1. Series and Parallel Resistor Combinations (2.5, 7.5)
Dr. S. M. Goodnick
September 17th, 2003
ECE201 Lect-10

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-10

3. Introduction
Complicated networks of resistors/ impedances can be replaced by a single equivalent resistor/impedance.
ECE201 Lect-10

4. Equivalent Resistance
i(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-10

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-10

6. Equivalent Impedance I I + + V V
Zeq – –
Zeq is equivalent to the network on the left in the sense that they have the same phasor I-V characteristics at the frequency w.
ECE201 Lect-10

7. Series Resistance R1 R3 R2
Req
Req = R1 + R2 + R3
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8. Series
Two elements are in series if the current that flows through one must also flow through the other. R1 R2
Series
Not Series R1 R2
ECE201 Lect-10

9. Series Impedance Z1 Z2
Zeq Z3
Zeq = Z1 + Z2 + Z3
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10. Example: Series Inductors
What is the equivalent impedance of two series inductors? L1 L2
ECE201 Lect-10

11. Series Inductors The equivalent impedance is Zeq = Z1 + Z2 = jw(L1+L2)
Two inductors in series are equivalent to a single inductor whose inductance is the sum of the two inductances.
Zeq = jw(L1+L2) = jwLeq
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12. Parallel Resistance R2 R1
Req R3
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13. Parallel
Two elements are in parallel if they are connected between (share) the same two (distinct) end nodes. R1 R2
Parallel
Not Parallel R1 R2
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14. Parallel Impedance Z1 Z2 Z3
Zeq
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15. Example: Parallel Capacitors
What is the equivalent impedance of two parallel capacitors? C1 C2
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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.
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17. Flash Example: Ladder Network
Find the equivalent resistance by making combinations of series and parallel resistors until only one resistor is left.
1kW
2kW
1kW
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18. Example #1: Bandpass Filter
10W
769pF
159mH
For w = 2.86  106, find the equivalent impedance.
ECE201 Lect-10

19. Now combine series impedances
Compute Impedances
10W
-j455W
j455W
Now combine series impedances
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20. Now combine parallel impedances
Bandpass Filter
10W+ j455W
-j455W
455.1W  88.7
Now combine parallel impedances
ECE201 Lect-10

21. Bandpass Filter
ECE201 Lect-10

22. Example #2: Loaded Bandpass Filter
10W
769pF
159mH
50kW
For w = 2.86  106, find the equivalent impedance.
ECE201 Lect-10

23. Class Examples Learning Extension E2.12 Learning Extension E2.13
ECE201 Lect-10