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