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). A i I c.

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Lecture 7 linear dependent sources
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).


Four types of linear dependent sources

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
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
Example

Find VR.

  • By Ohm’s law, VR = (R3)(G VX)

  • Extra equation specifying VX:


Nodal analysis with dependent sources
Nodal Analysis with Dependent Sources

R

V

R

V

1

b

3

a

R

I

+

IS

R

I

m

2

_

R

2

2

4



Linearity of i v relationship
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
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) / R I = (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