Lesson+23 - Lesson 23 Challenge 22 Classic Analog Filter...

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Challenge 22 Classic Analog Filter Design using MATLAB (Off Book) Challenge 23 Review Exam #2 now on-line HKN will be having a review session Monday March 17 at 7:20 in Larson 239. Lesson 23 Lesson 23 1 Lesson 23
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Challenge 22 What is the active filter’s “Q”? H(s) = - K B s/(s 2 + B s+ 0 2 ) (Standard form: B =bandwidth) 2 Lesson 23 Given a bandpass filter :
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H(s)= -Z f / Z i Z f = (1/sC 2 )||R 2 =(1/C 2 )/(s+(1/R 2 C 2 ) Z i = R 1 +(1/sC 1 )=(sR 1 C 1 +1)/(sC 1 ) H(s)= = ( - (1/R 1 C 2 )s)/(s+1/R 1 C 1 )(s+1/R 2 C 2 ) = - 250s/(s 2 +70s+1000) = - 3.57(70s)/(s 2 +70s+ 1000) 2 ) = - K B s/(s 2 + B s+ w 0 2 ) (Standard form) w 0 = resonate frequency = 1000) = 31.6 r/s, K =gain constant = -3.57, B =bandwidth = 70 r/s 3 Lesson 23
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H(s)= -3.57(70s)/(s 2 +70s+( 1000) 2 = - K B s/(s 2 + B s+ 0 2 ) 0 = resonate frequency = 1000 = 31.6 r/s K =gain constant = -3.57, B =bandwidth = 70 r/s Q= 0 /B = 0.45 ~ 0.5 Verification (textbook): s r BW s r s r B B / ; / ~ ; / ~ ~ , 70 82 12 47 35 2 2 2 1 2 0 2 2 1 ω ω ω ω 4 Lesson 23
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Product Alert AD9737A: 11-bit 2.5GSa/s, RF digital to analog converter The AD9739A is a 14-bit, high performance RF DAC s that are capable of synthesizing wideband signals from DC up to 3 GHz. Accepts digital input Sets the bandwidth requirements at the analog/digital boundary of the RF transmitter. Power Amps 5 Lesson 23
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How  do you design a filter that meets posted specifications?   Machines 6 Lesson 23
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After You Design, You Test 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 -5 -1 -0.5 0 0.5 1 X: 1.591e-005 Y: 0.9941 Time Amplitude X: 1.818e-005 Y: 1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 -5 -1 -0.5 0 0.5 1 X: 1.818e-005 Y: 1 Time Amplitude X: 1.591e-005 Y: 0.2016 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 -5 -1 -0.5 0 0.5 1 X: 1.818e-005 Y: 1 Time Amplitude X: 1.591e-005 Y: 0.04126 Input Output 3 /2 /2 7 Lesson 23 Passband Transition band Stopband
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Classic Analog Filters Digital Equivalents are called Infinite Impulse Response (IIR) Filters Classic analog filters generally posses feedback paths. Filters with feedback can be very frequency selective. Due to feedback, however, filters with feedback can exhibit instability, high internal gains, and require large to small electrical parameters. 8 Lesson 23
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Transfer function (proper) Frequency response ) ( ) ( ) p - (s ) z (s = ) ( i 1 N 0 i i 1 N 0 i 0 = 0 0 s D s N s a s b s h s H k N k k k N k k k k k ) (j ) (j j j = ) j (s 1 0 1 0 0 0 i j N i i j N i N i i i N i i i p z a b H ω ω ω ω ω 9 Lesson 23
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History: 1920’s – radio engineering Bessel, Butterworth, Chebyshev I Chebyshev II, and Cauer (Elliptic) Analog filter response. 10 Lesson 23
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Specifications Analog Prototype H P (s) -1, -3 dB, =1 r/s Tables or graphs Realized Analog Filter H(s) Transform Classical design strategy 11 Lesson 23
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Prototype 12 Lesson 23 -3dB @ 1 r/s
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13 Lesson 23
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Example – 1 st derive a prototype filter ( p =1 r/s) Next convert the prototype into a desired filter response.
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