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Lecture 7: Linear Dependent SourcesPowerPoint Presentation

Lecture 7: Linear Dependent Sources

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Lecture 7: Linear Dependent Sources

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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

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

- 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.

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

- 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

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