Nodal analysis

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Lecture 18 Summary of ideal devices, amplifier
examples
Reminder MIDTERM coming up one week from today
(Monday October 18th) This week Review and
examples
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Midterm

• Monday, October 18,
• In class
• One page, one side of notes

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Topics

• Today
• Summary of ideal circuits
• Amplifier examples
• Comparator
• Op-Amp

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Ideal devices
Wire Current in current out No voltage
differences
Resistor
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Ideal devices 2
Inductor
Ideal diode Reversed bias ? no current, open
circuit Forward bias ? no voltage drop, just like
a wire
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Ideal devices 3
V1 -
V2 -
Transformer
N1 and N2 are the number of turns of wire
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Ideal devices 4
Voltage source Voltage given, current can be
anything Note the voltage could be given as A
function of time

Current source Current given, voltage can be
anything Note the current could be given as A
function of time
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Ideal devices 5
V1 -
V2 -
Dependent Voltage source Voltage given as a
multiple of another Voltage or a current,
current can be anything

V1 -
Dependent Current source Current given as a
multiple of a different current or voltage,
voltage can be anything
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NPN transistor
Base
Collector
The Base-Collector junction must be reverse
biased. The model of the diode can be ideal, or
better with a 0.7 volt turn on Beta could be
anywhere from 40 to 400
Emitter
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NMOS transistor
Drain
Gate
If VGS is higher than the threshold VTH, then the
switch is closed.
D
G
Source
S
The resistance from the source to the drain
depends on the how much greater than threshold
VGS is, and how wide the transistor is.
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PMOS transistor
Source
If VGS is lower than the threshold VTH, then the
switch is closed.
S
G
Gate
Drain
D
The resistance from the source to the drain
depends on the how much below threshold (more
negative) VGS is.
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Amplifier
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Amplifier
Vrail
Vrail
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OP-AMPS AND COMPARATORS
A very high-gain differential amplifier can
function either in extremely linear fashion as an
operational amplifier (by using negative
feedback) or as a very nonlinear device a
comparator. Lets see how!
Differential ? V0 depends only on
difference (V ? V-)
The output cannot be larger than the supply
voltages. It will limit or clip if we attempt
to go too far. We call the limits of the output
the rails.
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WHAT ARE I-V CHARACTERISTICS OF AN ACTUAL
HIGH-GAIN DIFFERENTIAL AMPLIFIER ?

• Circuit model gives the essential linear part
• The gain may be 100 to 100,000 or more
• But V0 cannot rise above some physical voltage V0
  lt VRAIL
• And V0 cannot go below the lower rail V0
  gt V-RAIL
• CMOS based amplifiers can often go all the way to
  their power supplies, perhaps 5 volts

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I-V Characteristics of a real high-gain amplifier
Example Amplifier with gain of 105, with max V0
of 3V and min V0 of ?3V.
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I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN
DIFFERENTIAL AMPLIFIER (cont.)
Example Amplifier with gain of 105, with upper
rail of 3V and lower rail of ?3V. We plot the V0
vs VIN characteristics on two different scales
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I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN
DIFFERENTIAL AMPLIFIER (cont.)
Now plot same thing but with equal horizontal and
vertical scales (volts versus volts)

• Note
• (a) displays linear amplifier behavior
• (b) shows limit of linear region (VIN lt 30
  ?V)
• (c) shows comparator function (1 bit A/D
  converter centered at VIN 0) where lower rail
  logic 0 and upper rail logic 1

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EXAMPLE OF A HIGH-GAIN DIFFERENTIAL AMPLIFIER
OPERATING IN COMPARATOR (A/D) MODE
Simple comparator with threshold at 1V. Design
lower rail at 0V and upper rail at 2V (logic
1). A large (e.g. 102 to105 )
NOTE The actual diagram of a comparator would
not show an amplifier with offset power supply
as above. It would be a simple triangle, perhaps
with the threshold level (here 1V) specified.
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ONE-BIT A/D CONVERSION REQUIRED IN DIGITAL
SYSTEMS
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OP-AMPS AND COMPARATORS
A very high-gain differential amplifier can
function in extremely linear fashion as an
operational amplifier by using negative feedback.
Negative feedback ? Stabilizes the output
We can show that that for A ? ? (and Ri ? 0 for
simplicity)
Stable, finite, and independent of the properties
of the OP AMP !
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OP-AMPS TAMING THE WILD HIGH-GAIN AMPLIFIER
KEY CONCEPT Negative feedback
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OP-AMP very high gain ?predictable results
Analysis
Lets solve for V- then find VO from VO A (V -
V-)
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OP-AMPS Another Basic Circuit
Now lets look at the Inverting Amplifier
When the input is not so large that the output is
hitting the rails, we have a circuit model
R1
R2
VIN
V0
1K
9K
(?)
()
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Inverting amplifier analysis
Analysis
Solve for V- then find VO from VO - AV-