bjtmirr - c Copyright 2008 W Marshall Leach Jr Professor...

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c ° Copyright 2008. W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical and Computer Engineering. Current Mirrors Basic BJT Current Mirror Current mirrors are basic building blocks of analog design. Fig. 1 shows the basic npn current mirror. For its analysis, we assume identical transistors and neglect the Early e f ect, i.e. we assume V A →∞ . This makes the saturation current I S and current gain β independent of the collector- base voltage V CE . The input current to the mirror is labeled I REF . This current might come from a resistor connected to the positive rail or a current source realized with a transistor or another current mirror. The emitters of the two transistors are shown connected to ground. These can be connected to a dc voltage, e.g. the negative supply rail. Figure 1: Basic current mirror. The simplest way to solve for the output current is to sum the currents at the node where I REF enters the mirror. Because the two transistors have their base-emitter junctions in parallel, it follows that both must have the same currents. Thus, we can write the equation I REF = I O + 2 I O β Solution for I O yields I O = I REF 1+2 Note that this equation predicts that I O <I REF unless β →∞ . Because the Early e f ect has been neglected in solving for I O , the output resistance is in f nite. If we include the Early e f ect and assume that it has negligible e f ect in the solution for I O , the output resistance is given by r out = r 02 = V A + V CE 2 I O For a more accurate analysis, we can include the Early e f ect in calculating the output current. Consider the circuit if Fig. 2. If the transistors have the same parameters, we can write I C 1 = I S 0 exp μ V BE V T I B 1 = I C 1 β 0 I O = I S 0 μ 1+ V CB 2 V A exp μ V BE V T I B 2 = I O β 0 (1 + V CB 2 /V A ) 1
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By taking the ratio of I O to I C 1 ,weobta in I O = μ 1+ V CB 2 V A I C 1 Note that the voltage V CB is used for the Early e f ect, not the voltage V CE .Th isagreesw iththe Ebers-Moll model for the BJT that is used in SPICE. In deriving the small-signal π and T models, the derivations are simpli f ed by the use of V CE .Thu s V CE is used in most contemporary texts for the Early e f ect. The correct value is
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bjtmirr - c Copyright 2008 W Marshall Leach Jr Professor...

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