Transcript Review for Exam #1

Exam #1 Review
Dr. Holbert
February 18, 2008
LectR1
EEE 202
1
Basic Circuit Analysis Methods
•
•
•
•
While Obeying Passive Sign Convention
Ohm’s Law; KCL; KVL
Voltage and Current Division
Series/Parallel Resistance combinations
Rseries  R1  R2   RN   R j
1
1
1
1
1
 


R par R1 R2
RM
Ri
LectR1
EEE 202
2
Default Sign Convention
• Passive sign convention : current should
enter the positive voltage terminal
I
+
Circuit Element
–
• Consequence for P = I V
– Positive (+) Power: element absorbs power
– Negative (-) Power: element supplies power
LectR1
EEE 202
3
Ohm’s Law
V=IR
I
+
The
Rest of
the
Circuit
LectR1
R
V
–
EEE 202
4
KCL (Kirchhoff’s Current Law)
i1(t)
i5(t)
i2(t)
i4(t)
i3(t)
The sum of currents entering the node is
zero:
n
 i (t )  0
j 1
j
Analogy: mass flow at pipe junction
LectR1
EEE 202
5
KVL (Kirchhoff’s Voltage Law)
+
v1(t)
+
–
v2(t)
–
+
v3(t)
–
The sum of voltages around a loop is zero:
n
v
j 1
j
(t )  0
Analogy: pressure drop through pipe loop
LectR1
EEE 202
6
KVL Polarity
• A loop is any closed path through a circuit
in which no node is encountered more
than once
• Voltage Polarity Convention
– A voltage encountered + to – is positive
– A voltage encountered – to + is negative
LectR1
EEE 202
7
In General: Voltage Division
• Consider N resistors in series:
Ri
VRi (t )  VSk (t )
 Rj
• Source voltage(s) are divided between the
resistors in direct proportion to their
resistances
LectR1
EEE 202
8
In General: Current Division
• Consider N resistors in parallel:
iR j (t )   iS k (t )
R par
Rj
1
1
1
1
1
 


R par R1 R2
RN
Ri
• Special Case (2 resistors in parallel)
R2
iR1 (t )  iS (t )
R1  R2
LectR1
EEE 202
9
Equivalent Impedance
• If we wish to replace two parallel
resistances with a single resistor whose
voltage-current relationship is the same,
the equivalent resistance has a value of:
Req
R1 R2

R1  R2
• Parallel elements share the same two
(distinct) end nodes
LectR1
EEE 202
10
Steps of Nodal Analysis
1. Choose a reference (ground) node, V=0.
2. Assign node voltages to the other nodes.
3. Apply KCL to each node
but the reference node;
V1
V2
express currents in terms
R
of node voltages.
4. Solve the resulting system
V1  V2
of linear equations for the
I
R
nodal voltages.
LectR1
EEE 202
11
Steps of Mesh/Loop Analysis
1. Identify mesh (loops).
2. Assign a current to each mesh.
3. Apply KVL around each
I2
loop to get an equation in V
R +
–
R
terms of the loop currents.
I1
4. Solve the resulting system
of linear equations for the V = (I – I ) R
R
1
2
mesh/loop currents.
LectR1
EEE 202
12
Nodal and Loop Analyses
Nodal Analysis Recipe
1&2) Identify and label
N nodal voltages plus
the ground node
(V=0)
3) Apply KCL at N
nodes (supernode
makes constraint eq.)
4) Solve for the nodal
voltages
LectR1
Loop Analysis Recipe
1&2) Identify and label
M mesh currents
3) Apply KVL at the M
meshes (a current
source makes a
constraint equation)
4) Solve for the mesh
currents
EEE 202
13
Superposition Procedure
1. For each independent voltage and current
source (repeat the following):
a) Replace the other independent voltage sources with
a short circuit (i.e., V = 0).
b) Replace the other independent current sources with
an open circuit (i.e., I = 0).
Note: Dependent sources are not changed!
c) Calculate the contribution of this particular voltage or
current source to the desired output parameter.
2. Algebraically sum the individual contributions
(current and/or voltage) from each independent
source.
LectR1
EEE 202
14
Source Transformation
A voltage source in series with a resistor is
transformed into a current source in parallel
with that resistor; and vice versa.
Vs
+
–
Rs
Is
Rs
Vs  Rs I s
LectR1
EEE 202
15
Basic Approach to Finding the
Thevenin/Norton Equivalent
• Circuits with independent sources:
– Find Voc and/or Isc
– Compute RTh (= Voc / Isc)
• Circuits without independent sources:
– Apply a test voltage (current) source
– Find resulting current (voltage)
– Compute RTh (= Vtest / Itest)
LectR1
EEE 202
16
Thevenin/Norton Equivalent
RTh
Voc
+
–
Isc
Thevenin equivalent
circuit
LectR1
RTh
Norton equivalent
circuit
EEE 202
17
Op Amps
• Generally apply
KCL or nodal
analysis
• Ideal Op-Amp
Relations
i– = 0 = i+
v– = v+
LectR1
+
–
EEE 202
18