1
Chapter 9 Cascode Stages and Current Mirrors
9.1 Cascode Stage
9.2 Current Mirrors
CH 9 Cascode Stages and Current Mirrors 2
Boosted Output Impedances
SOSmout
EOEmout
RrRgR
rRrrRgR
1
||||1
2
1
CH 9 Cascode Stages and Current Mirrors 3
Bipolar Cascode Stage
1 2 1 1 2 1
1 1 2 1
[1 ( || )] ||
||
out m O O O
out m O O
R g r r r r r
R g r r r
Example 9.1
CH 9 Cascode Stages and Current Mirrors 4
CH 9 Cascode Stages and Current Mirrors 5
Maximum Bipolar Cascode Output Impedance
The maximum output impedance of a bipolar cascode is
bounded by the ever-present r between emitter and ground
of Q1.
11max,
11max, 1
Oout
Omout
rR
rrgR
Example 9.2
CH 9 Cascode Stages and Current Mirrors 6
CH 9 Cascode Stages and Current Mirrors 7
Example 9.3
Typically r is smaller than rO, so in general it is impossible
to double the output impedance by degenerating Q2 with a
resistor.
21
122
O
OoutA
rr
rrR
CH 9 Cascode Stages and Current Mirrors 8
PNP Cascode Stage
1 2 1 1 2 1
1 1 2 1
[1 ( || )] ||
||
out m O O O
out m O O
R g r r r r r
R g r r r
CH 9 Cascode Stages and Current Mirrors 9
Another Interpretation of Bipolar Cascode
Instead of treating cascode as Q2 degenerating Q1, we can
also think of it as Q1 stacking on top of Q2 (current source)
to boost Q2’s output impedance.
Vb2 determines the current level.
CH 9 Cascode Stages and Current Mirrors 10
False Cascodes
When the emitter of Q1 is connected to the emitter of Q2, it’s
no longer a cascode since Q2 becomes a diode-connected
device instead of a current source.
1
2
1
2
1
12
2
112
2
1
21
1
||||1
||||1
1
O
m
O
m
mout
O
m
OO
m
mout
rg
rg
gR
rrg
rrrg
gR
CH 9 Cascode Stages and Current Mirrors 11
MOS Cascode Stage
211
21211
OOmout
OOOmout
rrgR
rrrgR
Example 9.5
CH 9 Cascode Stages and Current Mirrors 12
CH 9 Cascode Stages and Current Mirrors 13
Another Interpretation of MOS Cascode
Similar to its bipolar counterpart, MOS cascode can be thought of as stacking a transistor on top of a current source.
Unlike bipolar cascode, the output impedance is not limited by .
CH 9 Cascode Stages and Current Mirrors 14
PMOS Cascode Stage
211
21211
OOmout
OOOmout
rrgR
rrrgR
CH 9 Cascode Stages and Current Mirrors 15
Example 9.6
RP will lower the output impedance, since its parallel
combination with rO1 will always be lower than rO1.
2121 )||)(1( OPOOmout rRrrgR
During manufacturing, a large parasitic resistor, RP ,has appeared
in a cascode as shown in Fig. 9. 11. Determine the output
resistance.
CH 9 Cascode Stages and Current Mirrors 16
Short-Circuit Transconductance
The short-circuit transconductance of a circuit measures its
strength in converting input voltage to output current.
0
outvin
outm
v
iG
CH 9 Cascode Stages and Current Mirrors 17
Example 9.7
1mm gG
Calculate the transconductance of the CS stage shown in
Fig. 9.13(a).
CH 9 Cascode Stages and Current Mirrors 18
Derivation of Voltage Gain
By representing a linear circuit with its Norton equivalent,
the relationship between Vout and Vin can be expressed by
the product of Gm and Rout.
outminout
outinmoutoutout
RGvv
RvGRiv
CH 9 Cascode Stages and Current Mirrors 19
Example 9.8
11 Omv rgA
Determine the voltage gain of the common-emitter stage shown in
Fig. 9.15(a).
CH 9 Cascode Stages and Current Mirrors 20
Comparison between Bipolar Cascode and CE Stage
Since the output impedance of bipolar cascode is higher
than that of the CE stage, we would expect its voltage gain
to be higher as well.
CH 9 Cascode Stages and Current Mirrors 21
Voltage Gain of Bipolar Cascode Amplifier
Since rO is much larger than 1/gm, most of IC,Q1 flows into the diode-connected Q2. Using Rout as before, AV is easily calculated.
1
1 2 2 1 2( || )
m m
v m O m O
G g
A g r g r r
Example 9.9
CH 9 Cascode Stages and Current Mirrors 22
1
1 2 2 1 2( || )
m m
v m O m O
G g
A g r g r r
Cascoding thus raises the voltage gain
by a factor of 65.8.
CH 9 Cascode Stages and Current Mirrors 23
Alternate View of Cascode Amplifier
A bipolar cascode amplifier is also a CE stage in series with
a CB stage.
CH 9 Cascode Stages and Current Mirrors 24
Practical Cascode Stage
Since no current source can be ideal, the output impedance drops.
)||(|| 21223 rrrgrR OOmOout
CH 9 Cascode Stages and Current Mirrors 25
Improved Cascode Stage
In order to preserve the high output impedance, a cascode
PNP current source is used.
)||(||)||( 21223433 rrrgrrrgR OOmOOmout
Example 9.10
CH 9 Cascode Stages and Current Mirrors 26
Compared to the ideal current source case, the gain
has fallen by approximately a factor of 3 because
the pnp devices suffer from a lower Early voltage
and β.
CH 9 Cascode Stages and Current Mirrors 27
MOS Cascode Amplifier
2211
21221 )1(
OmOmv
OOOmmv
outmv
rgrgA
rrrggA
RGA
CH 9 Cascode Stages and Current Mirrors 28
Improved MOS Cascode Amplifier
Similar to its bipolar counterpart, the output impedance of a MOS cascode amplifier can be improved by using a PMOS cascode current source.
oponout
OOmop
OOmon
RRR
rrgR
rrgR
||
433
122
CH 9 Cascode Stages and Current Mirrors 29
Temperature and Supply Dependence of Bias Current
Since VT, IS, n, and VTH all depend on temperature, I1 for
both bipolar and MOS depends on temperature and supply.
2 1 2 1 1 2 1
2
21
1 2
( ) ( ) ln( )
1
2
CC T S
n ox DD TH
R V R R I R R V I I
RWI C V V
L R R
CH 9 Cascode Stages and Current Mirrors 30
Concept of Current Mirror
The motivation behind a current mirror is to sense the
current from a “golden current source” and duplicate this
“golden current” to other locations.
CH 9 Cascode Stages and Current Mirrors 31
Bipolar Current Mirror Circuitry
The diode-connected QREF produces an output voltage V1
that forces Icopy1 = IREF, if Q1 = QREF.
REF
REFS
Scopy I
I
II
,
1
CH 9 Cascode Stages and Current Mirrors 32
Bad Current Mirror Example I
Without shorting the collector and base of QREF together, there will not be a path for the base currents to flow, therefore, Icopy is zero.
CH 9 Cascode Stages and Current Mirrors 33
Bad Current Mirror Example II
Although a path for base currents exists, this technique of
biasing is no better than resistive divider.
CH 9 Cascode Stages and Current Mirrors 34
Multiple Copies of IREF
Multiple copies of IREF can be generated at different
locations by simply applying the idea of current mirror to
more transistors.
REF
REFS
jS
jcopy II
II
,
,
,
CH 9 Cascode Stages and Current Mirrors 35
Current Scaling
By scaling the emitter area of Qj n times with respect to
QREF, Icopy,j is also n times larger than IREF. This is equivalent
to placing n unit-size transistors in parallel.
REFjcopy nII ,
CH 9 Cascode Stages and Current Mirrors 36
Example 9.14 : Scaled Current
A multistage amplifier incorporates two current sources of values
0.75mA and 0.5mA. Using a bandgap reference current of 0.25mA,
design the require current sources. Neglect the effect of the base
current for now.
CH 9 Cascode Stages and Current Mirrors 37
Fractional Scaling
A fraction of IREF can be created on Q1 by scaling up the emitter area of QREF.
REFcopy II3
1
CH 9 Cascode Stages and Current Mirrors 38
Example 9.15 : Different Mirroring Ratio
Using the idea of current scaling and fractional scaling, Icopy2 is 0.5mA and Icopy1 is 0.05mA respectively. All coming from a source of 0.2mA.
It is desired to generate two currents equal to 50uA and 500uA from a reference of 200uA. Design the current mirror circuit.
CH 9 Cascode Stages and Current Mirrors 39
Mirroring Error Due to Base Currents
11
1
n
nII REF
copy
CH 9 Cascode Stages and Current Mirrors 40
Improved Mirroring Accuracy
Because of QF, the base currents of QREF and Q1 are mostly supplied by QF rather than IREF. Mirroring error is reduced times.
11
12
n
nII REF
copy
CH 9 Cascode Stages and Current Mirrors 41
Example 9.16 : Different Mirroring Ratio Accuracy
154
10
154
2
1
REFcopy
REFcopy
II
II
Compute the Icopy1 and Icopy2 in this figure before and after adding a follower.
2
2
2
1
154
10
154
REFcopy
REFcopy
II
II
Before :
After :
CH 9 Cascode Stages and Current Mirrors 42
Example 9.17 : Different Mirroring Ratio Accuracy
Design this circuit for a voltage gain 100 and a power budget of 2mW. Assume VA,npn = 5V, VA,pnp = 4V, IREF = 100uA, and VCC = 2.5V.
The gain is smaller than 100 because low Early voltages and VT, a fundamental constant of the technology, independent of the bias current.
CH 9 Cascode Stages and Current Mirrors 43
PNP Current Mirror
PNP current mirror is used as a current source load to an
NPN amplifier stage.
CH 9 Cascode Stages and Current Mirrors 44
Generation of IREF for PNP Current Mirror
CH 9 Cascode Stages and Current Mirrors 45
Current Mirror with Discrete Devices
Let QREF and Q1 be discrete NPN devices. IREF and Icopy1 can
vary in large magnitude due to IS mismatch.
CH 9 Cascode Stages and Current Mirrors 46
MOS Current Mirror
The same concept of current mirror can be applied to MOS
transistors as well.
CH 9 Cascode Stages and Current Mirrors 47
Bad MOS Current Mirror Example
This is not a current mirror since the relationship between VX and IREF is not clearly defined.
The only way to clearly define VX with IREF is to use a diode-connected MOS since it provides square-law I-V relationship.
CH 9 Cascode Stages and Current Mirrors 48
Example 9.20 : Current Mirror ?
This circuit is not a current mirror because the gates of MREF
and M1 are floating.
Is this current mirror? Explain what happens.
CH 9 Cascode Stages and Current Mirrors 49
Example 9.21 : Current Scaling
Similar to their bipolar counterpart, MOS current mirrors
can also scale IREF up or down (I1 = 0.2mA, I2 = 0.5mA).
CH 9 Cascode Stages and Current Mirrors 50
CMOS Current Mirror
The idea of combining NMOS and PMOS to produce CMOS
current mirror is shown above.
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