El problema de la información: “Qué”, “cuánto”

k the frictional damping constant, and U the elastic resisting torque per unit angle of de fle ction.

Equations (5.6 ), (5.7) and (5.8) and the di fferentiated forms of (5.7 ) and (5.8) constitute a set of simultaneous line ar

di1 di2

di fferential equations. Elimination of _i1 , _i2,

err ,

and -in-

produce s a differential equation which give s the dependence o f

e

on W

p� -t (k + "J,P + o)-f-&

+(\J + 1b°-

+ w,R + w2.D )�

Rt where _W1 =

L specifies the )low frequency (R + R R

(5.9 )

cuto ff o f the

de tector coil and R _t = f o g + R '

(R + R + _f R ) L the total resistance

O g

in series with e . Other quantities not previously de fined are

W, =

L)

s

R

t

-+ f<.

0

-+ R

L

G-

7..

R

_-f

+ Ro + R�

W 1

R_l ,._

ct "-

cl

y

er �� +R .. J es

=

(

Qf

+ Ro -t-1\ ) L

I

The solution to the third order linear differential equation (5.9) is the sum of the complementary function, repre senting the transient condition, and the particular integral, re pre senting the steady state condition.

be considered.

The steady state solution only will

For harmonic re sponse the particular integral is given by

(}

=

y

�ii'\, wt - QJ

(5.10)

(�,'2. -+ Y-1..2.

2..

where X ::-

w/�� t w

I

Ll - ( k -t

1JJ ,

P t D ) w

1. (5.1 1 )

X

-=

w

( LA � �

+ V0₁R + w_2.D - \Jw'")

(5.1 2 )

(5. 13) To simplify the investigation of the particular integral

with respect to frequency response, the following parameters,

given by equations (5.14) to 5.22), are introduced :

(i) The feedback factor

f ,

where

0

_

A D

I

-

G-U

(5.14)

and S. = G/U₁ , the current sensitivity of the galvanometer. '

(ii) The modified galvanometer elastic resisting torque U , where (5. 15) I

Since

f

is always non-zero and positive, then U

>

U and the elastic resisting torque of the galvanometer is increased by the application of feedback.

(iii) The natural galvanometer resonant frequency f , ₀ where

{

=

I

(U

111 ff

(5_I .16)

(iv ) The modified resonant frequency of the galvanometer f , ₀ where

1

1 11

P

(5.17)

(v) The galvanometer open circuit relative damping factor _Oo V

as defined by Harris ( 1 959)

(5.18)

(vi) The modified galvanometer open circuit relative damping factor

I

Y where

oo '

R W.

1 u '

(5. 1 9)

(vii ) The galvanometer electromagnetic damping factor

f

,

as

defined by Harris ( 1959)

This D ₀ =

applies G2 R + R _{s g}

when the galvanometer is critically damped and , where R _s is the external damping resistance . (viii ) The modified galvanometer ele ctromagnetic damping factor

I •

f ,

where

D w ..

I

::: ---

2 u ·

D is de fined wi th re ference to equation (5.9).

(5.21 )

(ix) The ratio of the forcing frequency to the modified resonant frequency o f the galvanometer � , where

(5.22)

It is also convenient to introduce the following parameters :

The de finitions Tepley ( 1 961 a) (5 . 23) (5.24) (5.25 ) (5.26)

Substitution o f the parame ters de fined by equations ( 5.1 4 ) to (5.26 ) into ( 5 . 1 1 ) and (5.12 ) gives,

(5.27) and

Squaring and adding equations (5.27 ) and (5.28 ) and substituting in equation (5.10) results in a solution

where

and M is the magnification factor of the system and is defined by M =

8

rflo.1,.

/ Q O

• Here M is given by

=(��)l.+ {l + � IT�t' + to' ) - E ( t'+ �: )] +

�. [ 2( � / + i.')'- E] } t f/.' { f• +J [2 (�1 tt:)'--1]

- ¼ [ l ( �-

1

)]1 + 1

1t

_{(5. 29)}

Equation (5.29) is the trans fer function of the system. This expression may be simpli fied by considering the physical magnitude

of certain parameters. In Appendix I it is shown that

(3 >> / ,

P-> /

> )

't

01 and

tf

1 +

'£

0

1

c::_<

I

.

Incorporating these approximations, and noting that 0.5< E

<

1.0, equation

(5.29) simplifies to

* =ctfc<f+ f1 + ¼ �i' +j,.[2 (�/r-0 J}

+ { �,. - 2 - ¼ �a'} + �

}f (5.30 )

The parameters 0( and € are given by equations (5.23) and (5.26 ). An expression for

�t'

is obtained in Appendix I, viz

35.

5.4.2 Pr ct · cal De sign Consideration�.

The particular value s of the design constants in equation ( . 30) are specified by the characteristics of the galvanome ter

and the associate d optical-transistor amplifier. The spe cifications of the galvanome ter , a standard laboratory model Tinsley type

4500A, are f _O • 5 cps, Rg 460 .I\., , S

i 1 500mm/

µA

at 1m, and a critical damping resistance of 1 2k JI., . The value o f damping

1. resistance applies for

y

using equation (5.20 ) , that R _s

For

t

/£2. - J2 . ( 1 2k .t\, )

it can be shown, 1 7kfL • For the optical-transistor amplifier, the only parameter required is the voltage gain (A) measure d at the output across which the galvanome ter feedback c rcuit is conne cted. This parame ter varie s with

feedback resistance. However, the variation over the range o f Rf considered is small compared with the measured value of 1 04 and is neglected in the pre sent analysis.

may be negle cted _{since Rf} ) ) R + ₀ R _{g •}

The output re sistance R ₀ Substituting the values of the known constants into equations (5.1 4) , (5.1 5 ) , (5.23 ) and (5.31 ) produces a set of practic al design and equations

p ;: 7· { 't. JO' I � f

( I

r

0 -

0 · S JI -t-f

o< = 2 ·'l7 £

I

B r ' = r;. i( /£ '

(5.32 ) ( • 33 ) (5. 34) ( 5 . 35 ) The frequency re sponse curve i s obt ained by plott ing M, from equation (5.30 ), against frequency. For selected values o f the feedback resistance frequency re sponse eurves were calcula;ed in order to determine the optimum fe edback required for a high

frequency cutoff of 3 cps. The se calculations were carried out on an IBM 1 620 computer at the University of Canterbury ' s

Mobil Computer Laboratory. Theoretical response curves for various values of feedback resistance are shown in Figure 5.2.

Also shown is the frequency response of the system without feedback. This curve was obtained using the transfer function derived by

Tepley (1961a) for a galvanometer-photocell amplifier without feedback. (Equation 5.30 cannot be used since it is not valid for R_r>oO.) Clearly, the required high frequency response to 3 cps cannot be obtained without feedback. When the feedback resistance is reduc .. d, th•· .,idband frequency increases, the bandwidth decreases, and the mode of operation approaches that of an oscillograph . The high frequency peaks result from the inability to minimize the �� term in the transfer function.

Figure 5.3 shows that R_f = 1. 2 M.Jl; produces the desired response curve with a high frequency cutoff near 3 cps. Also shown is the experimental curve for Rf - 1.17M A . A close agreement is obtained between the theoretical and experimental curves, indicating that the approximations made in the theory are valid.

The undesirable high frequency peak may be removed in subsequent stages of amplification thus giving a flat response over the required bandwidth (0.3-3 cps).

LO -SPEED M ·, RECORDING.

Signals in the micropulsat�on frequency range may be recorded on magnetic tape using either the frequency -modulat±on recording process or the direct recording process. Although the frequency- modulation process has the advantage of reliable recording at

frequencies down to

D.c.

,

it is not suitable for long term unattended operation since a faster tape speed, and thus more frequent tape changes, are required to achieve the same high frequency response compared with the direct recording process. For the present application it is therefore more convenient to use the direct recording process.

37.

Within broad limitations the bandwidth obtainable with direct recording is independent of the recording head charac teristics,

and depends on the long wavelength and short wavelength losses which are de termined by the tape speed and the characteristics

of the playback head. These losses are superimposed on the

ideal re cord-playback characteristic which rises linearly with frequency at a rate of 6db/octave .

The principal short wavelength or high frequency loss is due to the finite gap-width of the playback he ad. The output from the he ad drops to zero when the wavelength of the signal re corded on the tape is equal to the e ffective length of the gap between the pole pieces of head. The particular heads used in both the re cord and playback systems had effective gap-widths

of 2 . 5 x 10-4 ins . To obtain substantial high frequency re sponse

with this head gap requires a record tape speed of approximately 2 in / hr / cps. Thus a tape speed of 6 in / hr is sufficient to re cord frequencie s up to 3 cps.

The long wavelength loss , which affects the low frequency

response, is a function of the overall head dimensions , and occurs

when a half-wavelength re corded on the tape is longer than the length of tape in contact with the playback head. Microscope measurements indicated that the length of tape in contact with the playback he ads is approximately 0.1 5 ins. Using this value, and a tape speed of b in / hr , results in a low frequency cutoff of approximately 0.02 cps.

At normal tape speeds the sensitivity and maximum undistorted output obtainable on playback varies with bias current. As the signal and bias currents in the record he ad at very low frequencies differ from those required at audio frequencie s , the optimum values

of the se currents must be established experimentally. The chosen

bias frequency of 500 cps is sufficiently high to prevent mixing or modulation of the signal frequencie s during playback. From

greater than 0.1mA. 5. 6

_su __

_{R_Y_.}

The design criteria considered in this chapter indicate that it i s possible to construct micropulsation recording instrument tion

which satisfies the conditions specified in the introduction. In particular, a theoretical minimum detectable signal of 2

mt

i s attainable in the 0.3-3 cps band using a 42,000 turn coil,

containing a specified 3% grain-oriented silicon steel core,in conjunction with a galvanometer-photocell amplifier utilizing feedback. In order to record frequencies up to 3 cps on

magnetic tape u sing the direct recording process, a minimum tape speed of 6 in / hr is required.

39.

CHAPTER VI

THE PORTABLE RF:CORDING .SYSTEM

6.1. GENER L .

The overall function of the transistorized recording system is to detect fluctuations of the N-S component of the geomagnetic field and to record the resulting data on magnetic tape for later study.

The equipment constructed to the specifications set out in Chapter V is illustrated in Figure 6.1 and shown in block diagram form in Figure 6.2. The detector coil consists of 35,200 turns of copper wire wound on a high perme ability core. This feeds

to a transistorized galvanometer-photocell amplifier and then to

high and low gain tape amplifiers. The overall recording bandwidth is 0.08 - 3.3 cps with a dynamic range of �1db. The tape deck operates with a tape transport speed of 6.5 in/hr and contains four recording channels. At this speed a 600 ft reel of tape lasts about six weeks. One channel records data at high sensitivity and a second records at low sensitivity, while the remaining two channels are used for timing purposes. Time pulses at half-minute intervals and time signals from a broadcast

receiver are recorded on the timing channels. A 50 cps transist­ orized electro-mechanical tuning fork provides the frequency standard necessary for the tape transport drive and timing systems. The complete system operates from a regulated battery supply and draws 320mA at 24 volts.

Descriptions and circuit diagrams of the individual components of the recording system are included in Appendix I I.

6.2 C LIBRATION .

Absolute calibration of the recording system was ac compli shed by placing the dete ctor coil in a vertical position at the centre

of the existing 1 00m dial!lleter two turn ground loop. According

to Vozoff ( 1 961 ) , c alibrations of this type are accurate to

approximately 1% for frequencie s le ss than 100 cps and loops of

diame ter less than 200m. For convenience the loop was driven

by a constant current sour ce . The voltage induced from the loop into the de tector coil was me asured on the re cord level me ter and this provided a calibration fo r the data re cording channels. The

current in the calibration windings of the detector coil which was required to give the same de fle ction on the level me te r was also measured. From current readings taken at selected frequencies within the pass-band an averaged calibration constant was obtaine d

for the detector coil.

Routine calibration is carried out using a 0.9 cps calibration osc illator whic h is incorporated in the re cording equipment. Once every 24 hours the o scillator is automatically switched on for

five minutes and a current is passed through the calibration windings of the dete ctor coil. When the tapes are replayed the se

calibration signals provide a daily che ck on the overall sensitivity of the data re cording channe ls.

6.3 OPER TIO •

The transistorized recording system has proven most reliable

in operation. Only one component failure, other than an occasional galvanometer lamp, oc curred during eight months o f continuous

recording.

With the de tec tor coil axis in the geomagne tic N-S direction,

man-made interference was not as trouble some as expected, and the Rolleston field station was considere d a satisfactory, if not ideal , recording site for Pc1 mic ropulsations. �uantitative comparisons of noise signal levels with those noted in Chapter IV from

41.

amplitude -time charts are not possible since data recorded on the

portable system are displayed only in frequency-time form,

intensity modulated with respect to amplitude. However additional ob servations with the portable equipment have been made over a short period of time at an extremely quiet site in t he Lake Tekapo region ,

120 miles from Christchurch. Qualitative comparisons of the electromagnetic background noise indicate that the nighttime level at Rolleston is comparable with that at Tekapo. As expected, the daytime background noise at Rolle ston contains much more impulsive activity.

To minimize interference from AC power lines and ot her

equipment operating at t he Rolle ston field station quiet site, the re cording equipment was placed in a field hut 25 yds from the neare st AC power line, and the detector coil was burie d a further 10 yds away.

CHAPTER VII

In document RELACIÓN ENTRE EL NIVEL DE CONOCIMIENTO DE CONSENTIMIENTO INFORMADO Y SU FORMA DE APLICACIÓN POR ALUMNOS DE VIII SEMESTRE DE LA CLÍNICA ODONTOLÓGICA DE LA UNIVERSIDAD CATÓLICA DE SANTA MARÍA AREQUIPA 2014 (página 46-50)