{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw8_solutions

# hw8_solutions - Homework 8 Solutions ECE 2B Winter 2011...

This preview shows pages 1–4. Sign up to view the full content.

Homework 8 Solutions ECE 2B Winter 2011 H.O. #26 Problem 9.26 For the circuit shown in Fig. P9.26: (a) Obtain an expression for H ( ! ) = V o / V i in standard form. (b) Generate spectral plots for the magnitude and phase of H ( ! ) , given that R 1 = 1 " , R 2 = 2 " , L 1 = 1 mH, and L 2 = 2 mH. (c) Determine the cutoff frequency ! c and the slope of the magnitude (in dB) when ! / ! c 1 and when ! / ! c 1. L 2 L 1 R 1 R 2 + _ V i + _ V o V 1 Figure P9.26: Circuit for Problem 9.26. Solution: (a) At node V 1 , KCL gives: V 1 - V i R 1 + V 1 j ! L 1 + V 1 R 2 + j ! L 2 = 0 . Also, voltage division gives V o = R 2 V 1 R 2 + j ! L 2 . Solution is H ( ! ) = V o V i = j ! L 1 R 2 ( R 1 + j ! L 1 )( R 2 + j ! L 2 )+ j ! L 1 R 1 . To express denominator in standard form, we factor out R 1 R 2 and expand terms: H ( ! ) = j ! L 1 / R 1 1 + j ! L 1 R 1 1 + j ! L 2 R 2 + j ! L 1 R 2 = j ! L 1 / R 1 1 + j ! L 1 R 1 + L 2 R 2 + L 1 R 2 + j ! L 1 L 2 R 1 R 2 2 = j ! K 1 + j 2 #! / ! c +( j ! / ! c ) 2 , where K = L 1 R 1 , ! c = R 1 R 2 L 1 L 2 , # = ! c 2 L 1 R 1 + L 2 R 2 + L 1 R 2 . (b) For R 1 = 1 " , R 2 = 2 " , L 1 = 1 mH, and L 2 = 2 mH, K = 10 - 3 , ! c = 10 3 rad/s , # = 1 . 25 . All rights reserved. Do not reproduce or distribute. ©2009 National Technology and Science Press

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Hence, H ( ! ) = j × 10 - 3 ! 1 + j 2 . 5 ! / ! c +( j ! / ! c ) 2 , with ! c = 10 3 rad/s. M [ dB ] = 20log | H ( ! ) | Spectral plots of M [dB] are " ( ! ) are shown in Figs. P9.26(a) and (b). 10 1 10 2 10 3 10 4 10 5 10 6 - 80 - 60 - 40 - 20 0 ω M (dB) 10 1 10 2 10 3 10 4 10 5 10 6 - 100 0 100 ω Figures P9.26(a) and (b) ϕ (deg) (c) Low-frequency asymptote ( ! / ! c 1): H ( ! ) j 10 - 3 ! = M [ dB ] has slope of + 20 dB/decade . High-frequency asymptote ( ! / ! c 1): H ( ! ) - j 10 - 3 ! 2 c ! = - j 10 3 ! = M [ dB ] has slope of - 20 dB/decade . All rights reserved. Do not reproduce or distribute. ©2009 National Technology and Science Press
Problem 9.33 For the op-amp circuit of Fig. P9.33: (a) Obtain an expression for H ( ! ) = V o / V i in standard form. (b) Generate spectral plots for the magnitude and phase of H ( ! ) , given that R 1 = R 2 = 100 " , C 1 = 10 μ F, and C 2 = 0 . 4 μ F.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

hw8_solutions - Homework 8 Solutions ECE 2B Winter 2011...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online