theorems
Motivations
Nodal and Mesh analysis are adequate for the analysis of any resistive circuits. However, for a large, complex circuit, these methods involve tedious computation. Objectives:
To reduce the manual computational effort
Superposition
A direct result of the linearity property
Recall Linearity Theorem
y = a1u1 + a 2 u 2 + + a mum
The total response y is the sum of the responses ai u i. Each a iu i is the response of the circuit to u i acting alone.
Superpositi
Introduction
Thevenins Theorem is a very important and useful theorem. It is a method for the reduction of a portion of a complex circuit into a simple one. It reduces the need for repeated solutions of the same sets of equations.
Thevenins Theor
Norton Equivalent Circuit
Any two-terminal linear network, composed of voltage sources, current sources, and resistors, can be replaced by an equivalent two-terminal network consisting of an independent current source in parallel with a resistor.
No
Problem Statements
a Network of Sources and Resistors
o
+
iL
Maximum Power Transfer
vL RL b
o
Whats the maximum power that can be delivered
to a load? Whats the value of RL that maximizes the power? Whats the efficiency of power transfer?
M
ELECTRICAL ENGINEERING DEPARTMENT
CALIFORNIA POLYTECHNIC STATE UNIVERSITY
EE 112
EXAM 2
FALL 2003
Print your Name:.
1 (20)
2 (20)
3 (20)
Nov. 3, 2003
Total
PROBLEM #1
Find I1 in the following circuit. Then find the power delivered by each of the independe
ELECTRICAL ENGINEERING DEPARTMENT
CALIFORNIA POLYTECHNIC STATE UNIVERSITY
EE 112
EXAM 2
FALL 2003
Print your Name:.
1 (20)
2 (20)
3 (20)
Nov. 3, 2003
Total
PROBLEM #1
Find I1 in the following circuit. Then find the power delivered by each of the independe
# This file is a general .xdc for the Nexys4 rev B board
# To use it in a project:
# - uncomment the lines corresponding to used pins
# - rename the used ports (in each line, after get_ports) according to the top
level signal names in the project
# Clock
Background Nodal Analysis
KVL + KCL + Ohms law sufficient in analyzing any resistive circuits difficult to use as the complexity of circuits increased
Nodal Analysis Mesh Analysis
developed based on Kirchhoffs laws provide two systematic methods
Outline
Series and parallel connections Voltage sources in series Current sources in parallel Resistors in series
Equivalent resistance Voltage-divider
Resistors in parallel
Equivalent resistance Current -divider
Y- Transformations
HW2: 2
Chapter 2, Solution 1 v = iR i = v/R = (16/5) mA = 3.2 mA
Chapter 2, Solution 2 p = v2/R Chapter 2, Solution 3 R = v/i = 120/(2.5x10-3) = 48k ohms Chapter 2, Solution 4 (a) (b) i = 3/100 = 30 mA i = 3/150 = 20 mA R = v2/p = 14400/60 = 240 ohms
Cha
Sol Tut #1 SEE 1003 2004/2005I Chapter 1, Solution 9
1
1
2
Chapter 1, Solution 2 i = dq/dt = 3 mA i = dq/dt = (16t + 4) A i = dq/dt = (-3e-t + 10e-2t) nA i=dq/dt = 1200 cos 120 t pA i =dq/dt = - e -4t (80 cos 50 t + 1000 sin 50t ) A
(a) q = idt
Circuit Elements
Circuit element is a mathematical model of a real device Active element: is capable of generating energy Examples: generators, batteries Passive element: absorbs (dissipates) energy Examples: resistors, capacitors, inductors
Activ
Kirchhoffs Laws
Reminder: there will be a Quiz on Chapter 1 next Monday (Jan.23)
Review
Electric Circuit Voltage Current Ohms Law
> _ Vs + i
+
R
_
v
A more complex circuit
a R1 b R2 c v1 R3 v2
d
Objective: determine voltage and current in a
# This file is a general .xdc for the Nexys4 DDR Rev. C
# To use it in a project:
# - uncomment the lines corresponding to used pins
# - rename the used ports (in each line, after get_ports) according to the top
level signal names in the project
# Clock s