bias for integrated circuits

8/13/2019 Bias for Integrated Circuits

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EEEB273 Electronics Analysis & Design II

Lecturer: Dr Jamaludin Bin Omar 3

Reference: Neamen, Chapter 10

Learning Outcome

Able to describe and:

Analyze and design a simple two-transistor BJTcurrent-source circuit to produce a given bias current.

Analyze and design more sophisticated BJT current-source circuits, such as the three-transistor circuit,cascode circuit, Wilson circuit, and Widlar circuit.

Analyze the output resistance of the various BJTcurrent-source circuits.

3.0)

Fig 3.50: Common-emittercircuit with a single biasresistor in the base.

3.0.1) Single Base Resistor Biasing

Advantages Simple

Disadvantages No biasstabilization, i.e. Q-point varies with Requires largeresistors (Ms),i.e. uses largearea, which is animportant issue inIC design.

3.0)

Fig 3.53: Common-emitter

circuit with an emitterresistor and voltage dividerbias circuit in the base.

3.0.2) Voltage Divider Biasing and Bias Stability

Advantages Smaller resistorsrequired (k range)RE has providedbias stabilizationand negativefeedback

Disadvantages Resistor size isstill undesirablefor IC design

3.0)

Simple transistor circuitbiased with both positiveand negative dc voltages.

3.0.3) Positive and Negative Voltage Biasing

Advantages Used fordifferential amplifierbiasing

Allows, in certainapplication, forelimination of CCand allows use ofdc input voltagesas input signals

Disadvantages Resistor size isstill undesirablefor IC design

3.0)

Bias stabilization: biasing usesconstant current sources

Avoid devices consuming largearea, i.e. avoiding the use of moderateand large resistors (which consumelarge area on IC)

3.0.4) The main issues required for biasing in IC design


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Can be a currentsource that establishesthe quiescent collector

current ICQ as shown inFigure 10.1

Advantages: Emitter current becomes

independent of andRB Collector current and C-E

voltage are independent oftransistor gain, forreasonablevalues

Value ofRB (henceRin) canbe increased withoutaffecting bias stability

Figure 10.1:Bipolar circuit withcurrent-sourcebiasing

3.1)

Simplest: Two-transistor current source Need to improve approximation ofI

O

= IREF

Need to improve stability ofIO by having higheroutput resistance

Improved current source topologies Basic 3-transistor: better approximation ofIO = IREF Cascode: higher output resistance by factor of Wilson: higher output resistance by factor of /2 Widlar: higher output resistance by (1 +gmRE)

3.2.1) Pre-summary of Current Source circuits

3.2)

Sum currents at the various nodes in thecircuit to find the relation between thereference current and the bias current.

To find the output resistance, place a testvoltage at the output node and analyse thesmall-signal equivalent circuit. Keep in mindthat the reference current is constant, whichmay make some of the base voltage constantor at signal ground.

3.2)

Problem-Solving Technique

Figure 10.2: (a) Basic two-transistor current source

(b) Two-transistor current source withreference resistorR1

3.2.2) Two-transistor Current Source

3.2)

Also called Current Mirror,with two matched transistors, Q1 & Q2

VBE1 = VBE2 = VBEIB1 =IB2IC1 =IC2

Q1 is diode-connected

Reference currentIREF established byR1

(10.1)

3.2.2) Two-transistor Current Source (Cont)

3.2)

1R

VVVI BEREF

+

=

Sum currents at collector of Q1

IC1 =IC2 andIB2 =IC2/

Output current:

3.2.2.1) Current Relationship


22 2

BCREF III +=

+

==

21

2REF

CO

III


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In actual transistors, the Early voltage (VA) is

finite. So,ro is also finite. Then the collector current is a function of the collector-emitter voltage. Thus, the stability ofIO is affected by

the bias conditions in the load circuit.

Refer to Fig 10.3. The voltage VIapplied to base of Q0is a dc voltage. When VI is changed, VCE2 changes sinceB-E voltage of Q0 is essentially a constant. A variation inVCE2 in turn changes the output currentIO, because ofthe Early effect. Fig 10.4 shows thatIO versus VCE2 characteristics at aconstant B-E voltage.

3.2.2.2) Significance of Output Resistance, ro


Fig 10.3: The dc equivalent ofsimple amplifier biased withtwo-transistor current source

3.2.2.2) Significance of Output Resistance, ro(Cont)


Fig 10.4: Output current versuscollector-emitter voltage,showing the Early voltage

The ratio of load current to reference current, takingthe Early effect* into account, is

*Refer toEquation 3.16in Neaman

where VA is the early voltage and the factor (1 + 2/)

accounts for the finite gain.



+

+

+

=

A

CE

A

CE

REF

O

V

V

V

V

I

I

1

2

1

1

21

1

VCE1 = VBE

VCE2 = VI VBE0 V

The differential change in IO with respect to a changein VCE2 is

(10.7)



+

+

=

A

BEA

REF

CE

O

V

VV

I

dV

dI

1

11

212

Assuming VCE2


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In practice, Q1 and Q2 may not be exactly identical.If >> 1, base currents can be neglected. The current-voltage relationship, neglecting Early effect, is then

and

Therefore, (10.10)

3.2.2.3) Mismatched Transistors


1

2

/

22

/

11

S

S

REF

O

VV

SCO

VV

SCREF

I

I

I

I

eIII

eIII

TBE

TBE

=

=

=

Thus, any deviation in the bias current f rom the ideal,as a function of mismatch between Q

1

and Q2

, is directlyrelated to the ratio of the reverse-saturation currents IS1and IS2.IS is a strong function of temperature. Therefore, inmost IC fabrication of current sources, Q1 and Q2 mustbe close to one another so that their temperatures willbe the same in order for the circuit to operate properly.

Also, parametersIS1 and IS2 are functions of cross-sectional area of B-E junctions. Hence, Equation(10.10) allows scaling ofIO with respect toIREF byhaving transistors of different sizes.

3.2.2.3) Mismatched Transistors (Cont)


Current source circuits that have improvedload current stability against changes in andchanges in output transistor collector voltageare: Basic Three-Transistor Current Source: better

approximation ofIO = IREF Cascode Current Source: higher output

resistance by factor of Wilson Current Source: higher output

resistance by factor of /2 Widlar Current Source: higher output resistance

by (1 + gmRE)

3.2.3) Improved Current-Source Circuits

3.2)

3.2.3.1) Basic Three-Transistor Current Source

3.2.3) Improved Current-Source Circuits (Cont)

Fig 10.5: Basic three-transistor current source

Assume that alltransistors are identical:

VBE1 = VBE2 = VBEIB1 =IB2IC1 =IC21 = 2 =

Note: Current in Q3 issubstantially smallerthan in either Q

1

and Q2

,i.e. 3 <

Sum currents at collector of Q1IREF =IC1 +IB3IC1 =IC2 andIB2 =IC2/

IB1

=IB2

,IE3

= 2IB2

,IE3

= (1+3)I

B3

Therefore,

3.2.3.1) Basic Three-Transistor Current Source (Cont)


( ) ( )

( ) ( )

++=

++=

++=

++=

3

2

3

22

3

21

3

31

1

21

1

2

1

2

1

CC

CREF

BC

ECREF

II

II

II

III

Assuming VBE3 = VBE, Reference Current is

Advantages:

Better approximation ofIO toIREF

IO is less sensitive to variation in



11

3 2

R

VVV

R

VVVVI BEBEBEREF

++

=


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Fig 10.6:(a) Two-transistor

current mirror(b) Three-transistor

current mirror(c) Variation in bias

currents with achange in



Output Resistance,rOThe output resistance looking into thecollector of output transistor Q2 of the basic3-transistor shown in Fig 10.5 is the same asthat of the 2-transistor current source, that is

(10.18)

This means any mismatch between Q1and Q2 produces a deviation in the biascurrent from the ideal, as given by Equation(10.10).



22

1

OCE

O

rdV

dI=

3.2.3.2) Cascode Current Source


Fig 10.7: (a) Bipolar cascode current mirror(b) Small-signal equivalent circuit

Current-source circuits withRo much greater than thatof the two-transistor circuit, such as the cascode circuit.

For a constantIREF, base voltages of Q2 andQ4 are constant, which implies these terminalsare at signal ground.

Fig 10.7(b) can be rearranged as follows.

3.2.3.2) Cascode Current Source (Cont)


Since gm2Vbe2 = 0, then

Vbe4 = - Ix (ro2 || r4)

Summing currents at output node yields



( )

( ) ( )

+=

+=

4

42424

4

4244

||||

||

o

oxxoxmx

o

oxxbemx

r

rrIVrrIgI

r

rrIVVgI

Combining terms

(10.20)

The output resistance has increased by afactor of compared to the 2-transistor currentsource, which increases the stability of thecurrent source with changes in output voltage.



( ) 4441 oox

xO rrr

I

VR ++==


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3.2.3.3) Wilson Current Source


Another configuration of a 3-transistor current source.

Fig 10.8: Wilsoncurrent source

Assume that all transistorsare identical:

VBE1 = VBE2 = VBEIB1 =IB2IC1 =IC2

Current levels in all threetransistors are nearly thesame, therefore

1 = 2 =3 =

3.2.3.3) Wilson Current Source (Cont)


Sum currents at the collector of Q1I

REF

=IC1

+IB3

(10.21)

At the emitter of Q3

(10.22)

At the collector of Q2

(10.23)

+=+=

212 2223 CBCE IIII

333

22

11

21

1

21

CCE

C II

II

+

+=

+

+

=

+

=



ReplacingIC1 withIC2

IREF =IC2 +IB3

(10.24)

Solve for the output current:

(10.25)

)2(

21

13

++

== REFOC III

33

2

1 CCREF

III +

+

+=



Equation (10.25) is essentially thesame as that of previous 3-transistor

current source.

The difference between the two 3-transistor current-source circuits isthe output resistance.



In Wilson current source: the outputresistance looking into the collector of Q3 is

which is approximately a factor /2 larger thanthat of either the 2-transistor source or the basic3-transistor source.

This means that, in the Wilson current source,the change in bias current IO with a change inoutput collector voltage is much smaller.

)2/(2/33

ooO

rrR =

3.2.3.4) Widlar Current Source


In all the previous current source circuits, the loadcurrent and reference currents have been nearly equal. For the two-transistor current source in Fig 10.2(a), if aload current ofIO = 10A is required, for V

+= 5V and V

--=

-5V, the resistance value needed is

In ICs, resistors on the order of 1Mrequire largeareas and are difficult to fabricate accurately.Therefore, need to limit IC resistor values to the lowkrange.

=

=

+

kI

VVVR

REF

BE 9301010

)5(7.0561


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3.2.3.4) Widlar Current Source (Cont)


A Widlar current source, Fig 10.9,meets the objective of limiting ICresistor values to the low krange.

A voltage difference is producedacross resistorRE, so that the B-Evoltage of Q2 is less than the B-Evoltage of Q1.

A smaller B-E voltage produces asmaller collector current, which in turnmeans that the load currentIO is lessthan the reference currentIREF.

Fig 10.9: Widlarcurrent source



Current RelationshipIf Q

1

and Q2

are identical and if >>1 for bothtransistors, then

and

Thus,

and )ln(

)ln(

2

1

/

2

/

1

2

1

S

OTBE

S

REFTBE

VV

SCO

VV

SCREF

I

IVV

I

IVV

eIII

eIII

TBE

TBE

=

=

==

=



Combining: (10.28)

From the circuit: (10.29)

Finally: (10.30))ln(

)ln(

221

21

O

REFTEO

EOEEBEBE

O

REFTBEBE

I

IVRI

RIRIVV

I

IVVV

=

=

=

Equation (10.30) gives the relationship

between the reference and bias currents.



Output ResistanceThe output resistance looking into thecollector of Q2 in Fig 10.9 can be expressedas

(10.31)

This output resistance can be determined byusing the small-signal equivalent circuit inFig 10.10(a).

OC

O

RdV

dI 1

2

=



Fig 10.10(a): Small-signal equivalent circuit fordetermining output resistance of W idlar current source



KCL equation at the base of Q1

Noting V1=Vx1:

or 111

11

11

11

11

1

1

11

111

1

11

||||1

||

||

11||

Rrg

rR

Rr

Vg

rV

I

R

Rr

VVg

r

VI

o

m

o

o

xm

x

x

o

o

xm

xx

=

++==

++=


8/10





Next calculate the approximate value forRo1

If IREF = 1mA, for = 100then r1 = 2.6kandgm1 = 38.5mA/V Assume R1 = 9.3kandro1 = then Ro10.026k= 26

For IO = 12A,r2 = 217k

Ro1 is in series with r2 andRo1


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Transistors are connected in parallel to increase theeffective B-E area of the device, hence increasing theload current. Circuit symbols as shown in Fig 10.14 can be used toindicate parallel output transistors.

3.2.4) Multitransistor Current Mirrors (Cont)

3.2)

Fig 10.14: Equivalent circuit symbols(a) two transistors in parallel,(b) three transistors in parallel, and(c) Ntransistors in parallel

Generalized Current Mirror As shown in Fig 10.15

Obtain severalIOs asmultiples of a singleIREFo pnp to source currento npn to sink current

Effect of finite :IO to be less thanIREF sinceIREF supplies all base currents.It becomes more severe asmore transistors are added.

3.2.4) Multitransistor Current Mirrors

Fig 10.15: Generalisedcurrent mirror

The minimum output voltage, VO(min), of

the current mirror influences the maximumsymmetrical output voltage, VOUT, swing of

the load circuit being biased.

The minimum output voltage for the two-

transistor current source is:VO(min) = VC2 = V

-+ VCE2 (sat)

where VCE2 (sat) may be in the order of0.1 to 0.3 V

3.2.5) Output Voltage Swing

3.2)

For the cascode and Wilson current

sources:VO(min) = VC2 = V

-+ VBE + VCE2 (sat)

The value may be in the order of 0.7 to 0.9 V

Note: Increase in VO(min) means reduced

maximum output voltage swing of the loadcircuit, which is critical in the low-power

applications.

3.2.5) Output Voltage Swing (Cont)

3.2)

3.3.1) Load Current and Output Resistance

3.3) !!" #

3.3.2) Comparison of Current Source Circuits

3.3) !!" #

WidlarTwo-transistor


10/10


Lecturer: Dr Jamaludin Bin Omar 3-

3.3.2) Comparison of Current Source Circuits (Cont)

3.3) !!" #

Two-transistor Cascode


3.3) !!" #

Two-transistor Three-transistor


3.3) !!" #

Three-transistor Wilson

$ % Test 2 Semester 2 2000/01

Assume that all transistors to be matched, with current gain .a) Starting with currentIat collector of Q1, find current at locations

marked with number 1 to number 12 in Figure above, expressed

in terms of I and . (18 marks)b) Find current atIREF andIO in terms ofIand . FindIO in terms of

IREF. (4.5 marks)c) CalculateIO whenIREF = 7 mAand = 50. (2.5 marks)

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