25-02-2013, 09:14 AM
SYNTHESIS OF CIRCUITS
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INTRODUCTION
In synthesis there are far too many design approaches to enumerate here, and plenty of scope for anyone to invent new ones. It is a less clearly defined problem and then, there are many ways to approach a solution. There is need of judgement as well as calculation. It is (arguably at least) more difficult, more open-ended, more interesting than analysis. Yet analysis remain vital - to test the design ideas before putting them into practice.
Because so much of synthesis is concerned with filter design, it is easy to suppose that all design is restricted to the frequency domain. Not so. Often there are clear requirements in both domains, and usually they conflict. For example, a filter’s performance may be specified as a particular pass-band in the frequency domain, and
at the same time it may be required to have a restricted transient response. This could occur in a radar system where bursts of oscillation are used, and the response to one burst must die away before the next pulse is received.
Usually the requirements are in conflict and a synthesis procedure consists in finding a compromise. In the last example, the better the discrimination is made in the frequency domain, the worse is the transient response.
Analysis of sampled data:
This is at first sight a less obvious candidate for synthesis procedures. Yet the concept of a filter is very general and very powerful. When we calculate the average of a set of readings (measurements), we are “smoothing out the fast variations” (high frequency components) — we are finding the “DC component” and this process is a numerical low-pass filter. The analogy with frequency-domain filters becomes closer when we envisage working out, say, the average of the last five temperature readings in a series of continuously sampled measurements. Or for instance when the annual inflation rate is updated every month. The general theme of digital filtering encompasses any linear operation on the data, and includes integration and differentiation.
I.F. filter for a TV receiver
In this case, as in most practical cases, the output is not fixed specifically. Instead we only fix some restrictions to its shape. In all practical cases we are not interested in obtaining a predetermined fixed function as filter characteristic. Instead, we want an approximation to an ideal case that satisfy certain restrictions. This is particularly suitable since as the problem of synthesis not always has an exact solution, this has to be found as an approximation within a set of “realizable functions”.
Digital Filters
Digital filters are algorithms for digital computers or circuits. Digital filtering is any linear operation performed on data which has been sampled at equally spaced intervals.
It includes smoothing (averaging), integrating, separating signals (filtering) and predicting.
Examples are the Fourier transform (or Fast Fourier Transform), important in signal processing work, the Simpson rule or the trapezoidal rule of integration, the central difference formula of numerical derivative, etc. All these can be regarded as digital filters.
We can also find equivalent digital filters to analogue filters. Low-pass and other analogue filters have their digital counterparts. But digital filters have additionally some special properties which make them well suited for digital communication systems, especially when large distances are involved. It is then that analogue systems are at a particular disadvantage because the attenuation continuously degrades the signal-to-noise ratio. In digital systems, the signal is completely regenerated at intervals and then re-transmitted with no loss of information.
There are no impedance-matching problems in the digital domain. Also, two or more digital filters can have genuinely identical characteristics. These filters are also programmable so that their characteristics can be changed easily and rapidly - even almost continuously if needed.