chapter 16 - Chapter 16: Filter Circuits Exercises Ex....

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 16: Filter Circuits Exercises Ex. 16.3-1 1 () 1 1 1250 1250 1250 1 1250 n n Ts s s T s s = +  == =  +  + Problems Se ction 16.3: Filters P16.3-1 Equation 16-3.2 and Table 16-3.2 provide a third-order Butterworth low-pass filter having a cutoff frequency equal to 1 rad/s. 2 1 (1 ) ( 1 ) n Hs ss s = + ++ Frequency scaling so that c = 2 100=628 rad/s ω π : 3 22 2 2 1 628 247673152 ( 628)( 628 628 ) ( 628)( 628 394384) 11 628 628 628 L sss s === + + + P16.3-2 Equation 16-3.2 and Table 16-3.2 provide a third-order Butterworth low-pass filter having a cutoff frequency equal to 1 rad/s and a dc gain equal to 1. 2 1 ) ( 1 n s = ) + Multiplying by 5 to change the dc gain to 5 and frequency scaling to change the cutoff frequency to ω c = 100 rad/s: 3 2 2 5 5100 5000000 ( 100)( 100 100 ) ( 100)( 100 10000) 1 1 100 100 100 L s = + + + 16-1
Background image of page 1

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

View Full DocumentRight Arrow Icon
P16.3-3 Use Table 16-3.2 to obtain the transfer function of a third-order Butterworth high-pass filter having a cutoff frequency equal to 1 rad/s and a dc gain equal to 5. 3 2 5 () (1 ) ( 1 ) n s Hs ss s = + ++ Frequency scaling to change the cutoff frequency to c 100 rad/s ω = 3 33 22 2 2 5 55 100 ( 100)( 100 100 ) ( 100)( 100 10000) 1 1 100 100 100 H s sss s   ⋅⋅  == = + + + P16.3-4 Use Table 16-3.2 to obtain the transfer function of a fourth-order Butterworth high-pass filter having a cutoff frequency equal to 1 rad/s and a dc gain equal to 5. 4 5 0.765 1 1.848 1 s n = + ++ + Frequency scaling can be used to adjust the cutoff frequency 500 hertz = 3142 rad/s: 4 4 5 3142 0.765 1 1.848 1 3142 3142 3142 3142 5 2403.6 3142 5806.4 3142 H s s ss ss =  +++   = + 16-2
Background image of page 2
P16.3-5 First, obtain the transfer function of a second-order Butterworth low-pass filter having a dc gain equal to 2 and a cutoff frequency equal to 2000 rad/s: () 2 2 2 8000000 2828 4000000 1.414 1 2000 2000 L Hs ss == ++    Next, obtain the transfer function of a second-order Butterworth high-pass filter having a passband gain equal to 2 and a cutoff frequency equal to 100 rad/s: 2 2 2 2 2 2 100 141.4 10000 1.414 1 100 100 H s s Finally, the transfer function of the bandpass filter is () () () ( ) 2 22 16000000 141.4 10000 2828 4000000 BL s HsH s H =⋅ = P16.3-6 2 2 2 2 250 250000 1 4 250 250 62500 250 1 B s s P16.3-7 First, obtain the transfer function of a second-order Butterworth high-pass filter having a dc gain equal to 2 and a cutoff frequency equal to 2000 rad/s: 2 2 2 2 2 2 2000 2828 4000000 1.414 1 2000 2000 L s s Next, obtain the transfer function of a second-order Butterworth low-pass filter having a pass- band gain equal to 2 and a cutoff frequency equal to 100 rad/s: 16-3
Background image of page 3

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

View Full DocumentRight Arrow Icon
() 2 2 2 20000 141.4 10000 1.414 1 100 100 H Hs ss == ++    Finally, the transfer function of the band-stop filter is () () () ( ) ( ) ( ) 22 2 43 2 1 0 2 141.4 10000 20000 2828 4000000 141.4 10000 2828 4000000 2 282.8 40000 56560000 810 141.4 10000 2828 4000000 NLH s s s Hs HsHs ss ss ss s s ++ + =+ = + = P16.3-8 2 2 2 2 2 250 4 62500 1 44 250 250 62500 250 1 N s s + =− = P16.3-9 2 24 2 250 4 250 4 250 2 250 250 62500 1 L P16.3-10 2 2 2 4 4 250 250 62500 250 1 H 16-4
Background image of page 4
Section 16.4: Second-Order Filters P16.4-1 The transfer function is () 0 2 1 s Vs RC Ts s s s R CL C == ++ so 2 0 00 11 1 , and C KQ LC RC Q L ω ωω = R C R 2 0 1 Pick 1 F. Then 1 H and 1000 L R Q CC µ = = = P16.4-2 The transfer function is 0 2 1 1 s Is LC s s R C so 2 0 1 , and C LC RC Q L = R C R 2 0 1 Pick 1 F then 25 H and 3535 L R Q = = = 16-5
Background image of page 5

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

View Full DocumentRight Arrow Icon
P16.4-3 The transfer function is 2 1 2 22 1 1 () 11 2
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/10/2011 for the course PHYSICS physics taught by Professor Physics during the Spring '11 term at HKU.

Page1 / 36

chapter 16 - Chapter 16: Filter Circuits Exercises Ex....

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online