homework #6 for smart structure technologies at korea advanced institute of science and technolo

8/15/2019 Homework #6 for Smart Structure Technologies at Korea Advanced Institute of Science and Technolo

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Homework #6Dias Bakhtiyarov

Question 2 (20 points): Three elements specify A/D throughput (sampling rate): conversiontime, acquisition time, and transfer time. Conversion time is the time required y the A/Dconverter to produce a digital value that corresponds to the analog input. Acquisition timecorresponds to the time needed y the associated analog circuitry to acquire a signal. Transfer time corresponds to the time needed to transfer data from the interface to the computer!smemory. Throughput is the rate at "hich all three can e completed. Throughput is often themost important factor in choosing a data acquisition interface.

(a) If we are interested in measurin si na! responses up to 2 kH" what shou!d $e thetheoreti%a! minimum &'D throu hput

# $%& should e the 'iquist frequency. %ence, theoretical minimum sampling frequency $%&.

($) In rea!ity the a%tua! throu hput of the &'D has to $e faster than the theoreti%a!minimum throu hput *p!ain why

*n reality, if our sampling rate is e+actly $%& for measuring signal responses up to # $%&, thenit may happen that the sampling points that "e record are going to correspond to every half the

period of the signal. This implies that the recorded response is &ero. %ence, higher samplingfrequency results in more accurate digiti&ation of signal.

(%) In %!ass we dis%ussed a$out a!iasin + *p!ain two %ommon te%hni,ues that %an $e usedto minimi"e a!iasin + (-e !earned one te%hni,ue in %!ass and you need find the otherte%hni,ue+)

ne of the techniques of minimi&ing aliasing is to apply a roll-off, i.e. apply lo"-pass filter sothat frequencies higher than the 'iquist frequency are eliminated. o"-pass filter can econstructed using simple C circuit.


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Another "ay to minimi&e aliasing is to perform oversampling or super-sampling of input signal.0ampling of input signal at much higher rate than 'iquist frequency eliminates the influence of overlapping of higher frequency signals due to their smaller amplitudes.

(d) .ost mu!ti/%hanne! ana!o input %ir%uits share a %ommon &'D %onverter+ he !ar er thenum$er of input %ir%uits $ein %onverted the !ower the per %hanne! throu hput+ If you wishto samp!e 10 %hanne!s at 20 kH" ea%h what shou!d $e the minimum throu hput of a dataa%,uisition system

#11 $%&

Question (20 points): Consider the circuit sho"n elo". The circuit consists of an amplifier providing 2#d3 gain, a filter, "hich causes an attenuation of 4#d3 at the frequency of interest,and follo"ed y a voltage divider.

5ig 4: 6ultistage amplification due to the interface circuit and data acquisition system

(a) 5ind the input and output voltage ratio ( E o /E i) across the 71 Ω resister.

( ) This implies that the actually gain in data acquisition can e different from "hat has eenspecified in the amplifier. %o" can "e find out the effective gain of the entire data acquisitionsystem in real testing8


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Question 3 (20 points): *n class, "e learned "hen aliasing occurs and ho" it is related to thesampling frequency (or the 'yquist frequency) of the data acquisition system. Ans"er thefollo"ing questions related to aliasing.

(a) A 41 %& sine "ave is sampled at 4# %&. Compute the ma+imum frequency that can erepresented in the resulting discrete signal. Compute the alias frequency.

( ) Assume that the measured signal has a comple+ periodic signal of the form: y(t) A 4 sin # π(#9)t A # sin # π (;9)t A 2 sin # π (4#9)t. *f the signal is sampled at 411 %&, determine thefrequency content of the resulting discrete response signal.

Question 4 ( 0 points): An analog-to-digital converter converts an analog voltage valuemeasured from the sensor (or the interface circuit) into a inary num er through a process calledquanti&ation that "e learned in class.

(a) Assume that 411 m< and 4< analog signals are processed y using an =- it or a 4#- it A/Dconverter to a full-scale output range of 1-41


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( ) 'e+t, an A/D converter "ith the follo"ing specification listed "ill e used in an environment

in "hich the A/D converter temperature changes y±

41 oC. ?stimate the total 60 error asedon the follo"ing equation:

Total 60 error:

###

T LQ E eeee ++±=

: %ere,Qe

, Le

andT e

are quanti&ation error, linearityerror and temperature error, respectively.

A/D Converter specification

5ull-space output range: 1-41<

The num er of its: 4# its

inearity:±

# its

Temperature drift: # its/9 oC

(c) Among the three sources of error descri ed a ove, fine out the one that has the mostdominant contri ution to the total error. %o" much improvement can "e gain in terms of reducing error (or improving the resolution) y changing the num er of its to 47- its instead of 4# its8 *s it a good investment of your fund8

homework #6 for smart structure technologies at korea advanced institute of science and technolo

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