dc biasing of bjt

DC Biasing of BJTs

BiasingBiasing

Biasing:Biasing: T The DC voltages applied to a transistor in order to turn it on so that it can amplify the AC signal.

Operating PointOperating Point

The DC input establishes an operating or quiescent point called the Q-pointQ-point.

The Three States of OperationThe Three States of Operation

• Active or Linear Region OperationActive or Linear Region OperationBase–Emitter junction is forward biasedBase–Collector junction is reverse biased

• Cutoff Region OperationCutoff Region OperationBase–Emitter junction is reverse biased

• Saturation Region OperationSaturation Region OperationBase–Emitter junction is forward biasedBase–Collector junction is forward biased

No matter what type of configuration a transistor is used in, the basic relationships between the currents are always the same, and the base-to-emitter voltage is the threshold value if the transistor is in the “on” state

BC

CBE

BE

II

III

VV

ββ

=≅+=

=)1(

7.0

• The operating point defines where the transistor will operate on its characteristics curves under dc conditions.

• For linear (minimum distortion) amplification, the dc operating point should not be too close to the maximum power, voltage, or current rating and should avoid the regions of saturation and cutoff

DC Biasing CircuitsDC Biasing Circuits

• Fixed-bias circuit

• Emitter-stabilized bias circuit

• Voltage divider bias circuit

• DC bias with voltage feedback

I. Fixed BiasI. Fixed Bias

• The fixed-bias configuration is the simplest of transistor biasing arrangements, but it is also quite unstable

•For most configurations the dc analysis begins with a determination of the base current

•For the dc analysis of a transistor network, all capacitors are replaced by an open-circuit equivalent

Fixed-bias circuit

The dc equivalent circuit of the fixed bias circuit where the capacitor is replaced with an open-circuit

The Base-Emitter LoopThe Base-Emitter Loop

From Kirchhoff’s voltage law:

+VCC – IBRB – VBE = 0

Solving for base current:

B

BECCB R

VVI

−=

Collector-Emitter LoopCollector-Emitter Loop

Collector current:

BIIC

β=

CCCCCE RIVV −=

From Kirchhoff’s voltage law:

0=−+ CCCCCE VRIV

Example: Determine the following for the fixed-bias configuration of the figure shown:

(a) IBQ and ICQ (b) VCEQ (c) VB and VC (d) VBC

β = 75

SaturationSaturation

• Saturation conditions are normally avoided because the base-collector junction is no longer reverse-biased and the output amplified signal will be distorted

•For a transistor operating in the saturation region, the current is a maximum value for the particular design. Change the design and the corresponding saturation level may rise or drop

•The highest saturation level is defined by the maximum collector current as provided by the specification sheet

SaturationSaturation

Ω=== 00

satCC

CECE I

V

I

VR

C

CCC R

VI

sat=

SaturationSaturation

When the transistor is operating in saturation, current through the transistor is at its maximum possible value.

CRCCV

CsatI =

V 0CEV ≅

In the previous example, the saturation level for the network is given by:

mAk

V

R

VI

C

CCCsat

45.52.2

12 =Ω

==

Load Line AnalysisLoad Line Analysis

CCCCCE RIVV −=

The variables IC and VCE are related by the equation:

Load Line AnalysisLoad Line Analysis

IICsatCsat

ICC = VCCCC / RCC

VCECE = 0 V

VVCEcutoffCEcutoff

VCECE = VCCCC

ICC = 0 mA

The Q-point is the operating point:• where the value of RB sets the value of IB

• that sets the values of VCE and IC

The end points of the load line are:

Circuit Values Affect the Q-PointCircuit Values Affect the Q-Point

[Movement of the Q-point with increasing level of IB]

Circuit Values Affect the Q-PointCircuit Values Affect the Q-Point

[Effect of an increasing level of RC on the load line the Q-point]

Circuit Values Affect the Q-PointCircuit Values Affect the Q-Point

[Effect of lower values of VCC on the load line the Q-point]

II. Emitter-Stabilized Bias CircuitII. Emitter-Stabilized Bias Circuit

Adding a resistor (RE) to the emitter circuit stabilizes the bias circuit.

Base-Emitter LoopBase-Emitter Loop

From Kirchhoff’s voltage law:

0 RI-V-RI- EEBEBBCC =+V

0R1)I(-V-RI-V EBBEBBCC =+βSince IE = (β + 1)IB:

EB

BECCB 1)R(R

V-VI

+β+=

Solving for IB:

Collector-Emitter LoopCollector-Emitter Loop

From Kirchhoff’s voltage law:

0 CC

VC

RC

I CE

V E

RE

I =−++

Since IE ≅ IC:

)R (RI– V V ECCCCCE +=

Also:

EBEBRCCB

CCCCECEC

EEE

V V RI– V V

RI - V V V V

RI V

+===+=

=

Example: Determine the following for the emitter bias network of the figure shown:

(a) IB (b) IC (c) VCE (d) VC (e) VE (f) VB (g) VBC

+16 V

β = 75

Improved Biased StabilityImproved Biased Stability Stability refers to a circuit condition in which the currents and voltages will remain fairly constant over a wide range of temperatures and transistor Beta (β) values

Adding RE to the emitter improves the stability of a transistor

β IB(µA) IC(mA) VCE(V)

75 30.24 2.27 9.91

100 28.81 3.63 9.11

[For Emitter Bias Case]

β IB(µA) IC(mA) VCE(V)

75 47.08 3.53 4.23

100 47.08 4.71 1.64

[For Fixed Bias Case]

Saturation LevelSaturation Level

EC

CCC RR

VI

sat +=

Load-line AnalysisLoad-line Analysis

VCEcutoff:: ICsat:

The endpoints can be determined from the load line.

mA 0 I

V V

C

CCCE

==

ERCR

CCVCI

CE V 0V

+=

=

)( ECCCCCE RRIVV +−=

III. Voltage Divider BiasIII. Voltage Divider Bias

This is a very stable bias circuit.

The currents and voltages are nearly independent of any any variations in β .

Exact Analysis:

21 || RRRTh =21

2

2 RR

VRVE CCRTh +

==

)( ECCCCCE RRIVV +−=

0=−−− EEBEThBTh RIVRIE

Applying Kirchhoff’s voltage law in the clockwise direction in the Thevenin network,

ETh

BEThB RR

VEI

)1( ++−=β (Substituting IE = (β+1)IB)

Approximate Analysis:

Approximate AnalysisApproximate Analysis

Where IB << I1 and I1 ≅ I2 :

Where βRE > 10R2:

From Kirchhoff’s voltage law:

21

CC2B RR

VRV

+=

E

EE R

VI =

BEBE VVV −=

EECCCCCE RI RI V V −−=

)R (RIV V

II

ECCCCCE

CE

+−=≅

Voltage Divider Bias AnalysisVoltage Divider Bias Analysis

Transistor Saturation LevelTransistor Saturation Level

EC

CCCmaxCsat RR

VII

+==

Load Line AnalysisLoad Line Analysis

Cutoff:Cutoff: Saturation:Saturation:

mA0I

VV

C

CCCE

==

V0VCE

ERCRCCV

CI

=

+=

IV. DC Bias with Voltage Feedback IV. DC Bias with Voltage Feedback

Another way to improve the stability of a bias circuit is to add a feedback path from collector to base.

In this bias circuit the Q-point is only slightly dependent on the transistor beta, β .

Base-Emitter LoopBase-Emitter Loop

)R(RR

VVI

ECB

BECCB +β+

−=

From Kirchhoff’s voltage law:From Kirchhoff’s voltage law:

0RI–V–RI–RI– V EEBEBBCCCC =′

Where IWhere IBB << I << ICC::

CI

BI

CI

CI' ≅+=

Knowing IKnowing ICC = = ββ IIBB and I and IEE ≅≅ I ICC, the loop , the loop

equation becomes: equation becomes:

0RIVRIRI– V EBBEBBCBCC =β−−−β

Solving for ISolving for IBB::

Collector-Emitter LoopCollector-Emitter Loop

Applying Kirchoff’s voltage law:Applying Kirchoff’s voltage law:

IERE + VCE + I’CRC – VCC = 0

Since ISince I′′ CC ≅≅ I ICC and I and IEE ≅≅ I ICC::

IC(RC + RE) + VCE – VCC =0

Solving for VSolving for VCECE::

VCE = VCC – IC(RC + RE)

Base-Emitter Bias AnalysisBase-Emitter Bias Analysis

Transistor Saturation LevelTransistor Saturation Level

EC

CCCmaxCsat RR

VII

+==

Load Line AnalysisLoad Line Analysis

Cutoff:Cutoff: Saturation:Saturation:

mA 0I

VV

C

CCCE

==

V 0VCE

ER

CR

CCV

CI

=

+=

Bias Stabilization Bias Stabilization

The s tability of a sys tem is a measure of the sens itivity of a ne twork to varia tions in its pa ramete rsIn any amplifie r employing a trans is tor the collector current IC is sens itive to each of the following pa rameters :

• β: increase with increase in tempera ture

• |VBE| : decrease about 2.5 mV per oC increase in tempera ture

• ICO (reverse sa tura tion current): doubles in va lue for every 100 increase in tempearture

Shift in dc-bias point (Q-point) due to change in tempera ture : (a ) 250C; (b) 1000C

A be tte r bias circuit is one tha t will s tabilize or mainta in the dc-bias initia lly se t, so tha t the amplifie r can be used in a changing-tempera ture environment

Stability Factors: S(ICO), S(VBE), and S(β)

CO

CCO I

IIS

∆∆=)(

BE

CBE V

IVS

∆∆=)(

ββ

∆∆= CIS )(

Networks tha t a re quite s table and re la tive ly insens itive to tempera ture varia tions have low s tability factors

The higher the s tability factor, the more sens itive is the ne twork to varia tions in tha t parameter

S(ICO):

Emitter-Bias Configuration

)/()1(

)/(1)1()(

EB

EBCO RR

RRIS

++++=

ββ

)1()( += βCOIS

1)1(

1)1()( =→

++=

ββCOIS

E

BCO R

RIS ≅)(

For RB/RE >> (β+1),

For RB/RE << 1,

For the range where RB/RE ranges between 1 and (β+1),

[Variation of stability factor with the resistor ratio RB/RE for the emitter-bias configuration]

)1()( += βCOIS

)/()1(

)/(1)1()(

ETh

EThCO RR

RRIS

++++=

ββ

)/()1(

)/(1)1()(

CB

CBCO RR

RRIS

++++=

ββ

Fixed-Bias Configuration:

Voltage-Divider Bias Configuration:

Feedback-Bias Configuration:

S(VBE):

EBBE RRVS

)1()(

++−=β

βEmitter-bias configuration:

Fixed-Bias Configuration:B

BE RVS

β−=)(

EBBE RRVS

)1()(

++−=β

β)1(/

/)(

++−=⇒

ββEB

EBE RR

RVS

E

EEBE R

RRVS

1/

)1(

/)( −=−≅

+−≅⇒

ββ

ββ

For (β+1)>>RB/RE

This shows that the larger the resistance RE, the lower is the stability factor and the more stable is the system

S(β):

Emitter-bias configuration:

)/1(

)/1()(

21

1

EB

EBCC

RR

RRIIS

+++

=∆∆=

ββββ

1

1)(β

β CIS =

)/1(

)/1()(

21

1

ETh

EThC

RR

RRIS

+++

=ββ

β

Fixed-Bias Configuration:

Voltage-Divider Bias Configuration:

Feedback-Bias Configuration:

))1((

)()(

21

1

βββ

+++

=CB

CBC

RR

RRIS

Summary

The total effect on the collector current can be determined using the following equation:

ββ ∆+∆+∆=∆ )()()( SVVSIISI BEBECOCOC