# 0.5 Sampling with automatic gain control  (Page 15/19)

 Page 15 / 19

There are two basic approaches to an AGC. The traditional approach uses analog circuitry to adjust the gain before the sampling. The more modern approach uses the output of the sampler to adjust thegain. The advantage of the analog method is that the two blocks (the gain and the sampling) are separate and do not interact.The advantage of the digital adjustment is that less additional hardware is required since the DSP processing is already presentfor other tasks.

A simple digital system for AGC gain adjustment is shown in [link] . The input $r\left(t\right)$ is multiplied by the gain $a$ to give the normalized signal $s\left(t\right)$ . This is then sampled to give the output $s\left[k\right]$ . The assessment block measures $s\left[k\right]$ and determines whether $a$ must be increased or decreased.

The goal is to choose $a$ so that the power (or average energy) of $s\left(t\right)$ is approximately equal to some specified ${\mathbf{s}}^{2}$ . Since

${a}^{2}{\left(\text{avg},\left\{,{r}^{2},\left(t\right),\right\}|}_{t=kT}\approx \text{avg}\left\{{s}^{2}\left(kT\right)\right\}\approx \text{avg}\left\{{s}^{2}\left[k\right]\right\},$

it would be ideal to choose

${a}^{2}\approx \frac{{\mathbf{s}}^{2}}{\text{avg}\left\{{r}^{2}\left(kT\right)\right\}},$

because this would imply that $\text{avg}\left\{{s}^{2}\left(kT\right)\right\}\approx {\mathbf{s}}^{2}$ . The averaging operation (in this case a movingaverage over a block of data of size $N$ ) is defined by

$\text{avg}\left\{x\left[k\right]\right\}=\frac{1}{N}\sum _{i=k-N+1}^{k}x\left[i\right]$

Unfortunately, neither the analog input $r\left(t\right)$ nor its power are directly available to the assessment blockin the DSP portion of the receiver, so it is not possible to directly implement [link] .

Is there an adaptive element that can accomplish this task? As suggested in the beginning of "Iteration and Optimization" , there are three steps to the creation of a viableoptimization approach: setting a goal, choosing a solution method, and testing. As in any real life engineering task, a propermathematical statement of the goal can be tricky, and this section proposes two (slightly different) possibilitiesfor the AGC. By comparing the resulting algorithms (essentially, alternativeforms for the AGC design), it may be possible to trade off among various design considerations.

One sensible goal is to try to minimize a simple function of the difference between the power of the sampled signal $s\left[k\right]$ and the desired power ${\mathbf{s}}^{2}$ . For instance, the averaged squared error in the powers of $s$ and $\mathbf{s}$ ,

$\begin{array}{cc}\hfill {J}_{LS}\left(a\right)& =\text{avg}\left\{\frac{1}{4},{\left({s}^{2}\left[k\right]-{\mathbf{s}}^{2}\right)}^{2}\right\}\hfill \\ & =\frac{1}{4}\text{avg}\left\{{\left({a}^{2}{r}^{2}\left(kT\right)-{\mathbf{s}}^{2}\right)}^{2}\right\},\hfill \end{array}$

penalizes values of $a$ which cause ${s}^{2}\left[k\right]$ to deviate from ${\mathbf{s}}^{2}$ . This formally mimics the parabolic form of the objective [link] in the polynomial minimization example of the previous section.Applying the steepest descent strategy yields

$a\left[k+1\right]=a\left[k\right]-\mu {\left(\frac{d{J}_{LS}\left(a\right)}{da}|}_{a=a\left[k\right]},$

which is the same as [link] , except that the name of the parameter has changed from $x$ to $a$ . To find the exact form of [link] requires the derivative of ${J}_{LS}\left(a\right)$ with respect to the unknown parameter $a$ . This can be approximated by swapping the derivative and the averaging operations to give

$\begin{array}{c}\\ \hfill \frac{d{J}_{LS}\left(a\right)}{da}& =& \frac{1}{4}\frac{d\text{avg}\left\{{\left({a}^{2}{r}^{2}\left(kT\right)-{\mathbf{s}}^{2}\right)}^{2}\right\}}{da}\hfill \\ & \approx & \frac{1}{4}\text{avg}\left\{\frac{d{\left({a}^{2}{r}^{2}\left(kT\right)-{\mathbf{s}}^{2}\right)}^{2}}{da}\right\}\hfill \\ & =& \text{avg}\left\{\left({a}^{2}{r}^{2}\left(kT\right)-{\mathbf{s}}^{2}\right)a{r}^{2}\left(kT\right)\right\}.\hfill \end{array}$

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are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
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learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
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Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
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Kamaluddeen
yes
narayan
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Damian
yes that's correct
Professor
I think
Professor
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if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
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