Calculate the effective transconductance gm as the ratio


Response to the following problem:

This problem explores the linearization of the transfer characteristics of the differential pair achieved by including emitter-degeneration resistances Re in the emitters (see Fig.). Consider the case I = 200 μA with the transistors exhibiting Vbe = 690 mV at iC = 1 mA and assume α ?1.

(a) With no emitter resistances Re, what value of VBE res lts when vid = 0?

(b) With no emitter resistances Re, use the large-signal model to find iC1 and iC2 when vid = 20 mV.

(c) Nowfind the value of Re that will result in the same iC1 and iC2 as in (b) but with vid = 200 mV. Use the large-signal model.

(d) Calculate the effective transconductance Gm as the ratio of the difference current, (iC1 - iC2), to vid in the cases without and with the Re's. By what factor is Gm reduced? How does this factor relate to the increase in vid? Comment.

2151_the emitters.jpg

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Electrical Engineering: Calculate the effective transconductance gm as the ratio
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