The effect of BJT mismatches can be reduced signifi cantly if we insert suitable resistances in series with the emitters, as shown in Fig. P4.70. Ignoring base currents and applying KVL we get R1II 1...

The effect of BJT mismatches can be reduced signifi cantly if we insert suitable resistances in series with the emitters, as shown in Fig. P4.70. Ignoring base currents and applying KVL we get R1II 1 VBE1 5 R2IO 1 VBE2, that is, R2IO 5 R1II 1 DVBE, where DVBE 5 VBE1 2 VBE2. If we impose R1II @ DVBE, then we get R2IO > R1II , or IO > (R1yR2)II , indicating that the ratio of the currents is established by the resistors. In particular, with equal resistors, we get accurate mirroring regardless of any mismatches between the two BJTs. This technique, particularly popular in the days of unmatched discrete devices, is still used in current ICs so long as the resistors don’t take up too much chip area. As an additional benefi t, emitter degeneration raises the output resistance, resulting in a much fl atter output-port i-v characteristic. If desired, one can add a beta helper to reduce the error even further. (a) Let the BJTs be grossly mismatched such that Is2 5 2Is1. Assuming VA 5 `, VCE2(EOS) 5 0.3 V, and negligible base currents, fi nd IO if II 5 1.0  mA and R1 5 R2 5 0. What is the value of vC2(min), the lower limit of the linear region of operation? (b) Repeat part (a) if R1 5 R2 5 100 V. (c) Repeat (a) if R1 5 R2 5 1.0 kV. (d) Find the values of R1 and R2 (5 R1) that will result in an output current error of 1% or less.