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By Ian Hickman

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

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So e''' e^""' represents a sinusoidal function which is increasing or decreasing - or staying the same amplitude if σ equals zero. The law of indices states that to multiply together two powers of the same n u m b e r it is only necessary to add the indices: 4 X 8 = 2 ' X 2 ' = 2 ' = 32, for example. Similarly, e^' é^' = + j-)', thus expressing compactly in a single term the frequency and rate of growth (or decline) of a sinusoid. It is usual to use s as shorthand for σ -f ί ω ; s is called the complex frequency variable.

For any phase angle less than φη, there are two different possible values of Uo, the larger at a frequency below V[(l/Ti)(l/T2)], the smaller at a frequency above. (f) Using the circle diagram. If you are better at geometry than at calculus or complex numbers, the circle diagram enables you to find the attenuation at the frequency where the phase shift φ is maximum. The bold triangles with bases (üo)oc = Κ and Uj = 1 are similar, as they have three equal angles, φ^, is common, each has an angle a, and each has an angle 9 0 ° + a.

B o d e , D . V a n Westrand C o m p a n y Inc, N e w Y o r k 1945. 2 . T r a n s f e r F u n c t i o n s , C a t h o d e R a y , p a g e 177, W i r e ­ l e s s W o r l d , A p r i l 1962. 3. State Variables for Engineers (Chapter 3), Da R u s s o , R o y , C l o s e ; J o h n W i l e y a n d S o n s , Inc. 1965. Chapter 3 Active components If passive components are the cogs and pinions of a circuit, an active component is the mainspring. The analogy is not quite exact p e r h a p s , for the mainspring stores and releases the energy to drive the clockwork, whereas an active c o m p o n e n t drives a circuit by controlling the release of energy from a battery or power supply in a particular manner.

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