# hw1_sol - 3. In order to find the slope of the PWL...

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Unformatted text preview: 3. In order to find the slope of the PWL segments, we first need to find the derivative of the i- v function: i = . 01 v ( 1 + v 3 125 )- 1 2 ⇒ i ( v ) = ∂ i ∂ v = . 01 ( 1 + v 3 125 )- 1 2- 1 2 × . 01 v × 3 v 2 125 × ( 1 + v 3 125 )- 3 2 Since i is on the order of several mA throughout the segment 0V-10V, in the rest of this solution we will express i in mA , and i ( v ) in mA V . a) i ( v = 1 . 5 ) = 14 . 802 , i ( v = 1 . 5 ) = 9 . 479 ⇒ i PW L ( v ) = i ( 1 . 5 )+ i ( 1 . 5 ) × ( v- 1 . 5 ) = 14 . 802 + 9 . 479 ( v- 1 . 5 ) = 9 . 479 v + . 584 The original function and its PWL approximation on the segment 0V-3V are shown in Fig. 3a. Figure 3a. The given i- v function (solid line) and its 1-segment PWL approximation (dashed) Calculating the relative error of this approximation gives the following results: v [ V ] 1 2 3 i [ mA ] 9.96 19.39 27.21 i PW L [ mA ] 0.584 10.06 19.54 29.02 δ [ % ] (see note) 1.00 0.77 6.65 Note: the relative error at v = 0 is large, due to the exact value of...
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## This note was uploaded on 02/21/2010 for the course ECE 442 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw1_sol - 3. In order to find the slope of the PWL...

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