# Lecture 7: Linear Dependent Sources - PowerPoint PPT Presentation

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Lecture 7: Linear Dependent Sources. Today we will look at special voltage and current sources called dependent sources . A dependent source has a voltage or current that depends on a different voltage or current somewhere in the circuit (or even in a different, detached circuit). A i I c.

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Lecture 7: Linear Dependent Sources

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### Lecture 7: Linear Dependent Sources

Today we will look at special voltage and current sources called dependent sources.

A dependent source has a voltage or current that depends on a different voltage or current somewhere in the circuit (or even in a different, detached circuit).

Ai Ic

Gm Vc

+

_

+

_

Av Vc

Rm Ic

### Four Types of Linear Dependent Sources

Parameter being sensed

(controlling voltage/current)

Constant of proportionality

Output

Voltage-controlled voltage source … V = Av Vc

Current-controlled voltage source … V = Rm Ic

Current-controlled current source … I = Ai Ic

Voltage-controlled current source … I = Gm Vc

### Analyzing Circuits with Linear Dependent Sources

• Circuits with linear dependent sources can be analyzed using the tools we have learned so far.

• A dependent voltage source acts like an independent ideal voltage source: it tells us what its voltage is, but the current is unknown.

• Similarly, a dependent current source tells us what its current is, but the voltage is unknown.

• We just need to write an extra equation that specifies what the controlling voltage or current is.

### Example

Find VR.

• By Ohm’s law, VR = (R3)(G VX)

• Extra equation specifying VX:

R

V

R

V

1

b

3

a

R

I

+

IS

R

I

m

2

_

R

2

2

4

Va

Vb

| +

+

I2

### Linearity of I-V Relationship

• Whenever a circuit is composed only of the elements we have studied so far,

• Ideal Independent Voltage and Current Sources

• Linear Dependent Voltage and Current Sources

• Resistors

the I-V relationship is always a line. Simple examples:

i

i

i

+

_

v

v

v

### Equivalent Circuits

I

• Consider the simple circuit composed of a voltage source and resistor.

• This circuit has a linear I-V relationship:

I = (V – VS) / RI = (1/R) V – VS / R

• With proper choice of VS and R, this circuit can mimic any other circuit we have studied so far.

VS

v

VS/R