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ECE201 Lect-8 1
Circuits with Resistor Combinations (2.6, 7.7)
Dr. Holbert
September 13, 2001
ECE201 Lect-8 2
Solving Circuits with Series and Parallel Combinations
• The combination of series and parallel impedances can be used to find voltages and currents in circuits.
• This process can often yield the fastest solutions to networks.
• This process may not apply to complicated networks.
ECE201 Lect-8 3
Series and Parallel Impedances
• Impedances are combined to create a simple circuit (usually one source and one impedance), from which a voltage or current can be found
• Once the voltage or current is found, KCL and KVL are used to work back through the network to find voltages and currents.
ECE201 Lect-8 4
1k
1k
2k
1k
2k
1k
+
-10V
+
-
V1
+
-
V3
+
-
V2
Example: Resistor Ladder
Find V1, V2, and V3
ECE201 Lect-8 5
1k
1k
2k
1k
2k
1k
+
-10V
+
-
V1
+
-
V3
+
-
V2
Example: Resistor Ladder
Find an equivalent resistance for the network with V1 across it, then find V1 using a
voltage divider.
ECE201 Lect-8 6
1k
1k
+
-10V
+
-
V1
Example: Resistor Ladder
V5k1k1
k1V101
V
ECE201 Lect-8 7
1k
1k
2k
1k
2k
1k
+
-10V
+
-
5V
+
-
V3
+
-
V2
Example: Resistor Ladder
Find an equivalent resistance for the network with V2 across it, then find V2.
ECE201 Lect-8 8
Example: Resistor Ladder
1k
2k
1k
+
-10V
+
-
5V
+
-
V2 1k
V5.2k1k1
k1V52
V
ECE201 Lect-8 9
1k
1k
2k
1k
2k
1k
+
-10V
+
-
5V
+
-
V3
+
-
2.5V
Example: Resistor Ladder
V25.1k1k1
k1V5.23
V
ECE201 Lect-8 10
Example: Notch Filter
Find Vout
Use = 1500
1k
0.1100
+
-10V 0
+
-
Vout
70.4mH
100F
ECE201 Lect-8 11
Vout1k
0.1100
+
-10V 0
+
-
j106
-j6.67
Example: Notch Filter
Find the equivalent impedance of the resistor, inductor, and capacitor.
ECE201 Lect-8 12
Vout1k
100
+
-10V 0
+
-
7.12 -89.99
Example: Notch Filter
Combine resistor and impedance.
ECE201 Lect-8 13
Example: Notch Filter
Vout1k+
-10V 0
+
-
100.3 -4.07
ECE201 Lect-8 14
Example: Notch Filter
0k107.400.31
0k10V10outV
37.0-V09.9outV
ECE201 Lect-8 15
Example: Notch Filter
Find Vout
Use = 377
1k
0.1100
+
-10V 0
+
-
Vout
70.4mH
100F
ECE201 Lect-8 16
Example: Notch Filter
Vout= 1.23V -0.17
ECE201 Lect-8 17
Frequency ResponseMagnitude of Vout
0
2
4
6
8
10
250 300 350 400 450 500
Frequency
ECE201 Lect-8 18
Using MATLAB to Solve Circuits
ECE201 Lect-8 19
MATLAB
• MATLAB can perform computations with complex numbers.
• You can use it as a calculator to compute phasors and impedances for AC SS analysis.
• You can also use it to automate computations of frequency responses.
ECE201 Lect-8 20
Using MATLAB
• Entering a complex number:
>> 1+2jans =
1.0000 + 2.0000i• Multiplying complex numbers:>> (1+2j)*(3+4j)ans =
-5.0000 +10.0000i
ECE201 Lect-8 21
Example: Notch Filter
Find Vout
Use = 1500
1k
0.1100
+
-10V 0
+
-
Vout
70.4mH
100F
ECE201 Lect-8 22
Compute Impedances
>> omega = 377
omega =
377
>> xl = j*omega*70.4e-3
xl =
0 +26.5408i
>> xc = 1/(j*omega*100e-6)
xc =
0 -26.5252i
ECE201 Lect-8 23
Equivalent Capacitor/Inductor Impedance
>> zeq = (0.1+xl)*xc
/(0.1+xl+xc)
zeq =
6.8687e+03 - 1.0981e+03i
ECE201 Lect-8 24
Voltage Divider
>> vin = 10
vin =
10
>> vout = vin*1e3
/(100+zeq+1e3)
vout =
1.2315 + 0.1697i
ECE201 Lect-8 25
Magnitude and Angle>> abs(vout) ans = 1.2432>> angle(vout) ans = 0.1369>> angle(vout)*180/pi ans = 7.8461
ECE201 Lect-8 26
Class Examples
• Learning Extension E2.14
• Learning Extension E2.15
• Learning Extension E7.12