International University

School of Electrical Engineering

ANALOG ELECTRONICS

Lecture # 1: Introduction to
Analog Electronics

Assoc. Prof. .Nguyen Binh Duong, Room O2.206

Email: nbduong@hcmiu.edu.vn

Textbook: Microelectronic Circuit Design, A.S.Sedra

& K.C. Smith, 6th ed., Oxford University Press.
 Microelectronic Circuits
by Sedra and Smith
• PART I Devices and Basic Circuits
– CHAPTER 1 Signals and Amplifiers
– CHAPTER 2 Operational Amplifiers
– CHAPTER 3 Semiconductors
– CHAPTER 4 Diodes
– CHAPTER 5 MOS Field-Effect Transistors (MOSFETs)
– CHAPTER 6 Bipolar Junction Transistors (BJTs)
• PART II Integrated-Circuit Amplifiers
– CHAPTER 7 Building Blocks of IC Amplifiers
– CHAPTER 8 Differential and Multistage Amplifiers This course: Analog
– CHAPTER 9 Frequency Response
Electronics
– CHAPTER 10 Feedback
– CHAPTER 11 Output Stages and Power Amplifiers
– CHAPTER 12 Operational-Amplifier Circuits
• PART III Digital Integrated Circuits
– CHAPTER 13 CMOS Digital Logic Circuits
– CHAPTER 14 Advanced MOS and Bipolar Logic Circuits
– CHAPTER 15 Memory Circuits

2
 Applications of Electronic Devices

Chips…

Sand…
Chips on Silicon wafers
 ICs and Applications
• Processors
– CPU, DSP, Controllers
• Memory chips
– RAM, ROM, EEPROM
• Analog
– Mobile,
Audio/video processing
• Programmable
– PLA, FPGA
• Embedded systems
– Vehicles’s comonents,
Factories’ equipments
– Network cards
• System-on-chip (SoC) Electrical appliances
 History of Development
Audion (Triode)
1906
1906 1906, Lee De Forest •1906 Lee de Forest
(“Triode”)
•Vacuum tube devices
continued to evolve
•1940 Russel Ohl (PN
1947
1947 junction)
•1947 Bardeen and
First point contact
Brattain (Transistor)
transistor (germanium)
1947, John Bardeen and
Walter Brattain
Bell Laboratories
 History of Development (cont.)
•1950 William Shockley (Junction
1958 transistor)
•1952 Single crystal silicon is fabricated
•1954 First commercial silicon transistor
•1954 First transistor radio (Regency TR-
1)
•1955 First field effect transistor - FET
First integrated •1952 Geoffrey W. A. Dummer (IC
circuit
(germanium), 1958
concept)
Jack S. Kilby, Texas •1954 Oxide masking process developed
Instruments
•1958 Jack Kilby (Integrated circuit)
Contained five
components, three
types:
transistors resistors
and capacitors
History of Development (cont.)
•1959 Planar technology invented
•1960 First MOSFET fabricated
– At Bell Labs by Kahng
•1961 First commercial ICs
– Fairchild and Texas Instruments
•1963 CMOS invented
– Frank Wanlass at Fairchild Semiconductor
– U. S. patent # 3,356,858
– Standby power reduced by six orders of magnitude
 History of Development (cont.)
• 1982 Intel 80286
•1971 Microprocessor invented – 1.5 m silicon gate
– Intel produces the first 4-bit CMOS process
microprocessor the 4004 – 1 polysilicon layer
– The 4004 was a 3 chip set – 2 metal layers
• 2 kbit ROM IC – 134,000 transistors
First • 320 bit RAM IC – 6 to 12 MHz clock
• 4-bit processor speed
• Each housed in a 16- – Die size 68.7 mm2
pin DIP package • 2000 Pentium 4
– Processor: – 0.18 m silicon gate
• 10 m silicon gate CMOS process
PMOS process – 1 polysilicon layer
• ~2300 transistors – 6 metal layers
• Clock speed: 0.108 – Fabrication: 21 mask
MHz layers
• Die size: 13.5 mm2 – 42,000,000 transistors
– 1,400 to 1,500 MHz
2000 Pentium 4 clock speed
– Die size 224 mm2
 2006 0.13 µm silicon
gate CMOS process
MOORE’s Law
 Then (C64, 1983) and (iPhone, 2013)

• 5000 nanometer process • 45 nanometer process

• 1.023 MHz (CPU) • A7 quad-core processor
• 10,000s of transistors • 100,000,000 transistors
• 160 x 200 x 16 color • 4.8 Retina+ 1080 HD
display resolution display
• $1300 dollars at release • > $600 dollars at release
(adjusted for inflation)
Electron Microscope view of
MOS Transistor
Insulating Layer (gate
oxide) now just 1.2 nm
thick

For reference:
Human hair: 100,000 nm
Silicon atom: 0.1 nm

32 nm wide
 Analog IC design in Vietnam
• Several companies starting analog centers
• Multinationals-eSilicon, TI, Intel, Renesas,
Marvel etc.
• Vietnam start ups- ICDREC, Wechip (but
dead after 2 years), Trung Nam… etc.
• Big demand for skilled designers
• Interesting and profitable activity
https://www.semiconvn.com/home/tuyen-dung-ky-su/tuyen-dung-ky-su-vi-
mach/120-tuyen-dung-ky-su-thiet-ke-vi-mach/90--ic-design-companies-in-
vietnam-cong-ty-thiet-ke-vi-mach-o-viet-nam.html
14
 Course Information
1. Timetable
 16 sessions, 1 session per week
 After 8 sessions, a midterm exam
2. Grading criterion
 30% for quizzes, homework, assignments, projects
 30% for midterm examination
 40% for final examination
 Lecture notes can be found on the Blackboard
 Students who are absent four sessions or more will be
forbidden to attend the final examination.
3. Relationship to Other Modules
 Pre-requisite: Electronics Devices
Textbooks:
Microelectronic Circuits, 4th Edition by Sedra and Smith
(www.sedrasmith.org)
 Class Participation
 ASK QUESTIONS!!!
− I will make an effort to periodically stop and see if everyone understands
the lecture material. However, you should stop me at any time if you have
any questions.
− If you are confused about something, ask me your questions

OFFICE HOURS
− You are also encouraged to see me at the office. My office is O2.206.
− Take advantage of office hours. It’s a resource that too many students
seem to neglect.
 Analog Signals
• Triangle signal

• Rectangular signal

• Sinusoidal signal

• Sine wave => important

 Analog to Digital Conversion

Figure : An analog signal is converted to an approximate digital

equivalent by sampling. Each sample value is represented by a
18
3-bit code word. Practical converters use longer code words.
 Signals and Noise

Figure : After noise is added, the original amplitudes of a digital signal

19
can be determined. This is not true for an analog signal.
Electronic circuits in modern
systems

 Analog electronic circuits

 Digital electronic circuit 20
21
Example Applications of Analog and
Mixed-Signal Integrated Circuits
 Mixed-Signal Integrated Circuits

Transistors are the most important devices in the electronic

circuits
The degree of device integration continues to follow Moore’s law, the number of
transistors inside an IC could be doubled every 24 months at a density that also
minimizes the cost of a transistor.
 Bipolar Transistor (NPN-type)
 The BJT (Bipolar Junction
Transistors) is a three-terminal
device (Collector, Emitter,Base) .

 BJT transistor is a current-

controlled device.

Equivalent circuit 24
 FET Transistor
 The FET (Field-Effect
 Transistor) is a three-terminal
device (Drain, Gate, Source)

 FET transistor is a voltage-

controlled device.

Equivalent circuit

25
Analog Integrated Circuit Design
– There is a strong need for excellent analog
and mixed-signal designers.
– To prepare a career in the field of mixed-
signal integrated circuits, this course is the
first step.

26
 Kirchhoff’s Laws
• Kirchhoff’s Current Law (KCL): The algebraic sum of all of the currents at
a node in a circuit equals zero.
• Kirchhoff’s Voltage Law (KVL): The algebraic sum of all of the voltages
around any closed path in a circuit equals zero.
 Divider Circuits
• Current and voltage divider circuits using resistors
 Source Transformations
 Source transformations can be a useful way to simplify circuits

 THEVENIN AND NORTON EQUIVALENTS

– Can represent any sources made up of sources (both independent and
dependent) and resistors
– Converting to a Thevenin equivalent

29
30
 Voltage, Current Sources,
Dependent Source
• A voltage source delivers a constant voltage regardless of the current it produces
• A current source delivers a constant current regardless of the output voltage
Example
 The Sinusoidal Signal
T : period of the function (s)
f : frequency of the function (Hz)
1
f 
T
ω : angular frequency (radians/second)
 2f 2 T
Φ: phase angle (degree)
180
(number of degrees)  (number of radians)
v Vm cost    
Vm : maximum amplitude (V)
A sinusoidal voltage/current
source produces a voltage/current Vrms: root mean square value
that varies sinusoidally with time. t0 T
1 Vm
Vrms   Vm2 cos t   dt 
2

Ωt + Φ : the argument of the sinusoid T t0 2

The Phasor

Euler’s identity: e j cos   j sin 

For a given sinusoidal voltage function:

The phasor is a complex number that carries the amplitude and phase
angle information of a sinusoidal function.

The phasor transform of the given sinusoidal function is:

V Vm e j P Vm cost   

 Complex Numbers Tutorial
Transition between rectangular and polar forms :
From polar form to rectangular form : Complex plane

ce j ccos   j sin  
c cos   jc sin 
a  jb
From rectangular form to polar form :

a  jb ce j
where : c  a2  b2
b
tan   n a  jb c c (cos   j sin  )
a
Complex Numbers

Angle in Angle in sin  cos  tan 

degrees rad.
0 0
30 /6
45 /4
60 /3
90 /2 36
ACTIVE DEVCES
REVIEW: Diode

38
REVIEW: Diode

39
Example
The diode circuit shown in Fig has VS= 10 V, Vm = 50 mV, and RL= 1 k.
Determine the instantaneous diode voltage v D. Assume rD=5.11Ω, VD=0.7V
 TRANSISTOR

 Two main roles:

 Amplifier circuit
 Switching circuit
REVIEW: BJT - DC and AC ANALYSIS

VCC=20V

42
 REVIEW: BJT - DC ANALYSIS

DC ANALYSIS MODEL (NPN)

For PNP, reverse the polarities
of the diode and voltage supply.
IB and IB remain as shown but
will have negative values.
43
 REVIEW: BJT - DC ANALYSIS
A transistor amplifier is biased so
that the Q-Point is located on the
• DC analysis DC Loadline.

DC load line
=>IE=IC+IB= IB(1+β) ≈ IB.β=IC. Since β>>1
If I C 0 then VCE ( off ) VCC
Equation of DC load line
VCE VCC  I C ( RC  RE ) VCC
If VCE 0 then I C ( sat ) 
RC  RE
 VCC VCE  I C ( RC  RE )
REVIEW: BJT - DC ANALYSIS

 is constant for a particular transistor. It's

value is less than but close to 1, normally 0.98-
0.9995. a is the gain of a
Common-Base amplifier.
 is constant for a particular transistor, typically
in the range of 100 to 200 but may be 50-
2000. Since the value of 
may vary significantly among transistors of the
same type, a
-tolerant circuit design is desirable.  is the
Common-Emitter current gain. 45
Example
 VCC 20
I C ( sat )  
RC  RE 40 Equation of DC load line
VCE VCC  I C ( RC  RE )

VCE ( off ) VCC 20V

 REVIEW: BJT - AC ANALYSIS

AC signal model of BJT

Supposing that
C, Cπ
are negligible

DC block: Zc=1/C is large

=> Zc =0(Ω) at AC mode.
 REVIEW: BJT - AC ANALYSIS

vout vL  ic .( RC // RL )  g m v ( RC // RL )
Here
vin v
vout vL  g m vin ( RC // RL )   ib ( RC // RL )
 If Vin =A.sin(t) then Gain of AC signal
vout  g m ( RC // RL ) A sin(t ) vout
AV   g m ( RC // RL )
vin
g m and r can be found by :
g m I C / 25x10  3
r  / g m
where I C I CEQis bias current

Small signal model

By superposition , total collector current is :iC _ Total I CQ  ic
DC AC

By superposition , total collector voltage is :vCE _ Total VCEQ v c

DC AC
DC component is created by the DC biasing circuit.
 AC component is created by small signal vC

The total current at collector : iC_Total The total voltage at collector : vCE_Total
We know that iC _ Total  I CQ  ic  ic iC _ Total  I C

But v c v out  ic .( Rc / / RL ), or v c  (iC _ Total  I C ) R where R  ( Rc / / RL )

Replace vc  (iC _ Total  I C ) R in equation vCE _ Total VCE  v c

We have : vCE _ Total VCE  iC _ Total R  I C R

If iC _ Total 0
then vCE ( off ) VCE  I CQ R
If vCE _ Total 0
then iC ( sat ) VCE / R  I CQ
 DC Biasing + AC signal

 The AC load line of a given

amplifier will not follow the plot of
the dc load line.
 This is due to the DC load of an
amplifier is different from the ac
load.
 AC load line and DC load line
intersects at Q-Point (Static
Operation Point) Q (VCE, IC)
 AC load line

 Case (a): Limited by saturation

 The maximum of output current : iC(AC)= (VCEQ/R)sin(t)
 The maximum of output voltage: vCE(AC)=vout= VCEQsin(t)
 Case (b): Limited by cut-off:
 The maximum of output current : ic(AC)= I CQsin(t)
 The maximum of output voltage: vCE(AC)=vout= (ICQ)sin(t)
 Case (c): Centered Q-point
 The maximum of output current : ic(AC)= I CQsin(t)
 The maximum of output voltage: vCE(AC)=vout= VCEQsin(t)
 REVIEW: BJT - AC ANALYSIS
DETERMINING IMPEDANCE
TO FIND Zin: 1. Remove the input source.
2. Leave the load connected.
3. Short other independent voltage sources; open other independent
current sources.
4. If there are no dependent sources, the input impedance is
determined by inspection, otherwise continue to step 5.
5. Keep in mind that current could flow in the circuit. Either a)
manipulate the circuit using resistance reflection rule to ground
out the independent sources, b) apply a test source to the input
TO FIND Zout: 1. Remove the load .
2. Turn off the input source, but leave the source (resistance)
connected.
3. Short other independent voltage sources; open other independent
current sources.
4. If there are no dependent sources, the output impedance is
determined by inspection, otherwise continue to step 5.
5. Keep in mind that current could flow in the circuit. Either a)
manipulate the circuit using resistance reflection rule to ground out
the independent sources, b) apply a test source to the output,
When calculating the gain, vout/vin, assume that sources and load (if
shown) are connected. 54
 REVIEW: BJT - AC ANALYSIS
EQUATIONS FOR AC ANALYSIS

55
 REVIEW: BJT - AC ANALYSIS

56
 REVIEW: BJT - AC ANALYSIS
BJT HIGH-FREQUENCY ANALYSIS

57
 REVIEW: BJT - AC ANALYSIS
BJT HIGH-FREQUENCY ANALYSIS THE MILLER EFFECT
The existance of C complicates the above model. The Miller effect says that the
model can be approximated by removing C and replacing it with another gate-to
source capacitance CM. K is the voltage gain across C (assuming that C
represents an open circuit).

58
REVIEW: METAL OXIDE SILICON FIELD-EFFECT TRANSISTORS -
MOSFETs

59
REVIEW: METAL OXIDE SILICON FIELD-EFFECT TRANSISTORS -
MOSFETs

In MOSFET circuits, there must

be a resistor between gate and
ground since the gate/substrate
junction has a capacitance that
can accumulate a destructive
charge. The resistance
should be high (around 1M) to
preserve the high input
impedance characteristic.
60
 REVIEW: METAL OXIDE SILICON FIELD-EFFECT TRANSISTORS -
MOSFETs

https://www.quora.com/What-are-th
e-pros-and-cons-of-BJT-versus-FET
-transistor
 The Three Modes of Operation:

CUTOFF - The region where the gate voltage is lower than the threshhold voltage Vt so
that no current flows through the drain.
TRIODE - The region where vDS is lower than the excess gate voltage and the
characteristic curve is a curve. For small signals of VDS, the FET behaves like a voltage-
controlled resistor. In the operating region, the characteristic curve may be thought of as
a straight line, the slope of which is the inverse of the drain-to-source resistance.
SATURATION - The region where vDS is greater than the excess gate voltage and the
characteristic curve is a horizontal line. Drain current is a function of gate voltage vGS.
REVIEW: METAL OXIDE SILICON FIELD-EFFECT TRANSISTORS -
MOSFETs

64
REVIEW: METAL OXIDE SILICON FIELD-EFFECT TRANSISTORS -
MOSFETs

THRESHHOLD VOLTAGE - Vt - the gate-to-source voltage at which an

FET begins to conduct, usually 1 to 3 volts in an n-channel enhancement
MOSFET.

EXCESS GATE VOLTAGE or EFFECTIVE VOLTAGE - The gate-to-

source voltage in excess of the threshhold voltage, i.e. vGS - vt

ASPECT RATIO - W/L - the ratio of the channel width to the channel
length (distance from source to drain). CMOS (complementary MOS) -
employing both n channel (NMOS) and p-channel (PMOS) on the same
chip.

GATE CAPACITANCE - The gate and substrate are separated by a

thin, non-conducting metal oxide layer which causes the gate to act like
a capacitor. It is necessary to connect a resistor between gate and
ground to prevent a destructive charge from accumulating. The resistor
should be on the order of 1 Meg to preserve the high impedance input
characteristic.
66
 REVIEW: METAL OXIDE SILICON FIELD-EFFECT TRANSISTORS -
MOSFETs

Where:
REVIEW: METAL OXIDE SILICON FIELD-EFFECT TRANSISTORS -
MOSFETs
Example
The voltage VA is usually referred to
as the Early voltage
The Early voltage VA
The π equivalent circuit

The T equivalent circuit

Determine the Output resistance
REVIEW: MOSFETs

93
REVIEW: MOSFETs

94
REVIEW: MOSFETsΠ

95
 REVIEW: MOSFETs
FREQUENCY ANALYSIS
Small capacitances exist between
the gate and drain and between
the gate and source. These effect
the frequency characteristics of the
circuit

THE MILLER EFFECT

The existance of Cgd complicates the above model. The Miller effect says
that the model can be approximated by removing Cgd and replacing it with
another gate-to source capacitance CM. K is the voltage gain across Cgd
(assuming that Cgd represents an open circuit).

96
 THE POLES OF AN AMPLIFIER
REVIEW: MOSFETs

97
REVIEW: EQUATION SUMMARY

98
REVIEW: TYPES OF SINGLE-TRANSISTOR AMPLIFIERS

99
REVIEW: TYPES OF SINGLE-TRANSISTOR AMPLIFIERS

10
0
 Amplifier Configurations
Voltage Amplifier: Voltage input and Voltage output

The controlled source is a Voltage-controlled-Voltage Source

Av = OPEN Circuit Voltage Gain can be found by applying a
voltage source with Rs=0, and measuring the open circuit output 10
voltage(no load or RL=infinity) 1
Amplifier Configurations

10
2
 Amplifier Configurations
Current Amplifier: Current input and Current output

10
3
 Amplifier Configurations
Transconductance Amplifier: Voltage input and Current output

10
4
 Amplifier Configurations
Transresistance Amplifier: Current input and Voltage output

10
5
Amplifier Configurations

10
6
 Amplifier Configurations
Final Summary of Transistor Amplifier Analysis

1) a.) Determine DC operating point. Make sure the transistors are biased into active mode (
forward active for BJTs and Saturation for MOSFET. Do not confuse the two terms as
saturation means a completely different thing for a BJT) and b.) calculate small signal
parameters gm, r, ro etc…
2) Convert to the AC only model.
• DC Voltage sources are replaced with shorts to ground
• DC Current sources are replaced with open circuits
• Large capacitors are replaced with short circuits
• Large inductors are replaced with open circuits
3) Use a Thevenin circuit where necessary on each leg of transistor
4) Replace transistor with small signal model
5) Simplify the circuit as much as necessary and solve for gain.
6) Solve for Input Resistance: With the load resistance attached… a.) Apply a test input
voltage and measure the input current, Rin=vt/it or b.) Apply a test input current and measure
the input voltage, Rin= vt/it
7) Solve for Output Resistance: With all input voltage sources shorted and all input current
sources opened… a.) Apply a test voltage to the output and measure the output current R
=vt/it or b) Apply a test current to the output and measure the output voltage, R out= vt/it

10
7
Transistor Amplifier Configurations

10
8
Transistor Amplifier Configurations

10
9
Transistor Amplifier Configurations

11
0
Transistor Amplifier Configurations

11
1
Transistor Amplifier Configurations

11
2
Transistor Amplifier Configurations

11
3
 Transistor Amplifier Configurations
Common Collector: AC V lt Voltage Gain

11
4
 Transistor Amplifier Configurations
Common Drain Conversion from DC to AC Equivalent Circuit

DC
Circuit

AC
Circuit

11
5
 Transistor Amplifier Configurations
Common Emitter and Common Source
DC Circuit converted to AC Equivalent (reduced)

AC Circuit

AC Circuit
(reduced)

11
6
 Transistor Amplifier Configurations
Common Drain AC Voltage Gain

11
7
 Transistor Amplifier Configurations
Common Collector/Drain Input Resistance

11
8
 Transistor Amplifier Configurations
Common Collector Output Resistance

11
9
 Transistor Amplifier Configurations
Common Drain Output Resistance

12
0
Transistor Amplifier Configurations

12
1
 Transistor Amplifier Configurations

Note: since R7 was originally defined as the load, the current gain should
actually be (+1) (R4||ro)/(R4||ro+R7) using a current divider. 12
2
 Transistor Amplifier Configurations
Common Base and Common Gate
DC Circuit

Base (or Gate) is neither an input or output

Input is Emitter (or Source)
Output is Collector ( or Drain)

12
3
 Transistor Amplifier Configurations
Common Base: DC Circuit converted to AC Equivalent (reduced)

DC
Circuit

Note: let’s ro go to infinity which

makes the math dramatically easier

AC
Circuit

12
4
Common Base AC Equivalent (reduced)

12
5
 Common Base Voltage Gain

Thus,

12
6
 Common Base Voltage Gain

Thus

12
7
Common Base Voltage Gain

12
8
 Transistor Amplifier Configurations
Common Base Input Resistance

Input Resistance: With the load resistance

attached apply a test input
voltage and measure the input current,
Rin=vx/I

From before,

12
9
Common Base Input Resistance

Input Resistance
is very small!
13
0
Transistor Amplifier Configurations
Common Base Output Resistance

Replace RL by a voltage
source, vx

13
1
Common Base Output Resistance

13
2
Transistor Amplifier Configurations

13
3
 Transistor Amplifier Configurations
Common Gate Solution
The Common Gate solution can be found by recognizing
that the following translations can be made in our small
signal model:

13
4
Transistor Amplifier Configurations

13
5
 You can combine or Cascade configurations to produce “High Performance”
amplifiers with High input impedance, low output impedance and huge voltage gains.

Multistage
Amplifier
Configurations
Multistage Amplifier Configurations
For AC-Coupled amplifiers (capacitors between stages), the DC
solution reduces to three parallel and independent circuits!

13
7
Multistage Amplifier Configurations
For AC-Coupled amplifiers (capacitors between stages), the AC solution
reduces to three circuits, each of which has a load dependent on the input
resistance of the next stage! Continued….

13
8
Multistage Amplifier Configurations
Continued….(For AC-Coupled amplifiers (capacitors between stages), the AC
solution reduces to three circuits, each of which has a load dependent on the
input resistance of the next stage!)

13
9
Multistage Amplifier Configurations
Multistage Amplifier Configurations

141
 Amplifier Configurations
• TYPES OF AMPLIFIERS
 Amplifiers always increase (or at least maintain) the signal power.
The gain of an amplifier is expressed as a voltage gain,
transconductance gain (voltage input, current output),
transresistance (current input, voltage output) or current gain.
Thus, there are four basic types of amplifiers, depending on what
it is that they amplify (voltage or current) and what it is that you
want as their output (voltage or current).

 One can model any amplifier as any of the four types, but the
intended use of the amplifier usually makes one choice usually
the best. In other words, an amplifier is usually designed to be a
particular type.
142
 AMPLIFIERS
• TYPES OF AMPLIFIERS

143
144
• NOTE 1: in general use Z (for impedance) rather
than R, since most inputs and outputs are not
purely resistive!
• NOTE 2: RS is shown as a resistor at the input of
the amplifier that effectively attenuates the input
signal if the amplifier is not ideal (i.e. if the
voltage input amplifiers have input resistances
less than infinity or if the current input amplifiers
have input resistances greater than zero).

145
BASIC AMPLIFIER PARAMETERS

146
147
BASIC AMPLIFIER PARAMETERS

148
 BASIC AMPLIFIER PARAMETERS
• “White” noise is noise that has a flat frequency spectrum (i.e. contains all
frequencies in equal proportion). In practice, noise is only “white” over a finite
bandwidth. The sound from an FM receiver between channels is more-or-less white.

• White noise can be really useful for determining the frequency response of circuits
using a spectrum analyzer - all frequencies are equally represented in the spectrum of
white noise, so you can input it into a circuit you are testing and look at which frequencies
come out! If you average over a long enough time, you can obtain a frequency
response for the circuit under test. 149
BASIC AMPLIFIER PARAMETERS

• DISTORTION of a signal occurs when the amplified version of the

signal coming out of the amplifier is not simply a scaled copy of the input
signal, but is differently shaped (distorted).

• Distortion can be noted as a difference in waveform shape the ideal

scaled copy of the input, a difference in the spectrum of the input and
output signals, or sometimes observed by listening to the output of an
amplifier (if it is used for audio).

• Distortion is due to nonlinearities, generally because the semiconductor

(or tube) amplifier are not perfectly linear. In some cases, distortion can
come from amplifier saturation ("clipping," or the amplifier simply reaching
one of the voltage or current extremes beyond which it cannot swing).

150
BASIC AMPLIFIER PARAMETERS
• Another common type of distortion in amplifiers that use both PNP and
NPN transistors at their outputs is crossover distortion, which is caused
by the slight "gap" in voltage between one type of transistor turning off
and the other turning on.
• The term total harmonic
distortion (THD) represents the
percentage of the total output signal
of an amplifier that is at frequencies
other than the one put in... in other
words, you drive the amplifier with a
pure sinewave at a frequency fo and
make a ratio of the power in the
harmonics (i.e. sum of signal
frequencies other than fo, with
amplitudes given by Ai(fi)) to the input
signal power.

151
AMPLIFIER POWER SUPPLIES & EFFICIENCY

• All amplifiers need some type of power supply to supply the extra
energy that is delivered to the load.
• Most analog amplifiers use two power supply voltages or “rails,” as
shown below,
• Some amplifiers use only a single power
supply voltage, but sometimes they internally
"split" that single voltage into two rails by
making an artificial "ground" voltage half way
from "real ground" to the supply voltage.
• The efficiency of an amplifier reflects the
amount of power delivered to the load as a
fraction of the total power drawn from the
power supply, and can be computed using:

152
 LARGE AND SMALL SIGNALS
• Most circuits are linear if the input signals are small enough! If the signal
amplitude is increased enough some type of nonlinearity will make itself obvious!
All semiconductor devices (and vacuum tubes!) are very nonlinear, and the only
reason we get nice, clean amplifier outputs is that we are keeping signal swings
small enough through various techniques.
• Examples of large signal effects (as discussed above in "Distortion"):
• Amplifier clipping (saturation) -> here you have a case where the amplifier’s
output cannot swing above and below certain maximum and minimum voltages
(that makes sense)... you have probably heard clipping when someone turned up
a stereo too loud!
• Amplifier distortion due to transistor nonlinearities -> this is simplest to
understand by considering that basically, all transistors are nonlinear devices and
we work very hard to “coax” linearity out of them over certain ranges of signal
level... this type of distortion can be minimized but can never be completely
avoided.
• Amplifier exploding (very nonlinear) due to extremely large input signal:

When we talk about transfer functions, AC small signal equivalent

models, Bode plots, etc., we are always assuming that the circuit is
in small-signal operation! 153
 TRANSFER FUNCTIONS
• You already know that stereo equipments are having frequency range over
which the amplifier will operate properly.
• Amplifiers are either DC or AC coupled, meaning that the inputs are sensitive
to both DC and AC signals ("DC-coupled") or only AC signals ("AC-coupled).
You should note that oscilloscope amplifiers always have the option of
choosing one or the other coupling modes.
• Capacitors can be used at the inputs and outputs of amplifiers to “block” DC
signals, as long as they are large enough to "look like shorts" in the frequency
range of interest... This type of amplifier is called AC- or capacitively-coupled.
• The frequency response of such an AC-coupled circuit cannot extend to zero
Hz.
• Here is a brief complex number review for your reference so you can
compute transfer functions of circuits:

154
 TRANSFER FUNCTIONS
POLES & ZEROS -> WHAT DO THEY MEAN?
Transfer Function Notation:

z1 through zN are the “zeros,” or the complex frequencies at which the

numerator becomes zero (the transfer function goes to zero)...
p1 through pM are the “poles,” or the complex frequencies at which the
denominator becomes zero (the transfer function goes to infinity)...
• The “order” of the system = N + M
• A zero alone would make the output amplitude of a circuit increase
forever with increasing frequency. In real circuits, one cannot have a
zero without a pole to “cancel” it out at some frequency.

155
 TRANSFER FUNCTIONS
SIMPLE FILTERS
• The cutoff (or 3dB) frequency is the point at which the response is 3 dB
lower than in the passband ( ~ 0.707 times the passband amplitude).
HERE IS A GOOD IDEA TO GET A SENSE FOR CIRCUIT
BEHAVIOR: Look at the circuit first before doing any math! The
capacitors are all infinite impedance for DC and their impedance
decreases toward zero as the frequency increases.
FIRST-ORDER RC LOW-PASS FILTER:

156
 TRANSFER FUNCTIONS
The general form is

where K is the gain for low frequencies and A = K0

• The pole is at S = -0
• The “cutoff” frequency is at
FIRST-ORDER RC HIGH-PASS FILTER:

The general form is

where K is the gain for high frequencies

• The pole is at S = -0 and the zero is at S = 0
157
• The cutoff frequency is the same as for the low-pass filter.
 BODE PLOTS
THE BASIC IDEA: The point is to be able to draw a "quick" sketch of a
transfer function of a circuit.
Assume: you have an equation for the transfer function.
ADD up the individual responses of all of the poles and zeros of the transfer
function.
They each affect the frequency response “only” after they take effect at their
respective “break” frequencies....
• a pole makes the amplitude fall with frequency by 20 dB /decade and “has
no effect” before its break frequency
• a zero makes the amplitude rise with frequency by 20 dB/decade and “has
no effect” before its break frequency
• a pole causes the phase to fall from 0° to -90° over two decades of
frequency starting one decade before the break frequency -> the phase is
-45° at its break frequency
• a zero causes the phase to rise from 0° to +90° over two decades of
frequency starting one decade before the break frequency -> the phase is
+45° at its break frequency
• the effects of poles or zeros at “zero” frequency have already “maxed
out” by the time you start your plot (i.e. phase is -90° for a pole at zero
frequency, and +90° for a zero at zero frequency) 158
 HOW TO MAKE A GAIN PLOT
1) Write the transfer function equation in a form so that you can see the break
frequencies of the poles and zeros.
2) Try to begin the sketch at a frequency where you know the gain (from
looking at the equation).
If it is not obvious, draw a rough draft of the curve and select the frequencies
corresponding to the "flat" parts, plug those frequencies in for "S", estimate the
gain and convert to dB.
Remember about poles and/or zeros that may have already “taken effect” at low
enough frequencies that they are “maxed out” before you start your sketch.
3) For each zero, add a +20 dB/decade slope to the slope of the sketch at the
break frequency of that zero.
4) For each pole, add a -20 dB/decade slope to the slope of the sketch at the
break frequency of that pole.
5) Draw a “smooth” curve over the sketch (the curves differ by about 3 dB at
each single break)...

159
 HOW TO MAKE A PHASE PLOT
1) Write the transfer function equation in a form so that you can see the
break frequencies of the poles and zeros.
2) Try to begin the sketch at a frequency where you know the phase (from
looking at the equation).
Remember about poles and/or zeros that may have already “taken effect” at
low enough frequencies that they are “maxed out” before you start your sketch.
One way to make it easier is to start out assuming 0° at "super low"
frequencies, then shift the whole phase sketch:
a) + 90° for any zeros at "zero frequency"
b) - 90° for any poles at "zero frequency"
c) +/- 180° if there is a negative sign
Remember that a negative sign on a gain is a 180° phase shift!
3) Each zero contributes a phase slope of +45° per decade starting one
decade below and lasting through one decade above the break frequency.
The phase contribution from that zero is “half way there” (or contributing
+45°) at the break frequency.
The contribution of that zero to phase at frequencies less that one tenth of the
break frequency and greater than ten times the break frequency is zero!
160
 HOW TO MAKE A PHASE PLOT
4) Each pole contributes a phase slope of -45° per decade starting one
decade below and lasting through one decade above the break
frequency.
The phase contribution from that pole is “half way there” (or
contributing -45°) at the break frequency.
The contribution of that pole to phase at frequencies less that one tenth of
the break frequency and greater than ten times the break frequency is
zero!
5) Draw a “smooth” curve over the sketch (the curves differ by about 6° at
each single break).

161