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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. 1 www.ice77.net 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 0V 0 Simple current mirror (BJT) 1.5mA 1.0mA 0.5mA 0A -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 2 www.ice77.net 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 11 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 11 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 3 www.ice77.net 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 0V 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). 4 www.ice77.net 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 5 www.ice77.net 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 0V 0 Base current corrected simple current mirror 1.2mA 0.8mA 0.4mA 0A -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 6 www.ice77.net 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 11 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 11 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. 7 www.ice77.net 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 34 0V 0 Widlar current source 1.2mA 0.8mA 0.4mA 0A -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 8 www.ice77.net 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. 9 www.ice77.net 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 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 0V 0 Wilson current mirror (BJT) 4.0mA 2.0mA 0A -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) 10 www.ice77.net 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.
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