Download Current mirrors

Current mirrors
Current mirrors are important blocks in electronics. They are widely used in
several applications and chips, the operational amplifier being one of them.
Current mirrors consist of two branches that are parallel to each other and
create two approximately equal currents. This is why these circuits are called
current mirrors. These currents are used to load other stages in circuits and
they are designed in such a way so that current is constant and independent
of loading.
Current mirrors come in different varieties:





Simple current mirror (BJT and MOSFET)
Base current corrected simple current mirror
Widlar current source
Wilson current mirror (BJT and MOSFET)
Cascoded current mirror (BJT and MOSFET)
For best performance, transistors should be matched, temperature should be
the same for all devices and collector-base/drain-gate voltages should also be
matched. This will provide equal currents on both sides of the current mirror.
All of the circuits have a compliance voltage which is the minimum output
voltage required to maintain correct circuit operation: the BJT should be in the
active/linear region and the MOSFET should be in the active/saturation
region.
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Simple current mirror
Two implementations exist for the simple current mirror: BJT and MOSFET.
BJT
The BJT implementation of the simple current mirror is used as a block in the
operational amplifier.
VCC
Vo
3.600V
1.472mA
R1
VCC
IREF
Vo
Io
I
2k
3.600V
V1
3.6Vdc
Q1
Q2
1.425mA
23.47uA
23.47uA 655.3mV
Q2N3642
650.0mV
V2
1.425mA
I
0
Q2N3642
-1.449mA
-1.449mA
0.65Vdc
1.425mA
0V
1.472mA
0V
0
0V
0
Simple current mirror (BJT)
1.5mA
1.0mA
0.5mA
0A
-0.5mA
0V
IC(Q2)
50mV
-I(R1)
100mV
150mV
200mV
250mV
300mV
350mV
400mV
450mV
500mV
V_V2
Simple current mirror currents (BJT)
The compliance voltage is roughly given by
Vo (min)  VCE 2( sat )  0.2V
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The collector resistor is given by
R
VCC  VBE1
I REF
The collector current is given by
 VVBE
 V
I C  I S  e T  11  CE


VA





From KCL analysis at the collector of Q1, the reference current is defined as
I REF  I C  2 I B  I C  2

2 

 I C 1 
o
 o 
IC
where βo is the value of β for VCB=0V (Q1 is diode-connected).
The output current is given by
 VVBE
 V
I o  I C  I S  e T  11  CE


VA





When VCB=0V the Early effect is eliminated and it does not affect the
equation. As the value of VCB increases, β values for both transistors no
longer match and the output current is no longer flat but it’s tilted with a slope
of 1/ro.
The output resistance is
R0  r0 
3
V A  VCE
Io
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MOSFET
The MOSFET implementation of the simple current mirror is as follows:
VDD
Vo
3.600V
537.8uA
R1
IREF
VDD
Vo
Io
I
2k
3.600V
V1
3.6Vdc
2.524V
M2
537.8uA
M1
0A
M2N6760
2.500V
V2
537.8uA
0A
M2N6760
2.5Vdc
537.8uA
0V
537.8uA
0V
I
0
0
0V
0
Simple current mirror (MOSFET)
600uA
400uA
200uA
0A
0V
-I(R1)
0.4V
ID(M2)
0.8V
1.2V
1.6V
2.0V
2.4V
2.8V
3.2V
3.6V
V_V2
Simple current mirror currents (MOSFET)
The parameters for the transistors are W=900n, L=90n and VTN=0.25V.
The compliance voltage is roughly given by
Vo (min)  V DS 2( sat )  VGS 2  VTN  2.5V  0.25V  2.25V
Note: the subscript N is added to VT to avoid confusion with the thermal
voltage (VT=25mV).
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The drain resistor is given by
R
V DD  VGS 1
I REF
Both transistors work in the active/saturation region and their drain current is
given by
I D  K n VGS  VTN  1    V DS  VGS  VTN 
2
Since no current enters the gates, reference and output currents match.
When VDS-VGS+VTN=0V the channel-length modulation is eliminated and it
does not have affect the equation. If the value of VDS-VGS+VTN≠0V, the output
current is no longer flat but it’s tilted with a slope of 1/ro.
Currents are related by the following expression:
Io
I REF

W2 / L2
W1 / L1
 1  V DS 2

 1  V DS1



The above relationship says that current in the two branches of the current
mirror depends on the aspect ratio of the two transistors.
The output resistance is
R0  r0 
5
1
I o
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Base current corrected simple current mirror
The currents of the BJT implementation of the simple current mirror are
somewhat dependent on the value of β for both transistors. In order to
minimize this dependency and decrease the error in current matching, a
transistor is added to the original simple current mirror circuit.
VCC
Vo
3.600V
1.194mA
VCC
R1
3.600V
IREF
VCC
2k
Q3
1.211V
913.6nA
Q1
1.193mA
Q2N3642
Vo
Io
I
3.600V
38.73uA
V1
Q2N3642
-39.64uA
650.5mV
19.82uA
1.200V
V2
3.6Vdc
Q2
19.82uA
-1.213mA
1.193mA
1.2Vdc
1.193mA
0V
1.233mA
0V
I
0
Q2N3642
-1.213mA
0
0V
0
Base current corrected simple current mirror
1.2mA
0.8mA
0.4mA
0A
-0.4mA
0V
-I(R1)
50mV
IC(Q2)
100mV
150mV
200mV
250mV
300mV
350mV
400mV
450mV
500mV
V_V2
Base current corrected simple current mirror currents
The compliance voltage is roughly given by
Vo (min)  VCE 2( sat )  0.2V
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The collector resistor is given by
R
VCC  VBE 3  VBE1
I REF
The collector current is given by
 VVBE
 V
I C  I S  e T  11  CE


VA





From KCL analysis at the collector of Q1, the reference current is defined as
I REF  I C1  I B 3  I C 
2I C
V  V BE 3  V BE1
 CC
   1
R
The output current is given by
 VVBE
 V
I o  I C  I S  e T  11  CE


VA





The output resistance is
R0  r0 
V A  VCE
Io
Note: the MOSFET implementation of this circuit does not exist since current
does not enter the gate of a MOSFET.
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Widlar current source
The Widlar current source, a variation of the simple current mirror, was
advanced by Bob Widlar in the mid 1960s. The only difference between the
two circuits is the introduction of an emitter resistor. This additional
component forces the currents in the two branches of the circuit to be unequal
so this is why the circuit is called a source rather than a mirror. This specific
circuit is used as a block in the operational amplifier.
VCC
Vo
3.600V
1.019mA
R1
VCC
IREF
Vo
Io
I
2.9k
3.600V
700.0mV
V1
V2
3.6Vdc
Q1
Q2
992.6uA
Q2N3642
9.188uA
16.88uA 645.9mV
-1.010mA
R2
506.7uA
0.7Vdc
506.7uA
0V
1.019mA
0V
I
0
Q2N3642
515.9uA
-515.9uA
17.54mV
0
34
0V
0
Widlar current source
1.2mA
0.8mA
0.4mA
0A
-0.4mA
0V
-I(R1)
50mV
IC(Q2)
100mV
150mV
200mV
250mV
300mV
350mV
400mV
450mV
500mV
V_V2
Widlar current source currents
Note: the circuit presented here has been designed so that IC1 is twice the
value of IC2.
The compliance voltage is roughly given by
Vo (min)  VCE 2 ( sat )  V R 2  0.2V  I E 2 R2
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The collector resistor is given by
R1 
VCC  V BE1
I REF
The base voltage is defined by
VB  V BE1  V BE 2  I E 2 R2  VBE 2  I o R2
The difference in base-emitter voltages is
VBE1  V BE 2  I o R2
The base-emitter voltages are given by
I
VBE1  VT ln REF
 IS



and
I 
VBE 2  VT ln o 
 IS 
Subtracting base-emitter voltages again,
I
VBE1  VBE 2  VT ln REF
 IS

I 
I
  VT ln o   VT ln REF

 IS 
 Io



so that
I
VBE1  V BE 2  I o R2  VT ln REF
 Io



and the emitter resistor is
R2 
VT  I REF
ln
I o  I o



Note that if the condition IREF=Io is forced, the argument of the logarithm is 1
which produces 0 and therefore a 0Ω resistance (simple current mirror
configuration). This is why reference and output currents do not match.
The output resistance is higher than the one for the simple current mirror:
Ro  ro 1  g m R2 || r 
Note: the MOSFET implementation of the Widlar current source is not used
and if it were, it would behave similarly to the simple current mirrors.
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Wilson current mirror
Two implementations exist for the Wilson current mirror: BJT and MOSFET.
This circuit employs 3 transistors (4 in the improved version). The major
advantages of this circuit over the simple current mirror is that it has a higher
output impedance and strongly reduces the base error of the BJT
implementation.
BJT
The BJT implementation of the Wilson current mirror was invented by George
R. Wilson at Tektronix in 1967.
Ro
VCC
Vo
3.600V
2.266mA
R1
IREF
Io
I
VCC
1k
Q3
35.55uA
1.334V
3.600V
I
Q2
666.9mV
35.07uA
35.07uA
-2.265mA
V2
3.6Vdc
666.9mV
2.230mA
1.400V
V1
Q2N3642
-2.281mA
Q1
Q2N3642
2.245mA
Vo
1.4Vdc
2.245mA
0V
2.266mA
0V
2.210mA
0
0
Q2N3642
-2.246mA
0V
0V
0
Wilson current mirror (BJT)
4.0mA
2.0mA
0A
-2.0mA
-4.0mA
0V
-I(R1)
0.2V
IC(Q3)
0.4V
0.6V
0.8V
1.0V
1.2V
1.4V
1.6V
1.8V
2.0V
V_V2
Wilson current mirror currents (BJT)
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The compliance voltage is roughly given by
Vo (min)  V BE 2  VCE 3( sat )  0.7V  0.2V  0.9V
The output resistance is very high and it’s given by
Ro 
  ro 3
2
An improved version of the above circuit exists. It uses an additional transistor
which improves linearity when higher current levels are needed.
Ro
VCC
Vo
3.600V
2.265mA
R1
I
1k
IREF
Io
1.335V
Q4
2.195mA
Q2N3642
667.9mV
34.84uA
Q3
35.83uA
I
-2.230mA
Q2
-2.265mA
1.400V
V1
Q1
667.1mV
35.35uA
35.35uA
Vo
3.600V
Q2N3642
-2.300mA
2.230mA
Q2N3642
VCC
2.264mA
V2
3.6Vdc
667.1mV
2.230mA
1.4Vdc
2.264mA
0V
2.265mA
0V
Q2N3642
-2.265mA
0V
0
0
0V
0
Improved Wilson current mirror (BJT)
4.0mA
2.0mA
0A
-2.0mA
-4.0mA
0V
-I(R1)
0.2V
IC(Q3)
0.4V
0.6V
0.8V
1.0V
1.2V
1.4V
1.6V
1.8V
2.0V
V_V2
Improved Wilson current mirror currents (BJT)
11
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MOSFET
The MOSFET implementation of the Wilson current mirror looks like the
following:
Ro
VDD
Vo
3.600V
319.5uA
R1
IREF
Io
I
VDD
2k
2.961V
M3
318.8uA
0A
I
3.600V
V1
IRF830
M1
319.5uA
M2
0A
0A
IRF830
IRF830
2.700V
V2
3.6Vdc
1.480V
1.480V
Vo
2.7Vdc
318.8uA
0V
319.5uA
0V
318.8uA
0
0
0V
0V
0
Wilson current mirror (MOSFET)
400uA
300uA
200uA
100uA
0A
0V
-I(R1)
0.4V
ID(M3)
0.8V
1.2V
1.6V
2.0V
2.4V
2.8V
3.2V
3.6V
V_V2
Wilson current mirror currents (MOSFET)
The parameters for the transistors are W=1μ, L=45n and VTN=0.3V.
The compliance voltage is roughly given by
Vo (min)  VGS 2  V DS 3( sat )  VGS 2  VGS 3  VTN   1.5V  1.5V  0.3V  2.7V
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Currents are related by the following expression:
Io
I REF

W2 / L2
W1 / L1
 1  V DS 2

 1  V DS1



The output resistance is very high and it’s given by
Ro  ro 3 2  g m 3 ro1 
An improved version of the above circuit exists. It uses an additional transistor
which improves overall match in the two branches.
Ro
VDD
Vo
3.600V
319.0uA
R1
I
IREF
Io
2k
VDD
2.962V
M4
319.0uA
M3
319.0uA
0A
0A
I
IRF830
IRF830
1.481V
M1
319.0uA
0A
IRF830
3.600V
V1
M2
V2
2.7Vdc
319.0uA
0V
319.0uA
0V
319.0uA
0
0A
IRF830
2.700V
3.6Vdc
1.481V
1.481V
Vo
0
0V
0V
0
Improved Wilson current mirror (MOSFET)
400uA
300uA
200uA
100uA
0A
0V
-I(R1)
0.4V
ID(M3)
0.8V
1.2V
1.6V
2.0V
2.4V
2.8V
3.2V
3.6V
V_V2
Improved Wilson current mirror currents (MOSFET)
13
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Cascoded current mirror
The cascoded current mirror resembles a stack of two simple current mirrors
and it looks very much like the improved version of the Wilson current mirror
(with a diode connection at Q1/M1 instead of Q2/M2). Therefore, this circuit is
made up by 4 transistors. The major advantages over the simple current
mirror is that this circuit has a higher output impedance and it eliminates Early
effect with the MOSFET implementation.
BJT
The BJT implementation of the cascoded current mirror is as follows:
Ro
VCC
Vo
3.600V
2.267mA
R1
I
1k
IREF
Io
1.333V
Q4
2.198mA
Q2N3642
Q3
2.131mA
33.87uA
VCC
3.600V
Q2N3642
-2.164mA
-2.233mA
Q2N3642
Q1
2.164mA
Q2
666.3mV
34.40uA
34.40uA
-2.199mA
1.400V
V1
667.2mV
666.3mV
Vo
I
34.89uA
V2
3.6Vdc
2.164mA
1.4Vdc
2.131mA
0V
2.267mA
0V
Q2N3642
-2.199mA
0V
0
0
0V
0
Cascoded current mirror (BJT)
4.0mA
2.0mA
0A
-2.0mA
-4.0mA
0V
-I(R1)
0.2V
IC(Q3)
0.4V
0.6V
0.8V
1.0V
1.2V
1.4V
1.6V
1.8V
2.0V
V_V2
Cascoded current mirror currents (BJT)
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The compliance voltage is roughly given by
Vo (min)  VBE 2  V BE 4  V BE 3  VCE 3( sat )  VBE 2  VCE 3( sat )  0.7V  0.2V  0.9V
Note: VBE4 and VBE3 cancel each other so the base and collector voltages of
Q2 are the same.
The collector resistor is given by
R
VCC  VBE 4  V BE1
I REF
The output resistance is very high and it’s given by
Ro 
15
  ro 3
2
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MOSFET
The MOSFET implementation of the cascoded current mirror is as follows:
Ro
VDD
Vo
3.600V
231.1uA
R1
I
1k
IREF
Io
3.369V
M4
231.1uA
M3
0A
230.9uA
IRFJ132
VDD
3.600V
IRFJ132
1.685V
V1
1.609V
M1
231.1uA
0A
M2
1.685V
IRFJ132
2.700V
V2
3.6Vdc
230.9uA
2.7Vdc
230.9uA
0V
231.1uA
0V
0A
IRFJ132
Vo
I
0A
0
0
0V
0V
0
Cascoded current mirror (MOSFET)
300uA
200uA
100uA
0A
0V
-I(R1)
0.4V
ID(M3)
0.8V
1.2V
1.6V
2.0V
2.4V
2.8V
3.2V
3.6V
V_V2
Cascoded current mirror currents (MOSFET)
The parameters for the transistors are W=450n, L=45n and VTN=0.2V.
The compliance voltage is roughly given by
Vo (min)  VGS 2  VGS 4  VGS 3  V DS 3( sat )  VGS 2  VDS 3( sat )  VGS 2  VGS 3  VTN
 2VGS  VTN  2  1.6V  0.2V  3.0V
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Note: the compliance voltage appears to be a little lower (around 2.4V).
The drain resistor is given by
R
V DD  VGS 4  VGS 1
I REF
Currents in each branch are related by the following expression:
Io
I REF

W 2 / L2
W1 / L1
Note: the channel-length modulation factor is not present here since for this
circuit there is no Early effect.
The output resistance is very high and it’s given by
Ro  ro 2  ro 3 1  g m 3 ro 2 
17
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