Analog-to-Digital Conversion by Marcel Pelgrom

By Marcel Pelgrom

The layout of an analog-to-digital converter or digital-to-analog converter is without doubt one of the such a lot attention-grabbing initiatives in micro-electronics. In a converter the analog international with all its intricacies meets the world of the formal electronic abstraction. either disciplines has to be understood for an optimal conversion resolution. In a converter additionally method demanding situations meet know-how possibilities. glossy structures depend upon analog-to-digital converters as an important a part of the advanced chain to entry the actual global. And processors desire the final word functionality of digital-to-analog converters to offer the result of their complicated algorithms.

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During the factoring there are a few possibilities for the poles: • sn = 0 which results in a constant term starting at t = 0. • A real valued root spn . In the time domain this factor will result in an exponential term e−spn t . • A real valued root s = −spn < 0. In the time domain this factor will result in an exponentially decaying function. • A real valued root s = −spn > 0. A design example of this exponentially growing function is in the analysis of a latch. 2 with roots s = −s ± j s . In the • A second order polynomial (s + sp2 )2 + sp1 p2 p1 time domain pair of roots results in an exponentially decaying sinusoidal function if the real part of the root −sp2 ≤ 0.

As a path for ds the center line through the coil is chosen. The path is continued outside the coil in a direction perpendicular to the flux and than closed via a route with negligible flux. Only the path through the coil contributes to the integral. This path encircles the number of windings Nw times the current in the coil. B · ds = BLc = μ0 Nw I The integral is unequal to zero only inside the coil, where the vectors align, so the vector notation is omitted and B simply equals the value of the field inside the coil.

An integration results in a division by s. When an analysis in the frequency domain is carried out, the real part of s is set to zero leaving the radial frequency j ω as the running variable. This is a quick route to come to a Bode analysis, see Fig. 50. : N(s) s m + bm−1 s m−1 + · · · + b1 s + b0 = n D(s) s + an−1 s n−1 + · · · + a1 s + a0 = 2 ) (s + szm )(s + sz(m−1) )((s + sz2 )2 + sz1 2 ) (s + spn )(s + sp(n−1) )((s + sp2 )2 + sp1 18 2 Components and Definitions = Nn−1 (s) N2 (s) Nn (s) + + 2 ) (s + spn ) (s + sp(n−1) ) ((s + sp2 )2 + sp1 The roots of the numerator polynomial (s = −szm , s = −sz2 ± j sz1 ) are called “zeros” and the roots of the denominator polynomial (s = −spn , s = −sp2 ± j sp1 ) are the “poles”.

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