EE40 Lecture 12 Josh HugLogistical ThingsFilteringTransfer FunctionsUsing a Transfer FunctionSlide 6Transfer FunctionBode Magnitude PlotBode Magnitude Plot in Context of CircuitBode Phase PlotBode Phase Plot in Context of CircuitMultiple FrequenciesTime vs. Frequency DomainSlide 14Slide 15Filtering ExampleMore complex filteringPhase EffectsMagnitude and Phase DemoBode PlotsLoglog PlotsSlide 22Slide 23Manual Bode Plots2nd Order Filter Example2nd order Bode PlotsActive filter exampleMagnitude Plot UnitsBel and Decibel (dB)Logarithmic Measure for PowerDecibels for measuring transfer function magnitude?Transfer Function in dBExample1EE40 Summer 2010HugEE40Lecture 12Josh Hug7/21/20102EE40 Summer 2010HugLogistical 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 1,2,33EE40 Summer 2010HugFiltering•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 amounts4EE40 Summer 2010HugTransfer Functions5EE40 Summer 2010HugUsing a Transfer Function6EE40 Summer 2010HugUsing a Transfer Function7EE40 Summer 2010HugTransfer Function8EE40 Summer 2010HugBode Magnitude PlotLinear Scale Log Scale9EE40 Summer 2010HugBode Magnitude Plot in Context of Circuit10EE40 Summer 2010HugBode Phase PlotLinear Scale Semilog Scale11EE40 Summer 2010HugBode Phase Plot in Context of Circuit12EE40 Summer 2010HugMultiple 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”13EE40 Summer 2010HugTime vs. Frequency Domain14EE40 Summer 2010HugMultiple Frequencies•The “1” button on a phone is a combination of a 697 Hz tone and a 1209 Hz tone15EE40 Summer 2010HugMultiple Frequencies•Bill and Ted saying the word “bogus” is a more complex set of frequencies16EE40 Summer 2010HugFiltering Example•If we apply a filter with the frequency response on the right to the signal on the leftThen we’ll get:17EE40 Summer 2010HugMore complex filteringEach frequency individually scaled18EE40 Summer 2010HugPhase EffectsIf we shift the phase of the larger sine, we getOriginal “1 button” tone19EE40 Summer 2010HugMagnitude and Phase Demo•Let’s try the ever risky live demo20EE40 Summer 2010HugBode 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 plots21EE40 Summer 2010HugLoglog Plots22EE40 Summer 2010HugLoglog Plots23EE40 Summer 2010HugLoglog Plots24EE40 Summer 2010HugManual Bode Plots•On board, using handout25EE40 Summer 2010Hug2nd Order Filter Example•Also on board26EE40 Summer 2010Hug2nd order Bode Plots•Also on board•This is where we stopped in class27EE40 Summer 2010HugActive filter example•On board28EE40 Summer 2010HugMagnitude Plot Units29EE40 Summer 2010HugBel 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 magnitude30EE40 Summer 2010HugLogarithmic 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 range21log10PP dBNote: 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.dB:31EE40 Summer 2010HugDecibels for measuring transfer function magnitude?22IVP 32EE40 Summer 2010HugTransfer Function in dB33EE40 Summer
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