PTATref - Design of PTAT Current Reference Jim Hellums Iin...

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Design of PTAT Current Reference Jim Hellums Q1 Q1 R R Q2 Q2 Q4 Q3 Iin Iin Io Io n n m 1 1 1 (b) (a) The following design equations show why the PTAT circuit (b) on the right above is better than circuit (a) on the left. We start by writing the KVL equation for the standard circuit shown in figure (a). V BE 1 = V BE 2 + I E 2 R (1) where V BE for forward-bias is given by, V BE = V T ln ± I c I s ² (2) with V T = kT/q being the Thermal voltage. Assuming the bipolar transistor’s current gain, β , is large and the same for all transistors, (i.e. I B 0), then I o = I E 2 , so after we do some algebra to solve for the output current, we arrive at the following equations: I o R = V T ³ ln ± I in I s 1 ² - ln ± I o I s 2 ²´ (3) I o = V T R ln ± I in I s 1 · I s 2 I o ² (4) I o = V T R ln ± I in I o · I s 2 I s 1 ² (5) Since the base-emitter diode reverse leakage current I s is a function of the emitter area, and because Q2 has n times the area then I s 2 = nI s 1 . Therefore we can substitute and get I o = V T R ln ± n · I in I o ² (6) 1
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Since eqn (6) is non-linear we will not try to algebraically reduce it any further, but note that I o is a function of I in . Normally a PNP or PMOS current mirror with an 1:1 ratio is used to force I in = I o . This gives a supply-independent, self-biased current reference circuit with the well known design equation.
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This note was uploaded on 09/19/2010 for the course EE 7326 taught by Professor Jimhellums during the Spring '08 term at University of Texas at Dallas, Richardson.

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PTATref - Design of PTAT Current Reference Jim Hellums Iin...

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