ECE 3710 E: Circuits and Electronics

Jeff Dugger

Lecture 4: 08/31/00

Voltage Sources

+-

Vs

Provide potential to generate current

I

V

Vs

Ideal Voltage Source

Provides Voltage Independent of Current

Current determined byCircuit

Current Sources

Is

I

V

Is

Provides Current Independent of Voltage

Ideal Current Source

Voltage is determined by the Circuit

Ohm’s Law and Resistance

+

-V I R

V = I R

I = VR1

I

V

OR

Units: Ohms ( ) = Volts / Amp (V/A)

R1

I = VG

Ohm’s Law and Conductance

+

-V I

V = I R I

V

OR

Units: Siemens ( S ) = Amps / Volt (A/V)

R1

= GG

Series Resistance

R1

Vs R2

R3

I

V1

V2

V3

-Vs + V1 + V2 + V3 = 0

Vs = V1 + V2 + V3

Apply KVL:

Vs = R1 I + R2 I + R3 I

Apply Ohm’s Law:

= (R1 + R2 + R3) I

Define Equivalent Resistance:

Req = R1 + R2 + R3

Vs = Req I

Voltage Divider

I

R1

Vs R2

V1

V2

V2 = R2 IApply Ohm’s Law:

Use Equivalent Resistance to find I:

I = VsR1 + R2

1

Substitute:

V2 = VsR1 + R2

R2

Parallel Resistance

V

Is = G1 V + G2 V + G3 V

Apply Ohm’s Law:

= (G1 + G2 + G3 ) V

Define Equivalent Conductance:Geq = G1 + G2 + G3

Is = Geq V

G1 =

G2 =

G3 =

R1

1

R2

1

R3

1R1 R2 R3I1 I2 I3

Apply KCL: Is = I1 + I2 + I3

Is

Parallel Resistance

R1 R2 R3I1 I2 I3

Is = I1 + I2 + I3Apply KCL:

Or, Define Equivalent Resistance:

G1 =

G2 =

G3 =

V = Req Is

R1

1

R2

1

R3

1

Req = Geq

1=

1 / R1 + 1 / R2 + 1 / R3

1

VIs

Current Divider

R1 R2I1 I2

I2 = G2 VApply Ohm’s Law:

Use Equivalent Conductance to find V:

V = IsG1 + G2

1

Substitute:

I2 = IsG1 + G2

G2

VIs

Current Divider

R1 R2I1 I2

I2 = G2 VApply Ohm’s Law:

Use Equivalent Conductance to find V:

V = IsG1 + G2

1

Substitute:

I2 = IsR1 + R2

R1

VIs

Or, in terms or Resistance:

Series-Parallel Circuit

Vs R2I1

V1

V3R3

R1

I2 I3

Series-Parallel Circuit

Vs R2I1

V1

V3R3

R1

I2 I3

Circuit Analysis Example

VsR1IR3

R2

I2

R5

R4

V

Circuit Analysis Example

RaIV

Series Combination: Ra = R1 + R2

VsR3I2

R5

R4

Circuit Analysis Example

I

Rb

V

Parallel Combination: Rb = R4 || R5

VsR3I2Ra

Circuit Analysis Example

IV

Rb

VsR3RaI2

Circuit Analysis Example

IV

KCL at this node

Is = Ga V + Gb(V - Vs)= (Ga + Gb) V - Gb Vs

Rb

VsR3RaIs

V = Ga + Gb

GbVs + Ga + Gb

1Is

Circuit Analysis Example

IV

KCL at this node

Is = Ga V + Gb(V - Vs)= (Ga + Gb) V - Gb Vs

Rb

VsR3RaIs

V = Ra + Rb

RaVs + Ra || Rb Is

Open and Short Circuits“Open Circuit”

“Short Circuit”

R very large

R very small

R = I

V

R = 0I

V

Any current No voltage

No current Any voltage