ECE201 Lect-61 Series and Parallel Resistor Combinations (2.5, 8.5) Dr. Holbert February 6, 2006.
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Transcript of ECE201 Lect-61 Series and Parallel Resistor Combinations (2.5, 8.5) Dr. Holbert February 6, 2006.
ECE201 Lect-6 1
Series and Parallel Resistor Combinations (2.5, 8.5)
Dr. Holbert
February 6, 2006
ECE201 Lect-6 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.
ECE201 Lect-6 3
Introduction
• Complicated networks of resistors/ impedances can be replaced by a single equivalent resistor/impedance.
ECE201 Lect-6 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.
ECE201 Lect-6 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.
ECE201 Lect-6 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 .
ECE201 Lect-6 7
Series Resistance
R1
R3
R2 Req
Req = R1 + R2 + R3
ECE201 Lect-6 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
ECE201 Lect-6 9
Zeq
Series Impedance
Z1
Zeq = Z1 + Z2 + Z3
Z3
Z2
ECE201 Lect-6 10
Example: Series Inductors
• What is the equivalent impedance of two series inductors?
L2L1
ECE201 Lect-6 11
Series Inductors
• The equivalent impedance is
Zeq = Z1 + Z2 = j(L1+L2)
• Two inductors in series are equivalent to a single inductor whose inductance is the sum of the two inductances.
Zeq = j(L1+L2) = jLeq
ECE201 Lect-6 12
Parallel Resistance
ReqR3R2R1
321
1111
RRRReq
ECE201 Lect-6 13
Parallel
Two elements are in parallel if they are connected between (share) the same two (distinct) end nodes.
Parallel
Not Parallel
R1
R2
R1
R2
ECE201 Lect-6 14
Parallel Impedance
Z3Z1 Z2 Zeq
321
1111
ZZZZ
eq
ECE201 Lect-6 15
Example: Parallel Capacitors
• What is the equivalent impedance of two parallel capacitors?
C1 C2
ECE201 Lect-6 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
2121
1
111
CCj
CjCj
eq
eq
Z
ZZZ
ECE201 Lect-6 17
Flash Example: Ladder Network
Find the equivalent resistance by making combinations of series and parallel resistors until only one resistor is left.
1k
1k
2k
1k
2k 1k
ECE201 Lect-6 18
10
769pF
159H
Example #1: Bandpass Filter
For = 2.86 106, find the equivalent impedance.
ECE201 Lect-6 19
10
-j455
j455
Compute Impedances
Now combine series impedances
ECE201 Lect-6 20
-j45510 j455
Bandpass Filter
Now combine parallel impedances
455.1 88.7
ECE201 Lect-6 21
Bandpass Filter
3.1k7.2045510455
45510455
jj
jj
ECE201 Lect-6 22
Example #2: Loaded Bandpass Filter
For = 2.86 106, find the equivalent impedance.
10
769pF
159H
50k
ECE201 Lect-6 23
Class Examples
• Learning Extension E2.12
• Learning Extension E2.13
• Learning Extension E8.10