EE40 Lec 12 Transfer Function Function Bode Plots Plots Filters Prof Nathan Cheung 10 08 2009 Reading Hambley Chapter 6 1 6 5 EE40 Fall 2009 Slide 1 Prof Cheung OUTLINE Fourier Analysis Concept Transfer Function dB scale First Order Low Pass and High Pass Filters Bode Plots Log magnitude vs log frequency plot Linear Phase vs log frequency plot Asymptotic Frequency Behavior EE40 Fall 2009 Slide 2 Prof Cheung Fourier Synthesis of Waveforms Any waveform can be constructed by adding sinusoids that have the proper amplitudes f frequencies i and d phase h Example p Fourier Components p of A Square q Wave EE40 Fall 2009 Slide 3 Prof Cheung Transfer Function Transfer function is a function of frequency A complex quantity Both magnitude and phase are function of frequency Vin Two Port filter network Vout Vout Vout H f out in Vin Vin H f H f EE40 Fall 2009 Slide 4 Prof Cheung Example Response of a Two Frequency Signal H f1 H f2 i generall in EE40 Fall 2009 Slide 5 Prof Cheung Cascade of Two Port Networks H f H 1 f H 2 f EE40 Fall 2009 Slide 6 Prof Cheung Origin of Decibel dB unit The bel abbreviated B is named after Alexander Graham Bell who did much pioneering work with sound and the way o r ears respond to sound our so nd Our O r ears respond to sounds ranging from an intensity less than 10 16 W cm2 to intensities larger than 10 4 W cm2 where we begin to experience pain This is a range of more than 1x1012 times from the softest to the loudest sounds Logarithm provide a convenient way to represent these values because they compress this scale into a range of 12 rather than a range of a billion A bel is defined as the logarithm of a power ratio It gives us a way to compare power l l with levels i h eachh other h andd with i h some reference power EE40 Fall 2009 Slide 7 Prof Cheung The Decibel dB Unit A bel symbol B is a unit of measure of ratios of power levels B log10 P1 P2 where P1 and P2 are power levels one bel corresponds to a ratio of 10 1 10dB Log10 sscale The bel is too large for everyday use so the decibel dB equal to 0 1B is more commonlyy used 1dB 10 log10 P1 P2 1B dB are used to measure Electric power Gain or loss of amplifiers transmission loss of optical fibers EE40 Fall 2009 Slide 8 Prof Cheung Decibel Exercise Exercise Express a power of 50 mW in decibels relative to 1 watt 10 llog10 50 x 10 33 13 dB Exercise Express a power of 100 mW in decibels relative to 2 mW 10 log g10 50 17 dB dBm to express absolute values of power relative to a milliwatt dBm 10 log10 power in milliwatts 1 milliwatt 100 mW 20 dBm 10 mW 10 dBm EE40 Fall 2009 Slide 9 Prof Cheung Decibel dB as voltage or current ratios 2 2 V1 V1 10 log 20 log V2 V2 20dB 2 I1 I1 10 log 20 log I2 I2 1B Vo or I log10 sca ale P V I 2 Note 1 Bel of voltage yields 2 Bels of Power EE40 Fall 2009 Slide 10 Prof Cheung Some useful dB values to memorize H f 100 10 1 0 1 0 01 0 01 2 H f dB 40 20 0 20 40 40 6 3 3 14 20 6 2 1 2 5 10 2 EE40 Fall 2009 Slide 11 Prof Cheung Bode Plots A Bode plot is a straight line approximation of H Plot of transfer function magnitude vs frequency y axis i iis th the 20 20 log l off th the magnitude it d off th the ttransfer f function in dB and x axis is x axis axis is or f in log scale dB log f or log EE40 Fall 2009 Slide 12 Prof Cheung Bode Plots Plot of transfer function phase vs frequency y axis is the phase of transfer function in degrees li linear scale l x axis is or f in log scale degrees log f or log EE40 Fall 2009 Slide 13 Prof Cheung Decade Octave and Log Scale Log10 scale How about the Log axis Shifted by Log10 2 2 or 0 798 0 798 2 f rad sec Note Log g x y y Log g x Log g y EE40 Fall 2009 Slide 14 Prof Cheung Frequency Response The shape of the frequency response of the complex ratio of phasors VOUT VIN is a convenient means of classifying a circuit behavior and identifying key parameters VOUT VIN Gain Break point Break point VOUT VIN G i Gain High Pass Low Pass Frequency Frequency These are log ratio vs log frequency plots EE40 Fall 2009 Slide 15 Prof Cheung A Quick Quiz High Pass or Low Pass EE40 Fall 2009 Slide 16 Prof Cheung Example Low Pass Circuit R2 VIN R1 VT AVT C A 100 R1 100 000 VOUT R2 1000 C 10 uF Transfer Function H VOUT VIN A H 1 j B VOUT AZ c VIN Z R Zc with i B 1 R 2C 100 rad s VOUT A 1 jwC A A VIN R 2 1 j C 1 j R 2C 1 j 1 R 2C EE40 Fall 2009 Slide 17 Prof Cheung First Order Bode Magnitude Plot The break frequency describes the frequency where the trends on the Bode plot are changed 1 20 log H 20 log A 20 log 1 B 2 1 2 dB dB 40 dB B EE40 Fall 2009 0 dB Slide 18 B 20dB dec Prof Cheung Bode Magnitude Plot First order Low Pass Filter 1 20 log H 20 log A 20 log 1 B 2 1 2 dB 40 B 100 A Actual value 20 0 20 1 10 100 1000 10000 100 100 1 j 2 log Radian Frequency Slope 20dB dec or 6dB octave for B EE40 Fall 2009 Slide 19 Prof Cheung Bode Phase Plot First order Low pass Filter A H tan 1 B 1 j B Phase 180 with B 1 R 2C 100 rad s 90 0 1 10 100 1000 90 Radian Frequency log scale 180 Actual value at B is 45o 100 0 100 0 Phase Phase 0 45 45 1 j 2 45 EE40 Fall 2009 Slide 20 Prof Cheung Bode Plot Actual versus Straight Line Approximation First Order Low Pass Filter Phase Magnitude EE40 Fall 2009 Slide 21 Prof Cheung Bode Plot of a High Pass Filter Vout j c j L H Vs j L R 1 j c c R R L Pole will cause decrease by 20db dec after c so magnitude is flat after c EE40 Fall 2009 Slide 22 Prof Cheung Bode Magnitude Plot of a High Pass Filter 1 20 log H 20 log j c 20 log 1 j c EE40 Fall 2009 Slide 23 Prof Cheung Bode Phase Plot of a High Pass Filter …
View Full Document
Unlocking...