Transistor #
A junction transistor consists of a silicon (or germanium) crystal in which a layer of n-type silicon is sandwiched between two layers of p-type silicon. Alternatively, a transistor may consist of a layer of p-type between two layers of n-type material. In former case transistor is known as p-n-p transistor and in later case n-p-n transistor.
Transistor is also known as Bipolar Junction transistor, as both electron and holes are participated in the conduction of transistor.
Diagrams of transistor #
As shown in the above diagram, the three portions of a transistor are known as emitter, base, and collector. The arrow on the emitter – base junction is biased in the forward direction.
Construction of BJT #
Emitter
The section on one side of the junction that supplies charges carriers (i.e., electrons or holes) is called the emitter. The emitter is always forward biased with respect to base so as it can supply a large number of majority carriers.
Base
The middle section which forms two pn-junction the emitter and the collector, is called the base. The base-emitter junction is forward biased, allowing low resistance for the emitter circuit and the base-collector junction is reverse biased and provided high resistance in the collector circuit. The base is very lightly doped and very thin so that all charge carriers are easily passed through the junction.
Collector:
The section on the side of junction that do the job of gathering these charge carriers (electrons or holes) from the base is called collector. The function of collector is to remove charges from its junction with the base. The collector is always reverse biased with respect to base. The doping of the collector is between the heavy doping of the emitter and base area of a transistor.
Note
- Order of doping in transistor:
- Order of Width:
- Collector width is always largest, reason is given below:
As we know that the main function of collector is to collect the charge carriers in the collector region. Because due to the interaction of the charge carrier the colector region becomes heat up, as all the heat dissipated through this region and the transistor may burn out. So, in order to save the transistor from burning the collector is always larger than that of the emitter and base region.
Region of operation of transistors #
SN |
Emitter-Junction |
Collector-Junction |
Region of Operation |
---|---|---|---|
1. |
Forward-biased |
Reverse-biased |
Active |
2. |
Forward-biased |
Forward-biased |
Saturation |
3. |
Reverse-biased |
Reverse-biased |
Cutoff |
4. |
Reverse-biased |
Forward-biased |
Inverted |
Different configurations of Transistor #
SN |
Configura-tion Name |
Common Terminal |
Input Term |
Output Term |
Circuit diagram |
Input Characteristics |
Output Characteristics |
Transfer Characteristics |
Amplifi-cation factor |
---|---|---|---|---|---|---|---|---|---|
1. |
Common Emitter (CE) |
E |
B |
C |
IB versus VBE at constant VCE |
IC versus VCE at constant IB |
IC Versus IB |
|
|
2. |
Common Base(CB) |
B |
E |
C |
IE versus VEB at constant VCB |
IC versus VCB at constant IE |
IC Versus IE |
|
|
3. |
Common Collector (CC) |
C |
B |
E |
IE versus VBC at constant VCE |
IE versus VEC at constant IE |
IB Versus IB |
|
Comparison of different configurations of Transistors #
SN |
Characteristics |
C-B |
C-E |
C-C |
---|---|---|---|---|
1. |
Input resistance |
Very low (about 20 ) |
Low (about 1k ) |
Very high (about 500 k ) |
2. |
Output resistance |
Very high (about 1M ) |
High (about 40 k ) |
Low (about 250 k ) |
3. |
Voltage gain |
Very high |
Moderate |
Less than 1 |
4. |
Current gain |
1 |
High |
Very high |
5. |
Phase shift between input and output |
0o or 360o |
180o |
0o or 360o |
6. |
Application |
For high-frequency circuits as preamplifier |
For audio frequency circuits |
For impedance matching |
Relation between amplification factors . #
Important points about CB, CE & CC configurations #
CB Configuration
In the case of CB-configuration current gain A is less than unity, voltage gain AV is high (approximately equal to that of CE stage), input resistance, Ri is lowest and output resistance Ro is highest of the three configurations. The CB stage has few applications. It is sometimes used to match a very low-impedance source, to derive a high-impedance load. It is also used as a constant-current source. Its main application is in cascade amplifier (CE-CB) which is used in video amplifiers to increase bandwidth.
CE Configuration
In the case of CE-configuration we see that only the common-emitter stage is capable of both a voltage gain and current gain greater than unity. This configuration is the most widely used among the three configurations. We also observe from the above table that the magnitudes of Ri and Ro lies between those for the CB and CC configurations. It may be remember that CE-configuration is usually used in the intermediate stages.
CC Configuration
In the case of CC-configuration, we observe that voltage gain is approximately unity while the current gain Ai is very high. Input impedance, Ri is the highest and output impedance, Ro is the lowest of the three configurations. That’s why this circuit finds wide application as a buffer stage between a high-impedance source to drive a low impedance load. It is also used for impedance matching applications.
Operating Point of Transistor: (Q-Point)
For the proper operation of a transistor, in any application, we set a fixed levels of certain currents and voltages in a transistor. These value of currents and voltages define the point at which transistor operates. This point is known as operating point or quiescent point or simply Q-point. Since the level of the currents and voltage are fixed therefore, the operating point is also called d.c. operating point.
Or in other words, zero signal values of VCE and IC are called the operating point or Q-points. Here zero signal means in the absence of signal.
Stabilisation of operating point (Q-Point):
Here it is important to note that in order to avoid thermal runaway or the self-destruction of transistor because of rise in temperature and to overcome the effect of inherent variations of transistor parameters, it is very necessary to stabilise the operating point or to fix the operating point at all connection, we require stabilisation.
Thus stablisation may be defined as the process of making operating point independent of temperature changes or inherent variations in transistor parameters.
Thermal Runaway of a Transistor:
A transistor is said to be unstabilised when its operating point in shifted. Usually unstabilization in a transistor is occurred because of the change in collector current. The collector current in a transistor changes rapidly due to following two reasons namely:
- If the transistor is replaced by another one of same type. Because no two transistor can have same transistor parameters (i.e. )
(ii) The temperature changes affects IC. It can be more clearly understood by the equation IC = IB + (1 + ) ICO. We know that leakage current (ICBO or ICO) increases due to increase in temperature, results increase in collector current IC. The rise in collector current further increases the temperature resulting in further increase in ICBO. Such a cumulative effect leads to thermal runaway.
Stability Factor
It is defined as the rate of change of collector current with respect to any one out of three , while keeping two quantities constant. i.e
Steps for finding the stability factor of a transistor
Step 1: Apply the KVL the input of the given circuit, write the expression and get equation (1).
Step 2:
Step 3: Calculate the value of IB from equation (1) in terms of IC and other parameters and substitute in equation (2) which gives equation (3).
Step 4: Differentiate equation (3) with respect to IC and put S = and then solve for S.
Following are the basic Formulae used for the DC analysis of a transistor
- When given in the question then, we can consider as
- Apply KCL & KVL in input and output of the biasing circuit of the transistor to get the the value of Q-Point or operating point.
- For the BJT to be biased in its linear or active operating region the following must be followed:
1. The base-emitter junction must be forward-biased (p-region voltage more positive), with a resulting forward-bias voltage of about 0.6 to 0.7 V.
2. The base-collector junction must be reverse-biased (n-region more positive), with the reverse-bias voltage being any value within the maximum limits of the device.
- Operation in the cutoff, saturation and linear region of the BJT characteristics are provided as follows:
1. Linear-region operation:
Base-emitter junction forward-biased
Base-collector junction reverse-biased
2. Cutoff-region operation:
Base-emitter junction reverse-biased
Base-collector junction reverse-biased
3. Saturation-region operation:
Base-emitter junction forward-biased
Base-collector junction forward-biased
For example
Determine the dc bias voltage VCE and the current IC
RTH = R1 ||R2=
ETH = =
IB = = = 6.05
IC = = (140) (6.05 )
= 6.05 mA
VCE = VCC – IC(RC + RE)
= 22V – (0.85 mA) (10 k + 1.5 k )
= 22V – 9.78 V
Biasing of the transistor
It is used to stabilize the Q-Point of a Transistor. Different types of Biasing are used in a Transistor as details given below:
SN |
Parameter of Comparison |
Fixed bias or Base resistance |
Collector to base of Feedback blasting |
Emitter Resistance biasing |
Potential Divider or Self Biasing |
---|---|---|---|---|---|
1. |
Configuration |
||||
2. |
Emitter resistance |
Not used |
Not used |
Used |
Used |
3. |
Negative feedback |
Not used |
Included |
Not used |
Included |
4. |
Stability factor |
S = 1 + |
|
|
(where RB = Rth = R1 + R2) When RE>>RB |
5. |
Q-point stability |
Poor |
Moderate |
Moderate |
Very Good |
AC Analysis of Transistor: (CB Configuration):
Where
AC Analysis of Transistor: ( CE Configuration:
Where
The input impedance is determined by the following ratio:
The voltage Vbe is across the diode resistance as shown in Fig.. The level of re is still determined by the dc current IE. Using Ohm’s law gives
Substituting yields
However, is usually sufficiently larger than one to permit the approximation + 1 = , so that
Approximate Model:
Two-Port Circuit Parameters: {hybrid (h)-parameter} of Transistor circuits.
Hybrid (h-parameter) equivalent Model of Transistor #
For the hybrid equivalent model the parameters are defined at an operating point that may or may not reflect the actual operating conditions of the amplifier.
h11 input resistance hi
h12 reverse transfer voltage ratio hr
h21 forward transfer current ratio hf
h22 output conductance ho
are the h-parameters of the transistor circuit.
Where
Ohms
unit less
unit less
Siemens
h-model for CE configuration of Transistor: #
h-model for CB configuration of Transistor #
- Approximate h-model of a Trans istor: ()
Comparison of h-model and (CE & CB Configuration): #
Where and
and
Summary of meaning of h-parameter:
Table-A:
SN |
H-parameter |
Meaning |
Condition |
---|---|---|---|
1. |
h11 hi |
Input impedance |
Output short circuited |
2. |
h21 hf |
Forward current gain |
Output short circuited |
3. |
h12 hf |
Reverse voltage gain |
Input open |
4. |
h22 h0 |
Output admittance |
Input Open |
Table-B:
SN |
H-Particular Parameter |
CE |
CC |
CB |
---|---|---|---|---|
1. |
hi |
hie |
hic |
hib |
2. |
hf |
hre |
hrc |
hrb |
3. |
hf |
hfe |
hfe |
hfb |
4. |
ho |
hoe |
hoc |
hob |
Approximate conversion formulas for hybrid parameters:
Common collector to Common emitter:
hic = hie
hrc = 1
hfe = – (1 + hfa)
hoc = hoc
Common base to Common emitter:
hjb =
hrb =
hfb =
hob =
Following are the important formulae for the analysis of Amplifiers:
- Current gain or current amplification,
- Input Impedance,
- Voltage amplification,
Hybrid –
High frequency transistor small signal ac equivalent circuit.
The hybrid model includes parameters that do not appear in the other two models primarily to provide a more accurate model for high-frequency effects. For lower frequencies approximations to the model can be made with the result that the re model introduced earlier will result. The hybrid model appears in Fig. with all the parameters necessary for a full-frequency analysis.
All the capacitors that appear in Fig. are stray parasitic capacitors between the various junctions of the device. They are all capacitive effects that really only come into play at high frequencies. For low to mid-frequencies their reactance is very large and they can be considered open circuits. The capacitor Cu is usually just a few picofarads (pF) to a few tens of picofarads, whereas the capacitance Cu typically extends from less than 1 pF to a few picofarads. The resistance rb includes the base contact, base bulk, and base spreading resistance levels. The first is due to the actual connection to the base. The second includes the resistance from the external terminal to the active region of the transistor, and the last is the actual resistance within the active base region. It is typically a few ohms to tens of ohms. The resistors rue ru and ro are the resistances between the indicated terminals of the device when the device is in the active region. The resistance ru (using the symbol to agree with the hybrid terminology) is simply as introduced for the common-emitter re model. The resistance ru.
It is important to note in Fig. that the controlled source can be a voltage-controlled current source (VCCS) or a current-controlled current source (CCCS), depending on the parameters employed.
Since the use of the model is totally dependent on finding the parameter values for the equivalent network, it is important to be aware of the following relationships to extract the parameter values from the data typically provided:
model for the small-signal operation of the BJT:
Voltage controlled current source (trans-conductance amplifier):
Then
- transconductance,
Current controlled current source (current amplifier):
T- mode for the small –signal operation of the BJT:
BJT Transistor and its equivalent small- signal model is given below:
- model for the small-signal model with
High frequency of the BJT:
Important Points about the BJT:
- When a transistor is biased in the forward- active mode of operation, the current at one terminal of the transistor (collector current) is controlled by the voltage across the other two terminals of the transistor (base- emitter voltage). This is the basic transistor action.
- The principle currents in the device are determined by the diffusion of these minority carriers.
- The common base gain , which leads to the common emitter current gain is a function of three factors i.e emitter injection efficiency, base transport factor, and recombination factor.
- A common- collector (CC) configuration is also called emitter follower because its voltage gain is close to unity. i.e emitter follows the input signal.
- Common drain amplifier is also called as source follower.
- CC (emitter follower) configuration has very high input resistance and very low output resistance.
- Darlington pair is nothing but a cascade connections of two common collector transistor, which posses very high input resistance and high current gain.
Summary:
Important Formulae:
S.N |
Given Circuit |
Various Parameters |
||
---|---|---|---|---|
Quantity |
Exact Formulae |
Approximate (rb = 0, r0 = ) |
||
1. |
Ai |
|
|
|
Rj |
|
|
||
R0 |
r0 |
|||
R0’ |
r0||RC |
|
||
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|
|
2 |
Quantity |
Exact |
Approximate |
|
---|---|---|---|---|
Ai |
|
|
||
Rj |
|
|
||
R0 |
|
|
||
R0’ |
RE||r0 |
r0 || Re |
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