Discussion 8 Current Mirrors 1. Motivation Typical biasing schemes introduced in Chapters 4 and 5 fail to establish a constant collector current if the supply voltage or temperature is subject to change. Although highly undesirable, these are unavoidable effects in transistor operating conditions. So how could we supply a constant current while avoiding supply and temperature dependence? The answer is using current mirrors. 2. Bipolar Current Mirror Assume that there is a “golden current”, IREF , that is essentially independent of external conditions. Our goal is to produce Icopy that has same characteristics as IREF. In short, the black box could be realized as shown below. Neglecting the base currents for now, note that QREF(diode-connected) and Q1 have equal VBE. Therefore, IREF = IS, REF exp(VVT) Icopy = IS, 1 exp(VVT) and hence, Icopy = IIS,S,REF I REF If QREF and Q1 are identical(IS,REF and IS,1), Icopy=IREF. Note that this holds true even though VT and IS vary with temperature. Example) Explain why the following circuits are bad current mirrors.Example) Find the expression for Icopy in terms of IREF. 3. Effect of Base Current Thus far, we have neglected the base current at node X by all transistors, an effect leading to a significant error as the number of copies increases. This error is due to a fraction of IREF that through the base rather than the collector of QREF. Let us analyze the error with the following diagram. For a large β and moderate n, the second term in the denominator is negligible and Icopy ≈ nIREF. However, as the number of copied current(n) increases, so does the error in Icopy. Let us try to suppress the error by introducing an emitter follower QF that is interposed between the collector of QREF and node X. Note that we have assumed IC,F ≈ IE,F. Now, we have reduced the effect of the base current by a factor of β. In other words, emitter follower allows room for more copied currents.Example) [HW 7, Problem 1] Find the expression for Icopy in terms of
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