By Ian Hickman

This e-book is meant for the practicing digital engineer explaining analog digital circuits as easily as attainable. Its objective is to take the reader inside of digital circuits explaining precisely what they do by using vector diagrams

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W e have given the particular value of ω where ω = l/CR the title ωο. 1e by ωο, they simply become 0 , 0 . 2, 0 . 5 , 1 , 1 0 etc. If. A s ω increases from 0 to infinity, φ decreases from 0° to - 9 0 ° whilst V o decreases from unity to zero. W e now have a universal picture which applies to any low-pass circuit like Figure 2 . 1 a . W e simply multiply the ω values in Figure 2 . I f by l/lirCR to get its actual frequency response. e. the Μ part of Μ L Φ) and arg V o or φ against a linear base of frequency, as in Figure 2 .

Let's give this value of ω the label ω„. At ω,, the output voltage v,, = iXc = {vJR){\/ ]ω„Γ), so ω,CR V. ) 1 ( ] ω ) - 7 Γ + jωC/? 2) This equation can be factorized into + a) (s + ¿ ) , where Ö and ¿ a r e the roots of the equation ^ R ¿ a - where Xcv is the reactance of the capacitor at ω„. Clearly, for given values of L and C, as R becomes very small the output voltage at resonance will be much larger than the input voltage. )V(L/C) is often called the magnification + c / ? e. -a and -b are the positions of the poles on the p o l e - z e r o diagram.

Clearly then the sum l\ + A increases as we move up the ]ω axis; so you might be tempted to think that the magnitude of VO, which is propor­ tional to (l//|)(l//2), will decrease. But not so: for in percentage terms, /, initially decreases faster than /: increases, so the magnitude of the transfer function |7(]ω)| = |VO/VI| actually increases. At ω = 0 . e. there is a ^peak' of miniscule dimensions at frequencies well below the resonant frequency. 2, |7(ίω)| is already back to unity. As R decreases, the positions of the poles migrate away from each other around a semicircle of radius equal to unity centred on the origin.

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