Analog Integrated Circuit (IC) biasing and active loads BJT Current Sources

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2 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

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Electronics II
-

A
nalog IC Biasing and Active Loads


1

Analog Integrated Circuit (IC) b
iasing and active
loads



BJT Current Sources


Preamble


Biasing BJT Circuits to Achieve Forward
-
active
Mode


Single Base Resistor Biasing

















Voltage Divider Biasing and Bias Stability

















Advantages



Simple

Disadvantages



No bias stabilisation,
i.e.
Q
-
point varies
with




Requires large
resistors (M

’s), i.e.
uses=large=area,=
which=is=an=
important=issue=in=fC=
design.
=
Advantages=
=


Smaller resistors
required (k


range)



R
E

has provided
bias stabilisation
and negativ
e
feedback

Disadvantages



Resistor size is
still undesirable
for IC design

Advantages



Simple

Disadvantages



No bias stabilisation,
i.e.
Q
-
point varies
with




Requires large
resistors (M

’s), i.e.
uses=large=area,=
which=is=an=
important=issue=in=fC=
des
ign.
=
Advantages=
=


Simple

Disadvantages



No bias stabilisation,
i.e.
Q
-
point varies
with




Requires large
resistors (M

’s), i.e.
uses=large=area,=
which=is=an=
important=issue=in=fC=
design
=
Figure
1
: Common
-
emitter circuit
with a single bias resistor in the
base.


Figure
2
: Common
-
emitter
circuit with an emitter resistor
and voltage divider bias circuit
in the base.


Electronics II
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A
nalog IC Biasing and Active Loads


2

Positive and Negative Voltage Biasing














Figure
3
:

Simple transistor circuit
biased with both positive and
negative dc voltages.


The
main issues required for biasing in IC design
:



Bias stabilisation



Avoiding devices consuming large area, i.e. avoiding the use of
moderate and large resistors



Integrated
Circuit Biasing




Can be a current source that establishes the
quiescent collector current ICQ as shown in
Figure 4.



Advantages:

o

Emitter current becomes independent of


and
R
B

o

Collector current and C
-
E voltage are
independent of transistor gain, for
reas
onable


values

o

Value of
R
B

(hence
R
in
) can be increased
without affecting bias stability



What type of circuits can be designed to establish bias current I
O
?

Advantages



Used
for
differential
amplifier biasing



Allows, in
certain
application, for
elimination of C
C

and allows use of
dc input voltages
as input signals

Disadvantages



Resistor size is
still undesirable
for IC design.

Figure
4
: Bipolar circuit with
ideal current
-
source biasing
.

Electronics II
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A
nalog IC Biasing and Active Loads


3

Two
-
Transistor Current Source a.k.a Current Mirror




Basic building block in IC current
source
design



Q
1

is diode
-
connected



Q
1

and
Q
2

are matched
, i.e.
identical,













The
reference current

is given by:




Current relationship
:

o

At collector node of
Q
1
, i.e. at point X:

o

Therefore, output current is



(1.2)



**




Output resistance,
r
o
:

o

Eq. (1.2) assumes Early voltage,
V
A

=

.

o

When Early effect is taken into account
,
V
A

and
r
o

is finite.

o

Stability of
I
O

is affected by the bias
conditions in the load circuit.

(Remember, want
I
O

=
I
REF

for biasing)


V
BE1

=
V
BE2
= V
BE

I
B1

=
I
B2

I
C1

=
I
C2

X

Figure
5
: Two
-
transistor current
source with reference resistor
R
1
.

(1.1)

Connected
as a diode;

when
supplies are
connected,
BE
-
junction
is forward
biased.

Electronics II
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A
nalog IC Biasing and Active Loads


4

o

Hence, assumin
g
V
CE1

(=
V
BE
) <<
V
A
,



o

A more general equation to calculate
dI
O
:



where
R
O

is the output resistance of the current source and is
different for different types of current sources.


**


Mismatched Transistors


In most IC fabrication of current sources,

Q
1

and
Q
2

will be directly adjacent
to each other. Hence, they can be very well matched.


However,
if
Q
1

and
Q
2

are mismatched

and


>>1, base currents can be
neglected to give:



and



Therefore,



I
S1

and

I
S2

are:



reverse
-
saturation currents for
Q
1

and
Q
2

respectively



functions of cross
-
sectional area of the B
-
E junctions


Hence,
(1.4) allows scaling of
I
O

with respect to
I
REF

by having
transistors of different sizes
.


Improved Current Source Circuits


Let’s look at current source circuits that have improved load current stability
against:



changes in




changes in output transistor collector voltage


(1.3)

(1.4)

Electronics II
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A
nalog IC Biasing and Active Loads


5

Figure
6
: Basic three
-
transistor
current source.

A)

Basic Three
-
Transistor Current Source




Assume
all transistors identical.







(1.5)




Note: Curren
t in
Q
3

substantially
smaller


than in either
Q
1

and
Q
2
, i.e.

3

<

.




The
reference current

is given by:


(1.6)




Current relationship
:

o

Summing the currents at point X:

o

Therefore, output current is



(1.7)





Advantage
:

1.

Better

approximation of
I
O

to

I
REF


2.

I
O

less sensitive to variation
in






Output resistance,
r
o
:

o

Looking into the collector of the output transistor
Q
2

in the three
-
transistor current source,

r
o

is the
same as in the two
-
transistor
current source
:


(
1.8)

V
BE1

=
V
BE2
= V
BE

I
B1

=
I
B2

I
C1

=
I
C2


1

=

2

=


X

Usually assume
V
BE3

=
V
BE
. Hence,
the term “
2V
BE
”.
=
Electronics II
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A
nalog IC Biasing and Active Loads


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If

there exists any mismatch between
Q
1

and
Q
2
, the bias current deviation
from the ideal is as given in eq. (1.4).

**

B)

Cascode Current Source




Designed such that
R
O

is greater than that of the two
-
transistor
circuit
.



Assumption: all the transistors
are matched.
Hence,
I
O



I
REF
.


Figure
7
: (a) Bipolar cascode current mirror; (b) small
-
signal equivalent circuit
(Note: Voltage source
V
x

is connected to the output to enable calculation of output
resistance
R
O
).


Base voltag
es of
Q
2

and
Q
4

are constant, which implies these terminals (K
and L in Figure 7) are signal ground.


Figure 7(b) can be rearranged to give Figure 8.








K

L

K

L

Electronics II
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A
nalog IC Biasing and Active Loads


7

Figure
9
: Basic three
-
transistor
current source.






Figure
8
: Small
-
signal equivalent circuit of the cascode current mir
ror rearranged.

From Figure 8, summing currents at the output node yields:




and since
, the
output resistance

is given by:



(1.9)



Hence, the
output resistance has increased by a factor of


compared to
t
he two
-
transistor current source.


Advantage: Increases current source stability with changes in output
voltage.



C)

Wilson Current Source



Another configuration of a three
-
transistor current source.



Assume
all transistors

identical.









Current levels

in all three transistors
are nearly the same, therefore



1

=

2

=

3

=





At

point X:

(1.10)

V
BE1

=
V
BE2
= V
BE

I
B1

=
I
B2

I
C1

=
I
C2


X

Y

Electronics II
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A
nalog IC Biasing and Active Loads


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Nodal equation at emitter of
Q
3
, i.e. point Y:


(1.11)




Using the current relationships of a transistor, eq. (1.11) becomes:



(
1.12)




Therefore, by substituting (1.12) into (1.10), the
output current

is:




(1.13)







The
output resistance

for the Wilson current source, looking into the
collector of
Q
3
:


(1.14)




Widlar Current Source


In all the previous current source
circuits, the load current and reference
currents have been nearly equal.


For the two
-
transistor current source (Figure 5), if a load current of
I
O

=
10

A is required, for
V
+

= 5V and
V
-

= 5V, the resistance value needed is:



This current relationship is essentially the same as of the pr
evious three
-
transistor current source (given by eq. 1.7).
The difference is in the higher
output resistance of Wilson current source.


Electronics II
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A
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Figure
10
: Widlar current
source.


Resi
stors in the order of 1M


require large area and are difficult to fabricate
accurately for IC application. Hence, the
resistor values are limited to the
low kilohm range
.



The Widlar current source, shown below, meets the above requirement.




Voltage diff
erence across
R
E

enables
V
BE2

<
V
BE1




Hence,
I
O

<
I
REF
.




Q
1

and
Q
2

are identical

and
β

>>1
for both transistors.




Hence,
.


Thus,

(1.15)



Similarly,

which rearranges to give:


(1.15)


From
Figure 10

(KVL at
R
E
,
Q
1

and
Q
2
)
,


(1.16)



Hence, by substituting (1.14) and (1.15) into
(1.16), the
current
relationship

of the Widlar current source is:



(1.17)



**

Electronics II
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A
nalog IC Biasing and Active Loads


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The output resistance looking into the collector of
Q
2

is given by:




which can be determined by using the small
-
signal equivalent circuit in
Figure 11(a).


The output res
istance looking into the base of
Q
1

is given by





is in series with
, and since
, the effect of

can be
neglected, meaning that the base of

Q
2

is essentially at signal ground.






















Figure
11
: (a) Small
-
signal equivalent circuit for determining output resistance of
Widlar current source, (b) simplified equivalent circuit for determining output
resistan
ce, and (c) equivalent circuit after a Norton transformation.

Electronics II
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A
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11


Therefore, output resistance at the collector of
Q
2

can be determined from
Figure 11(b) or 11(c) to give:


(1.18)

Normally,
, therefore


(1.19)


where
.


Hence, the output resistance of the Widlar current source is a factor

larger than that of the simple two
-
transistor current source.



Multitransistor Current Mirrors


The reference transistor

V
BE

voltage can also be applie
d to multiple
transistors to generate multiple load currents as shown below.



Figure
12
: Multitransistor current mirror.


The relationship between each load current and the reference current,
assuming all transistors are matched
and
V
A

= ∞, is:



(1.20)


Electronics II
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A
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The collector of multiple output transistors can be connected together,
changing the load current versus current relationship. An example of such a
circuit is shown in Figure 13.




Figure
13
: Mul
tioutput
transistor current source
(assuming all transistors are
matched and

β

is very large such
that the base currents can be
neglected,
I
1

=
I
2

=
I
3

=
I
REF

).






Generalized Current Mirror




Figure
14
: Generalized current
mi
rror
.




Obtain several output
currents (
I
O
’s) from a
single reference current
I
REF
.



pnp transistors

to ‘source’
currents



npn transistors to ‘sink’
currents



Effect of finite


-

I
O

to be
less than
I
REF

since
I
REF

supplies all base currents.
It becomes more s
evere as
more transistors are added.




= 3
I
REF

Equivalent circuit
symbol of three
transistors in parallel

Electronics II
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A
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Summary of current source circuits




Two
-
transistor

(Figure 5)

Three
-
transistor

(Figure 6)

Cascode

(Figure 7a)

Wilson

(Figure 9)

Widlar

(Figure 10)

Multiple
transistor

(Figure 12)

Load current,
I
O







Output
resistance,
R
O

r
o2

r
o2




r
o

Finite
β

error
*





-


*Finite
β

error = discrepancy between
I
O

and
I
REF

since the reference current supplies all base currents.