Basic Electronics

Basic Electronics

Prof. Rajput SandeepAssist. 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

Electron Drift Current

Electron DiffusionCurrent

Hole Drift CurrentHole Diffusion

Current

no net current!

EC

EV

EF

Ei

p-Type Material n-Type Material- qVBI

+ + ++ ++ + + + ++ ++ + + + + ++

0DiffusionDrift

nDqnEqJJJ nnnnn

no net current!

EC

EV

EFEi

n vs. E

p vs. E

In Equilibrium (no bias)Total current balances due to the sum of the individual components

0DiffusionDrift

pDqpEqJJJ ppppp

Open Circuited p-n Junction

PN Junction I-V Characteristics

Forward Bias (VA > 0)

I

Hole Drift Current


Electron DiffusionCurrent

Hole Diffusion Current IP

IN

Current flow is dominated by majority carriers flowing across the junction and becoming minority carriers

VA

Current flow is proportional to e(Va/Vref) due to the exponential decay of carriers into the majority carrier bands

Lowering of potential hill

by VA

PN III

Hole Diffusion Current negligible due to large energy barrier

Hole Drift Current


Electron Diffusion Current negligible due to large energy barrier

Reverse Bias (VA < 0)


Increase of potential hill

by VA

Current flow is constant due to thermally generated carriers swept out by E fields in the depletion region

Current flow is dominated by minority carriers flowing across the junction and becoming majority carriers

Where does the Reverse Bias Current come from? Generation near the depletion region edges “replenishes” the current source.


Putting it all together

for Ideal diodeVref = kT/q

-I0


Current-Voltage Characteristics of a Typical Silicon PN Junction

1exp0 kT

qVII

Diode Equation

Lecture : 2 Current Components in a P-N

Diode


Quisineutral Region Quisineutral Region

x”=0 x’=0Total on current is constant throughout the device. Thus, we can characterize the current flow components as…

-xp xn

J

Current Components in a P-N Diode

PN -junction diode structure used in the discussion of currents. The sketch shows the dimensions and the bias convention. The cross-sec-tional area A is assumed to be uniform.


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.


Hole density in the quasi-neutral n-region of an ideal short base diode under forward bias of Va volts.


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.


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.


J elec

x

n-region

J = J elec + J hole

SCL

Minority carrier diffusioncurrent

Majority carrier diffusionand drift current

Total current

J hole

Wn–Wp

p-region

J

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


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 breakdown2. Avalanche breakdown

And based on the above classifications of breakdown of diode, we have the two special types of diode as

1. Zener breakdown2. 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.

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

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 re-gion, they get accelerated by the electric field and that even for larger time (as dis-tance 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 the applications and instead Zener diode is used in the application circuits of break-down diodes such as regulating power supply.

Breakdown Diodes Differences between Zener breakdown and Avalanche breakdown:

Zener breakdown Avalanche breakdown

1. The Zener breakdown occurs in HIGH 1. The avalanche breakdown occurs in doping diodes. LOW doping diodes.

2. The breakdown occurs within the 2. The breakdown occurs outside the depletion region. depletion region.

3. The breakdown voltage is lesser than 3. The breakdown voltage is more than zener that of avalanche breakdown. 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 break-down increases and hence breakdown voltage decreases.

Temperature Effect on 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 gapK is a voltage man constantA is a constant independent of temperature

The following graph shows the effect of temperature on the characteristics of diode

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 in-crease with increase in temperature. The minority charge carriers are also known as thermally generated carriers and the reverse current depends on minority carriers only. Hence as the number of minority charge carriers increase, the reverse cur-rent would also increase with temperature as shown in the figure given on the pre-vious 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 SandeepAssist. Prof., EC Dept.HCET ,Siddhpur.

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

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 ni

2as 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.

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.

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.


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


What is a Transistor?

Semiconductors: ability to change from conductor 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

amplified Lee De Forest improves on Fleming’s original vac-

uum tube to amplify signals Made use of third electrode Too bulky for most applications

The Transistor is Born

Bell Labs (1947): Bardeen, Brattain, and Shockley

Originally made of germa-nium

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

NPN

n p nE

B

C

Cross Section

PNP

p n pE

B

C

Cross Section

B

C

ESchematic Symbol

C

Schematic Symbol

B

E Collector doping is usually ~ 109

Base doping is slightly higher ~ 1010 – 1011

Emitter doping is much higher ~ 1017

Junction Transistor

B

CE

IE IC

IB

-

+

VBE VBC

+

-

+- VCE

B

CE

IE IC

IB-

+

VEB VCB

+

-

+ -VEC

NPN : IE = IB + IC

VCE = -VBC + VBE

PNP : IE = IB + IC

VEC = VEB - VCB

Lecture : 6 Transistor Current Components


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 doping 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.

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 - I pC 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 I co 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.

Transistor Current Components

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.

- Electrons+ Holes

VBE

VCB

+-

+

-n+

n

p-

IneIpe

-I co

Bulk-recombina-tion Current

Inc

Current flow for an NPN BJT in the active region

Inc

IneIpe

For CB Transistor IE= Ine+ Ipe

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.

ICOBulk-recombination current

Current flow for an NPN BJT in the active region

Lecture : 7 Transistor Configurations


Various Regions (Modes) of Operation of BJT

Most important mode of operation Central to amplifier operation The region where current curves are practically flat

Active:

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

Circuit Diagram

+_VCC

IC

VCE

IB

Collector-Current Curves

VCE

IC

Active Region

IB

Saturation Region Cutoff Region IB = 0

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.

BJT’s have three regions of operation:1) Active - BJT acts like an amplifier (most common use)2) Saturation - BJT acts like a short circuit3) Cutoff - BJT acts like an open circuit BJT is used as a switch by switching

between these two regions.

rsat

Vo

_ +

C

B

E

Saturat ion Region Model

Vo

_ +

C

B

E

Active Region Model #1

dc IB

IB

Ro

Vo

_ +

C

B

E

Active Region Model #2

dc IB ICEO

RBB

VCE (V)

IC(mA)

IB = 50 A

IB = 0

30

5 10 15 20 0

0

IB = 100 A

IB = 150 A

IB = 200 A

22.5

15

7.5

Saturation Region

Active Region

Cutoff Region

C

E

B

When analyzing a DC BJT circuit, the BJT is replaced by one of the DC circuit models shown below.

DC Models for a BJT:


DC and DC

= Common-emitter current gain = Common-base current gain

= IC = IC

IB IE

The relationships between the two parameters are:

= = + 1 1 -

and are sometimes referred to as dc and dc because the relationships being dealt with in the BJT are DC.

Output characteristics: NPN BJT (typical)

VCE (V)

IC(mA)

IB = 50 A

IB = 0

30

5 10 15 20 0

0

IB = 100 A

IB = 150 A

IB = 200 A

22.5

15

7.5

Cdc FE

B

I = = h I

Note: Two key specifications for the BJT are Bdc and

Vo (or assume Vo is about 0.7 V)

Note: The PE review text sometimes uses dc instead of dc. They are related as follows:

Input characteristics: NPN BJT (typical)

VBE (V)

IB(A)

200

0.5 1.0 0

0

VCE = 0

150

100

50

VCE = 0.5 V

VCE > 1 V

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

dcdc

dc

= + 1

Find the approximate values of bdc and adc from the graph.

dc

dc

- 1

dc


Figure: Common-emitter characteristics displaying exaggerated secondary effects.


Figure: Common-emitter characteristics displaying exaggerated secondary effects.


Common-Base BJT Configuration

+ _ + _

IC IE

IB

VCB VBE

EC

B

VCE

VBEVCB

Region of Operation IC VCE VBE VCB

C-B Bias

E-B Bias

Active IB =VBE+VCE ~0.7V 0V Rev. Fwd.

Saturation Max ~0V ~0.7V -0.7V<VCE<0 Fwd. Fwd.

Cutoff ~0 =VBE+VCE 0V 0V Rev. None/Rev.

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.

Input Characteristics

This curve shows the relationship between of input current (IE) to input voltage (VBE) for various levels of output voltage (VCB).


Output Characteristic

Satu

ratio

n R

egio

n IE

IC

VCB

Active Region

CutoffIE = 0

0.8V 2V 4V 6V 8V

mA

2

4

6

IE=1mA

IE=2mA

Breakdown Reg.


Common-Collector BJT Configuration

Emitter-Current Curves

VCE

IE

Active Re-gion

IB

Saturation Region

Cutoff RegionIB = 0

The Common-Collector biasing circuit is basically equivalent to the common emitter biased circuit except instead of looking at IC as a function of VCE and IB we are looking at IE.Also, since ~ 1, and = IC/IE that means IC~IE

Lecture : 8 Ebers-Moll BJT Model


Ebers-Moll BJT Model

The Eber-Moll Model for BJTs is fairly complex, but it is valid in all re-gions of BJT operation. The circuit diagram below shows all the compo-nents of the Eber-Moll Model:

E C

B

IRIF

IE IC

IB

RIERIC

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 IB = IE - IC

IE = IF - RIR

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 CircuitThe 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:

iBr

iE

iCiB

B C

E

r = ( + 1) * VT

IE

@ = 1 and T = 25Cr = ( + 1) * 0.026

IE

Recall: = IC / IB

The Early Effect (Early Voltage)

VCE

ICNote: Common-Emitter Configuration

-VA

IB

Green = Ideal IC

Orange = Actual IC (IC’)

Early Effect ExampleGiven: The common-emitter circuit below with IB = 25A, VCC = 15V, = 100 and VA = 80.Find: a) The ideal collector current

b) The actual collector current

Circuit Diagram

+_VCC

ICVCE

IB

b = 100 = IC/IB

a)IC = 100 * IB = 100 * (25x10-6 A)IC = 2.5 mA

b) IC’ = IC VCE + 1 = 2.5x10-3 15 + 1 = 2.96 mA

VA 80

IC’ = 2.96 mA

Lecture : 9Transistor Biasing


The Thermal Stability of Operating Point SIco

The Thermal Stability Factor : Sico

SIco = ∂Ic

∂Ico

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

Vbe, β

The Fixed Bias Circuit

15 V

C

E

B

15 V

200 k 1 k

The Thermal Stability Factor : SIco

SIco = ∂Ic

∂Ico

General Equation of SIco Comes out to be SIco ═ 1 + β 1- β (∂Ib/∂IC)

Vbe, β

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 largeIndicating high un-stability

Ib

Rb

RC

RC

The Collector to Base Bias Circuit

VCC

RC

C

E

B

RF

Ic

Ib

VBE+

- IE

The General Equation for Thermal Stability Factor, SIco = ∂Ic

∂Ico

Comes out to be SIco ═ 1 + β 1- β (∂Ib/∂IC)

Vbe, β

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 CircuitVCC

RC

C

E

B

VCC

R1

RE R2

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,

This shows that SIco is inversely proportional to RE and It is less than (1+β), signifying better thermal stability

VCC

RC

C

E

B

RE

RTh

VTh _ +

Thevenin Ckt

IC

Ib

IC

Ib

IC

Thevenins Voltage

Self-bias ResistorRth = R1*R2 & Vth = Vcc R2

R1+R2 R1+R2

ThRRR

E

EIcoS

1

1

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.

Substituting the active region model into the circuit to the left and analyzing the circuit yields the following well known equation:

VCC

RC

C

E

B

VCC

R1

RE R2

VCC

RC

C

E

B

RE

RTh

VTh _ +

2Th CC Th 1 2

1 2

RV = V and R = R R R + R

dc Th o CEO Th EC

Th dc E

CEO dc CBO

V - V + I R + R I =

R + + 1 R

where I = + 1 I

ICEO has little effect and is often neglected yielding the simpler relationship:

dc Th oC

Th dc E

V - V I =

R + + 1 R

Test for stability: For a stable Q-point w.r.t. variations in bdc choose:

Th dc ER << + 1 R Why? Because then

dc Th o dc Th o Th oC dc

Th dc E dc E E

V - V V - V V - V I = (independent of )

R + + 1 R + 1 R R

Voltage divider bias-ing circuit with emit-ter feedback

Replacing the input circuit by a Thevenin equivalent circuit yields:

Lecture : 10 Transistor at Low Frequencies


A Practical C E Amplifier Circuit

VCC

RC

C

E

B

VCC

R1

RE R2

Rs Ci RL

Co

CE vi

vo

+

+

vs

+

_ _

_

io

ii

Common Emitter (CE) Amplifier

Input Signal Source

Graphical Analysis of the CE configuration,

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 .

If changes in operating currents and voltages are small enough, then IC and VCE waveforms are undistorted 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:

The minus sign indicates a 1800 phase shift between input and output signals.

2061802060008.0

18065.1~

~~

bevcev

vA

BJT Amplifier using Coupling and Bypass Capacitors

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.

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.

Lecture : 11AC analysis of BJT Amplifier


D C Equivalent for the BJT Amplifier (Step1)

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.

DC Equivalent Circuit

A C Equivalent for the BJT Amplifier (Step 2)

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 con-nected to ground.

R1IIR2=RB

Rin

Ro

A C Equivalent for the BJT Amplifier

100kΩ4.3kΩ3

R CRR

30kΩ10kΩ2

R 1RBR

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).

All externally connected capacitors are assumed as short circuited elements for ac signal

A C Analysis of CE Amplifier

1) Determine DC operating point and calculate small signal parameters2) Draw the AC equivalent circuit of Amp. • DC Voltage sources are shorted to ground • DC Current sources are open circuited • Large capacitors are short circuits • Large inductors are open circuits3) Use a Thevenin circuit (sometimes a 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 model5) Simplify the circuit as much as necessary. Steps to Analyze a Transistor Amplifier6) Calculate the small signal parameters and gain etc.

Step 1

Step 2

Step 3

Step 4

Step 5

π-model used

Lecture : 12 Hybrid Parameter Model


Hybrid-Pi Model for the BJT

The hybrid-pi small-signal model is the intrinsic low-frequency representation of the BJT.

The small-signal parameters are con-trolled by the Q-point and are indepen-dent of the geometry of the BJT.

Transconductance:

qKT

TV

CI

mg TV ,

Input resistance: Rin

mgo

CI

TVor

Output resistance:

CI

CEV

AV

or

Where, VA is Early Volt-age (VA=100V for npn)

Hybrid Parameter Model

hi

hrVohohfIiVi

Ii 2

2'

Io

Vo

1

1'

11 12

21 22

i i o i i r o

o i o f i o o

V h I h V h I h VI h I h V h I h V

Linear Two port DeviceVi

Ii Io

Vo

11 12

21 22

0 0

0 0

i i

o ii o

o o

o ii o

V Vh hV II V

I Ih h

V II V

h-Parameters

h11 = hi = Input Resistanceh12 = hr = Reverse Transfer Voltage Ratioh21 = hf = Forward Transfer Current Ratioh22 = ho = Output Admittance

The Mid-frequency small-signal models

b

e

hoe

hie

hrevce hfeib vbe

ib ic

vce

c

e

+ _

+ +

_ _

h-parameter model

b

e

rd gmv vbe

ib ic

vce

c

e

+ +

_ _

hybrid- model

r v

+

_

b

e

ib vbe

ib ic

vce

c

e

+ +

_ _

re model

re

fe ac o

Alternate names:h = = =

m C C

o fe doe

ore ie

m

38.92g = I (Note: Uses DC value of I ) n

where n = 1 (typical, Si BJT) 1 = h r =

h

h = 0 r = h = g

e BB

o fe

o e ie

re

oe doe

26 mVr = (Note: uses DC value of I ) I

= h r = h

h = 01h = 0, or use r =

h

Three Small signal Models of CE Transistor

BJT Mid-frequency Analysis using the hybrid-p model

b

e

rd gmv vi

ii io

vo

c

e

+ +

_ _

mid-frequency CE amplifier circuit

r v

+

_

RC RL RTh vs

+

_

is

RS

A common emitter (CE) amplifier

VCC

RC

C

E

B

VCC

R1

RE R2

Rs Ci RL

Co

CE vi

vo

+

+

vs

+

_ _

_

io

ii

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 modelThe resulting mid-frequency circuit is shown below.

si

iv

s

i

i

o

s

osvCLoLLm

i

ov RZ

ZA

vv

vv

vv

ARRrRRgvv

A , where,, ''

R where,, 21 RRrRIv

Z ThThi

ii Co

ovo

oo Rr

iv

Zi

i

oi i

iA

An AC Equivalent Circuitro

Small-Signal Analysis for Gain Av (Using Π-model)

3,3

RCRCRorLR R

ivbev

bevov

ivov

vA

Lbemo RvgLRoIv

Rs

Rs

LR

orRC

Rbevmgov

3

r

BR

SR

rB

RLRmgvA

r

BR

SR

rB

Rivbev

From input circuit

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.

rRRrBRR

rBR

21xixv

in

)(xixv

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.

CRorCRR

mgorC

R

xixv

out

bevxvxvxi

But vbe=0.

since ro is usually >> RC.

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

An Emitter Follower (CC Amplifier) Amplifier

THANKS

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