Lecture 22 2
Introduction
• For analysis, series resistors/impedances can be replaced by an equivalent resistor/ impedance.
• Parallel resistors/impedances can be replaced by an equivalent resistor/ impedance.
Lecture 22 3
Introduction
• Complicated networks of resistors/ impedances can be replaced by a single equivalent resistor/impedance.
Lecture 22 4
Equivalent Resistancei(t)
+
-
v(t)
i(t)
+
-
v(t)Req
Req is equivalent to the resistor network on the left in the sense that they have the same i-v characteristics.
Lecture 22 5
Equivalent Resistance
• The rest of the circuit cannot tell whether the resistor network or the equivalent resistor is connected to it.
• The equivalent resistance cannot be used to find voltages or currents internal to the resistor network.
Lecture 22 6
Equivalent ImpedanceI
+
-
V
I
+
-
VZeq
Zeq is equivalent to the network on the left in the sense that they have the same phasor I-V characteristics at the frequency .
Lecture 22 8
Series
Two elements are in series if the current that flows through one must also flow through the other.
R1 R2
Series
R1 R2
Not Series
Lecture 22 10
Example: Series Inductors
• What is the equivalent impedance of two series inductors?
L2L1
Lecture 22 11
Series Inductors
• The equivalent impedance is
j(L1+L2)
• Two inductors in series are equivalent to a single inductor whose inductance is the sum of the two inductances.
Lecture 22 13
Parallel
Two elements are in parallel if they are connected between the same two nodes.
Parallel
Not Parallel
R1
R2
R1
R2
Lecture 22 15
Example: Parallel Capacitors
• What is the equivalent impedance of two parallel capacitors?
C1 C2
Lecture 22 16
Parallel Capacitors
• The equivalent impedance is
• Two capacitors in parallel are equivalent to a single capacitor whose capacitance is the sum of the two capacitances.
21
1
CCj
Lecture 22 17
Example: Ladder Network
• Ladder networks are used in analog-to-digital converters to provide reference voltages that are 1/2, 1/4, 1/8, etc. of a source voltage.
Lecture 22 19
Ladder Network
Find the equivalent resistance by making combinations of series and parallel resistors until you have only one resistor left.
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