(a) Straight-line approximation of magnitude response (b) straight-line approximation of phase angle responseįigure 4 Comparison of Bode plot approximation with the actual frequency response function.StudyDaddy Engineering What are Bode plots? Use a well labelled diagram to aid your explanation. When all the asymptotic approximations are combined, the complete frequency response approximation is obtained.įigure 4 depicts the results of the asymptotic Bode approximation when compared with the actual frequency response functions.įigure 3 Bode plot approximation for a second-order frequency response function. The two denominator terms have similar behavior, except for the fact that the slope is −π/4 and that the straight line with slope −π/4 rad/decade extends between the frequencies 0.1ω 2 and 10ω 2, and 0.1ω 3 and 10ω 3, respectively.įigure 3 depicts the asymptotic approximations of the individual factors in equation 13, with the magnitude factors shown in Figure 3(a) and the phase factors in Figure 3(b). The numerator first-order term, on the other hand, can be approximated, that is, by drawing a straight line starting at 0.1ω 1 =0.5, with slope +π/4rad/decade (positive because this is a numerator factor) and ending at 10ω 1 = 50, where the asymptote +π/2 is reached. If we now consider the phase response portion of equation 13, we recognize that the first term, the phase angle of the constant, is always zero. You see that the individual factors are very easy to plot by inspection once the frequency response function has been normalized in the form of equation 9. The numerator term, with a 3-dB frequency ω 1 = 5, is expressed in the form of the first-order Bode plot of Figure 1(a), except for the fact that the slope of the line leaving the zero axis at ω 1= 5 is +20 dB/decade each of the two denominator factors is similarly plotted as lines of slope −20 dB/decade, departing the zero axis at ω 2 = 10 and ω 3 = 100. The constant corresponds to the value −46 dB, plotted in Figure 3(a) as a line of zero slope. \Įach of the terms in the logarithmic magnitude expression can be plotted individually. RC Low-Pass Filter Bode PlotsĬonsider the RC low-pass filter. The individual Bode plots of these four distinct terms are all well approximated by linear segments, which are readily summed to form the overall Bode plot of more complicated frequency response functions. Simple poles or zeros (1 + jωτ) or (1 + jω/ω o).ĭ. Moreover, there are only four distinct types of terms present in any frequency response function:Ĭ. The advantage here is that Bode (logarithmic) plots can be constructed from the sum of individual plots of individual terms. The product of terms in a frequency response function becomes a sum of terms because log( ab/c) = log( a) + log( b) − log( c). While logarithmic plots may at first seem a daunting complication, they have two significant advantages:ġ.
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