ΗΛΕΚΤΡΙΚΕΣ ΜΕΤΡΗΣΕΙΣ

.

2012

1

:

(). ,

/:

. ()

.

:

1. , ..

2. , ..

3. , ..

(Measurements and Instrumentation)

:

/

/ Soft measurements

/

(.. )

, ..

.

( ) .

( !)

. ,

.

5

, ,

.

Oscilloscopes, Analyzers, Meters (5) Oscilloscopes (1) Spectrum Analyzer (Signal Analyzer) (2) Network Analyzer (1) Logic Analyzers (1) EMI/EMC, Phase Noise, Physical Layer Test (2) Bit Error Ratio Test (BERT) Solutions (2) Digital Multimeter, Voltmeters (1) Power Meters & Power Sensors (1) Frequency Counter Products (1) Noise Figure Analyzers & Noise Sources (1) LCR Meters & Impedance Measurement Products (1) Dynamic Signal Analyzers, Mechanical & Physical Test (1) Generators, Sources, Supplies (5) Signal Generator (Signal Source) (1) Pulse Generator Product Portfolio (1) Data Generators & Analyzers (1) DC Power Supplies (3) DC Electronic Loads (3) AC Power Sources / Power Analyzers (2) Modular Products and Systems (3) Modular Mainframes and Controllers (1) Modular Bit Error Rate Test Systems (1) Modular Data Acquisition and Switching (1) Modular Digital IO (1) Software for Modular Products and Systems (1) Accessories & Options for Modular Products (1) Additional Test & Measurement Products (11) Data Acquisition - DAQ (3) Wireline Communications Test Equipment (2) Application-Specific Test Systems and Components (2) Photonic Test & Measurement (3) GPIB, USB, Accessories, Racks (3) Used Agilent T&M Equipment (4) Services (1) Application Engineering Services (1)

6

1.

-

2. , ,

3.

,

4. , ,

Wheatstone Kelvin , , RC, RL Q Maxwell Hay Owen, Schering Wien

[ ]

5.

6.

[ ] [ ] []

7. -

7

1.

1. -

2.

3.

4.

5.

9

1.1 -

[d Arsonval-1890]

FD: (deviation)

FC:

( [Weston-1900])

F: (damping)

.

(eddy currents)

.

FD FC

11

:

( ),

.

(taut band) ,

.

, .

:

1. 5 50

2. () 1 k 50 k

3. 5 mV 250 mV

F = B I l (= Tesla m)

,

F = 2 B I l

F = 2 B I l

( r

)

TD = F r = 2 B I l N r [Nm]

A ( = 2 r l)

TD = B I N A [Nm]

. ,

TC = K0, :

TC = TD,

B I N A = K 0

0 = c I, c: , :

1.

2. ( ) 12

1.2

, (1)

(2).

, .

/ (

).

,

.

:

TD = K I I , : 13

(

, TD = K I2).

.

,

.

. (

).

:

1. 0,02 0,1

2. () 7,5 k

3. 30 V 600 V

4. 25 500 Hz

5. 0,1 0,25 %

1.3

:

, . ,

.

14

( ).

, . ,

, ( marketing ),

.

. , ,

.

() . , ,

.

.

15

:

, ..

.

-1. ( )

-2. ,

-3. , , .

-4.

+1.

+2.

:

1. 50 m

2. () 10 k

3. 10 V 750 V

4. 15 150 Hz

5. 0,5 %

16

1.4

: ()

. .

, 1-200 kV.

, -

. = V2, .

.

:

1. 30 V 50 kV

2. 15 Hz 300 kHz

3. 0,5 %

1.5

( )

. , ,

. ,

. (

)

. mm

( ).

17

,

.

.

R = 0 ( )

.

, .

R 0 .

.

.

G

R

18

2. , ,

1.

2.

3.

4.

5.

19

2.1

.

, . , ..

V kV .

, .. nV.

.

. ,

,

. ,

. ,

, .

.

, R

, () .

Rm . , Rm

.

sm

vIR R

=+

svIR

=

A

vs

R

Rm vs

R

21

()

. .

() Rm

Rm. , Rm

.

R.

1ss m s sm m

v Rv RI v R vR R R R

= = + +

vs

: 1.

.

2.

.

=

. ,

2 Vm

m

RV VW V R V

= = =

,

:

1mm

RV I

= =

50 10 100 k/V.

, .

V vs Rm

I = 0

vs

R R Im

22

. = 100 k/V. , 61 1 10 10 A 10 A100000m

I

= = = = .

Rm = 2000 ,

3 6 32 10 10 10 20 10 V 20 mVm m mV R I = = = =

20 mV .

(. ).

2.2

, .. ,

. ,

.

.

Rsh, , (shunt resistance).

. 99

() 0,1 mA. Rsh 1 .

(1) (2)

(3) .

(1) Vm = Rm Im = 0,1 mA 99 = 9,9 mV.

Vm = Rsh Is Is = Vm / Rsh = 9,9 mV / 1 = 9,9 mA.

, : I = Is + Im =9,9 + 0,1 = 10 mA.

(2) (3) , .

50 % 25 % . .

, .

,

Is

Rm

Rsh

m

23

(

).

,

. make-before-break (. . ).

:

, Ayrton:

: (R1 + R2 + R3) || Rm (R1 + R2) || (Rm + R3) (R1) || (Rm + R2 +

R3). 24

. 10

10 V.

() 0,1 () 1 .

() Rm = 0,1 10/(10 + 0,1) = 0,99 . 1 ,

(1 0,99)/1 100 = 1%.

() Rm = 1 10/(10 + 1) = 0,909 . 1 ,

(1 0,909)/1 100 = 9,1%.

.

,

.

. ,

.

(clamp meter),

.

2.3

,

. ,

. , ,

. ,

RS, (multiplier resistance).

9 Rm

10 .

25

. 100 Rm = 1 k

.

100 V 0,75 , 0,5

0,25 ;

( )m S m S m S mm m

V VV I R R R R R RI I

= + + = =

100 V m = 100 , RS =999 k.

, 75 V, 50 V 25 V ( ).

, .

,

(

).

:

RS Rm

26

12 V

70 k

50 k +

V

.

50 , Rm = 1700 10, 50 100 V.

61 1 1 110 50 10 1700 198,3 km m m mR R V I R V I R R R

+ = = = =

V = 50 100 V:

62 2 2 250 50 10 1700 998,3 km m m mR R V I R V I R R R

+ = = = =

63 3 3 3100 50 10 1700 1,9983 Mm m m mR R V I R V I R R R

+ = = = =

1 198,3 kR = 10 V

1 2 2 16

2 250 50 10 1700 998300 800 km m m mR R R V I R V I R R

R R+ + = =

= =

1 2 3 3 1 26

3 3100 50 10 1700 998300 800000 1 Mm m m mR R R R V I R V I R R R

R R+ + + = =

= =

.

, 1

100 V. , = 1 / 100 V = 10 k/V. .

.

. 5 V (, ) () 20 k/V

() 200 k/V, ( ).

27

() 20 k/V 5 V 20 k/V = 100 k. ,

50 k 50 k || 100 k = 33,3 k, 12 33,3/(70 +

33,3) = 3,87 V.

(B) 200 k/V 5 V 200 k/V = 1 M. ,

50 k 50 k || 1 M = 47,62 k, 12 47,62/(70 +

47,62) = 4,86 V.

. 200 500 k/V

, .

10 /V

10 G/V.

2.4

( )

. ,

:

: 10 Hz 300 kHz

: 300 kHz 3 GHz

: 3 GHz 30 GHz

: > 30 GHz

nV kV n

k . ,

50/60 Hz 1 V 10 kV 1 10 kA.

: (peak), (RMS) (average)

.

28

1.

.

2. , ,

(Square), (Mean)

(Root):

( )2

1

2

2 1

1 TRMS

T

f f t dtT T

=

1 = 0.

3. , ,

( )2

12 1

1 TAVG

T

f f t dtT T

=

RMS.

(dc-direct current). , .. RMS

Vdc VRMS.

(

Hz)

, . , ,

.

29

, ,

, .

(rectification) (rectifiers)

, (diodes).

-.

,

. ,

(.. , Zener, Schottky, Gunn, LED, . ) (, ,

.). :

.

:

( )

30

(

) .

.

= 0,637

= / 2 = 0,707

,

(. 0,637 ). ,

(. 0,707

). 0,707/0,637 = 1,11.

.

. 100

Rm = 1 k 100 VRMS.

31

.

.

IAVG = 100 .

100 A 157 A

0,637 0,637AVG

peak mII I= = = = .

( ) ( )

mI

=

2 VF,

( , ).

VF = 0,7 V. 1,414

VRMS,

61, 414 2 1,414 2 1,414 100 2 0,7 1000

157 10890,7 k

RMS F RMS Fm S m

m S m

S

V V V VI R RR R I

R

= = =

+

=

, .. 75 V.

75 , . .

, Im = 157 , IRMS = 0,707 Im = 111 ()

VRMS = 100 V (), R = 100 V / 111 = 900,9 k,

= 900,9 k / 100 V = 9 k/V

() () .

() ,

( 100 mV). , 0,5

0,7 V ,

.

( ) 32

.

.

. (. ) 250 mA.

1 mA Rm = 1700 .

Np = 4 Ns = 500

(VF = 0,7 V). 20 k.

RL.

,

1. ( ) Im = IAVG/0,637 = 1 mA/0,637 = 1,57

mA

2. ( )

Em = Im (Rs + Rm) + 2 VF = 1,57 103 (20000 + 1700) + 1,4 = 35,5 V

3. ( RMS)

Es = 0,707 35,5 V = 25,1 V [RMS]

4. ( RMS)

Im = 1,11 IAVG = 1,11 mA [RMS]

5. ( RMS)

Is = Ip Np / Ns = 250 mA 4/500 = 2 mA

6. , Is = +

2 mA = 1,11 mA + IL IL = 2 1,11 = 0,89 mA

RL = Es / IL = 25,1V / 0,89 mA = 28,2 k

33

2.5

.

. (

) ,

, .

. (break-in cable)

.

34

3.

1.

2. ,

3.

4.

5.

6.

37

. , , ,

, . ,

/ ,

. ,

.

3.1

100 , (tolerance) 10 .

90 110

100 10 . .

(). , 1000 900 1100 .

|1000 900| / 1000 = 0,1 10 %.

- .

, * , :

: | *| ( )

: | *| / (, , .. %)

, , 3 V 1%,

2,97 V 3,03 V, . 0,06 V. ,

400 V 1%, 396 V 404 V,

. 8 V.

ppm (parts-per-million)

, ..

ppm/C. 2 100 ppm/C,

39

100 2000000 2001000000

=

, 2 200 .

. 1,14 k 1,26 k

1,2 k. ; ,

25 C 500 ppm/C,

75 C;

1,26 k 1,2 k = +0,06 k

1,2 k 1,14 k = 0,06 k

= 0,06 k

0,06 k 100% 5%1,2 k

=

25 C R = 1,2 + 0,06 k = 1,26 k

500500 ppm 1,26 k 0,63 C1000000

R = =

= 75 25 = 50 C

R = 0,63 /C 50C = 31,5

, 75 C 1,26 k = 1,2915 k

3.2 ,

1% 1 .

, 1 1% = 0,99 1,01 .

1%

(accuracy) .

.

40

!: .

100 V 2% (.

2 V 100 V) 10 V

2 V 100% 20%

10 V

= , . 8 12 V.

,

.

(resolution)

. .., ,

(

. ,

. , (

) .

, , 1 ( ).

(

) . ,

/(max Xmin)

.

(precision) , :

. ..

41

(, -, .) (

). ,

.

, .

.. ,

10:43:20. ,

!

.

,

: 1/100

. , 1/10

!

, .

( ).

, .

: , ,

.

, (calibration error)

. -

( ). 42

, .

( )

. ,

.

.

.

3.3

. :

. ,

.

( )

- ( , )

.

. ,

( ).

. ,

(..

V ).

,

,

. .

43

3.4

,

, ,

.

. , ,

.

.

:

. ( , ..)

. (nulling) .

. .

. , ,

, (.. ), .

.

, .

( )

(. ).

, Murphy

.

= , = [( ) + ( )]

= , % = [(% ) + (% )]

= / , % = [(% ) + (% )]

= , % = (% )

44

3.5

, .

. ,

,

.

( ), ,

, .

(outliers) .

.

3.6

, ,

,

.

(..

) 0

:

(swamping resistance)

. ,

Rm

Rsh

.

45

9 ,

1% 0,1%. :

,

. , ,

( ) Rm.

.

0,004 /C.

0,0002 /C

0,0006 /C. 0C,

2 ;

:

R =

R =

RT =

= = 0,004 /C

= = 0,0002 /C

= = 0,0006 /C

0C: R + R

C:

RT = R (1 + ) + R (1 + )

:

RT = (R + R) (1 + )

,

R (1 + ) + R (1 + ) = (R + R) (1 + )

:

R (1 + 0,004 ) + R (1 + 0,0002 ) = (R + R) (1 + 0,0006 )

:

0,0034 R = 0,0004 R

0,0034 8,50,0004

RR R = =

8,5 2 17R = =

46

4. , ,

1.

2. Wheatstone Kelvin

3.

4. , , RC, RL Q

5. Maxwell Hay

6. Owen, Schering Wien

47

4.1

Ohm,

.

. (

):

;

,

. , . ,

.

, ,

, ( )

. ,

. :

A IV +

V

A

I + IV

+

R E

I

+

+ A

E + EA

+

R E

I

V

+ EA

I

B

: IV

vo vs Rs RX

RX vo vs Rs

VH

IH

IL

VL

vs ( Rs)

( ). . .

vo vs Rs

VH

IH

IL

VL RX

50

4.2 WHEATSTONE KELVIN

4.2.1 Wheatstone (Samuel Hunter Christie in 1833, Sir Charles Wheatstone 1843)

Wheatstone (

):

S .

x

SPRQ

=

0, 1

Rx, 2, VP = VQ VR = VS

1 P = I2 Q I1 Rx = I2 S.

.

. P

Q ( ), 0,05%

0,1% S, Rx ( P +

S + Q) (0,05 + 0,05 + 0,1)%, .

0,2%.

,

.

Thevenin (

):

G

+

+ G

S Rx

+

VP +

VQ

VR

+

VS

Q P

I1 I2

51

r = P || Rx + Q || S

xR S B

x

R SV V ER P S Q

= + +

.

Wheatstone. P = 3,5 k, Q = 7 k, S = 4 k, R = 2 k.

= 10V, 1 /mm

2,5 k. R .

,

r = P || R + Q || S = 3,5 k || 2 k + 7 k || 4 k = 3,82 k

( ) ( )1 A 3,82 k + 2,5 k 6,32 mVR S g gV V I r r = + = =

66,32 mV 632 10

10 VR S

B

V VR SR P S Q E

= = = + +

R, :

6632 10R R SR R P S Q

+ = + + +

R Sg

g

V VIr r

=+

G

rg r

VR VS

Ig

52

R = 5,46772

4.2.2 Kelvin (William Thomson Lord Kelvin, 1861)

Wheatstone, ,

, 5 ( 1012 ).

Kelvin, (

Q S Wheatstone). Kelvin

(: Q

Qx):

: , .

, 1 2i R i r IS= + 1 2 1 2rIS i R i r IS R i iR

= =

.

1 2 1 2 1 2x x xpi P i p IQ IQ i P i p IQ P i iP

= + = =

.

+

G EB

S R

Qx P i1

I

r

p

i1

i2

i2

I i2

I

I + i1

53

1 2

1 2

x

pP i iIQ P

rIS R i iR

=

, p rP R= xQ P

S R= ,

Wheatstone. P, R, p, r

. Qx:

xSPQR

=

10 1 0,2%.

0,1 .

4.2.3

(.. )

, . .

. , ,

(..

).

(

(surface leakage current).

.

, .

, (guard

wire)

(surface leakage current)

.

V

V E

I I

I +

+

54

:

, , ,

(megohmeter megger [

]).

( 100 5000 V)

( ) .

V V = E

+

I

55

4.3

,

, , , .

/

.

:

.

.

, :

: 1 2

3 4

Z ZZ Z

=

,

.

1

G

2

3 4

56

4.4 , , RC, RL Q

4.4.1 ( De Sauty)

, 1/3 = 2/4.

31 13 4 1 3 4 4

1 1xx

x

jjC RC C C

R R C R C R R

= = =

,

. , C1 .

: (G) ()

(null detector) D.

4.4.2 CR LR

Cp

( , ,

). ()

( ) (

).

.

:

2 2 2 2

,s s s sp ps s

R X R XR XR X+ +

= =

()

2 2

2 2 2 2,p p p p

s sp p p p

R X R XR X

R X R X= =

+ +

D

Cx

R3 R4

C1

Cp Rp

Ls Rs

57

(

).

, .

, s sLs s

X LQR R

= = , QL [5, 1000]

, 1p

Cp p p

XD

R C R= = , DC [0,0001, 0,1]

.

4.4.3 CR, LR, Q

4.4.3.1 -

1 4

3

1 3

4

s

s

R RRR

C RCR

=

=

() Rs R1.

D

Cs

R3 R4

C1

R1 Rs

p pL

p p

R RQ

X L= =

sC s s

s

RD C RX

= =

58

4.4.3.2 -

1 4

3

1 3

4

p

p

R RRR

C RCR

=

=

( )

4.4.3.3

, .

1 4

3

1 4

3

s

s

R RRR

L RLR

=

=

4.5 MAXWELL HAY

4.5.1 Maxwell

Maxwell ( Maxwell-Wien) .

D

Cp

R3 R4

C1

R1

Rp

D

R3 R4

L1

R1

Ls

Rs

59

():

1

3 4

sRRR R

=

:

3 1

4

sLC RR

=

:

1 4

3

3 1 4

s

s

R RRR

L C R R

=

=

4.5.2 Hay

Hay .

:

1 4

3

3 1 4

p

p

R RRR

L C R R

=

=

, .

D

R3 R4

R1 Ls

Rs

C3

D

R3 R4

R1

C3

Rp

Lp

Maxwell

Hay

60

4.6 OWEN, SCHERING WIEN

4.6.1 Owen

Owen

/.

:

21

3

1 2 3

s

s

RR CC

L C R R

=

=

4.6.2 Schering

Schering /.

:

43

1

31

4

s

s

RR CCRC CR

=

=

4.6.3 Wien ()

:

3 4 3 4

12

fR R C C

=

R2

Ls

Rs

D

R3

C3

C1

R4 R3

Cs C1

Rs

D

C3

D

R3

R4

R1

C3

R2

C4

61

Agilent-E4981A Capacitance Meter

64

5.

1.

2.

3.

65

5.1

(operational amplifier op-amp)

.

: !

o ( ) o o o

()

6

Out

+

V+

V 4

5

Offset null

1

7

2

3

Inverting input

Non-inverting input

67

1 2oi i i i i+ = + + +

: offset null ( ) .

2 1dv v v=

( )2 1 , : o dv Av A v v A= =

, 105 108 , Ri 105 1013 , Ro 10 100 0 , VCC 5 24 V

+

VCC

VCC

i1

i2

io

i+

i

Avd

Ro Ri

vd vo

v1

v2

68

vout VCC ():

CC out CCV v V

.

( ) ( ).

.

vout/vin .

.

, 741 :

, = 2105

++

10 k

1

o

i

vs

20 k

741

vo

i

+

10 k

vd

vs

20 k

2 M

50

200000 v1

i o

69

, Ri = 2

, Ro = 50

;

, :

1 11

1

1

1

10000 2000000 20000200 301 1002 3

23

s o

s o

s o

s o

v v v vv

v v vv v v

v vv

= +

=

+=

vd = v1,

( )1 0 0 1400 200000v v v v = +

0 26667067 53333333 1,9999699oo s

s

vv vv

+ =

.. vs = 2 V, v= 3,9999398 V v1 = 20,066667 V

1 0 0,19999 mA20000v vi = =

.

.

.

.

io

+

v1

v2

+ 741

vo 5 k 40 k

vs

20 k

70

9 io vs = 1 V 0,65 mA. , .

, : = 9,00041 io

= 0,657 mA vs = 1 V. .

5.1.1

(inverting amplifier)

:

1 11 2

1

i o

f

v v v vi iR R

= =

1 2 0v v= = ()

1

i o

f

v vR R

=

1

fo i

Rv v

R=

:

v1

+

v2 = v1

+

vo

+

i2 = 0

i1 = 0

+

+

vi Ri

+

vo

++

R1 0 A

vi

Rf

vo

v1

v2

i1

i2

71

5.1.2

(non-inverting amplifier)

1

1 fo iR

v vR

= +

= 1 Rf = 0 (.)

R1 = (.)

( = 1 voltage follower

)

5.1.3 ()

(summer)

1 2 31 2 3

f f fo

R R Rv v v v

R R R

= + +

+

v1

+ R1 0 A

vi

Rf

vo

v2

+

v3

v1

v2

R1

R2

R3

+ 0 A

Rf

vo

0 A

72

5.1.4 (differential amplifier)

12

2 22 1

131

4

1

1o

RRR Rv v v

RRRR

+

= +

,

vo = 0 v1 = v2.

312 4

RRR R

=

( )2 2 11

oRv v vR

=

R2 = R1 R3 = R4 (v2 v1).

.

5.1.5

.

:

( )32 2 11 4

21oRRv v v

R R

= +

v2

R1

+v1 R3

+

va

R2

vo

vb

R4

73

( RG):

: 21v

G

RAR

= +

v1

R1

R2

R3

+

R2

+

vo

0 A

+

+

v2

R3

R4

R1

0 A

R

R

RG

v1 (inverting) R

R

+

R

vo

+

+

v2 (non-inverting)

R

74

5.1.6

:

( ) ( )0

1 to iv t v z dzRC

=

:

( ) ( ) ( )

0

1 10

R Ct

i oo i o o i

i i

v dvC dv v dt v t v v z dzR dt RC RC

=

= = =

5.1.7

:

( ) ( )iodv t

v t RCdt

=

:

R +

vi

iR

C

iC

+

+

vo

+

R

+

vi

C

+

vo

75

5.2

( ):

:

oi

RKR

=

.

1. (zero drift) 2. (bias)

(nulling) . www.analog.com/static/imported-files/tutorials/MT-055.pdf

:

( . 31).

Ri

+

vi +

Ro

vo

Rs

Rm

Ri

+

vi +

Ro

vo R1

C

Rm

76

5.3

1 fA (femto: 1015) 50 .

,

.

Rs

741 (IC741, : Philips)

78

6.

1.

2.

3.

4.

5.

6.

79

6.1

(

2. (2 1)

.

. [: , .]

0 8 V 3

. ADC :

, 1,5 2,5 V, 2 (0102) V.

, Vin, (

),

Vin k k:

, :

ADC:

: 1

2 1N [ LSB (least significant bit)]

. 800-1500 mV 8

010100002 (8010) 100101102 (15010). k 10mV.

:

111

110

101

100

011

010

001

000 1 3 4 5 2 6 7 8

1 V

( 0 )

max

2 1NX

82

= 1500 800150 80 1

+

= 700 mV/71 = 9,86 mV = 81

2 1= 1

255= 0,4%

,

. ,

. ,

.

6.3

:

V ( 0 V).

.

( - 0).

Vin

V0

t1 t2

t

V0

(gating)

0 t

83

( ) 0rampV t V mt=

m . ,

( )1 0 1ramp inV t V mt V= =

( )2 0 2 0rampV t V mt= =

,

2 1 inVt t tm

= =

( , ),

int n V nmT

T

= = ( : 1tn

T = +

)

, .

(comparator).

(1) LOGIC HIGH

(0) LOGIC LOWin ref o

in ref o

V V V V V VV V V V V V

+

+

> > = =

< < = =

, 1 ( )

0 .

84

6.4 ()

:

.

.

( - 0).

Vin

C

R

+

Vout Vref

Vin

C

R

+

Vout Vref

1: C Vin (, VC(0) = 0).

2: C Vref Vout = 0. ( , Vref . .).

85

,

( ) inoutV TV TRC

=

T s, T .

, .

Tx :

( ) ( )ref x inout x out xref

V T V TV T T V T TRC V

+ = + =

. ()

.

R C

. ,

.

,

( ).

:

Vin1

Vin2

Vin1 < Vin2

t

Vout

0

86

. ADC R = 100 k C =

0,01 F. Vref 10 V 10 ms.

6,8 V.

6,810ms 6,8ms10

inx

ref

VT TV

= = =

10 + 6,8 = 16,8 ms.

( 10 V 10 + 10 = 20 ms 30 mV 10 +

0,03 = 10,03 ms.)

6.5

:

.

.

(bit 1)

(bit 0) ( , ).

:

1. (most significant bit-MSB) 1

87

2.

(digital-to-analog converter, DAC)

3. ( ) DAC.

,

1, 0.

.

( 4 )

.

1000 8

1100 12

0100 4

1010 10

1110 14

0110 6

0010 2

1001 9

1011 11

1101 13

0111 7

1111 15

0101 5

0011 3

0001 1

DAC Digital-to-Analog Converter

( )

START

Vref

MSB

88

.

,

s (, 10 20 s).

DAC (

):

6.6

,

: (1) , (2) (3) .

, ,

() .

. ,

, +1

( ) 0 1 (

!). 1 0

. , 3 0,000

1,999, ( ,000 1,999) 89

1 2000 (2103). 5 1

200000. 4

. ,

.

.

.

. ,

( % + [LSD])

( % + [LSD])

LSD (least significant digit) ,

, . ,

3 (0,7% + 1).

, %, .

20 V, ; 3 ,

20,0 V ( ,

), 1 0,1 V. , ,

(0,7 20/100 + 0,1) = 0,24 V.

0,24 V 100% 1, 2%20 V

= , .19,86 20,24 V.

,

1,2 V. 3 (0,5 % + 3)

, 200, 20 2 V.

;

,

200 V ( , ). .

01.2. 1,2 0,5/100

= 0,006, .

1 8 8 8 8

90

, . 3 , 1,2

0,3, . 0,9 1,5 V, 25% ( !) ,

. .

20 V, .

1.20 ,

(1,20 0,5/100 + 0,03) = 0,036 V. 1,16 1,24 V

, 3%,

.

2 V, .

1.200 (1,200 0,5/100 + 0,003) = 0,009 V.

1,191 1,209 V 0,75%

( 1,200 V 0,75%).

,

/

.

(sampling),

(Sa/s, Samples per second),

.

!:

(, , .)

(, ).

. ,

()

( 85%) .

91

:

[1] Bell, D.A.: Electronic Instrumentation and Measurements, Reston (Prentice-Hall),

Reston,VA, 1983.

[2] , .-.: , , , 2001.

[3] Webster, J.G. (Ed.): Electrical Measurement, Signal Processing, and Displays, CRC

Press, Boca Raton FL, 2004. [ ] [ !]

[4] Sanderson, M. L.: Electrical Measurements, Chapter 27, pp. 439-498, in W. Boyles,

(Ed.): Instrumentation Reference Book, 4th Ed., Elsevier, 2010. [ ]

[5] Application Notes Agilent ( , .. Fluke,

Hameg, Tektronix, Metrix, Keithley Instruments, Honeywell, Gould, .):

http://www.home.agilent.com/agilent/facet.jspx?t=79831.g.1&cc=GR&lc=eng&sm=g&

pageMode=TM&pageMode=TM

:

[4A] 8 Hints for Making Better Digital Multimeter Measurements

[4B] 8 Hints for Successful Impedance Measurements

[4] Impedance Measurement Handbook, 4th Edition

:

[] Bentley, J.P.: Principles of Measurement Systems, 4th Edition, Pearson Education,

Harlow, England, 2005. [, ]

[] Regtien, P.P.L.: Electronic instrumentation, 2nd edition, VSSD, Delft, The

Netherlands, 2005.

[] Witte, R.A.: Electronic Test InstrumentsAnalog and Digital Measurements, 2nd

Edition, Pearson Education Press, New York, 2003.

:

[] Fraden, J.: Handbook of Modern SensorsPhysics, Designs, and Applications, 4th

Edition, Springer, New York, 2010. [ ]

93

:

1. [1]

2. http://www.tpub.com/neets/book3/7b.htm

3. http://electricinnn.blogspot.com/2009/11/galvanometer.html

4. http://www.geofex.com/

5. http://commons.wikimedia.org

6. http://www.csgnetwork.com/dimmerdelayproj.html

7. www.analog.com/static/imported-files/tutorials/MT-055.pdf 8. http://www.globalspec.com/

9. http://pioneer.netserv.chula.ac.th/~tarporn/311/HandOut/DmmPPT.pdf

94

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