EE40 Lecture 12 Josh Hug 7 21 2010 EE40 Summer 2010 Hug 1 Logistical Things HW6 due Friday at 5PM also short Midterm next Wednesday 7 28 Focus is heavily on HW4 5 6 and Labs P1 4 5 Will reuse concepts from HW 1 2 3 EE40 Summer 2010 Hug 2 Filtering For the past couple of lectures we ve discussed using phasors and impedances to solve circuits Usually we ve assumed we have some single frequency source and found the resulting output Last time in lecture we showed that we could apply two different frequencies at one time using superposition Each was scaled and shifted by different amounts EE40 Summer 2010 Hug 3 Transfer Functions EE40 Summer 2010 Hug 4 Using a Transfer Function EE40 Summer 2010 Hug 5 Using a Transfer Function EE40 Summer 2010 Hug 6 Transfer Function EE40 Summer 2010 Hug 7 Bode Magnitude Plot EE40 Summer 2010 Linear Scale Log Scale Hug 8 Bode Magnitude Plot in Context of Circuit EE40 Summer 2010 Hug 9 Bode Phase Plot EE40 Summer 2010 Linear Scale Semilog Scale Hug 10 Bode Phase Plot in Context of Circuit EE40 Summer 2010 Hug 11 Multiple Frequencies Real signals are often a combination of a continuum of many frequencies Radio antenna input Microphone input Intuitively Thunder contains a bunch of low frequency sounds Boiling kettles contains a bunch of high frequency sounds There is a mathematically well defined idea of what it means for a signal to contain many frequencies EE40 Summer 2010 Hug 12 Time vs Frequency Domain EE40 Summer 2010 Hug 13 Multiple Frequencies The 1 button on a phone is a combination of a 697 Hz tone and a 1209 Hz tone EE40 Summer 2010 Hug 14 Multiple Frequencies Bill and Ted saying the word bogus is a more complex set of frequencies EE40 Summer 2010 Hug 15 Filtering Example If we apply a filter with the frequency response on the right to the signal on the left Then we ll get EE40 Summer 2010 Hug 16 More complex filtering EE40 Summer 2010 Each frequency individually scaled Hug 17 Phase Effects If we shift the phase of the larger sine we get Original 1 button tone EE40 Summer 2010 Hug 18 Magnitude and Phase Demo Let s try the ever risky live demo EE40 Summer 2010 Hug 19 Bode Plots Hopefully I ve convinced you that magnitude and phase plots are useful Now the goal will be to draw them straight from the transfer function First some reminders on loglog plots EE40 Summer 2010 Hug 20 Loglog Plots EE40 Summer 2010 Hug 21 Loglog Plots EE40 Summer 2010 Hug 22 Loglog Plots EE40 Summer 2010 Hug 23 Manual Bode Plots On board using handout EE40 Summer 2010 Hug 24 2nd Order Filter Example Also on board EE40 Summer 2010 Hug 25 2nd order Bode Plots Also on board This is where we stopped in class EE40 Summer 2010 Hug 26 Active filter example On board EE40 Summer 2010 Hug 27 Magnitude Plot Units EE40 Summer 2010 Hug 28 Bel and Decibel dB A bel symbol B is a unit of measure of ratios of power levels i e relative power levels B log10 P1 P2 where P1 and P2 are power levels The bel is a logarithmic measure Zero bels corresponds to a ratio of 1 1 One bel corresponds to a ratio of 10 1 Three bels corresponds to a ratio of 1000 1 The bel is too large for everyday use so the decibel dB equal to 0 1B is more commonly used 1dB 10 log10 P1 P2 0 dB corresponds to a ratio of 1 1 10 dB corresponds to a ratio of 10 1 10 dB corresponds to a ratio of 1 10 dB are used to measure Electric power filter magnitude EE40 Summer 2010 Hug 29 Logarithmic Measure for Power To express a power in terms of decibels one starts by choosing a reference power Preference and writing Power P in decibels 10 log10 P Preference Exercise Express a power of 50 mW in decibels relative to 1 watt P dB 10 log10 50 x 10 3 13 dB Use logarithmic scale to express power ratios varying over a large range dB P1 10 log P2 EE40 Summer 2010 dB Note dB is not a unit for a physical quantity since power ratio is unitless It is just a notation to remind us we are in the log scale Hug 30 Decibels for measuring transfer function magnitude 2 P V I EE40 Summer 2010 2 Hug 31 Transfer Function in dB EE40 Summer 2010 Hug 32 Example EE40 Summer 2010 Hug 33
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