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 Vo IREF Io I 2k 3.600V 650.0mV

V1 V2

Q1 3.6Vdc 0.65Vdc 1.425mA Q2 1.425mA 1.425mA 1.472mA 0V 23.47uA 0V I 23.47uA 655.3mV Q2N3642 Q2N3642 0 0 -1.449mA -1.449mA

0 Simple current mirror (BJT)

1.5mA

1.0mA

0.5mA

-0.5mA 0V 50mV 100mV 150mV 200mV 250mV 300mV 350mV 400mV 450mV 500mV IC(Q2) -I(R1) 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

V V R  CC BE1 I REF

The collector current is given by

V  BE  V  I  I e VT 11 CE  C S   V    A 

From KCL analysis at the collector of Q1, the reference current is defined as

I  2  C   I REF  I C  2I B  I C  2  I C 1   o   o  where βo is the value of β for VCB=0V (Q1 is diode-connected).

The output current is given by

V  BE  V  I  I  I e VT 11 CE  o C S   V    A 

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

VA VCE R0  r0  I o

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MOSFET

The MOSFET implementation of the simple current mirror is as follows:

VDD Vo

3.600V 537.8uA

R1 VDD Vo IREF Io I 2k 3.600V 2.500V

V1 V2

3.6Vdc 2.5Vdc 2.524V 537.8uA 537.8uAM1 M2 537.8uA 537.8uA 0V 0V I 0A 0A M2N6760 M2N6760 0 0

0 Simple current mirror (MOSFET)

600uA

400uA

200uA

0A 0V 0.4V 0.8V 1.2V 1.6V 2.0V 2.4V 2.8V 3.2V 3.6V -I(R1) ID(M2) 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)  VDS 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

V V R  DD GS1 I REF

Both transistors work in the active/saturation region and their drain current is given by

2 I D  K n VGS VTN 1   VDS  VGS VTN 

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:

I o W2 / L2 1 VDS 2     I REF W1 / L1  1 VDS1 

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

1 R0  r0  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 VCC Vo IREF Io I 2k 3.600V 1.200V Q3 38.73uA 1.211V V1 V2 913.6nA Q2N3642 Q1 -39.64uA 3.6Vdc 1.2Vdc 650.5mV 1.193mA Q2 1.193mA 1.193mA 1.233mA 0V 0V I 19.82uA 19.82uA Q2N3642 Q2N3642 0 0 -1.213mA -1.213mA

0 Base current corrected simple current mirror

1.2mA

0.8mA

0.4mA

-0.4mA 0V 50mV 100mV 150mV 200mV 250mV 300mV 350mV 400mV 450mV 500mV -I(R1) IC(Q2) 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

V V V R  CC BE3 BE1 I REF

The collector current is given by

V  BE  V  I  I e VT 11 CE  C S   V    A 

From KCL analysis at the collector of Q1, the reference current is defined as

2I V V V I  I  I  I  C  CC BE3 BE1 REF C1 B3 C   1 R

The output current is given by

V  BE  V  I  I  I e VT 11 CE  o C S   V    A 

The output resistance is

VA VCE R0  r0  I o

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 Vo IREF Io I 2.9k 3.600V 700.0mV

V1 V2

Q1 3.6Vdc 0.7Vdc 506.7uA Q2 992.6uA 506.7uA 1.019mA 0V 9.188uA 0V I 16.88uA 645.9mV Q2N3642 Q2N3642 0 0 -1.010mA 515.9uA-515.9uA 17.54mV R2

0 Widlar current source

1.2mA

0.8mA

0.4mA

-0.4mA 0V 50mV 100mV 150mV 200mV 250mV 300mV 350mV 400mV 450mV 500mV -I(R1) IC(Q2) 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) VR2  0.2V  I E2 R2

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The collector resistor is given by

VCC VBE1 R1  I REF

The base voltage is defined by

VB  VBE1  VBE2  I E2 R2  VBE 2  I o R2

The difference in base-emitter voltages is

VBE1 VBE2  I o R2

The base-emitter voltages are given by

 I   I   REF  and  o  VBE1  VT ln  VBE 2  VT ln   I S   I S 

Subtracting base-emitter voltages again,

 I   I   I   REF   o   REF  VBE1 VBE 2  VT ln  VT ln   VT ln   I S   I S   I o  so that

 I   REF  VBE1 VBE 2  I o R2  VT ln   I o  and the emitter resistor is

V  I  T  REF  R2  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.

VCC Vo

3.600V 2.266mA

R1 IREF Io I VCC Vo 1k

Q3 2.245mA 3.600V 1.400V 35.55uA I 1.334V V1 V2 Q2N3642 -2.281mA 3.6Vdc 1.4Vdc Q1 666.9mV 2.245mA 2.266mA 0V Q2 2.230mA 2.210mA 0V 666.9mV 35.07uA 35.07uA 0 0 Q2N3642 Q2N3642 -2.265mA -2.246mA 0V

0 Wilson current mirror (BJT)

4.0mA

2.0mA

-2.0mA

-4.0mA 0V 0.2V 0.4V 0.6V 0.8V 1.0V 1.2V 1.4V 1.6V 1.8V 2.0V -I(R1) IC(Q3) V_V2 Wilson current mirror currents (BJT)

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The compliance voltage is roughly given by

Vo(min)  VBE 2 VCE3(sat)  0.7V  0.2V  0.9V

The output resistance is very high and it’s given by

  r R  o3 o 2

An improved version of the above circuit exists. It uses an additional transistor which improves linearity when higher current levels are needed.

VCC Vo

3.600V 2.265mA

R1 I IREF 1k

Io 1.335V Q4 VCC Vo Q3 2.195mA 2.264mA 35.83uA I 34.84uA 3.600V 1.400V Q2N3642 Q2N3642 -2.230mA -2.300mA V1 V2

667.9mV Q1 3.6Vdc 1.4Vdc Q2 2.230mA 667.1mV2.230mA 2.264mA 667.1mV 2.265mA 0V 35.35uA 35.35uA 0V Q2N3642 Q2N3642 -2.265mA -2.265mA 0 0 0V

0 Improved Wilson current mirror (BJT)

4.0mA

2.0mA

-2.0mA

-4.0mA 0V 0.2V 0.4V 0.6V 0.8V 1.0V 1.2V 1.4V 1.6V 1.8V 2.0V -I(R1) IC(Q3) V_V2 Improved Wilson current mirror currents (BJT)

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MOSFET

The MOSFET implementation of the Wilson current mirror looks like the following:

VDD Vo

3.600V 319.5uA

R1 IREF Io I VDD Vo 2k

M3 318.8uA 3.600V 2.700V I 2.961V 0A V1 V2

IRF830 3.6Vdc 2.7Vdc 1.480V 318.8uA M1 319.5uA 0V 319.5uA M2 318.8uA 0V 1.480V 0A 0A 0 0

IRF830 IRF830 0V

0 Wilson current mirror (MOSFET)

400uA

300uA

200uA

100uA

0A 0V 0.4V 0.8V 1.2V 1.6V 2.0V 2.4V 2.8V 3.2V 3.6V -I(R1) ID(M3) 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 VDS3(sat)  VGS 2  VGS3 VTN   1.5V 1.5V  0.3V  2.7V

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Currents are related by the following expression:

I o W2 / L2 1 VDS 2     I REF W1 / L1  1 VDS1 

The output resistance is very high and it’s given by

Ro  ro3 2  g m3ro1 

An improved version of the above circuit exists. It uses an additional transistor which improves overall match in the two branches.

VDD Vo

3.600V319.0uA

IREF I Io 2k

VDD Vo 2.962V M4 319.0uA M3 319.0uA 3.600V 2.700V I 0A 0A V1 V2

IRF830 IRF830 3.6Vdc 2.7Vdc 1.481V 1.481V 319.0uA M1 319.0uA 0V 319.0uA M2 319.0uA 0V 1.481V 0A 0A 0 0

IRF830 IRF830 0V

0 Improved Wilson current mirror (MOSFET)

400uA

300uA

200uA

100uA

0A 0V 0.4V 0.8V 1.2V 1.6V 2.0V 2.4V 2.8V 3.2V 3.6V -I(R1) ID(M3) V_V2 Improved Wilson current mirror currents (MOSFET)

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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:

VCC Vo

3.600V 2.267mA

R1 I IREF 1k Io

1.333V Q4 2.131mA Q3 2.198mA VCC Vo 33.87uA I 34.89uA Q2N3642 Q2N3642 3.600V 1.400V -2.233mA -2.164mA V1 V2 667.2mV 666.3mV Q1 3.6Vdc 1.4Vdc Q2 2.164mA 2.164mA 2.131mA 666.3mV 2.267mA 0V 34.40uA 34.40uA 0V Q2N3642 Q2N3642 -2.199mA -2.199mA 0 0 0V

0 Cascoded current mirror (BJT)

4.0mA

2.0mA

-2.0mA

-4.0mA 0V 0.2V 0.4V 0.6V 0.8V 1.0V 1.2V 1.4V 1.6V 1.8V 2.0V -I(R1) IC(Q3) V_V2 Cascoded current mirror currents (BJT)

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The compliance voltage is roughly given by

Vo(min)  VBE 2 VBE4 VBE3 VCE3(sat)  VBE 2 VCE3(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

V V V R  CC BE 4 BE1 I REF

The output resistance is very high and it’s given by

  r R  o3 o 2

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MOSFET

The MOSFET implementation of the cascoded current mirror is as follows:

VDD Vo

3.600V 231.1uA

R1 I IREF 1k Io

3.369V

M4 M3 231.1uA 230.9uA VDD Vo I 0A 0A 3.600V 2.700V IRFJ132 IRFJ132 V1 V2 1.685V 1.609V

M1 M2 3.6Vdc 2.7Vdc 231.1uA 230.9uA 230.9uA 1.685V 231.1uA 0V 0A 0A 0V

IRFJ132 IRFJ132 0 0 0V

0 Cascoded current mirror (MOSFET)

300uA

200uA

100uA

0A 0V 0.4V 0.8V 1.2V 1.6V 2.0V 2.4V 2.8V 3.2V 3.6V -I(R1) ID(M3) 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 VGS3 VDS3(sat)  VGS 2 VDS 3(sat)  VGS 2 VGS3 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

V V V R  DD GS 4 GS1 I REF

Currents in each branch are related by the following expression:

I W / L o  2 2 I REF 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  ro2  ro3 1 g m3ro2 

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