Download chapter 1 - UniMAP Portal

1.1
1.2
1.3
1.4
1.5
1.6
1.7
Introduction
Atomic Theory
Insulators, Conductors, and Semiconductors
Current in Semiconductors
P-N Junction
Bias
Summary
Electronic Systems
− Radio
− Television
− Computer
− Telephone
Vacuum Tubes
Vacuum Tube
1890s
Amplifier
To increase the
strength of ac signals
Rectifier
Able to operate
very well
−Large
−Fragile
−High power
consumption
To convert ac energy
to dc energy
Fig.1-1: Structure of a vacuum tube diode and triode
Transistor
1950s
A Semiconductor
Device
Single
small chip
commonly used as an
amplifier or an
electrically controlled
switch
Integrated circuits
1960s
− Smaller
− More rugged
− Less power
consumption
μicro-Processors
1980s
BJT
Fig.1-2: Transistor and symbols
PNP
P-channel
NPN
N-channel
JFET
BJT = Bipolar Junction transistor
JFET = Junction Field-Effect Transistor
(a)
Fig.1-3: (a) Integrated circuits
and (b) microprocessor
(b)
A microprocessor is a programmable
digital electronic component that
incorporates the functions of a central
processing unit (CPU) on a single
semiconducting integrated circuit (IC).
1.2.1 The Atom
 Atom is the smallest particle of an element
that retains the characteristics of that element.
 An atom consists of the protons and neutrons
that make up the nucleus (core) at the center
and electrons that orbit about the nucleus.
• The nucleus carries almost the total mass of
the atom.
• Neutrons are neutral and carry no charge.
• Protons carry positive charges.
• The electrons carry negative charges.
 The number of protons = the number of electrons Fig. 1-4: Bohr model of an atom
in an atom, which makes it electrically neutral or
balanced.
1.2.2 Valence Shell
-
Valence shell is the outermost shell
in an atom that determines the
conductivity of an atom.
The electrons in valence shell are
called valence electrons.
Shells or
orbital paths
1st shell (K): 2n2 = 2(1)2 = 2 electrons
Total:
n = the shell number
29 electrons
-
-
-
M
-
L
-
-
K
29 p
-
-
-
+
-
-
-
29 n
-
-
-
-
-
3rd shell (M): 2n2 = 2(3)2 = 18 electrons
1 electrons
-
-
2nd shell (L): 2n2 = 2(2)2 = 8 electrons
4th shell (N):
N
Valence
shell
-
-
Valence
electron
Fig.1-5: Bohr model of copper
atom (Cu)
Tabel 1-1: Electron contents of shells and subshells of the copper atom
Shell
K (n = 1)
L (n = 2)
M (n = 3)
N (n = 4)
Subshells
Capacity (2n2)
Content
s
2
2
s
2
2
p
6
6
s
2
2
p
6
6
d
10
10
s
2
1
p
6
0
d
10
0
f
14
0
1.2.3 Energy Bands
Energy
Energy
Conduction band
Energy gap
Conduction
E4 = 1.8eV
band
E3 = 0.7eV
E2
E1
E = energy level
Valence
band
Second band
(shell 2)
Valence band
First band
(shell 1)
Fig. 1-6: Energy band diagram for an unexited (no
external energy) atom in a pure (intrinsic) Si crystal.
Nucleus
Each orbital shell around the nucleus corresponds to a certain energy band.
A shell is separated from adjacent shells by energy gaps, in which no
electron can exist (forbidden band).
For an electron to jump from one orbital shell to another, it must absorb
enough energy to overcome its energy gap between the shells.
Energy
Energy
Conduction Band
Conduction Band
Forbidden Band
Forbidden Band
Valence Band
Valence Band
(a) Insulator
(b) Semiconductor
Energy
Conduction Band
Valence Band
(c) Conductor
Fig. 1-7: Energy band diagrams for three different materials
The amount of energy that the valence electrons must attain to be elevated to the
next level (conduction band) is measured in electron volts (1 eV = 1.6 x 10-19
joules), which is the energy gap between valence band and conduction band.
For conductors, semiconductors, and insulators, the valence to conduction-band
energy gaps are approximately 0.4, 1.1, and 1.8 eV, respectively
1.1.4 Covalent Bonding
Covalent bonding is the method
by which atoms complete their
valence shells by “sharing”
valence electrons.
The results of this bonding are:
1. The atoms are held together,
forming a solid substance.
2. The atoms are all electrically
stable, because their valence
shells are complete.
3. The completed valence shells
cause the atom to act as an
insulator.
-
+
-
-
-
+
-
-
-
-
-
+
-
-
-
-
+
-
-
-
+
-
-
Fig. 1-8: Covalent bonding in
a semiconductor crystal
1.1.5 Semiconductors
A semiconductors is a material that is between conductors and insulators in its
ability to conduct electrical current.
Play a significant role in the development of modern electronic device such as
diodes, transistors, and integrated circuits.
Class of semiconductor :
- Single-crystal : Ge, Si & C
- Compound : GaAs, CdS & GaAsP
-
-
- -
-
- -
-
-
-
-
-
-
-
-
-
Si
-
-
-
- -
-
Ge
-
-
- -
Fig. 1-9: Semiconductor atoms
- - - -
-
-
In terms of electrical
properties
Insulators
Materials
Semiconductors
Conductors
All materials are made up of atoms that contribute to
its ability to conduct electrical current
Insulators
A material that does not conduct electrical current under normal conditions.
Valence electrons are tightly bound to the atoms → very few free electrons.
Most good insulators are compounds rather than single-elemet materials.
Ex. : rubber, plastics, glass, mica, and quartz.
Conductors
A material that easily conducts electrical current.
Valence electrons are very loosely bound to the atoms → many free electrons.
Characterized by atoms with only one valence electron.
The best conductors are single-element materials.
Ex. : copper, silver, gold and aluminum.
Semiconductors
A material that is between conductors and insulators in its
ability to conduct electrical current.
In its pure (intrinsic) state is neither a good conductor nor a good insulator.
Characterized by atoms with four valence electron.
Ex. : - Single-crystal : Ge, Si & C
- Compound : GaAs, CdS & GaAsP
Comparison of a Semiconductor Atom to a Conductor
Atom
Core of Si atom has a net charge of +4 (14 protons – 10 electrons) and
+1 (29 protons – 28 electrons) for Cu atom.
A valence electron in Si atom feels an attractive force of +4 compared to Cu
atom which feels an attractive force of +1.
Force holding valence electrons to the atom in Si
> in Cu.
The distance from its nucleus of Copper’s valence electron (in 4th shell) >
silicon’s valence electron (in 3rd shell).
Valence electrons
Valence electrons
Core (+4)
(a) Silicon atom
Core (+1)
(a) Copper atom
Fig.1-10: Diagrams of the silicon and copper atoms
Conduction Electrons and Holes
(a)
When an electron jumps to the conduction
band, a vacancy is left in the vallence band,
this vacancy is called a hole and the
electron is said to be in an excited state.
Recombination occurs when a conductionband electron after within a few microseconds
of becoming a free, loss its energy and falls
(b)
back into a hole in the valence band.
The energy given up by the electron is in
the form of light and/or heat.
Fig.1-11: Creation of electron-hole pairs in a Si atom.
(a) energy diagram, and (b) bonding diagram
Electron and Hole Current
At the temperature room, at any instant, a number of free electrons that are
unattached to any atom drift randomly throughout the material. This condition occurs
when no voltage is applied across a piece of intrinsic Si (as illustrated in Fig. 1-12).
When a voltage is applied across the piece of intrinsic Si, as shown in Fig. 1-13,
the thermally generated free electrons in the conduction band, which are free to
move, are now easily attracted toward the positive end.
At the same time, there are also an equal number of holes in the valence band
created by electrons that jump into the conduction band (Fig. 1-14).
The movement of free electrons in a semiconductive material is called electron
current.
The movement of electrons in a valence band is called hole current.
Fig.1-13: Free electrons are attracted
toward the positive end
Fig.1-12: Free electrons are being
generated continuously while
some recombine with holes
Fig. 1-14: Hole current in intrinsic Si
Table 1-2: Few terms and processes that are frequently referred to in p-n junction theory
Terms/Processes
Definitions
Intrinsic semiconductor
the pure semiconductor, in which the number of free
electrons equals the number of holes in the crystal
structure.
Doping
the process of adding impurity atoms to the intrinsic
semiconductor in order to alter the balance between holes
and electrons (or to increase the conductivity of the
semiconductor).
N-type impurities (donor)
the type of impurities that add (donate) electrons to
intrinsic semiconductors, when combined.
P-type impurities
(acceptors)
the type of impurities that produce holes (accept electrons)
in intrinsic semiconductors, when combined.
Extrinsic semiconductor
the impure semiconductor that has been doped with ntype or p-type impurity atoms, resulting in imbalance
between the hole and electron densities.
Table 1-2: Few terms and processes that are frequently referred to in p-n junction theory
Terms/Processes
Ionization
Diffusion current
Definitions
the process of losing or gaining a valence electron. If a
neutral atom loses a valence electron, it is no longer neutral
and is called a positive ion. On the other hand, if a neutral
atom gains a valence electron, it is called a negative ion.
results when there is a non-uniform concentration of charge
carriers (electrons or holes) in the semiconductor; that is, if
there is a higher density of carriers in one region and lower
density in another, carriers start migrating from the region of
higher density to the region with lower density until a fairly
uniform concentration is established in the semiconductor.
The flow of these charge carriers during migration constitutes
a current flow called diffusion current, and the carriers are
said to diffuse from one region to another.
1.5.1 N-Type Semiconductor
An n-type semiconductor is produced when the intrinsic semiconductor is doped with ntype impurity atoms that have five valence electrons (pentavalent), such as arsenic (As),
antimony (Sb), Bismuth (B) and phosphorus (P). Pentavalent atom is called a donor atom.
-
-
-
-
-
Si
-
-
As
-
-
Si
-
Conduction band
Si
-
-
Energy
-
-
Excess
covalent
bond
electron
Electrons
(majority carriers)
Valence band
Si
-
- - - - - - - - - - - - - - - - - - - -
-
-
Fig. 1-15: N-type semiconductor. Four of As
atom’s valence electrons are used to form
the covalent bond with Si atoms, leaving one
extra electron
Holes
(minority carriers)
Fig. 1-16: Energy diagram (n-type
semiconductor)
1.5.2 P-type Semiconductor
A p-type semiconducotor is produced when the intrinsic semiconductor is doped with p-type
impurity atoms that have three valance electrons (trivalent), such as aluminum, boron,
and gallium. Trivalent atom is referred to as an acceptor atom.
-
-
-
-
-
Si
-
Al
-
-
Si
-
Conduction band
Si
-
-
Energy
-
-
-
-
-
Covalent
bond hole
-
-
-
-
-
-
-
Electrons
(minority carriers)
Valence band
-
Si
-
-
-
Fig. 1-14: P-type semiconductor. Three of
Al atom’ valence electrons are used in the
covalent bonds, leaving one hole
Holes
(majority carriers)
Fig. 1-15: Energy diagram (p-type
semiconductor)
1.5.3 Formation of The P-N Junction
The p-n junction is a fundamental component of many electronic devices and is
formed by joining, through a certain manufacturing process, a block of p-type
semiconductor to a block of n-type semiconductor.
- - - - - - - - - -
- - - - - - - - - -
N-type
P-type
N-type
Energy
P-type
Energy
-
- - - - - - - - - - - - -
-
-
-
-
Conduction band
Conduction band
-
- - - - - - - - - - - - -
-
-
-
-
Conduction band
Conduction band
Valence band
Valence band
(a)
Valence band
Valence band
(b)
Fig. 1-16: N-type and P-type semconductors (a) before and (b) at the instant they are joined
1.5.4 Formation of The Depletion Region
- - - - + - - - - + - - - - + -
- - - - - - - - - -
Depletion layer
Energy
- - - - - - - - - - - - -
Energy
-
-
-
-
-
- - - - - - - - - - - - -
-
-
-
-
-
Fig.1-17: When two materials are joined together, some of the free electrons in
n-type material diffuse to p-type material across the juction
Junction
N-type
-
-
-
+4
-
-
-
+4
+4
-
-
-
-
-
-
+4
-
+5
-
-
-
-
+4
-
-
-
-
+3
-
-
-
-
+4
-
P-type
-
+4
Total (+) = 21
Total (-) = 20
Net charge = +1
Fig.1-18: Depletion layer charges
-
-
+4
-
-
Total (+) = 19
Total (-) = 20
Net charge = -1
Several things to remember:
Each electron that diffuses across the junction leaves one positively charged
bond in the n-type material and produces one negatively charged bond in the p-
type material.
Both conduction-band electrons and valence-band holes are need for
conduction through the materials. When an electron diffuses across the junction,
the n-type material has lost a conduction-band electron. When the electron falls
into a hole in the p-type material, that material has lost a valence-band hole. At
this point, both bonds have been depleted of charge carriers.
Bias is a potential applied to p-n junction to obtain certain operating conditions.
This potential is used to control the width of the depletion layer.
By controlling the width of the depletion layer, we are able to control the resistance
of the p-n junction and thus the amount of current that can pass through the
device.
Table 1-1: The relationship between the width of depletion layer and the junction current
Depletion Layer Width
Junction Resistance
Junction Current
Minimum
Minimum
Maximum
Maximum
Maximum
Minimum
1.6.1 Forward Bias
Forward bias is a potential used to reduce the resistance of p-n junction.
A forward-biased p-n junction has minimum depletion layer width and junction
resistance.
There are two requirements to produce forward bias:
- The positive side of voltage source (denoted as bias voltage) is connected
to the p-type material of the p-n junction semiconductor and the negative
side is connected to the n-type material.
- Bias voltage must be greater than the barrier potential. Barrier potensial is an
energy hill that is created by the electric field between the positive and
negative ions in the depletion region on either side of the junction.
The resistor limits the forward current to a value that will not damage the
device.
Fig.1-19: A p-n junction connected for forward bias
The negative side of the bias-voltage source “pushes” the free electrons (the
majority carriers in n-type material) toward the p-n junction because like
charges repel.
The negative terminal also provides a continuous flow of electrons into the n region.
The free electrons obtain sufficient energy from the bias-voltage to overcome the
barrier potential of the depletion region and move on through into the p region.
Once in the p region, this free electron have lost too much energy overcoming the
barrier potensial and thus, the free electrons can’t remain in the conduction
band for longer. They immediately combine with holes in valence band.
Since unlike charges attract, the positive side of the bias-voltage source attracts the
valence electrons toward the left end of the p region.
The holes in the p region provide the medium or pathway for these valence electrons to
move through the p region.
The valence electrons move from one hole to the next toward the left.
The holes, which are the majority carriers in the p region, effectively (not actually) move
to the right toward the junction.
As the electrons flow out of the p region through the external connection and to the
positive side of the bias-voltage source, they leave holes behind in the p region; at the
same time, these electrons become conduction electrons in the metal conductor.
There is a continuous availability of holes effectively moving toward the p-n junction to
combine with the continuous stream of electrons as they come across the junction into
the p region.
Fig.1-20: A forward-biased p-n junction showing the flow of majority carriers
and the voltage due to the barrier potential across the depletion region
The Effect of Forward Bias on the Depletion Region
As more electrons flow into the depletion region, the number of positive ions is
reduced.
As more holes effectively flow into the depletion region on the other side of the p-n
junction, the number of negative ions is reduced.
This reduction in positive and negative ions during forward bias causes the
depletion region to narrow.
The Effect of Barrier Potential During Forward Bias
When forward bias is applied, the free electrons have enough energy to overcome
the barrier potential and effectively “climb the energy hill” and cross the depletion
region.
When the free electrons cross the depletion region, they give up an amount of
energy equivalent to the barrier potential.
The energy loss results in a volatge drop across the p-n junction equal to the barrier
potential.
An additional small voltage drop occurs across the p and n regions due to the
internal resistance of the material. This resistance is called the dynamic resistance.
For doped semiconductive material, the dynamic resistance is very small and can
usually be negleted.
1.6.2 Reverse Bias
Reverse bias is a potential that essentially “prevents” current through the diode.
A reverse-biased p-n junction has maximum depletion layer width and junction
resistance.
There are two requirements to produce forward bias:
- The positive side of voltage source (denoted as bias voltage) is connected
to the n-type material of the p-n junction semiconductor and the negative
side is connected to the p-type material.
- The depletion region is much wider than in forward bias.
Fig.1-21: A p-n junction connected for reverse bias.
The positive side of the bias-voltage source “pulls” the free electrons (the
majority carriers in n-type material) away from the p-n junction because unlike
charges attract.
As the electrons flow toward the positive side of the voltage source, additional positive
ions are created. This results in a widening of the depletion region and
a depletion of majority carriers.
In the p region, electrons from the negative side of the voltage source enter as valence
electrons and move from hole to hole toward the depletion region where they
create additional negative ions. This results in a widening of the depletion
region and depletion of majority carriers.
The initial flow of charge carriers is transitional and lasts for only a very short time after
the reverse-bias voltage is applied.
As the depletion region widens, the availability of majority carriers decreases.
As more of the n and p regions become depleted of majority carriers, the electrical field
between the positive and negative ions increases in strength until the potential
across the depletion region equals the bias voltage. At this point, the transition
current essentially ceases except for a very small reverse current.
Fig.1-22: The p-n junction during the short transition time
immediately after reverse-bias voltage is applied
Reverse Current
There is the extremely small current exists in reverse bias after the transition
current dies out. It is caused by the minority carriers in the n and p region that
are produced by thermally generated electron-hole pairs.
The small number of free minority electrons in the p region are “pushed” toward
the p-n junction by negative bias voltage.
When these electrons reach the wide depletion region, they “fall down the energy
hill” and combine with the minority holes in the n region as valence electrons
and flow toward the positive bias voltage, creating a small hole current.
The conduction band in the p region is at a higher energy level than the
conduction band in the n region. Therefore, the minority electrons easily pass
through the depletion region because they require no additional energy.
Fig.1-23: The extremely small reverse current in a reverse-biased diode is
due to the minority carriers from thermally generated electron-hole pairs
Reverse Breakdown
Normally, the reverse current is so small that it can be neglected. However, if the
external reverse-bias voltage is increased to a value called the breakdown
voltage, the reverse current will drastically increase.
The small number of free minority electrons in the p region are “pushed” toward
the p-n junction by negative bias voltage.
When these electrons reach the wide depletion region, they “fall down the energy
hill” and combine with the minority holes in the n region as valence electrons
and flow toward the positive bias voltage, creating a small hole current.
The conduction band in the p region is at a higher energy level than the
conduction band in the n region. Therefore, the minority electrons easily pass
through the depletion region because they require no additional energy.
1.7.1 Introduction
VD
A diode is a two-electrode (two-terminal)
Anode (A)
Cathode (K)
device that acts as an one-way conductor.
+
-
The p region is called the anode and the
n region is called the cathode.
The arrow in the symbol points in the
ID
direction of conventional current (opposite
to electron flow).
Fig. 1-24: The symbol for the p-n
junction diode
VF
The most basic type of diode is the p-n
A diode is forward-biased when the positive
terminal of the source is connected to the
-
+
junction diode.
IF
+
VBias
R
-
anode through a current-limiting resistor and
the negative terminal is connected to the
(a) Forward-biased diode
cathode.
A diode is reverse-biased when the negative
terminal of the source is connected to the
anode and the positive terminal is connected to
the cathode.
VD
+
VBias
When forward biased, a p-n junction diode
+
I≈0
R
conducts. When reverse biased, it effectively
blocks the flow of charge (current).
(b) Reverse-biased diode
Fig.1-25: Two different bias circuits
1.7.2 The Ideal Diode Model
The ideal diode behaves like a closed switch (ON) when forward biased, and like an open
switch (OFF) when it is reverse biased.
VA
VA
VA
IF = 0
IF > 0
VF
VK
IF
VF = 0
VK
ON
The behavior of the ideal diode can be
summarized as following:
VF < 0
VK
OFF
Fig.1-26: The behavior of the diode: (a) ideal
diode, (b) short circuit and (c) open circuit
If the diode is ON, current passes
from the anode to cathode. Therefore,
we can replace it with a short circuit.
If the diode is OFF, cathode voltage is
greater than anode voltage. Then, we
can replace it with an open circuit.
Diode ON : IF > 0; VF = 0 → VA = VK
Diode OFF: IF = 0; VF < 0 → VA < VK
This model is adequate for most troubleshooting when you are trying to determine wheter
the diode is working properly.
Based on the characteristics of a switch, it
can be stated that the ideal diode:
IF
1. When reverse biased (open switch):
a. The diode has infinite resistance.
b. The diode does not pass current.
c. The diode drops the applied voltage
across its terminals.
2. When forward biased (closed switch):
a. The diode has no resistance.
b. The diode does not limit the circuit
current.
c. The diode has no voltage drop
across its terminals.
Forward
operating
region
VR
II
I
III
IV
VF
Reverse
operating
region
IR
Fig.1-27: I-V characteristics of the ideal diode
Since the barrier potential and the forward dynamic resistance are neglected, the diode is
assumed to have a zero voltage across it when forward-biased, as indicated by the portion of
the curve on the positive vertical axis (Fig.1-27).
VF  0V
The forward current is determined by the bias voltage and the limiting resistor using Ohm’s law:
VBias
IF 
RLimit
(1-1)
Since the reverse current is neglected, its value is assumed to be zero, as indicated in Fig.1-27
by the portion of the curve on the negative horizontal axis.
I R  0V
The reserve voltage equals the bias voltage.
VR  VBias
Example 1-1:
For the diode circuits in Fig. 2-2 (a) and (c), determine if the diode is ON or OFF. Find VR, IR,
VF, and IF.
+12 V
+12 V
+
+
IR
VR
R = 2K
IR
VR
R = 2K
IR
IF
IR
IF
VF
VR
R = 2K
V2
-
-
VF
IF
+
VF
+
V2
V2
(a)
R = 2K
V2
-
-
VR
V1
+
VF
+
-
V1
+
+12 V
+
-
-
IF
+12 V
V1
(b)
(c)
Figure 1-28
V1
(d)
1.7.3 The Practical Diode Model
The practical model includes the barrier potential.
When the diode is forward-biased, it is equivalent to a closed switch in series with
a small equivalent voltage source (VF) equals to the barrier potential (0.7) with the
positive side toward the anode, as indicated in Fig.1-29(a).
This equivalent voltage source represents the barrier potential that must be
exceeded by the bias voltage before the diode will conduct and is not an active
source of voltage.
When the diode is reverse-biased, it is equivalent to an open switch just as in the
ideal model, as shown in Fig.1-29(b).
The barrier potential does not affect reverse bias.
Since the barrier potential is included and the dynamic resistance is neglected, the
diode is assumed to have a voltage across it when forward-bias, as indicated by the
portion of the curve to the right of the origin (in Fig.1-29(c)).
Since the barrier potential is included and the forward dynamic resistance are neglected, the
diode is assumed to have a voltage across it when forward-biased, as indicated by the
portion of the curve to the right of the origin (Fig.1-29(c)).
VF  0.7V
The forward current is determined as follows by first applying Kirchoff’s voltage law:
VBias  VF
IF 
RLimit
(1-2)
The diode is assumed to have zero reverse current, as indicated by the portion of the curve
on the negative horizontal axis.
IR  0 A
VR  VBias
This model is useful to troubleshoot in lower-voltage circuits and to design the basic diode
circuits.
Fig.1-29: The practical model of a diode
1.7.4 The Complete Diode Model
The complete model includes the barrier potential, the small forward dynamic resistance
(r ’d), and the large internal reverse resistance (r ’R).
When the diode is forward-biased, it acts as a closed switch in series with the equivalent
barrier voltage (VB) and the small forward dynamic resistance (r’d), as indicated in Fig.130(a).
When the diode is reverse-biased, it acts as an open switch in parallel with the large
internal reverse resistance (r’R), as shown in Fig.1-30(b).
The barrier potential does not affect reverse bias.
Since the barrier potential and the dynamic resistance are included, the diode is assumed
to have a voltage across it when forward-biased.
This voltage (VF) consists of the barrier potential voltage plus the small voltage drop across
the dynamic resistance, as indicated by the portion of the curve to the right of the origin.
The curve slops because the voltage drop due to dynamic resistance increases as the
current increases.
Fig.1-30: The complete model of a diode
For the complete model of a silicon diode, the following formulas apply:
VF  0.7 V  I r
'
F d
VBias  0.7 V
IF 
RLimit  rd'
(1-3)
(1-4)
For troubleshooting work, it is unnecessary to use the complete model, because it
involves complicated calculations. This model is generally suited to design
problems using a computer for simulation.
Exercise 1-1:
(a) Determine the forward voltage and forward current for the diode in
Fig.1-31(a) for each of the diode models. Also find the voltage across
the limiting resistor in each case. Assume r’d = 10 Ω at the determined
value of forward current.
(b) Determine the reverse voltage and reverse current for the diode in
Fig.1-31(b) for each of the diode models. Also find the voltage across
the limiting resistor in each case. Assume IR = 1μA.
RLimit
+
VBias
-
IF
RLimit
1 kΩ
+
VBias
10 V
(a) Forward-biased diode
-
IF
1 kΩ
10 V
(b) Reverse-biased diode
Fig.1-31: Two different bias circuits