Circuits with Series and Parallel ResistorsImpedances - PowerPoint PPT Presentation

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Circuits with Series and Parallel ResistorsImpedances

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Impedances are combined to create a simple circuit (usually one source and one ... zeq = (0.1 xl)*xc /(0.1 xl xc) zeq = 6.8687e 03 - 1.0981e 03i. Lecture 23. 24 ... – PowerPoint PPT presentation

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Title: Circuits with Series and Parallel ResistorsImpedances


1
Circuits with Series and Parallel
Resistors/Impedances
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.

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.

4
Example Resistor Ladder
  • Find V1, V2, and V3

5
Example Resistor Ladder
1kW
1kW
1kW

1kW
10V
2kW
2kW
-
  • Find an equivalent resistance for the network
    with V1 across it, then find V1 using a voltage
    divider.

6
Example Resistor Ladder
7
Example Resistor Ladder
1kW
1kW
1kW

1kW
10V
2kW
2kW
-
  • Find an equivalent resistance for the network
    with V2 across it, then find V2.

8
Example Resistor Ladder
9
Example Resistor Ladder
10
Example Notch Filter
70.4mH
0.1W
100W


1kW
10V ? 0?
Vout
100mF
-
-
  • Find Vout
  • Use w 1500

11
Example Notch Filter
Vout
  • Find the equivalent impedance of the resistor,
    inductor, and capacitor.

12
Example Notch Filter
7.12W ? -89.99?
100W


1kW
10V ? 0?
Vout
-
-
  • Combine resistor and impedance.

13
Example Notch Filter
14
Example Notch Filter
15
Example Notch Filter
70.4mH
0.1W
100W


1kW
10V ? 0?
Vout
100mF
-
-
  • Find Vout
  • Use w 377

16
Example Notch Filter
  • Vout 1.23V ? -0.17?

17
Frequency Response
18
Using MATLAB to Solve Circuits
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.

20
Using MATLAB
  • Entering a complex number
  • gtgt 12j
  • ans
  • 1.0000 2.0000i
  • Multiplying complex numbers
  • gtgt (12j)(34j)
  • ans
  • -5.0000 10.0000i

21
Example Notch Filter
70.4mH
0.1W
100W


1kW
10V ? 0?
Vout
100mF
-
-
  • Find Vout
  • Use w 1500

22
Compute Impedances
  • gtgt omega 377
  • omega
  • 377
  • gtgt xl jomega70.4e-3
  • xl
  • 0 26.5408i
  • gtgt xc 1/(jomega100e-6)
  • xc
  • 0 -26.5252i

23
Equivalent Capacitor/Inductor Impedance
  • gtgt zeq (0.1xl)xc
  • /(0.1xlxc)
  • zeq
  • 6.8687e03 - 1.0981e03i

24
Voltage Divider
  • gtgt vin 10
  • vin
  • 10
  • gtgt vout vin1e3
  • /(100zeq1e3)
  • vout
  • 1.2315 0.1697i

25
Magnitude and Angle
  • gtgt abs(vout)
  • ans
  • 1.2432
  • gtgt angle(vout)
  • ans
  • 0.1369
  • gtgt angle(vout)180/pi
  • ans
  • 7.8461
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