Transcript Basic Electronics

Basic Electronics
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur
Lecture : 1
Junction Diode Characteristics
Open Circuited p-n Junction

In Equilibrium (no bias)
Total current balances due to the sum of the individual components
no net current!
Electron Drift
Current
Hole Diffusion
Current
Electron Diffusion
Current
Hole Drift
Current
Open Circuited p-n Junction

In Equilibrium (no bias)
Total current balances due to the sum of the individual components
n vs. E
n-Type Material
- qVBI
p-Type Material
EC
++
Ei
EF
EV
+ + + + + + + + + + + + + + + + + EC
EF
Ei
EV
p vs. E
Jn  Jn
Drift
 Jn
Diffusion
 q   n nE  q  Dn n  0
Jp  Jp
Drift
 Jp
Diffusion
 q   p pE  q  D p p  0
no net current!
PN Junction I-V Characteristics

Forward Bias (VA > 0)
IN
Electron Drift
Current
Lowering of
potential hill
by VA
Electron Diffusion
Current
Current flow is
proportional to
e(Va/Vref) due to the
exponential decay of
carriers into the
majority carrier
bands
VA
Hole Diffusion
Current
Current flow is dominated
by majority carriers flowing
across the junction and
becoming minority carriers
I
IP
Hole Drift
Current
I  IN  IP
PN Junction I-V Characteristics

Reverse Bias (VA < 0)
Electron Drift
Current
Current flow is constant due to
thermally generated carriers
swept out by E fields in the
depletion region
Increase of
potential hill
by VA
Electron Diffusion Current negligible due
to large energy barrier
Hole Diffusion Current negligible
due to large energy barrier
Current flow is dominated by
minority carriers flowing across the
junction and becoming majority
carriers
Hole Drift
Current
PN Junction I-V Characteristics
 Where does the Reverse Bias Current come from?
Generation near the depletion region edges “replenishes” the current source.
PN Junction I-V Characteristics
 Putting it all together
-I0
for Ideal diode
Vref = kT/q
Current-Voltage Characteristics of a Typical Silicon PN Junction

Diode Equation
  qV  
  1
I  I 0 exp 
  kT  
Lecture : 2
Current Components in a P-N
Diode
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur
Current Components in a P-N Diode
Quisineutral Region
Quisineutral Region
x”=0
x’=0
Total on current is constant throughout the device.
Thus, we can characterize the current flow components as…
J
-xp
xn
Current Components in a P-N Diode
PN -junction diode structure used in the discussion of currents. The sketc
h shows the dimensions and the bias convention. The cross-sectional area
A is assumed to be uniform.
Current Components in a P-N Diode
Hole current (solid line) and recombining electron current (dashed line)
in the quasi-neutral n-region of the long-base diode of Figure 5.5. The
sum of the two currents J (dot-dash line) is constant.
Current Components in a P-N Diode
Hole density in the quasi-neutral n-region of an ideal
short base diode under forward bias of Va volts.
Current Components in a P-N Diode
The ratio of generation region width Xi to space charge region width
Xd as a function of reverse voltage for several donor concentrations in
a one-sided step junction.
Current Components in a P-N Diode
The current components in the quasi-neutral regions of a long-base diode
under moderate forward bias: J(1) injected minority-carrier current, J(2)
majority-carrier current recombining with J(1), J(3) majority-carrier
current injected across the junction. J(4) space-charge-region
recombination current.
Current Components in a P-N Diode
J
p-region
SCL
n-region
J = J elec + J hole
Total current
Majority carrier diffusion
and drift current
J h ole
J elec
Minority carrier diffusion
current
x
–Wp
Wn
The total current anywhere in the device is constant. Just outside the
depletion region it is due to the diffusion of minority carriers.
Lecture : 3
Breakdown Diodes
and
Temperature Effect on Diode
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur
Breakdown Diodes
 When the reverse voltage applied across diode becomes greater than
the breakdown voltage, then the diode breaks down and very high
current starts flowing in the circuit. There are generally two types of
breakdowns in a diode:
1. Zener breakdown
2. Avalanche breakdown
 And based on the above classifications of breakdown of diode, we
have the two special types of diode as
1. Zener breakdown
2. Avalanche breakdown
 The difference between the Zener Diode and avalanche Diode is the
doping level. The doping level of Zener diode is more than avalanche
diode or we can say diodes which have higher doping level undergo
Zener breakdown when reverse bias voltage is increased while diodes
with lesser doping level undergo Avalanche breakdown.
Breakdown Diodes
 Zener diode : As we have already mentioned doping level of Zener diode is very
high and hence width of depletion region is less. As we know
E = VB / d
VB is the barrier voltage
E is the electric field
d is the depletion width
 As doping is high, hence width (d) is less and as barrier voltage varies with doping
as stated by the formula:
 From the formula we can get that the voltage varies proportional to log of doping
and hence the barrier voltage is almost constant.
 So from the above discuss we find that Electric field in the depletion region would
be large as VB is almost constant and d has decreased. Due to this large electric field,
electrons from the outer shell of the atom in the depletion region are expelled out
and hence carriers are generated within the depletion region. The high electric field
in the depletion region pulls out large number of electrons from the large number of
atoms. This leads to large current flow and this type of breakdown is called Zener
breakdown.
Breakdown Diodes
 Avalanche diode : The diode which have lesser doping undergo avalanche breakdown
when high reverse voltage is applied. The lesser doping means the depletion width is
large and so electric field within depletion region is not so high.
 Hence the electric field would not be able to pull out electrons from the outer shell of
atoms and breakdown doesn’t occur in depletion region. But as the depletion region is
large and hence when the minority charge carriers move through the depletion region,
they get accelerated by the electric field and that even for larger time (as distance
through which acceleration is provided is large).
 Hence minority charge carriers acquire high velocity and so high kinetic energy.
When these charge carriers strike with atoms in the n-type and p-type regions, the
high kinetic energy gets converted to thermal energy and hence due to this energy
electrons from the outermost shell are pulled out and large current starts flowing. This
type of breakdown is called avalanche breakdown.
 But due to the high thermal energy, the temperature rises and diode gets burned. Due
to this reason the simple diodes (where avalanche breakdown occurs) is not used in th
e applications and instead Zener diode is used in the application circuits of breakdown
diodes such as regulating power supply.
Breakdown Diodes
 Differences between Zener breakdown and Avalanche breakdown:
Zener breakdown
1. The Zener breakdown occurs in HIGH
doping diodes.
2. The breakdown occurs within the
depletion region.
3. The breakdown voltage is lesser than
zener that of avalanche breakdown.
Avalanche breakdown
1. The avalanche breakdown occurs in
LOW doping diodes.
2. The breakdown occurs outside the
depletion region.
3. The breakdown voltage is more than
breakdown voltage.
 As Zener breakdown voltage is less than that of avalanche breakdown voltage, hence
Zener breakdown is said to occur before the avalanche breakdown.
 Hence we can say if we increase the doping of a diode, the chances of zener breakdo
wn increases and hence breakdown voltage decreases.
Temperature Effect on Diode
 The following graph shows the effect of temperature on the characteristics of diode
A-B curve: This curve shows the
characteristics of diode for different
temperatures in the forward biase. As we
can see from the figure given above, that
curve moves towards left as we increase
the temperature. We know with increase in
temperature,
conductivity
of
semiconductors increase. The intrinsic
concentration (ni) of the semiconductors is
dependent on temperature as given by:
Eg is the energy gap
K is a voltage man constant
A is a constant independent of temperature
Temperature Effect on Diode
 When temperature is high, the electrons of the outermost shell take the thermal energy
and become free. So conductivity increases with temperature. Hence with increase in
temperature, the A-B curve would shift towards left i.e. curve would rise sharply and
the breakdown voltage would also decrease with increase in temperature.
 A-C curve: This curve shows the characteristics of diode in the reverse biased region
till the breakdown voltage for different temperatures. We know ni concentration
would increase with increase in temperature and hence minority charges would increa
se with increase in temperature. The minority charge carriers are also known as therm
ally generated carriers and the reverse current depends on minority carriers only.
Hence as the number of minority charge carriers increase, the reverse current would
also increase with temperature as shown in the figure given on the previous page.
 The reverse saturation current gets double with every 10 C increase in temperature.
 C-D curve: This curve shows the characteristics of a diode in reverse biased region
from the breakdown voltage point onwards. As with increase in temperature, loosely
bonded electrons are already free and to free the other electrons, it would take more
voltage than earlier.
Lecture : 4
Junction Diode Switching Times
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur.
Junction Diode Switching Times
 The switching time of a diode is defined as the time which a diode
takes to change its state from forward biased state to reverse biased
state or in other words the forward current through diode doesn’t
reduce to reverse saturation current immediately as the reverse voltage
is applied. In fact it takes time for the current to reduce from forward
current to reverse saturation current. This time is also called reverse
recovery time.
 To discuss more about the switching time, we first need to discuss
charge distribution of diode in normal state, forward biased state and
reverse biased state assuming doping of p-type is more than n-type.
Apply the relation given below
n * p = ni2 at constant temperature (Mass action law)
Junction Diode Switching Times
 Now we apply the above relation to p-type : P i.e. the concentration of majority
carriers (holes) is larger as doping of p-side is high and we have the value of ni2 as
constant at fixed temperature. Hence from the above relation we find that number of
minority carriers (electrons) is less in p-type material while as doping of n-side is
normal, hence number of majority carriers (i.e. electrons) in n-side is not large with
the value of ni2as constant and hence number of minority carriers is larger as
compared to that in p-side.
 Npo is defined as the concentration of minority carriers in N-type material i.e. holes
and Pno is defined as the concentration of minority carriers in P-type material
i.e. electrons when diode is in un-biased.
Junction Diode Switching Times
 Charge distribution of diode in Forward Biased state : When diode is forward biased,
the majority carriers of both sides cross the junction and after reaching the other side,
the charge carriers start combining. So holes from p-side start moving towards n-side
and electrons from n-side start moving to p-side. When holes enter the n-side they
become the minority carriers and just at the junction there would be high
concentration of holes in n-side as the recombining has just started. Also all the holes
can not recombine at the junction.
 Hence when we move away from the junction in the n-side, the concentration of holes
is decreasing as more and more holes are recombining. This is also shown in the
figure below. Similarly in the p-side, concentration of the electrons is high near the
junction and it starts decreasing as we move away from the junction in the p-side.
Junction Diode Switching Times
 Charge distribution of diode in Reverse Biased state : When we reverse biased any
diode, the minority carriers from both sides cross the junction and then recombine
after reaching the other side. Hence the holes from n-side move towards p-side and
after reaching p-type material become majority carriers. These holes combine with
minority carriers of p-side i.e. electrons.
 So the minority carriers at junction i.e. holes in the n-side which are near junction
would immediately cross the junction on reverse biased and other holes move slowly.
Similar to the above, electrons of p-side move to n-side.
Junction Diode Switching Times
 Diode Reverse Recovery Time : Consider the following circuit of diode to analyze the
switching time of diode.
 So to change state from forward to reverse biase, the whole minority charge
distribution needs to be inverted as we can see from the figures above.
Junction Diode Switching Times
 Diode Reverse Recovery Time : Now let’s see what happens during the period in
which state changes. Firstly we are in forward biased state when voltage applied is +
V.
 So there are many minority carriers near the junction and then there is an exponential
decrease in the concentration of minority carriers and there is a continuous flow of
majority carriers across the junction. We assume the current as I in the forward biased.
We depict this in the following graph of current across the junction with time.
Junction Diode Switching Times
 Now we change the applied voltage to –V at time t=t1 i.e. diode is now reverse biased.
As minority carrier concentration in both sides was large near junction in the forward
biased, when we have instantly changed the state to reverse biased, those minority
arriers start moving in the opposite direction.
 And due to large concentration of such minority carriers, the amount of current
flowing remains the same.
Junction Diode Switching Times
 But the high reverse current continues for small time because the concentration
of the stored minority carriers start decreasing and the current also starts
decreasing exponentially as shown below:
 The time gap t2 - t1 in which the reverse current is high (i.e. equal to I) is known
as storage time and the time gap from t2 to t3 i.e. the time reverse current
becomes equal to reverse saturation current is known as transient time. The
total time from t1 to t3 is known as reverse recovery time.
Junction Diode Switching Times
 Effect Of Doping On Reverse Recovery Time : As we have already known that reverse
recovery time is the time it takes to invert the minority charge distribution of diode
from forward biased to minority charge distribution in reverse biased.
 Hence when we increase the doping of material, the concentration for minority charge
carriers decrease.
 Hence as the peaks of charge distribution have fallen, it takes lesser time to invert the
charge distribution.
 Hence we can say that with increase in doping, the reverse recovery time decrease and
with decrease in doping level the reverse recovery time increases.
Lecture : 5
Transistor Characteristics
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur
What is a Transistor?
 Semiconductors: ability to change from con
ductor to insulator
 Can either allow current or prohibit current
to flow
 Useful as a switch, but also as an amplifier
 Essential part of many technological
advances
A Brief History
 Guglielmo Marconi invents radio in 1895
 Problem: For long distance travel, signal must be am
plified
 Lee De Forest improves on Fleming’s original vacuu
m tube to amplify signals
 Made use of third electrode
 Too bulky for most applications
The Transistor is Born
 Bell Labs (1947): Bardeen, Bratta
in, and Shockley
 Originally made of germanium
 Current transistors made of doped
silicon
How Transistors Work
 Doping: adding small amounts of other elements to
create additional protons or electrons.
 P-Type: dopants lack a fourth valence electron (Boron,
Aluminum).
 N-Type: dopants have an additional (5th) valence electron
(Phosphorus, Arsenic).
 Importance: Current only flows from P to N.
Physical Structure of Transistor
Diodes and Bias
 Diode: simple P-N junction.
 Forward Bias: allows current to flow
from P to N.
 Reverse Bias: no current allowed to
flow from N to P.
 Breakdown Voltage: sufficient N to P
voltage of a Zener Diode will allow
for current to flow in this direction.
The Bipolar Junction Transistor
 Normally Emitter layer is heavily doped, Base layer is lightly doped and Collector
layer has Moderate doping.
The Two Types of BJT Transistors
PNP
NPN
n
E
p
n
C
E
p
n
p
B
B
Cross Section
Cross Section
C
C
B
B
E
Schematic Symbol



E
109
Collector doping is usually ~
Base doping is slightly higher ~ 1010 – 1011
Emitter doping is much higher ~ 1017
Schematic Symbol
C
Junction Transistor
IE
E
-
VCE +
IC
-
IE
-
C
E
+
VEC
IC
-
C
+
VBE
IB
VBC
+
VEB
-
-
+
+
B
B
NPN :
IE = IB + IC
VCE = -VBC + VBE
PNP :
IE = IB + IC
VEC = VEB - VCB
VCB
IB
Lecture : 6
Transistor Current Components
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur
Transistor Current Components
 In the figure we show the various components which flow across the forward-based
emitter junction and the reverse-biased collector junction. The emitter current IE
consists of hole current IpE (holes crossing from the emitter into base) and electron
current InE (electron crossing from base into the emitter).
 The ratio of hole to electron currents, IpE/InE, crossing the emitter junction is
proportional to the ratio of the conductivity of the p material to that of the n material.
In the commercial transistor the doping of the emitter is made much larger than the do
ping of the base. This future ensures (in a p-n-p transistor) that the emitter current
consists almost entirely of the holes. Such a situation is desired since the current
which results from electrons crossing the emitter junction from base to emitter does
not contribute carriers which can reach the collector.
Transistor Current Components
 Not all the holes crossing the emitter junction JE reach the collector junction Jc
because some of them combine with the electrons in the n – type base. If Ipc is the
hole current at Jc, there must be a bulk recombination current IpE - IpC leaving the
base, as indicated in figure. (actually, electrons enter the base region through the base
lead to supply those charges which have been lost by recombination with the holes
injected into the base across JE).
 If the emitter were open-circuited so that IE = 0, then IpC would be zero. Under these
circumstances, the base and collector would act as a reverse-biased diode, and the
collector current Ic would equal the reverse saturation current ICO. If IE ≠ 0, then, from
figure, we note that,


Ic = Ico – IpC
For a p-n-p transistor, Ico consists of holes moving across Jc from left to right
(base to collector) and electrons crossing Jc in the opposite direction. Since the
assumed reference direction for Ico in figure is from right to left, then for a p-n-p
transistor, Ico is negative. For an n-p-n transistor, Ico is positive.
Current flow for an NPN BJT in the active region
n
I co
-
Inc
+
VCB
-
p- Electrons
+ Holes
+
VBE -
Ipe
Ine
n+
Bulk-recombinati
on Current
 Most of the current is due to electrons moving from the emitter through base to the collector. Base
current consists of holes crossing from the base into the emitter and of holes that recombine with
electrons in the base.
Current flow for an NPN BJT in the active region
For CB Transistor IE= Ine+ Ipe
Bulk-recombination
current
ICO Inc
Ic= Inc- Ico
And Ic= - αIE + Ico
CB Current Gain, α ═ (Ic- Ico)
(IE- 0)
For CE Transistor, IC = βIb + (1+β) Ico
where β ═ α ,
1- α is CE Gain.
Ipe
Ine
Lecture : 7
Transistor Configurations
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur
Various Regions (Modes) of Operation of BJT
Active:
 Most important mode of operation
 Central to amplifier operation
 The region where current curves are practically flat
Saturation:
 Barrier potential of the junctions cancel each other out causing a
virtual short (behaves as on state Switch)
Cutoff:
 Current reduced to zero
 Ideal transistor behaves like an open switch
 There is also a mode of operation called inverse active mode, but it is rarely used.
Three Possible Configurations of BJT
 Biasing the transistor refers to applying voltages to the transistor to
achieve certain operating conditions.
1. Common-Base Configuration (CB) : input
= VEB & IE
output = VCB & IC
2. Common-Emitter Configuration (CE): input = VBE & IB
output= VCE & IC
3. Common-Collector Configuration (CC) :input = VBC & IB
(Also known as Emitter follower)
output = VEC & IE
Common-Emitter BJT Configuration
Region of Operation
Description
Active
Small base current controls a large collector current
Saturation
VCE(sat) ~ 0.2V, VCE increases with IC
Cutoff
Achieved by reducing IB to 0, Ideally, IC will also be
equal to 0.
IC
IC
VCE
Active Region
VCC
+
_
IB
Circuit Diagram
IB
Saturation Region
VCE
Cutoff Region IB = 0
Collector-Current Curves
Common-Emitter BJT Configuration
 BJT’s have three regions of operation:
1) Active - BJT acts like an amplifier (most common use)
2) Saturation - BJT acts like a short circuit
BJT is used as a switch by switching
3) Cutoff - BJT acts like an open circuit
between these two regions.
IC(mA)
Saturation Region
IB = 200 A
30
Active Region
IB = 150 A
22.5
IB = 100 A
15
B
IB = 50 A
7.5
Cutoff Region
When analyzing a DC BJT
circuit, the BJT is replaced
by one of the DC circuit
models shown below.
C
E
IB = 0
0
VCE (V)
0
5
10
15
20
DC Models for a BJT:
C
rsat
B
B
+
_
B
Vo
Vo
b dc IB
ICEO
b dc IB
IB
+
_
C
C
+
_
RBB
Vo
E
Saturat ion Region Model
E
Active Region Model #1
E
Active Region Model #2
Ro
DC b and DC 
 b = Common-emitter current gain
 = Common-base current gain
b = IC
IB

 = IC
IE
The relationships between the two parameters are:
=
b
b+1
b=

1-
  and b are sometimes referred to as dc and bdc because the
relationships being dealt with in the BJT are DC.
Common-Emitter BJT Configuration
 Output characteristics: NPN BJT (typical)
b dc =
IC(mA)
IB = 200 A
30
Note: The PE review text sometimes
uses dc instead of bdc. They are related
as follows:
IB = 150 A
22.5
IC
= h FE
IB
IB = 100 A
15
 dc =
IB = 50 A
7.5
IB = 0
0
0
5
10
15
20
VCE (V)
b dc
b dc + 1
b dc 
 dc
1 -  dc
 Find the approximate values of
bdc and adc from the graph.
 Input characteristics: NPN BJT (typical)
IB(A)
VCE = 0.5 V
200
VCE = 0
VCE > 1 V
150
100
50
The input characteristics look like the characteristics of a
forward-biased diode. Note that VBE varies only slightly, so
we often ignore these characteristics and assume:
Common approximation: VBE = Vo = 0.65 to 0.7V
Note: Two key specifications for the BJT are Bdc and
0
VBE (V)
0
0.5
1.0
Vo (or assume Vo is about 0.7 V)
Common-Emitter BJT Configuration
Figure: Common-emitter characteristics displaying exaggerated secondary effects.
Common-Emitter BJT Configuration
Figure: Common-emitter characteristics displaying exaggerated secondary effects.
Common-Base BJT Configuration
C
 The Table Below lists assumptions
that can be made for the attributes of
the common-base BJT circuit in the
different regions of operation. Given
for a Silicon NPN transistor.
VCE
IC
VCB
IE
E
VBE
+
_
+
_
IB
B
VCB
Region of
Operation
IC
Active
bIB
Saturation
Max
~0V
Cutoff
~0
=VBE+VCE
VCE
VBE
VCB
C-B
Bias
E-B
Bias
0V
Rev.
Fwd.
~0.7V -0.7V<VCE<0 Fwd.
Fwd.
0V
None/
Rev.
VBE
=VBE+VCE ~0.7V
0V
Rev.
Common-Base BJT Configuration
 Input Characteristics
This curve shows the relationship
between of input current (IE) to in
put voltage (VBE) for various leve
ls of output voltage (VCB).
Common-Base BJT Configuration
 Output Characteristic
IC mA
Breakdown Reg.
6
Saturation Region
Active Region
0.8V
IE
4
IE=2mA
2
IE=1mA
2V
4V
6V
8V
Cutoff
IE = 0
VCB
Common-Collector BJT Configuration
Emitter-Current Curves
 The
Common-Collector
biasing circuit is basically
equivalent to the common
emitter
biased
circuit
except instead of looking a
t IC as a function of VCE
and IB we are looking at IE.
Also, since  ~ 1, and
 = IC/IE that means IC~IE
IE
Active Regio
n
IB
VCE
Saturation Region
Cutoff Region
IB = 0
Lecture : 8
Ebers-Moll BJT Model
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur.
Ebers-Moll BJT Model
 The Eber-Moll Model for BJTs is fairly complex, but it is valid in all region
s of BJT operation. The circuit diagram below shows all the components of
the Eber-Moll Model:
E
IE
IC
C
 R IC
 R IE
IF
IR
IB
B
Eber-Moll BJT Model




R = Common-base current gain (in forward active mode)
F = Common-base current gain (in inverse active mode)
IES = Reverse-Saturation Current of B-E Junction
ICS = Reverse-Saturation Current of B-C Junction
 IC = FIF – IR
 IE = IF - RIR
IB = I E - IC
 IF = IES [exp(qVBE/kT) – 1]
IR = IC [exp (qVBC/kT) – 1]
 If IES & ICS are not given, they can be determined using various

BJT parameters.
Small Signal BJT Equivalent Circuit
The small-signal model can be used when the BJT is in the active region. The small
-signal active-region model for a CB circuit is shown below:
iB
iC
B
biB
r
r = (b + 1) * VT
IE
@  = 1 and T = 25C
r = (b + 1) * 0.026
IE
iE
E
Recall: b = IC / IB
C
The Early Effect (Early Voltage)
Note: Common-Emitter Configuration
IC
IB
-VA
VCE
Green = Ideal IC
Orange = Actual IC (IC’)
Early Effect Example
Given: The common-emitter circuit below with IB = 25A,
VCC = 15V, b = 100 and VA = 80.
Find: a) The ideal collector current
b) The actual collector current
Circuit Diagram
IC
VCC
b)
+
_
VCE
b = 100 = IC/IB
a)
IC = 100 * IB = 100 * (25x10-6 A)
IC = 2.5 mA
IB
IC’ = IC VCE + 1
VA
IC’ = 2.96 mA
= 2.5x10-3 15 + 1
80
= 2.96 mA
Lecture : 9
Transistor Biasing
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur.
The Thermal Stability of Operating Point SIco
 The Thermal Stability Factor : Sico
SIco = ∂Ic
∂Ico
Vbe, β
 This equation signifies that Ic Changes SIco times as fast as Ico
 Differentiating the equation of Collector Current IC & rearranging the terms
we can write
SIco ═
1+β
1- β (∂Ib/∂IC)
It may be noted that Lower is the value of SIco better is the stability
The Fixed Bias Circuit
15 V
15 V
200 k
RC
Rb
1k
C
B
RC
The Thermal Stability Factor : SIco
SIco = ∂Ic
Vbe, β
∂Ico
General Equation of SIco Comes out to be
SIco ═ 1 + β
1- β (∂Ib/∂IC)
Ib
E
Applying KVL through Base Circuit we can
write, Ib Rb+ Vbe= Vcc
Diff w. r. t. IC, we get (∂Ib / ∂Ic) = 0
SIco= (1+β) is very large
Indicating high un-stability
The Collector to Base Bias Circuit
VCC
RC
Ic
RF
Ib
C
B
+V
BE
-
IE
E
The General Equation for Thermal Stability
Factor,
SIco = ∂Ic
∂Ico Vbe, β
Comes out to be
SIco ═ 1 + β
1- β (∂Ib/∂IC)
Applying KVL through base circuit
we can write (Ib+ IC) RC + Ib Rb+ Vbe= Vcc
Diff. w. r. t. IC we get
(∂Ib / ∂Ic) = - RC / (Rb + RC)
Therefore, SIco ═
(1+ β)
1+ [βRC/(RC+ Rb)]
Which is less than (1+β), signifying better thermal
stability
The Potential Divider Bias Circuit
VCC
VCC
R1
RC
IC
C
Ib
B
E
R2
RE
I
C
The General Equation for Thermal Stability Factor,
SIco ═ 1 + β
1- β (∂Ib/∂IC)
Applying KVL through input base circuit
we can write IbRTh + IE RE+ Vbe= VTh
Therefore, IbRTh + (IC+ Ib) RE+ VBE= VTh
Diff. w. r. t. IC & rearranging we get
(∂Ib / ∂Ic) = - RE / (RTh + RE)
Therefore,
1 b
SIco 
VCC
Thevenin Ckt
RC
IC
Ib
C
B
RE 

1 b
 RE  RTh 
This shows that SIco is inversely proportional to
RE and It is less than (1+β), signifying better the
rmal stability
RTh
E
+
_
VTh
RE
Self-bias Resistor
Thevenins
Voltage
Rth = R1*R2 & Vth = Vcc R2
R1+R2
R1+R2
Potential-Divider Bias Circuit with Emitter Feedback
 Most popular biasing circuit :
 Problem: bdc can vary over a wide range for BJT’s (even with the same part number)
 Solution: Adding the feedback resistor RE. How large should RE be? Let’s see.
VCC
VCC
VCC
R1
RC
RC
C
C
B
B
IC =
RTh
+
_
VTh
RE
b dc  VTh - Vo  + ICEO  R Th + R E 
R Th +  b dc + 1 R E
where ICEO =  b dc + 1 ICBO
E
E
R2
Substituting the active region model into the
circuit to the left and analyzing the circuit
yields the following well known equation:
RE
ICEO has little effect and is often neglected
yielding the simpler relationship:
Voltage divider biasin
g circuit with emitter
feedback
Replacing the input circuit by
a Thevenin equivalent circuit
yields:
 R2 
VTh = VCC 
 and R Th = R1 R 2
R
+
R
 1
2
IC =
b dc  VTh - Vo 
R Th +  b dc + 1 R E
Test for stability: For a stable Q-point w.r.t. variations in bdc choose:
R Th <<  bdc + 1 R E
Why? Because then
IC =
b dc  VTh - Vo 
b  V - Vo 
 dc Th
R Th +  b dc + 1 R E
 b dc + 1 R E

 VTh
- Vo 
(independent of b dc )
RE
Lecture : 10
Transistor at Low Frequencies
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur.
A Practical C E Amplifier Circuit
VCC
VCC
Input Signal Source
R1
RC
io
C
Co
ii
Rs
+
vs
+
Ci
+
B
E
vi
_
R2
RE
_
Common Emitter (CE) Amplifier
RL
CE
vo
_
Graphical Analysis of the CE configuration,
 If changes in operating currents
and voltages are small enough,
then IC and VCE waveforms are u
ndistorted replicas of the input
signal.
 A small voltage change at the
base causes a large voltage
change at the collector. The
voltage gain is given by:
 An 8 mV peak change in vBE gives a 5
mA change in iB and a 0.5 mA change
in iC.
 The 0.5 mA change in iC gives a 1.65
V change in vCE .
~
~ vce 1.65180
Av  ~ 
 206180  206
v
0.0080
be
 The minus sign indicates a 1800
phase shift between input and ou
tput signals.
BJT Amplifier using Coupling and Bypass Capacitors
 In a practical amplifier design, C1 and C3 are
large coupling capacitors or dc blocking
capacitors, their reactance (XC = |ZC| = 1/wC)
at signal frequency is negligible. They are
fective open circuits for the circuit when DC
bias is considered.
 C2 is a bypass capacitor. It provides a low
impedance path for ac current from emitter to
ground. It effectively removes RE (required
for good Q-point stability) from the circuit
when ac signals are considered.


AC coupling through capacitors is used to inject an ac input signal and extract the ac
output signal without disturbing the DC Q-point
Capacitors provide negligible impedance at frequencies of interest and provide open
circuits at dc.
Lecture : 11
AC analysis of BJT Amplifier
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur.
D C Equivalent for the BJT Amplifier (Step1)
DC Equivalent Circuit
 All capacitors in the original amplifier circuit are replaced by open circuits,
disconnecting vI, RI, and R3 from the circuit and leaving RE intact. The the
transistor Q will be replaced by its DC model.
A C Equivalent for the BJT Amplifier (Step 2)
R1IIR2=RB
Ro
Rin
 Coupling capacitor CC and Emitter bypass capacitor CE are replaced by short
circuits.
 DC voltage supply is replaced with short circuits, which in this case is conne
cted to ground.
A C Equivalent for the BJT Amplifier
All externally connected capacitors are
assumed as short circuited elements for ac
signal
R  R R 10kΩ 30kΩ
B
1 2
R  R R  4.3kΩ 100kΩ
C 3
 By combining parallel resistors into equivalent RB and R, the equivalent AC
circuit above is constructed. Here, the transistor will be replaced by its
equivalent small-signal AC model (to be developed).
A C Analysis of CE Amplifier
Step 1
1) Determine DC operating point and
calculate small signal parameters
2) Draw the AC equivalent circuit of Amp.
Step 2
• DC Voltage sources are shorted to ground
• DC Current sources are open circuited
• Large capacitors are short circuits
• Large inductors are open circuits
3) Use a Thevenin circuit (sometimes a
Step 3
Norton) where necessary. Ideally the
base should be a single resistor + a single
source. Do not confuse this with the DC
Thevenin you did in step 1.
4) Replace transistor with small signal model
Step 4
5) Simplify the circuit as much as necessary.
Steps to Analyze a Transistor Amplifier
6) Calculate the small signal parameters and
gain etc.
Step 5
π-model used
Lecture : 12
Hybrid Parameter Model
Prof. Rajput Sandeep
Assist. Prof., EC Dept.
HCET ,Siddhpur.
Hybrid-Pi Model for the BJT
Transconductance:
I
gm  C ,VT  KT
q
V
T
Input resistance: Rin
b oV
bo
T
r 

I
gm
C
 The hybrid-pi small-signal model is the
intrinsic low-frequency representation
of the BJT.
 The small-signal parameters are control
led by the Q-point and are independent
of the geometry of the BJT.
Output resistance:
V V
ro  A CE
I
C
Where, VA is Early Voltage
(VA=100V for npn)
Hybrid Parameter Model
Io
Ii
Linear Two port Device
Vi
Vo
Ii
1
Vi
Io
hi
hrVo
hfIi
ho
1'
2
Vo
2'
Vi  h11Ii  h12Vo  hi I i  hrVo
I o  h21Ii  h22Vo  h f I i  hoVo
h-Parameters
Vi
h11 
Ii
Io
h21 
Ii
Vo  0
Vi
h12 
Vo
Ii  0
Vo  0
Io
h22 
Vo
Ii  0
h11 = hi = Input Resistance
h12 = hr = Reverse Transfer Voltage Ratio
h21 = hf = Forward Transfer Current Ratio
h22 = ho = Output Admittance
Three Small signal Models of CE Transistor
The Mid-frequency small-signal models
ib
ic
c
b
hie
+
vbe
Alternate names:
h fe = b ac = b o = b
+
hrevce
+
_
hfe ib
hoe
vce
_
_
e
e
h-parameter model
ib
ic
+
38.92
IC (Note: Uses DC value of I C )
n
where n = 1 (typical, Si BJT)
vce
b o = h fe
rd =
h re = 0
r = h ie =
c
b
+
+
vbe
r
_
v
gmv
rd
gm =
_
_
e
e
1
h oe
hybrid- model
ib
ic
c
b
+
vbe
+
bre
bib
vce
_
_
e
e
re model
re =
bo
gm
26 mV
(Note: uses DC value of IB )
IB
b o = h fe
b o re = h ie
h re = 0
h oe = 0, or use rd =
1
h oe
BJT Mid-frequency Analysis using the hybrid-p model
VCC
VCC
R1
A common emitter (CE) amplifier
RC
io
The mid-frequency circuit is drawn as follows:
 the coupling capacitors (Ci and Co) and the
 bypass capacitor (CE) are short circuits
 short the DC supply voltage (superposition)
 replace the BJT with the hybrid-p model
The resulting mid-frequency circuit is shown below.
C
Co
ii
Rs
+
+
+
B
Ci
E
vs
vi
R2
_
RL
RE
CE
vo
_
_
is
+
vs
ii
RS
vi
_
e
io
c
+
RTh
_
b
+
r
v
+
gmv
ro rd
RC
Zi 
An AC Equivalent Circuit
e
vo
Av    g m RL' , where, RL'  ro RL RC ,
vi
io
Ai 
ii
vo
_
_
mid-frequency CE amplifier circuit
RL
 Zi 
v o v o vi
Av s     Av 

v s vi v s
Z

R
s 
 i
vi
 RTh r , where, R Th  R1 R2
Ii
Zo 
vo
io
 ro RC
vi  o
Small-Signal Analysis for Gain Av (Using Π-model)
Rs
vo   g mv  R R ro 
beC
3 

R
L
Rs
From input circuit
R  ro R R ,  R
L
C 3
C
R3
vo  vo  vbe 
Av  v   v  v 
i  be  i 
vo
 I o RL  g v R
m be
L















v R r
i B
v 
be R   R r
S  B 






R

r








B
 Av   g m R
L R R r
B 
S







C-E Amplifier Input Resistance
 The input resistance, the total
resistance
looking
into the
amplifier at coupling capacitor C1,
represents the total resistance
presented to the AC source.
v x  i x (R r )
B
vx
R 
 R r  R R r
B
1 2
in i
x
C-E Amplifier Output Resistance
 The output resistance is the total
equivalent resistance looking into the
output of the amplifier at coupling
capacitor C3. The input source is set
to 0 and a test source is applied at the
output.
v
 x  gm v
be
R
ro
C
But vbe=0.
vx
Rout 
 R ro  R
C
C
ix
ix 
vx
since ro is usually >> RC.
An Emitter Follower (CC Amplifier) Amplifier
 Very high input Resistance
 Very low out put Resistance
 Unity Voltage gain with no phase shift
 High current gain
 Can be used for impedance matching
or a circuit for providing electrical
isolation