By Ian Hickman
This e-book is meant for the practicing digital engineer explaining analog digital circuits as easily as attainable. Its goal is to take the reader inside of digital circuits explaining precisely what they do by using vector diagrams
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Extra resources for Analog Electronics. Analog Circuitry Explained
On the other h a n d , the cartesian form is much more convenient than the polar when adding complex n u m b e r s . 1c, you will recall that this is shown for the particular case of that frequency at which the reactance of the capacitor equals R 28 Analog Electronics C 1Γ = Fm i R = /? 2 CR and Lf? circuits. (a) L/? low-pass circuit. (b) CR high-pass (bass-cut) lead circuit. e. where ωο = l/CR = 1/T), by using = ω/ωο instead of ω. Then when ω = 1/7= ωο, the normalized radian frequency = 1. F(jω) then simplifies to F(iωJ = ;ω/ωο —^ ^ .
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 . 1 g . 707 L - 4 5 ° . ) A t the same time, it is convenient to plot the magnitude on a logarithmic scale of decibels (unit symbol d B ) .
This has a finite pole and a finite zero both on the - σ axis, with the pole nearer the origin. I in a feedback amplifier (see Chapter 3) without the phase shift ever reaching 90° and with negligible phase shift at very high frequencies. 6b to f illustrate the response from several different points of view. N o t e that Κ is the value of the transfer function at infinitely high frequencies, where the reactance of C is zero, as can be seen by replacing C b y a short-circuit. When s = 0, F(s) gives the steady state transfer function at zero frequency, where the reactance of C is infinite, so , ^ 1/7: T2 1 / 7 : .