10/1/2004EE 42 fall 2004 lecture 141 Lecture #14 Example circuits, Zener diodes, dependent sources, basic amplifiers Reading: 4.10, 5.1, 5.8 Next: transistors.

10/1/2004 EE 42 fall 2004 lecture 14 1

Lecture #14 Example circuits, Zener diodes, dependent sources, basic amplifiers

Reading: 4.10, 5.1, 5.8

Next: transistors (chapter 6 and 14)

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Topics

Today:

Examples, circuit applications:

• Diode circuits, Zener diode

• Use of dependent sources

• Basic Amplifier Models

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Notes on Use of Models• Most of the diode models are piecewise defined:

– One function for reverse bias– Another for forward bias

• You will need to:– “Guess” which diode or diodes are reverse (or forward)

biased– Solve for V, I according to your guess– If result is impossible, guess again

• Rarely, both guesses may lead to impossibility.– Then you must use a more detailed model

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Example 1: Ideal Diode ModelFind ID and VD using the ideal diode model.

• Is the diode reverse biasedor forward biased?

• Make a guess, substitutecorresponding circuitfor diode.

• “Reality check”answer to see if we need to re-guess.

+-

ID

VD

+

_

2 V

1 kW

V

I

Reverse bias

Forward biasI

V+

_

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Guessing the Diode Mode: Graphing

• Look at the diode circuit as a Thevenin equivalent linear circuit attached to a diode.

VL = VD

IL = -ID

• Graph the diode I-V curve and the linear circuit I-V curve on the same graph, both in terms of ID and VD.

• This means draw the diode I-V curve normally, and draw the linear I-V curve flipped vertically (IL = -ID).

• See where the two intersect—this gives you ID and VD.

Linear circuit

IL

+VL

-

ID

VD

+

_

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Example 1: Ideal Diode Model

• Forward biased

• VD = 0 V

• ID = 2 mA

VD

ID

2 V

2 mA

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Guessing the Diode Mode: “Common Sense”

• Notice the polarity of the 2 Vfalling over the resistor and diode

• The 2 V is in same direction as VD

• Diode is probably forward biased

• It’s generally easier to guess reverse bias first since it is easy to check.

• No matter what piecewise model we use, reverse bias is always open circuit.

• So when you don’t know what to do, put in open circuit for the diode, and see if it violates reverse bias conditions (zero current, negative voltage).

+-

ID

VD

+

_

2 V

1 kW

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Example 1: Ideal Diode Model

• Guess reverse bias:

• Since no current

is flowing,

VD = 2 V (by KVL)

• This is impossible for reverse bias (must have negative VD) So the diode must be forward biased

• VD = 0 V

• ID = 2 V / 1 kW = 2mA

• Same as what we got graphically.

+-

ID

VD

+

_

2 V

1 k

+-

ID

VD

+

_

2 V

1 k

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Example 2: Large-Signal Diode Model

• The large-signal diode model takes into account voltage needed to forward bias, (VF = 0.7 for silicon)

to find ID and VD.

• To be in forward bias

mode, the diode needs

0.7 V. • The source only provides 0.5 V. • The resistor cannot add to the voltage since the diode could

only allow current to flow clockwise.

• Reverse bias => open circuit => ID = 0 A, VD = 0.5 V

+-

ID

VD

+

_

0.5 V

1 k

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Zener diodes

• A Zener diode is the name commonly used for a diode which is designed for use in reverse breakdown

• Since the diode breaks down sharply, at accurate voltage, it can be used as a voltage reference

• The symbol for a Zener diode:

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Zener diode as a simple regulator

• The Zener diode shown here will keep the regulated voltage equal to its reverse breakdown voltage.

~ Constant voltagepower supplyto load

R

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Resistor sizing

• How big should R be in the regulator shown?• If the load draws a current I, then the resistor

must carry that current when the unregulated voltage is at the lowest point, without letting the regulated voltage drop.

• Lets say the load draws 10 milliamps, the regulated voltage is 2 volts, and the minimum unregulated voltage (low point of ripple) is 2.5 volts)

The resistor must be • R=(2.5v-2v)/10 milliamps=500 ohms.

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Ripple calculation

• How much ripple will be observed on the unregulated supply?

• The maximum current will be:

• And we can estimate the amount of charge lost:

• So the ripple will be

R

VVI regulatedpeakdunregulate

peak

)(

tIQ

C

QV

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Dependent Voltage and Current Sources

• A linear dependent source is a voltage or current source that depends linearly on some other circuit current or voltage.

• We can have voltage or current sources depending on voltages or currents elsewhere in the circuit.

Sometimes a diamond-shaped symbol is used for dependent sources, just as a reminder that it’s a dependent source.

Circuit analysis is performed just as with independent sources.

+

-

c

d

Vcd+ -

V = Av x Vcd

Here the voltage V is proportional to the voltage across the element c-d .

OR

+-

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WHY DEPENDENT SOURCES? EXAMPLE: MODEL FOR AN AMPLIFIER

V0 depends only on input (V+ V-)

)VV(AV0

+

AV+

V

V0

Differential Amplifier

AMPLIFIER SYMBOL output

An actual amplifier has dozens (to hundreds) of devices (transistors) in it. But the dependent source allows us to model it with a very simple element.

EXAMPLE: A =20 Then if input (V+-V-) = 10mV; Vo = 200mV.

input

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EXAMPLE OF THE USE OF DEPENDENT SOURCE IN THE MODEL FOR AN AMPLIFIER

V0 depends only on input (V+ V-)

)VV(AV0

+

AV+

V

V0

Differential Amplifier

AMPLIFIER SYMBOL

+

+

V0AV1

+

V1

Ri

Circuit Model in linear region

AMPLIFIER MODEL

See the utility of this: this model, when used correctly mimics the behavior of an amplifier but omits the complication of the many many transistors and other components.

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NODAL ANALYSIS WITH DEPENDENT SOURCESExample circuit: Voltage controlled voltage source in a branch

Write down node equations for nodes a, b, and c.(Note that the voltage at the bottom of R2 is “known” so current flowing down from node a is (Va AvVc)/R2.)

R5

R4 VAA

+

ISS

R3R1 Va Vb

+

R6

Vc

R2

0R

VVR

VAVR

VV

3

ba

2

cva

1

AAa

0R

VVRV

RVV

5

cb

4

b

3

ab SS

6

c

5

bc IRV

RVV

CONCLUSION:

Standard nodal analysis works

AvVc

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NODAL ANALYSIS WITH DEPENDENT SOURCESFinding Thévenin Equivalent Circuits with Dependent Sources Present

Method 1: Use Voc and Isc as usual to find VT and RT (and IN as well)

Method 2: To find RT by the “ohmmeter method” turn off only the independent sources; let the dependent sources just do their thing.

See examples in text (such as Example 4.3) and in discussion sections.

Pay most attention to voltage-dependent voltage sources and voltage-dependent current sources. We will use these only.

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NODAL ANALYSIS WITH DEPENDENT SOURCESExample : Find Thévenin equivalent of stuff in red box.

With method 2 we first find open circuit voltage (VT) and then we “measure” input resistance with source ISS turned off.

Verify the solution:

ISS

R3Va

+ A v V cs

R6

Vc

R 2

A)-1(RRR

)AR(RRIV

632

326SSTH

A)-1(RRR

)R(RRR

632

362TH

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EXAMPLE: AMPLIFIER ANALYSISUSING THE AMPLIFIER MODEL WITH Ri = infinity:

A: Find Thévenin equivalent resistance of the input.

B: Find the Ratio of the output voltage to the input voltage (“Voltage Gain”)

Method: We substitute the amplifier model for the amplifier, and perform standard nodal analysis

You find : RIN and VO/VIN

+

+

V0AV1

+

V1

Ri

Circuit Model in linear region

AMPLIFIER MODEL

+ A

V-

V+V0

RF

RSVIN

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EXAMPLE: AMPLIFIER ANALYSISUSING THE AMPLIFIER MODEL WITH Ri = infinity:

How to begin: Just redraw carefully!

Method: We substitute the amplifier model for the amplifier, and perform standard nodal analysis

Verify the solution: RIN = VO/VIN = A1

A)R(1R SF

SF

F

A)R(1R

AR-

+

AV1

-

+V1

V-

V+

V0

RF

RSVIN

+ A

V-

V+V0

RF

RSVIN