قياسات وأجهزة نظري
DESCRIPTION
٢٢٦٧٦٧אא אאאאאאאאאא ٢٦٧ א א אאאא אאW אאW TRANSCRIPT
٢٢٦٧٦٧אא
٢٦٧ א
،،אא،אW
אא א א א א א אאאא،אאאאאאא
אאאא אאאאאאאWא
אאK אאאאאאא
א ،א אא א א אא א א ، א
א،אאאאאאאאאאאאאאאא
אא،אאאא،אK
א א ? ? ? ?אאאאאאאאK אאאאאאא
،א،אאאאאאאאאK
א אא א WאK
אאאא
٢٦٧ א
،אאאאKKK،
אא،אאאאאאאאK
אאאאאאאאא،אאאאאאא
אאאאאKאאא،אאאאא
אא،אאאאאאאאאאאאK
אאאאאאאאאאאK
אאאא،אאאא،אאאא،אK
א،אאא،אא،אאא
אאK ،אKKKKKK
אאאאאאאאאא
א
א
א
א
א
١
א٢٦٧ אא א
אאאא
- ١ -
אאWאאאK
אאאאWאאW • אאאאאK • אאאאאK • אאאאK • אאאK • אאK • אאאאאK
אאאWאאא١٠٠K٪
אאWK
Wאא • אאK • אKאK
אאWאאאK
א٢٦٧ אא א
אאאא
- ٢ -
אאאא
אאW • אאאאאK • אאאאאK • אאאאK • אאאK • אאK • אאאאאK
א٢٦٧ אא א
אאאא
- ٣ -
١ J١ Introduction אאאאא
אאאאאאאאK
אאאK
١ J٢ General Concepts אWאאK
אאאW F١E measured quantity F٢E Standard system F٣E measuring instruments F٤E measuring technology
אאW F١E Wאאאא
אKKKKKKKKKKKKK F٢E WאאאאאK
W FE אאאאThe international standards system
אאאאאאKאאאאא
אאאאK FE אאאאאThe primary standards system
אא،אאאאאאאאK
אאאאאאK FE אאאאThe secondary standards system
א٢٦٧ אא א
אאאא
- ٤ -
אאאאאאאKאאאאאא
אאKאאאאאאאFאאEא
אאאאאאK FE אאאThe working standard
אאKאאאאאאK
F٣E WאאאאאאאאאאאאK
F٤E Wאאאאאא
١ J٣ אאאElectrical And Electronic Instruments אאאאאאא
אאאKאאאאאא،אאאאאאאFE
FKEאאאאאאאאאאאא
،א،אאאא،אאאK
١ J٣ J١ אאא
Functions and Characteristics of Electrical and Electronic Instruments אאאאאא
אKאאא،אאאאK،אא
א٢٦٧ אא א
אאאא
- ٥ -
١٠٠٪אאאKKאא،אאאא،אאא
אא(amplifier)אאאK
١ J٣ J١ J١ אאאElectrical Units
א،אאאאאאאאאK،א
אאאאאאKאאאאאW
F١E אא(Q) F٢E אא(I) F٣E אאאאא(V) F٤E א(R) F٥E אאא(L) F٦E א(C)
א٢٦٧ אא א
אאאא
- ٦ -
F١ J١Eאאאא،אאאאאאאK
א א אאאW
א(Length) l (meter) m
א(Mass) m א(kilogram) kg
א(Time) t (second) s אא(Temperature) T (degree Kelvin)°K
א(Luminous intensity) (candela) cd
אא(Electric current) i (Ampere) A
אאאW אאאא(Electromotive force) V (Volt) V
א(Quantity of charge) Q (Coulomb) C
אא(Electrical resistance) R (Ohm) Ω א(Capacitance) C א(Farad) F
אאא(Inductance) L (Henry) H
F١ J١Eאא
١ J٤ אאError Sources in Measurements אאא
א،אW F١E אא(Instrumental Error)W
FE אFW J JE FE אFWאאאאאאאאE FE אFW–E FE אFW–E
F٢E אא(Gross Error)W FE א
א٢٦٧ אא א
אאאא
- ٧ -
FE אאא FE אאאאא
F٣E א(Environmental Error) FE אאאאWאאאאא
FE אאWאאאא
אאאאאאא
K אאאא
אאאאא،אאאאא (Expected Value) אאK
אא،אאאא(Error)אK אאאאW
א(Absolute Error)א(Percentage Error)K
א٢٦٧ אא א
אאאא
- ٨ -
אאAbsolute Error (eab) אאאאאK
אW nnab XYe −= F١ J١E
W : eab אא : Ynאא : Xn אא
אאFerERelative Error אאאאאK
אW
n
nn
n
abr Y
XYYe
)e(−
== F١ J٢E
אאPercentage Error (e%)
אאאאאK אW
%100Y
XY%100
Ye
)e(n
nn
n
ab% ×
−=×= F١ J٣E
אW אAccuracy
אאאK
א٢٦٧ אא א
אאאא
- ٩ -
אאRelative Accuracy (Ar) אא(Ar) אאאאאK
אא(Ar)W
rn
nn
n
nr e1
YXY
1YX
A −=−
−== F١ J٤E
W ArWאאK
Percentage Accuracy (a%)אאאאא(a%)אאאאאK
%100Y
XY%100%
YX
an
nn
n
n% ×
−−== F١ J٥E
%% e%100ErrorPercentage%100a −=−= F١ J٦E
W : a% אאא
F١ J١E
אאV49،אאאאאV50א،W
FE אא FE אא FE אא FE אא
אW FE אאeabW
volt14950XYe nnab =−=−= FE אאe%W
א٢٦٧ אא א
אאאא
- ١٠ -
%2%100V50
V49V50%100
Ye
en
ab% =×
−=×=
FE אאArW
98.05011
v50V49V50
1A r =−=−
−=
FE אאa%W
%98%2%100e%100a %% =−=−=
אאאאאאא
אKאא(Precision)אאאאאאאאאאאאאK
אא،אאאאאKKאW
n
nii X
XX1)ecision(Pr
−−= F١ J٧E
W (Precision)i Wאא(i)
iXWאא(i) nXW אאאאא (n)
א٢٦٧ אא א
אאאא
- ١١ -
F١ J٢E אאאאאאW
אאVi (volts)אא981 1022 1013 974 1005 1036 987 1068 1079 9910
F١ J٢EF١ J٢E
אאאא(Precision)אF٤EFW(P4%K אW
אF١ J٧WE
%100V
VV%100%P
n
ii ×
−−=
nאאא١٠אא אאאאאF٤E،Wi = 4
10Xאאאאא،W
1.10110
99107106981031009710110298X =+++++++++
=
P4% = %94.95%1001.101
1.10197%100 =×
−−
١ J٥ אאא Statistical Analysis of Errors in Measurements
א٢٦٧ אא א
אאאא
- ١٢ -
אאאא،אK،אאFאEא،
אאאאKFאאאאאאEKאאאאWאWאא،א
א،אאאאאאא،אאאאאאWא
،אאאK א،אאא،
אאאאאאאאאאאאאK
אאאאKאאאאKא
،אאאאאאKאאאאאאW אא(arithmetic mean)،אאאF(Average deviationאאא
(Standard deviation)K ١ J٥ J١ אאאאAverage value (arithmetic mean)
אאאאXnאאא)X.....X,X,X( n321אאאnKW
nX........XXX
X n321 ++++= F١ J٨E
١ J٥ J٢ אאdeviation
אאאאi)id(،אאא אאאiXאאאאאXKW
XXd ii −= F١ J٩E
א٢٦٧ אא א
אאאא
- ١٣ -
אאאאאKW 0 d .. . . d d d n321 =++++ F١ J١٠E
W
X........XXX....XXXX......XXXXd n21n
n
1i21i −−−−−++=−+−+−=∑
=
0XnX.dn
1ii
n
1ii =−= ∑∑
==
אאאאW
∑=
=n
1ii 0d F١ J١١E
אאK
١ J٥ J٢ J١ אאאAverage deviation אאא(D)אאאאKW
nd ... . d d d
D n321 ++++= F١ J١٢E
١ J٥ J٢ J٢ אאאStandard deviation אאא(S)אאאאK
W
)1n( or nd ...d d d
S2n
23
22
21
−++++
= F١ J١٣E
،אאאאא( n < 30 )אא(n-1)אאאא( n ≥ 30 )אאn،אאn
n-1K
F١ J٣E
א٢٦٧ אא א
אאאא
- ١٤ -
א،אאW FE אאאאXK FE אאidK
FE אאא∑=
n
1iid K
FE אאאDK FE אאאSK
א א X150.1 X249.7 X349.6 X450.2
F١ J٣EF١ J٣E
אW FE אאXW
9.49 4
2.50 6.49 7.49 1.50 X =+++
=
FE אאidW 2.0 9.49 1.50 d1 =−=
2.0- 9.49 7.49 d2 =−=
3.0- 9.49 6.49 d3 =−=
3.0 9.49 2.50 d4 =−=
FE אאא∑=
n
1iid W
0 3.0 3.0 2.0 2.0 d d d d d 4321
4
1ii =+−−=+++=∑
=
FE אאאDW
25.0 41
43.0 3.0 2.0 2.0
D ==+−+−+
=
א٢٦٧ אא א
אאאא
- ١٥ -
FE אאאSW
294.0 3
3.0 3.0 2.0 2.0 14
d d d d S
222224
23
22
21 =
+++=
−+++
=
١ J٦ אאLimiting Errors אאאא
אאFull scale readingKאאvoltmeterאא%2±Kאא
אאאא2%Kאאאאאא2%Kא
אאאאאK F١ J٤E
אאאא 300 v 2 %Kאאאאאא
120 vK א
אאW v6 v300 02.0 scale fullat Error Limiting =×=
אאא120 vW
% 5 % 100 120
6 v 120 at Error Limiting =×=
א٢٦٧ אא א
אאאא
- ١٦ -
١ J٧ אאElements of Electronic Instruments
אאאאF١ J١KEאW
F١ J١Eאא
F١E TransducerWאאא F٢E Signal ModifierWאאאא
אKאא؛אאאא،א
אאאאK F٣E Indicating DeviceW
אא(Voltmeter)א(Ammeter)K
אאאאאאWאאאאאאאא
אW،אא،אא،אא،אאאאאאKאא
אאאאאאאאאאK
Transducer Signal modifier Indicating device
א٢٦٧ אא א
אאאא
- ١٧ -
١ J٨ אאאאא
Selection, Usage and Care of Measuring Instruments אאא
K،אאאאאאאאאאאאאא،K
אאאאאאKאאאאאFא
אE(The operating and instructions manual)א،אאאאKאאאאא
אאאאאאאאאאאאאאFאאKEא،
אאאא،אKאאW،א،
،KאאאKאאאאאאאאאK
،אא،אאאאאאאאאאא
אK
א٢٦٧ אא א
אאאא
- ١٨ -
אא ١ J١ אא1.5 Aא،
1.46 AKאאא(eab)אא(e%)K
١ J٢ אאא2 kΩא،1.93 kΩא،W
FE אאK FE אאאK
١ J٣ אאאאאא30.15 Vא،א
29.9 VK ١ J٤ אא،אאאW
אא(volts) א 20.20 (1) 19.90 (2) 20.05 (3) 20.10 (4) 19.85 (5) 20.00 (6)
אאאאK
א٢٦٧ אא א
אאאא
- ١٩ -
١ J٥ אאאאאW
א(mm) אא2.211 2.182 2.203 2.214 2.175 2.196
א٢٦٧ אא א
אאאא
- ٢٠ -
FE אאK FEאאאאאK
١ J٦ אא98%אאאאW
FE אאאא175 V300 V FE אאאאאFE
١ J٧ אאאאאאא
٣٠٠K؟אא ١ J٨ א،אא
5.6 kΩאאאא،W
א(kΩ) א5.751 5.602 5.653 5.504 5.705 5.556 5.807 5.558
אאאאאאאK
א٢٦٧ אא א
אאאא
- ٢١ -
١ J٩ אא،אאאאW
א(kHz) אא5321 5482 5433 5354 5465 5316 5437 5368
א٢٦٧ אא א
אאאא
- ٢٢ -
אאאW FE אאאאK FE אאאK FE אאאK
١ J١٠ אאאא300V2%א
אאKאאאאאאא120א VK
אאאאאאאא
א
א
א
א
٢
א٢٦٧ א א
אאאא א
- ٢١ -
אאWאאאאאK
אאאאWאאW • אאאK • אאאאאאK • אאאאאאK • אאאאאאK
אאאWאאא١٠٠K٪
אאWK
אאW • אאK • אKאK
אאWאאאאK
א٢٦٧ א א
אאאא א
- ٢٢ -
٢ J١ Introduction אאאאFאE
אאאאW،אאאאאאאאאK
٢ J٢ אאאD'Arsonval Meter Movement אאאאאא
א،אWK ٢ J٢ J١ אאאConstruction of D'Arsonval Meter
אאא،F٢ J١E،אא(horseshoe)،אא(soft iron)،
אאא،אאאא،א
אאאKאאאאאאא
،אאאאאK
א٢٦٧ א א
אאאא א
- ٢٣ -
F٢ J١EאאאK
٢ J٢ J٢ אאאOperation of D'Arsonval Meter אאאא،א،א
אאאאאא،אאאאאKאאא،
אאאאא،אאאKאא
אKאא،אאאאאאאאא،אאא،אאאא
אאK
Moving Coil
N S
Spring
Core
South Pole
North Pole
א Permenant Magnet
Pointer
Scale
א٢٦٧ א א
אאאא א
- ٢٤ -
٢ J٢ J٣ אאאאאאאא
D'Arsonval Meter in Direct Current Circuits ٢ J٢ J٣ J١ אאאאאאא
D'Arsonval Meter as D.C Ammeter אאאא،אא
אאאאK،אאאא50µAKאא
אK،אאא،אאאאא(Rsh)אאא،א
אאאאKF٢ J٢EאאאאאאאאאאK
F٢ J٢EאאאאK
אאאIshאאImאאאKאאאאא
אאF٢ J٢E،W RshW אא RmW אאאFאE IshW אא אא ImW אאאאאאא IW אאאא
Ish
Im
I
Rsh
Rm +
_
Vm
א٢٦٧ א א
אאאא א
- ٢٥ -
F٢ J٢EאאאW mmm R I V ⋅= F٢ J١E
אRshאא،אאאא،אאW
shm V V = F٢ J٢E ،אאאאאאאאאאW
shm I I I += F٢ J٣E
אאאRshאא،אאאW
msh I I I −= F٢ J٤E
אאאאIshאVmא،RshW
( )m
mm
sh
shsh II
RI
IV
R−⋅
== F٢ J٥E
אאאאאאאא،אnאא،אnW
II nm
= F٢ J٦E
אאF٢ J٥EW
( )( ) ( ) 1-n
RI/III/RI
R m
mm
mmmsh =
−⋅
= F٢ J٧E
א٢٦٧ א א
אאאא א
- ٢٦ -
F٢ J١E אאאאאW
אRmΩ100אmA1Im =Kאאאא(Rsh)אאmA10I =K
אW אF٢ J٥WE
( ) Ω=×
××=
−⋅
=−
− 11.11
109100101
IIRI
R3
3
m
mmsh
אnאF٢ J٦EW
101011010n
3
3=
×
×=
−
−
אF٢ J٧EW
( ) Ω==−Ω
=−
= 11.119
100110
1001n
RR m
sh
٢ J٢ J٣ J١ J١ אאThe Ayrton shunt אאאאאאא
אRshאאאאK אאאאא
אRshאאאאאאא(range selector switch)אאאאאK
F٢ J٣EאאאאRsh, Ra Rb،RcK אאRshW
cbash RRRR ++= F٢ J٨E
RshאF٢ J٧EW )1n(/RR msh −= F٢ J٩E
W m1 II n = )١٠-٢(
א٢٦٧ א א
אאאא א
- ٢٧ -
F٢ J٣Eאאאא[I1]K
אאאcba R,R,RאאF٢ J٤KE
F٢ J٤Eאאאא[I2]K אא[I2]אאאRaאאRb+Rcא
RmאRb + RcאאאRm+ RaאאאW
macb RRRR VV ++ = F٢ J١١E
אאאאW
I
I1-Im
+
Im
I3 I2
Ra Rb
Rm
I1
shR
-
Rc
I
I2-Im
+
Im
I3 I2
Ra Rb
Rm
I1
shR
-
Rc
א٢٦٧ א א
אאאא א
- ٢٨ -
)RR(I)II)(RR( mamm2cb +=−+ F٢ J١٢E ،אW
)RR(I)RR(I)RR(I mamcbmcb2 +=+−+ F٢ J١٣E Im (Rb + Rc)אאאW
)RR(I)RRRR(I)RR(I mshmmcbamcb2 +=+++=+ F٢ J١٤E
א(Rb + Rc)א ( )
2
mshmcb I
RRIRR +=+ F٢ J١٥E
אאאRshא(Rb + Rc)א Ra אW
)RR(RR cbsha +−= F٢ J١٦E א[I3]F٢ J٥WE
F٢ J٥Eאאאא[I3]K
אRbאאRcאאRmHRaאRcאאאRm+ Ra+ RbאאאW
bamC RRRR VV ++= F٢ J١٧E
I
I3-Im
+
Im
I3 I2
Ra Rb
Rm
I1
shR
-
Rc
א٢٦٧ א א
אאאא א
- ٢٩ -
אאאאW )RRR(I)II(R mbamm3c ++=− F٢ J١٨E
אW )RRR(IRIRI mbamcmc3 ++=− F٢ J١٩E
RcImאאאW )RR(I)RRRR(IRI mshmmcbamc3 +=+++= F٢ J٢٠E
א(Rc)א ( )
3
mshmc I
RRIR += F٢ J٢١E
אאRbאאW )RR( R R cashb +−= F٢ J٢٢E
F٢ J٢E
אאF٢ J٦E،אא،אאאא(Ra, Rb & Rc)K
F٢ J٦EאאF٢ J٢KE אW
אאW 100A100mA10n =µ=
Im = 100 µA
Ra
Rb
Rm = 1 kΩ
Rc
mA10I1 = mA100I2 = A1I3 =
א٢٦٧ א א
אאאא א
- ٣٠ -
אאW ( )1nRRRRR mcbash −=++=
( ) Ω=−Ω= 1.101100k1R sh cb RR +W
( )2
mshmcb I
RRIRR
+=+
( )Ω=
+µ=+ 01.1
mA10010001.10A100
RR cb
W 09.901.11.10)RR(RR cbsha =−=+−=
cRW ( )
3
mshmc I
RRIR
+=
( )Ω=
Ωµ= 101.0
A11.1010A100
R c
bRW Ω=+−=+−= 909.0)101.009.9(1.10)RR(RR cashb
٢ J٢ J٣ J١ J٢ אאאאא Ammeter Loading Effect
אאאאאא،אאאא
אא،אאאאKאאאאא،אאאאF٢ J٧Eא
אאאאFIeEWIe = E / R1
א٢٦٧ א א
אאאא א
- ٣١ -
F٢ J٧EאאK
אאאאאFRmE،F٢ J٨E،א،W
)RR(EI m1m += F٢ J٢٣E
F٢ J٨EאאאK
אאE = 10Vא،R1 = 10 kΩ،אאF٢ J٧EW
mA1k10V10REI 1e =Ω==
אאאאאF٢ J٨E2 kΩאא،אW
( ) mA833.0k2k10V10)RR(EI m1m =Ω+Ω=+= Rmאא،אאאא
16.7%אאK אאא،א
אאאאKא،אאא،אאא10 ΩK
٢ J٢ J٣ J٢ אאאאאאא Voltmeter) JDCE
E
Y
Im XR1 Rm
E
Y
Ie XR1
א٢٦٧ א א
אאאא א
- ٣٢ -
אאאאאאאאאא
אאאKאאאאאאא،אא
אא،אאאאאאאKאאF10 mvEא،
אא،אא10א mvא،אא(RS)،
אאאאאא،F٢ J٩KE
א٢٦٧ א א
אאאא א
- ٣٣ -
F٢ J٩EאאאאאאK
אRSאא،VW ( )Smm RRVI += F٢ J٢٤E
( ) mmS RIVR −= F٢ J٢٥E א(Sensitivity (S))אW
FSI1S = F٢ J٢٦E W
FSIWאאאאאאאK אSW
Vvolt/ohmohmsvolt1
Ampere1S Ω===≡ F٢ J٢٧E
אRSW mS RVSR −⋅= F٢ J٢٨E
אאאRSאאVא،
אVאRSאאK F٢ J٣E
אאIFSאא100א µAאא،.1 kΩאאאאאאאא . 50 V
א אF٢ J٢٨E
mI RS mR
V
VRs Vm
א٢٦٧ א א
אאאא א
- ٣٤ -
mS RSVR −= אSW
V/k10A1001I1S S.F Ω=µ== SRSW
Ω=Ω−×Ω= k499k1)V50V/k10(R S
אאאאW
F٢ J٤E
אאאRS1, RS2, RS3אאF٢ J١٠KE
F٢ J١٠EאאאF٢ J٤KE
RS1 RS3 RS2
A50Im µ= Ω= k1R m
3 V 10 V 30 V
+−
א٢٦٧ א א
אאאא א
- ٣٥ -
אW אSW
V/k20A50/1I/1S FS Ω=µ== RS1אא3 VW
Ω=Ω−×Ω=−⋅= k59k1V3V/k20RVSR m11S RS2אא10 VW
Ω=Ω−×Ω=−⋅= k199k1V10V/k20RVSR m22S RS3אא30 VW
Ω=Ω−×Ω=−⋅= k599k1V30V/k20RVSR m33S F٢ J٥E
אאאRa, Rb, RcאאF٢ J١١KE
F٢ J١١EאאאF٢ J٥KE
אW אSW
V/k20A50/1I/1S FS Ω=µ== Raאא3 VW
Ω=Ω−×Ω=−⋅= k59k1V3V/k20RVSR m1a Rbאא10 VW
Ω=Ω−×Ω=−⋅=+ k199k1V10V/k20RVSRR m2ba Ω=Ω−Ω=−Ω= k140k59k199Rk199R bb
A50Im µ= Ω= k1R m
Ra Rc Rb
3 V 10 V 30 V
+−
א٢٦٧ א א
אאאא א
- ٣٦ -
Rcאא30 VW Ω=Ω−×Ω=−⋅=++ k599k1V30V/k20RVSRRR m3cba
Ω=Ω−Ω=+−Ω= k400k199k599)RR(k599R bac
٢ J٢ J٣ J٢ J١ אאאאא Voltmeter Loading Effect
אאאאאאא،א،אא
א،אאאאK F٢ J١٢Eאאא،א
אאRB،א،אאRBאW
BA
BR RR
REVB +
×= F٢ J٢٩E
V5k5k25
k5V30V
BR =Ω+Ω
Ω×=
F٢ J١٢EאאאK
אאאאא10kΩ،אאאאאא،אאאRB،
אאאReqW
VBeq R//RR =
VB
VB
RRRR
+×
=
E = 30V RB = 5KΩ
RA = 25KΩ
BRV
א٢٦٧ א א
אאאא א
- ٣٧ -
Ω=Ω+ΩΩ×Ω
= k33.3k10k5k10k5אא،א
א،אW
V53.3k25k33.3
k33.3V30RR
REV
Aeq
eqR B
=Ω+Ω
Ω×=
+×=
אאא29.4 %אאא،אאK
א،אאאאאאאא،אאאF٢ J١٢E
א،אא،אאאא500kΩK
٢ J٢ J٣ J٣ אאאאא D'Arsonval Meter as Ohmmeter
אאאא،אאאאאא
אאK אאאאא
אF٢ J١٣E،אאK
F٢ J١٣Eאאאא
X
Rz Ifs
E
Rm
א٢٦٧ א א
אאאא א
- ٣٨ -
אאאאF٢ J١٣E،FRzEFRmEFEEאא،FRxEאא
א]אX, YF٢ J١٣E[אאאK
אאאאאאFRxEW
xmz RRREI
++= F٢ J٣٠E
אאאאאאאFRxEא،W∞=xRאאW0I =א،0R x =:
mz RREI+
= F٢ J٣١E
FE, Rz, RmE،אאאאאFIFSKE
mzs.f RR
EI+
= F٢ J٣٢E
אmzx RRR +=،W
FSmz
I21
)RR(2EI =+
= F٢ J٣٣E
אאIfs،אאKא ( )mzx RR2R +=،W
( ) FSmz
I31
RR3EI =+
= F٢ J٣٤E
א( )mzx RR3R +=،W
( ) FSmz
I41
RR4EI =+
= F٢ J٣٥E
،אאאאאאא،אא،אאא(∞)
א٢٦٧ א א
אאאא א
- ٣٩ -
אא،אאFRxEאא(Rz + Rm)،،אאא][א
אא(Rz + Rm)KאאX, YF٢ J١٣E،אFshortEאאKא
אאא)Rz.( ٢ J٢ J٤ אאאאאאאא
D'Arsonval Meter in Alternating Current Circuits אאאאאאא
אKאאאאאאאאK
אאאאאאא،א،،،א
אאK،אאאא،א،אאאאאאאא
א،אאאא،אאאKאאאאFאאא
אKEאא(rectification)אאא(diode rectifier)،אK
٢ J٢ J٤ J١ אאאאא D'Arsonval Meter with Half Wave Rectification
אאאאאאא،אאאF٢ J١٠Eא،אא
אK
א٢٦٧ א א
אאאא א
- ٤٠ -
F٢ J١٤Eאא
אא،אאאאאאאאK
אאאאFאאE،،אאאאKא
Kאאאאאאא אאא(Eav)אאא(Erms)W
maxmax
av E318.0E
E =π
=Q F٢ J٣٦E
2E
E maxs.m.r =Q , s.m.rmax E414.1E =∴ F٢ J٣٧E
s.m.rs.m.rav E45.0E414.1318.0E =×=∴ F٢ J٣٨E
F٢ J٣٩E avav
s.m.r E22.245.0
EE ==∴
א[2.22]،אform factor)Eאאאאא،،אאא
אאאאאK
אא(Rs)W
RS
Rm
If.s
s.m.rE avE
א٢٦٧ א א
אאאא א
- ٤١ -
c.d
s.m.r
c.d
c.dmST I
E45.0IE
RRR ==+= F٢ J٤٠E
W TRWאאאK
mc.d
s.m.rm
c.d
c.dS R
IE45.0
RIE
R −=−= F٢ J٤١E
אאF٢ J٤١E،F٢ J٢٨Eא،אאאאאאאא
10 Vא،10 Vא4.5 Vאאאא،
אאאאאאאW F٢ J٤٢Ec.dc.a S45.0S =
אאTRW
c.dc.dc.d
c.dT ES
IE
R == F٢ J٤٣E
W
s.fc.d I
1S =
s.m.rc.as.m.rc.dc.d
s.m.rT ESES45.0
IE45.0
R === F٢ J٤٤E
s.m.rc.ac.dc.dmST ESESRRR ==+=∴ F٢ J٤٥E
F٢ J٦E
אאאאאאאFאF٢ J١٥EEאא،אאאV10E s.m.r =K
א٢٦٧ א א
אאאא א
- ٤٢ -
F٢ J١٥EאאאאF٢ J٦KE
אW אאאF٢ J٣٨WE
V5.41045.0E45.0EE s.m.rc.dav =×===
אאאאאF٢ J٢٦WE
V/k1V/1000I1Sfs
c.d Ω=Ω==
אאאאאF٢ J٤٢WE V/k45.0V/k145.0S45.0S c.dc.a Ω=Ω×==
אאאF٢ J٤٥WE Ω=×Ω=×=+= k5.4V5.4V/k1ESRRR c.dc.dmST
W Ω=×Ω=×=+= k5.4V10V/k45.0ESRRR s.m.rc.amST
אאאW Ω=Ω−Ω=Ω−Ω= k2.4k3.0k5.4300k5.4R S
אW
Ω=Ω=−×
×=−=
−k2.44200300
1011045.0R
IE45.0
R3m
c.d
s.m.rS
mA1I s.f =
RS
avE V10E s.m.r = Ω= 300R m
א٢٦٧ א א
אאאא א
- ٤٣ -
אאאאאאא،אא(Rsh)F٢ J
١٦EK
F٢ J١٦EאאאאK
אאא(D2)(reverse-biased)א،אאאאאK،אאא
א(D2)(forward-biased)،אאא(reverse-biased leakage current)،אאאא(D1)Kא
אא(Rsh)אאא(D1)،אאאא(D1)אאאאK
F٢ J٧E
אאאFאF٢ J١٧EEאאאאא،א50אΩ
אK אW
F١E אאאRSK F٢E אאאאK
RS
inE
s.fI
mR
א٢٦٧ א א
אאאא א
- ٤٤ -
F٣E אאאאK אW
F١EאאאRSW אאאאאאW
shshms.f RIRI ×=×
F٢ J١٧EאאאאF٢ J٧KE
אאאא،IshW
A100200
200A100R
RII
sh
msfsh µ=
ΩΩ×µ
=×
=
אאITW A200A100A100III shsfT µ=µ+µ=+=
אאW V5.4V1045.0E45.0EE s.m.ravc.d =×=×==
אאRTW
Ω=µ
== k5.22A200
V5.4I
ER
T
c.dT
אאאRS, RdאאאאאאRmאאאRshW
Ω= 200R m Ω= 200R sh
D1
D2
TI
A100I s.f µ=
RS
shI
s.m.rin V10E =
א٢٦٧ א א
אאאא א
- ٤٥ -
shm
shmdST RR
RRRRR
+×
++=
אאאRSW
shm
shmdTS RR
RRRRR
+×
−−=
Ω=Ω×=Ω+ΩΩ×Ω
−Ω−Ω×= k35.221035.22200200200200
50105.22R 33S
F٢EאאאאW
V/k5V5.4k5.22
ER
Sc.d
Tc.d Ω=
Ω==
F٣EאאאאW
V/k25.2V10k5.22
ER
Sc.a
Tc.a Ω=
Ω==
٢ J٢ J٤ J٢ אאאאא D'Arsonval Meter with Full Wave Rectification
אאאאאאאאאא
אאאאאאאאאKאא،אא
אאאאאאאאאKF٢ J١٨Eאאאאאאא
(bridge rectifier)K
א٢٦٧ א א
אאאא א
- ٤٦ -
F٢ J١٨EאאאאאאK
אא،אאאאKאאאאFא
אEא،،אאאאKאאאאאא
אאאאאאאK אאאאW
maxmaxav E636.0E2E =π
=Q F٢ J٤٦E
s.m.rmax E414.1E =Q F٢ J٤٧E
s.m.rs.m.rav E9.0E414.1636.0E =×=∴ F٢ J٤٨E
avav
s.m.r E11.19.0
EE ==∴ F٢ J٤٩E
א[1.11]אאאאאא،אאא،אאאאאK
אאא،אאאאא
Rm
RS If.s
א٢٦٧ א א
אאאא א
- ٤٧ -
אאאאא،אאאאאK
F٢ J٨E
אאאאאאאF٢ J١٩Eאא،אאאא،Er.m.s=10 VK
F٢ J١٩EאאאאF٢ J٨KE אW
אאאאW
V/k1mA11
I1SFS
c.d Ω===
אאW V9V109.0E9.0E s.m.rs.m.rc.d =×=×=
אאW mSc.dc.dT RRk9V9V/k1ESR +=Ω=×Ω=×=
Ω=Ω−Ω=∴ k5.8500k9R S
RS
Ω= 500R m
mA1I s.f = V10E s.m.r =
א٢٦٧ א א
אאאא א
- ٤٨ -
F٢ J٩E אאאאאאא
F٢ J٢٠Eאאאא،50 Ω،אאW
FE אאאRSK FE אאאאK FE אאאאK א FE אאאRSאאW
V9V109.0E9.0E s.m.rs.m.rc.d =×=×=
F٢ J٢٠EאאאאF٢ J٩KE
אאאאאאאW
V5.0500mA1RIRI mmshsh =Ω×=×=×
mA1500
V5.0Ish =
Ω=
אאאITW mA2mA1mA1III shmT =+=+=
אאRTW
RS
Ω= 500R m
mA1I s.f = TI
Ω= 500R sh
shI s.m.rin V10E =
א٢٦٧ א א
אאאא א
- ٤٩ -
Ω=== k5.4mA2V9
IER
T
c.dT
אאאRSW
shm
shmdST RR
RRR2RR
+++=
Ω+ΩΩ×Ω
+×+=Ω500500500500
502Rk5.4 S
Ω=Ω−Ω= k15.4350k5.4R S
FE אאאאW
c.dc.dT ESR ×=
V/500V9k5.4
ER
Sc.d
Tc.d Ω=
Ω==
FE אאאאW
V/450V10
k5.4ER
Ss.m.rs.m.r
Tc.a Ω=
Ω==
א٢٦٧ א א
אאאא א
- ٥٠ -
אא
F١E אאאאאאאא850 Ωאא100 µAK
F٢E אאאאאאאא
100 mA אאא 100 µAאא(Rm = 570 Ω)K
F٣E אאאאאאאא
150 Vאאא200 µAאא(Rm = 570 Ω)K
F٤E אאאאאאאא
אא(Im)100 µAK F٥E אאאאאאאאא
א20 kΩ/VK F٦E אאאאאאאאא
א50 kΩ/VK F٧E אאאאאאאאא
150 mAאאא1 mAאא105 ΩK
F٨E אאFאאא (2 kΩW
FE Aא0-10 Vאא18 kΩK FE Bא0-300 Vאא . 298 kΩ
א٢٦٧ א א
אאאא א
- ٥١ -
F٩E אאR1, R2& R3אאאאאאW
F١٠E אאR1, R2, R3& R4אאאאא
אW
Im = 50 µA
R3
R2
Rm = 1 kΩ
R1
mA1I1 = mA10I2 = mA100I3 =
Im = 50 µA
R3
R2
Rm = 1 kΩ
R1
mA1I2 = mA10I3 = mA100I4 = A100I1 µ=
R4
-
א٢٦٧ א א
אאאא א
- ٥٢ -
F١١E אאR3 J R1אאאאאW
F١٢E אאR5 J R1אאאאאW
R3 R2 R1
1 V 5 V 10 V
Rm = 2 kΩ
Im = 50 µA
א٢٦٧ א א
אאאא א
- ٥٣ -
F١٣E אאאא،אאאאRx
אאאא،אאK
F١٤E אא6 kΩ،אאאא10 kΩ/Vאא؛W1 V, 5 V, 10 V,
100 Vאאאא،3%אK
R3 R2 R1 R4 R5
1 V 5 V 10 V 50 V 100 V
Rm = 2 kΩ
Im = 50 µA
Im = 50 µA
Rsh=500 Ω = Rx
Rm = 2 kΩ R2= 4.6 kΩ
R= 1 kΩ
E = 1.5 V
E = 8 V
6 kΩ
10 kΩ
V0
א٢٦٧ א א
אאאא א
- ٥٤ -
F١٥E אAאא5 kΩ/VאX, Yאאא15אVאא30Vא،Bאא
אX, Yאא16.13Vאא50Vאא.B
F١٦E אא50 kΩאאאא20 kΩ/V±2%אא10 V
؟אא
F١٧E אאאאאאFאE
150 µApeak؟אאאאא، F١٨E אאאאא1אmAאא،
אאא،אאאאאאאK
E = 100 V
R
100 kΩ
V0
X
Y
V0
E = 12 V
50 kΩ
30 kΩ
א٢٦٧ א א
אאאא א
- ٥٥ -
F١٩E אאאאאא1mAאא،אאאאאא،אא
אאאK F٢٠E אאאאFאEא0.8 mA
אאאא؟אא
F٢١E אאאאFאEא0.8 mAאאאאאא؟א
F٢٢E אאאאא1אmA
א500א Ω،אאאאאא،אאאאאאא
אאאאא30 VrmsK F٢٣E אאאאא200אµA
א500א Ω،אאאאאאא،אאאאאא .50Vp-p
F٢٤E אאאFאEאא
אאאאאאאאאאW
Ω= 250R m
RD = 300 Ω
mA1I s.f =
RS
s.m.rin V20E =
א٢٦٧ א א
אאאא א
- ٥٦ -
F٢٥E אאאFאEאא
אאאאאאאאאאW
F٢٦E אאאFאEאאאאאאאאאאא
אK
F٢٧E אאאFאEאא
אאאאאאאאאאFאאא300 ΩKE
RS
Ω= 250R m
mA1I s.f = s.m.rin V20E =
Ω= 250R m Ω= 250R sh
RD2 = 300 Ω
RD1= 300 Ω
TI
mA1I s.f =
RS
shI s.m.rin V20E =
א٢٦٧ א א
אאאא א
- ٥٧ -
RS
Ω= 500R m
mA2I s.f = s.m.rin V20E =
אאאא
א
א
٣
א٢٦٧ א א
אא
- ٥٧ -
אאWאאאאאK
אאאאWאאW • אאאאK • אאאאאK • אאאאK • אאאK
אאאWאאאא١٠٠K٪
אאWK
אאW
• אאK • אKאK
אאWאאאאK
א٢٦٧ א א
אא
- ٥٨ -
٣ J١ (Introduction) אאאאאF
אאאאאאEאאאאא،אאא،אאאא
אאK א(parameters)א،
א،אאאאאK ،אאאאאאאאאאאאאאF٣ J١FEEK
אאאאאאאאאF٣ J١FEEKאאאאא
אאאאאאאאK
FEאא FEאאאאא F٣ J١EאאאאאאאאאK
א
א
א
א
א٢٦٧ א א
אא
- ٥٩ -
٣ J٢ אא(Digital Voltmeters [DVM]) אאאאאא
אאKאאאWאאא(A/D Converters)אאא(Decade Counting Units)א
אא(Display Unit)אאאאאאW
١K אאאאאא(Single-slope DVM's) ٢K אאאאא(Dual-slope DVM's) ٣K א(Voltage-to-Frequency Converters) ٤K אאאאא(Successive-Approximation DVM's)
אאאK ٣ J٢ J١ אאאאאא(Single-Slope DVM's)
א،אאאאאאאאאאאאאא
אאאאאאא،אK F٣ J٢Eאאא،אאאאא
،אא(-Vref)،אאאאאא(Vx)אKאאאא(Integrator)
(Comparator)،א(AND)אא(Counter)א(digital readout)KאאW
١K אאאאאאאK ٢K אאא(main gate control)Fא (1)
F٣ J٣EE،אSאא(leading edge)،אאאANDאא[High]K
٣K אS،אCאאאאKאאאאאאאאא]א
(2)F٣ J٣E[K
א٢٦٧ א א
אא
- ٦٠ -
٤K א[High]אא(Vx)אא ]א(3) F٣ J٣E[Kאא،אAND
[High]K
F٣ J٢EאK
٥K אאאClock]א(4) F٣ J٣E[אאאAND،אאאא[High]،
(5) F٣א]אאאאא J٣E[אאאא(Binary Counter)K
٦K אאVx،א،אאאאANDא،אא
(Clock)אאאאK ٧K אאאאאאאאVx،א
א(digital readout)אאK ٨K ،אאאא(main gate control)،
אאאאאKאא(falling edge)א
אאא א
א
א
-
+
-
+
Vref (−)
Vx
- R
C S
אS
1
5 3
4
2
א٢٦٧ א א
אא
- ٦١ -
אSאא،C،אאאK
F٣ J٣EאאאאאF٣ J٢E(Timing Diagram)K
F٣ J٣EאאאK
אאא( T )אאאא
א،אאאK אא[Vio(t)]W
∫ −−=t
trefio
1
dtVRC1)t(V F٣ J١E
)tt(VRC1)t(V 1refio −=∴ F٣ J٢E
t1אאאא،אאt2אאאאאאאW
אS
אS
Vx
2
3
1
4
5
t1 t2 T
א٢٦٧ א א
אא
- ٦٢ -
x2io2 V)t(V ttat =⇒= F٣ J٣E
)tt(VRC1V)t(V 12refx2io −==∴ F٣ J٤E
אאt1t2אTאא،W T = t2 – t1
TV
RC1V refx =∴ F٣ J٥E
ref
x
VV
RCTor = F٣ J٦E
אאאאTאאאVxK אאאאאאא،א
אאאFאאR, CאE،א،אאאאא
אאK F٣ J١E
אאאTt1t2אאאא،אאאΩ= k100Rאf1.0C µ=א،V5Vx =אא،V10Vref −=K
א אאF٣ J٦E،W
secm5sec105105101.010100
VV
RCT 363
ref
x =×=××××== −−
٣ J٢ J٢ אאאאא(Dual-Slope DVM's) אאאאא،א
F٣ J٤EK
א٢٦٧ א א
אא
- ٦٣ -
אאאA1אאRאC،אאאA2،אא
[Low]א،[High]אKאאW
١K אאאאאאW ١ J אS2CK ٢ J אS1אAK ٣ J אא(0000…...0)K
F٣ J٤EK
٢K אאאאאאF٣ J٥E،אK
٣K אאא[High]،אאANDא(Clock)אאK
عداد
دائرة تحكم منطقية
نبضات الساعة
S1
S2
C R B
A
Vref (-)
A1 A2
Vi -
+
-
+
א٢٦٧ א א
אא
- ٦٤ -
F٣ J٥EאאאF٣ J٤EK ٤K אאאאאאאt2
F٣ J٥E، [Overflow Pulse]אאאאאS1אBאא،Vrefא،א
(at time t2)אא(0000 ……0)K ٥K אCאt2t3אאא
א،אאאאאt3،אא[Low]،אאANDא(Clock)א
אא،אאאאt2t3אK
٦K אt3אאאאאאאK
אאS1אAW
∫ ≤≤−=t
t21in1
1
ttt dtVRC1)t(V F٣ J٧E
)tt(RCV
)t(V 1in
1 −−=∴ F٣ J٨E
)t(V)t(V ttat 2112 =⇒= F٣ J٩E
)tt(RCV
)t(V 12in
21 −−=∴ F٣ J١٠E
121 ttT If −= F٣ J١١E
خرج المكامل
خرج المقارنt1 t2 t3
א٢٦٧ א א
אא
- ٦٥ -
RCTV
)t(V 1in21 −=∴ F٣ J١٢E
אא،אt2t3،אV2(t)אW
∫+=t
tref212
2
dtVRC1)t(V)t(V F٣ J١٣E
)tt(VRC1)t(V)t(V 2ref212 −+=∴ F٣ J١٤E
0)t(V ttat 323 =⇒= F٣ J١٥E
1in23ref TVRC1)tt(V
RC1
=−∴ F٣ J١٦E
re, therefottT If 232 −= F٣ J١٧E
1in2ref TVTV = F٣ J١٨E
equal,which
1
2refin
ref
in
1
2
TT
VV VV
TT
=⇒= F٣ J١٩E
אאאאאאאא
אאT2K
F٣ J٢E אאאVrefאt2אאא-5 V،
אאאt2t3א؟Vi =1 VT1=1 secK א
אאF٣ J١٩E،W
sec2.0511
VV
TTref
in12 =×=×=
א٢٦٧ א א
אא
- ٦٦ -
٣ J٣ אאא(Digital Multimeter [DMM]) אאאאאאאLא
אא(Decade Counter)K F٣ J٦Eא
(Attenuator)،אא(Compensated Attenuator)א،אאאאאא
אאאאאK ،אאאא،אאאאאK
אא،אאאאLאאאאאאא،אאK
אאא،אאא(Rectifier)،אאאK
א(Current-to-Voltage Converter)אF٣ J٦EאאF٣ J٧EKאאאא
(Summing Junction)،Σi،אאKאאא،אאא،אIRאIiKאIR(Voltage drop)אאא
אאאKאאאאאLאאאא،אאאאאK
א٢٦٧ א א
אא
- ٦٧ -
F٣ J٦EאK
F٣ J٧EK
א
א
אא
DCV
OHMS
ACVDCMA DCV
DCMA OHMS
ACV
ACV
OHMS
DCMA
DCV
א
א
10 Ω
100 Ω
1 kΩ IR
Ii
تيار مجهول+
J
א٢٦٧ א א
אא
- ٦٨ -
אאאאKאאאאאאLא
אאאאאאאK
א٢٦٧ א א
אא
- ٦٩ -
אא
١K אאאאאאאאK ٢K אאאאאאK ٣K אאאאאאK ٤K אאאאאאאאK ٥K אאא( T )אאאאא،
אאאאאאאאK ٦K אאאאאאאK ٧K אאאאאאK ٨K אאאאאאK ٩K אאאK
١٠K אאאTt1t2אאא،אאאאΩ= k200Rאnf50C =א،V5Vx =،
אאV10Vref −=K
١١K אא،אאΩ= k250Rאnf75C =K
١٢K אאאVrefאt2אא5-א Vאאא،t2t3؟אVi =1.1 VT1=3 secK
١٣K אא،אאVi =1.5 VT1=2 secK
אאאא
א
א
٤
אא٢٦٧ א א
אא
- ٧١ -
אאWאאאאאK
אאאאאWאאW • אאאאK • אאאאאK • אאאאאK • אאאאאאK
אאאWאאאא١٠٠K٪
אאWK
אאW
• אאK • אKאK
אאWאאאאK
אא٢٦٧ א א
אא
- ٧٢ -
٤ J١ Introduction
אאאאאא،אא،،אא
א،אאK،אאאאא،אא
אאאאאK אאאאאאאאא
،אאאKאאא
אאא،K ،אאאאא
אאאK
٤ J٢ אאאאOscilloscope Block Diagram א(Cathode-Ray Tube or CRT)אא
אאאFאF٤ J١EEKאאאY, X ،אא
אאאK אאאאאא Y אא
אאאאאאאאא،אא S1 F٤ J١Eא،אאא C1 א
،אאאאאאאK،אאאאאS1d.c
אאאK אאYאאY،אאאא
אYאאאאKאאאאא(preamplifier).
אא٢٦٧ א א
אא
- ٧٣ -
F٤ J١EאאאK
א (time base) אאאאאאא(saw tooth waveform)אאא،
אאKאאאאאאאאאאאFאX KEאא
אאאאאK אאא،
אאC2אא،אא،אאאאאאאאא
X אאאKאאאKאF٤ J٢E][،zxאא
אאK
אא٢٦٧ א א
אא
- ٧٤ -
][][ F٤ J٢Eאא][،zxK
א،אאאאאאK S3] F٤ J١E[א
א،אאאאא،אאאאאאK
אאאאאא،אא،אS2F٤ J١EאאK
אאאאאאK אא (graticule)
אFאKEאאאאKאאאאY،א
אS1] F٤ J١ [(،Y][VOLTS/DIVאא.YאאאYא
אאYאKאVOLTS/DIVאYאאאאאאK
אאא[TRIGGER LEVEL]אאאאאKאא،אאTrigger levelAUTO،
א،אאאאא]?H?،? J?[K אאאאאאVARIABLE
CONTROLTIME/DIVKאTIME/DIVאVARIABLE CONTROLCalibrateאK
X J shiftאאאאאאK
אא٢٦٧ א א
אא
- ٧٥ -
،אINTENSITYFOCUSאאKאאא،אא
אאאאאFאEאK
٤ J٣ אאאאOscilloscope as a measuring instrument אאאאאאא
אאKאאא2 - 10MHz،אאאK
אאא،אאא(Calibration)אאKאא
Kאאא،אאאאאKאא50Hz،
TIME/DIV10ms/divאאא10 divאאK
٤ J٣ J١ אאאאאאVoltage Measurements
אאFאאEאאKF٤ J٣E(sine waves)KאAFא
אEא4.5div،אאא B FאאEא2 divאאKאאא[VOLTS/DIV]100mv،
FאאEאW
F٤ J٣EF JEK
אא٢٦٧ א א
אא
- ٧٦ -
Wave A: VA = (4.5 DIV) × 100 mv/DIV = 450 mv
Wave B: VB = (2.0 DIV) × 100 mv/DIV = 200 mv
٤ J٣ J٢ אאFrequency Measurements אאאא،אאא
Yא،א(CAL)אא،אא،א
א،אאא(T)W T = (Horizontal divisions/cycle) × (TIME/DIV)
א(F)،אא(T)،W F = 1/T.
אא[TIME/DIV]0.5 ms ،אא(T)א(F)אF٤ J٣EW
Wave A : TA = [(8.8 DIV) × 0.5 ms/DIV]/2 cycles = 2.2 ms
FA = 1/ (2.2ms) ≅ 455 Hz
Wave B : TB = [(8.8 DIV) × 0.5 ms/DIV]/6 cycles = 0.73 ms
FB = 1/(0.73ms) ≅ 1.36 kHz
٤ J٣ J٣ אLissajous Figures אאאא،
[Lissajous figures]אאKאאאאK
אאא(F2)Yאאאא(F1)X،אאא
אאאF٤ J٤EKאאאאאאK
אא٢٦٧ א א
אא
- ٧٧ -
F1/F2 = 5/3 F1/F2 = 3/2 ][][
F٤ J٤EאK
אאאאאאאWאאאא،א
FאאאFLEאאאEF2=LF1
٤ J٣ J٤ אPhase Angle Computation
א(Phase difference)אאאאW
אאWאאאאא(Channel-1 and 2)אאאא(CAL)،
אאא،אאK
F٤ J٥Eא،8 divisionsאא،אא1.4 divisions
אאKאאא (One cycle)360°،،8 div = 360°،W
1 div = 360°/8 = 45°
אא٢٦٧ א א
אא
- ٧٨ -
F٤ J٥EאK
אאאW θ = 1.4 div × (45°/div) = 63°
אאW،אאאאאא(Channel-1 and 2)،אאאא
F٤ J٦E،אאאK ،אאאא0°،א
אא45°אאFאאE،אאא 0°90°[0° < θ < 90°]אא،א[ellipse]
אאאאK
אא٢٦٧ א א
אא
- ٧٩ -
F٤ J٦E(1/1)אK
אאא90°אאא
אFאאKEאא90°180°[90° < θ < 180°]אאא
[ellipse]אאאאK
אאא180°אאאא،135°אאFא
אKE
אא٢٦٧ א א
אא
- ٨٠ -
F٤ J٧Eאא[θ]אאאאא[ellipse]K
F٤ J٧EאאK
א[θ] F٤ J٧EאאאW
Sin(θ) = Y1/Y2 W (Y1)WאאאאאאK (Y2)WאאאאאאK
אאאאאאאאאאאאK
אא٢٦٧ א א
אא
- ٨١ -
אאא
١ J אאאאאאאאK ٢ J אאK ٣ J אאאאאאאK ٤ J אאאאאאאK ٥ J אאאאאאK ٦ J אאאאאאאK
אאאא
אא
٥
אא ٢٦٧א א
אא
- ٨٣ -
אאWאאאאאאK
אאאאWאאW • אאאאאאאאK • אאאאאאאאK • אאאאאאאאK • אאאאאאאאK
אאאWאאאא١٠٠K٪
אאWK
אאW
• אאK • אKאK
אאWאאאאK
אא ٢٦٧א א
אא
- ٨٤ -
٥ J١ Introduction אאאאאא
אאאאאאאKאאאאאK
אאאאאאאKא،אאאאאא
אאאאאF،א،KE
אאאאאאאאאאאאאאK
٥ J٢ אאאאאאDirect Current Bridges ٥ J٢ J١Wheatstone Bridge
FF٥ J١EEאאאKא
(E)אאאKאFEאאאאאאK
F٥ J١EאאאK
A B G
I1
R1 R2
I2
I3 R3 R4 I4
E
אא ٢٦٧א א
אא
- ٨٥ -
אא،אאאFR4EאאFR2Eא،אא
אאאK ٥ J٢ J١ J١ אאCondition of Balance of Wheatstone Bridge
אאאאאABאא،אR1אאR2،W
2211 RIRI = F٥ J١E
אאR3אאR4،W
4433 RIRI = F٥ J٢E
אא،W 31 II = , 42 II = F٥ J٣E
אF٥ J١EאF٥ J٢WE
44
22
33
11
RIRI
RIRI
= F٥ J٤E
אF٥ J٣EאF٥ J٤EW
4
2
3
1
RR
RR
= F٥ J٦E
אF٥ J٦Eא،אאאW
3241 RRRR = F٥ J٧E
F٥ J١E אאאRxאאאF٥ J٢Eאא
אאK
אא ٢٦٧א א
אא
- ٨٦ -
F٥ J٢EאF٥ J١KE א
אא،אאאFF٥ J٧EEW
32x1 RRRR =
אאRxW
Ω=Ω
Ω⋅Ω== k40
k12k32k15
RRR
R1
32x
٥ J٢ J١ J٢אאGeneral solution of Wheatstone Bridge
אאאאאאKאאאאאKKאא
אאאאאאVthאrthאאא،RGאאאW
Gth
thG Rr
VI
+= F٥ J٨E
VthrthW
WVth
A B G
R1 = 12 kΩ R2 = 15 kΩ
R3 = 32 kΩ Rx
E
אא ٢٦٧א א
אא
- ٨٧ -
אאAB Vth FאRGאאKE
VthאאאאKF٥ J٣EVthW
221121th RIRIVVV −=−= F٥ J٩E
)RR
RRR
R(ER
RRER
RREV
42
2
31
12
421
31th +
−+
=+
−+
= F٥ J١٠E
אא ٢٦٧א א
אא
- ٨٨ -
Wrth rthאאאאא
אאABrthF٥ J٤KE
F٥ J٣EאVthK
F٥ J٤EאאאrthK
אאrthאאR1R3א،אאR2R4،אאאאאK
אאrthW
A B
R1 R2
R3 R4
E Vth
C
D
V1 V2 I2 I1
A B
R1 R2
R3 R4
C
D
≡ A B R1 R2
R3 R4
C
D
אא ٢٦٧א א
אא
- ٨٩ -
42
42
31
31th RR
RRRR
RRr+
++
= F٥ J١١E
F٥ J٢E אאאאאאF٥ J٥KE
F٥ J٥EאF٥ J٢KE א
אאאאW VthאF٥ J١٠EW
)RR
RRR
R(EV
42
2
31
1th +
−+
=
V278.0k5.7k6.1
k6.1k5.3k1
k16Vth =⎟⎟
⎠
⎞⎜⎜⎝
⎛Ω+Ω
Ω−
Ω+ΩΩ
×=
rthאF٥ J١١WE
42
42
31
31th RR
RRRR
RRr
++
+=
Ω=Ω+ΩΩ×Ω
+Ω+ΩΩ×Ω
= k096.2k5.7k6.1k5.7k6.1
k5.3k1k5.3k1
rth
אאאIGאF٥ J٨WE
A4.12120010096.2
V278.0Rr
VI
3Gth
thG µ=
Ω+Ω×=
+=
A B G
R1 = 1kΩ R2 = 1.6 kΩ
R3 = 3.5 kΩ
E = 6 V
R4 = 7.5 kΩ
RG = 200 Ω
אא ٢٦٧א א
אא
- ٩٠ -
٥ J٢ J١ J٣אאא Slightly unbalanced Wheatstone Bridge
אאאאא٥٪אאאF٥ J٦E،
אאW
F٥ J٦EאאK WVthאF٥ J١٠WE
⎟⎟⎠
⎞⎜⎜⎝
⎛+
−+
×=42
2
31
1th RR
RRR
REV
⎟⎟⎠
⎞⎜⎜⎝
⎛∆+
−×=⎟⎟⎠
⎞⎜⎜⎝
⎛∆+
−×=RR2
R21E
RR2R
R2REVth F٥ J١٢E
( ) ( )⎟⎟⎠
⎞⎜⎜⎝
⎛∆+×
×−
∆+×∆+
×=RR22
R2RR22
RR2EVth F٥ J١٣E
( )⎟⎟⎠
⎞⎜⎜⎝
⎛∆+×
∆×=
RR22REVth F٥ J١٤E
אאאאא∆Rא،2R،אאW
⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆×=
R4REVth F٥ J١٥E
A B
R R
R R+∆R
E Vth
אא ٢٦٧א א
אא
- ٩١ -
WrthאF٥ J١١WE ( )
RRRRRR
RRRR
RRRR
RRRR
r42
42
31
31th ∆++
∆+⋅+
+⋅
=+
++
= F٥ J١٦E
( )RR2RRR
2R
rth ∆+∆+⋅
+= F٥ J١٧E
∆RR،אאW ( )
R2
R2
RR2RR
2R
rth =+=⋅
+= F٥ J١٨E
F٥ J٣E
אאאאאF٥ J٧EאאאאאK
F٥ J٧EאF٥ J٣E
א WאאW
⎟⎟⎠
⎞⎜⎜⎝
⎛+
−+
×=42
2
31
1th RR
RRR
REV
V122.01025500
1000500
V10Vth =⎟⎟⎠
⎞⎜⎜⎝
⎛−
ΩΩ
×=
A B
500 Ω 500 Ω
500 Ω 525 Ω
10 V G125 Ω
אא ٢٦٧א א
אא
- ٩٢ -
42
42
31
31th RR
RRRR
RRr
++
+=
Ω=Ω+ΩΩ⋅Ω
+Ω+ΩΩ⋅Ω
= 1.506525500525500
500500500500
rth
אאאW
Gth
thG Rr
VI
+=
A3.1931251.506V122.0
IG µ=Ω+Ω
=
WאאW
⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆×=
R4REVth
V125.05004
25V10Vth =⎟⎟
⎠
⎞⎜⎜⎝
⎛Ω×
Ω×=
Ω== 500Rrth
אאאW
A200125500V125.0
RrV
IGth
thG µ=
Ω+Ω=
+=
٥ J٢ J٢Kelvin Bridge F٥ J٨E،אאא
KאאאאאאאK
אא ٢٦٧א א
אא
- ٩٣ -
F٥ J٨EאאאK אאאFאE
אאKאאאאאאאFRa, RbEא
،אRlcאאאKא1 µΩ 1ΩאK
٥ J٢ J٢ J١אאBalance of Kelvin Bridge Wאאאאאא
b
a
4
2
3
1
RR
RR
RR
== F٥ J١٩E
אאאאאאא،W
a
b
1
3
2
x
RR
RR
RR
== F٥ J٢٠E
a
b2
1
32x R
RRR
RRR
×=
×= F٥ J٢١E
E A B G
R1 R2
R3 Rx
Ra
Rlc
Rb
אא ٢٦٧א א
אא
- ٩٤ -
F٥ J٤E אRxאא،RaRb1000،R1=5Ω
21 R5.0R =K
א R1=5Ω21 R5.0R =،W
Ω=Ω
== 105.0
55.0
RR 1
2
אאW
a
b
2
x
RR
RR
=
W
Ω=×Ω
=×
= 01.01000
110R
RRR
a
b2x
٥ J٢ J٣אאאאאאDigital readout Bridges
א،אאאאאאאא،אאאאKKאא
אאאא،אאאאKF٥ J٩Eאא
אאAmplifierאאאאאאאא
אK
אא ٢٦٧א א
אא
- ٩٥ -
F٥ J٩EאאאאאאK
٥ J٢ J٤אאאאא Microprocessor – controlled Bridges
אאא،אאאאאKא،אאאאא
אאאאאאKאאא
אאאאאאאאאאאאאאאKאאאא
אאאאאאK ٥ J٢ J٥אאאApplications on D.C Bridges ٥ J٢ J٥ J١אאMurray Loop
אאאאאאאKאא
אאKאאאאאאאאKF٥ J١٠EאאKא،אא
Rb R2
A B
R3 Rx
E Amplifier FE
Logic circuits
دوائر ( )منطقية
Readout
אא ٢٦٧א א
אא
- ٩٦ -
،אאאאאאאאאK
F٥ J١٠Eאא
אאאאאאאאאLxאRxKאאאאאא
אLaאRaאאאאאLb-LxאRb-RxK
אאR2אאאאK
אWאא،W
( )x
xba
1
2
RRRR
RR −+
= F٥ J٢٢E
x1b1a1x2 RRRRRRRR −+=∴ F٥ J٢٣E
b1a1x1x2 RRRRRRRR +=+∴ F٥ J٢٤E
R1 R2
A B E G א
א
La
Lb
Lx א
א
אא
אא ٢٦٧א א
אא
- ٩٧ -
( ) ( )ba121x RRRRRR +=+∴ F٥ J٢٥E
אאRx
( )( )21
ba1x RR
RRRR
++
=∴ F٥ J٢٦E
אאאאF٥ J٢٦WE
aLR ρ
=Q F٥ J٢٧E
W ρWאאא LWא aWא
⎟⎟⎠
⎞⎜⎜⎝
⎛ ρ+
ρ+
=ρ
∴b
bb
a
aa
21
1
x
xx
aL
aL
RRR
aL
F٥ J٢٨E
אאאאאW
( )21
1
21
1x RR
LR2L2
RRR
L+
=+
=∴ F٥ J٢٩E
F٥ J٥E אאאאF٥ J١١Eא،
אאאKאא1760 m،אאאאאא100 Ωאאא
300 Ωאאאא،K
אא ٢٦٧א א
אא
- ٩٨ -
F٥ J١١EאאF٥ J٥KE
א
m880300100
m17601002RRLR2
L11
1x =
Ω+Ω×Ω×
=+
=∴
٥ J٣אאאאאאAlternating Current Bridges אאאאאאאא
אאאאאאאKאאאאאאא،
Kאאאאאאאא
(detector)אFF٥ J١٢KEE،אאאאאאאאאאא
(Oscillators)אאא(Amplifiers)אא.(Filters) אאאאא
،אאאאאאאאאK
100 Ω 300Ω
A B E G
1760 m
1760 m
Lx
אא ٢٦٧א א
אא
- ٩٩ -
F٥ J١٢EאאK
٥ J٣ J١אאאBalance of A.C Wheatstone Bridge אאאאא،אאאא
balanceא،אאאאאאאאKאאא b cאKא
אF٥ J١٣KE
F٥ J١٣EאאאאאK
b c a.c
detector
Z1 Z2
Z3 Z4
a.c source
a
d
b c
Z1 Z2
Z3 Z4
a.c source
a
d
I1 I2
I3 I4
אא ٢٦٧א א
אא
- ١٠٠ -
אאאbcאאאKאאbaא
אcaא،W 2211 ZIZI = F٥ J٣٠E
אאbdאאcdא،W
4433 ZIZI = F٥ J٣١E
אאאbcא،W 31 II = F٥ J٣٢E
42 II = F٥ J٣٣E
אF٥ J٣٠EאF٥ J٣١WE
44
22
33
11
ZIZI
ZIZI
= F٥ J٣٤E
F٥ J٣٢EF٥ J٣٣E،W
4
2
3
1
ZZ
ZZ
= F٥ J٣٥E
אF٥ J٣٥EW 3241 ZZZZ = F٥ J٣٦E
אאF٥ J٣٥EF٥ J٣٦EאאW
44
22
33
11
ZZ
ZZ
θ∠θ∠
=θ∠θ∠
F٥ J٣٧E
F٥ J٣٨E( ) ( ) ( ) ( )33224411 ZZZZ θ∠θ∠=θ∠θ∠
אF٥ J٣٨Eא،אאאאאאW
3241 ZZZZ = FאאאE F٥ J٣٩E
F٥ J٤٠E ) אאאאE3241 θ∠+θ∠=θ∠+θ∠
אא ٢٦٧א א
אא
- ١٠١ -
F٥ J٦E אאאאאF٥ J
١٤EW °∠Ω= 30300Z1
°∠Ω= 0150Z2
°−∠Ω= 40250Z3
אאאZxK
F٥ J١٤EאאF٥ J٦KE
א אאאFאF٥ J٣٩WEE
3241 ZZZZ =
Ω=Ω
Ω×Ω=== 125
300250150
ZZZ
ZZ1
324x
אאאאFאF٥ J٤٠WEE °−=°−°−+°=θ∠−θ∠+θ∠=θ∠ 7030)40(01324
אאאאW °−∠Ω= 70125Zx
°∠Ω= 30300Z1 °∠Ω= 0150Z2
°−∠Ω= 40250Z3 x4 ZZ =
b c a.c
detector a.c source
a
d
אא ٢٦٧א א
אא
- ١٠٢ -
W )70(sin125j)70(cos12570125Zx °−+Ω°−=°−∠Ω=
5.117j75.42Zx −Ω=
אאא42.75 ΩאאאΩ= 5.117XC،W
C15.117XC ω
=Ω=
Ω×ω=
5.1171C
،אאא60 HzאW
F58.225.117602
1C µ=Ω××π×
=
F٥ J٧E אאאF٥ J١٥Eאאא،ZxK
F٥ J١٥EאאאF٥ J٧KE
A B d
R1=400Ω R2=200Ω
R3=300Ω Zx
E=6 V
L2=15.92 mH
C3=0.4 µF
F=1 kHz
אא ٢٦٧א א
אא
- ١٠٣ -
א אאאW
F١E אZ1W
°∠Ω=+Ω= 04000j400Z1
F٢E אZ2W 3
222 1092.15j200LjRZ −××ω+Ω=ω+=
ωW sec/rad19.628310002f2 =×π×=π=ω
אZ2W
Ω+Ω=×××+Ω= − 100j2001092.1519.6283j200Z 32
°∠Ω=Ω+Ω= 6.266.223100j200Z2
F٣E אZ3W
Ω××
−Ω=ω
−=−6
333
104.019.62831j300
C1jRZ
°−∠Ω=Ω−Ω= 13.53500400j300Z3
אZ4אאאאא،W WאW
Ω=Ω
Ω×Ω=== 5.279
4005006.223
ZZZ
ZZ1
324x
WאאW °−=°−°−+°=θ∠−θ∠+θ∠=θ∠ 53.260)13.53(6.261324
אאZxאאW Ω−Ω=°−∠= 8.124j25053.265.279Zx
،אאאאאא250 Ωאא124.8א Ωא،W
אא ٢٦٧א א
אא
- ١٠٤ -
C18.124XC ω
=Ω=
F28.18.12419.6283
1C µ=×
=
٥ J٣ J٢אאאSimilar Angle Bridge אאאאאאאKאא
אאאא،אאאKאאאאאא
F٥ J١٦E،אאאאאW F١E אZ1W
11 RZ = F٥ J٤١E
F٢E אZ2W
22 RZ = F٥ J٤٢E
F٣E אZ3W
3C33 XjRZ −= F٥ J٤٣E
F٤E אZ4W
Cxx4 XjRZ −= F٥ J٤٤E
F٥ J١٦EאאאאK
d
R1 R2
R3
Cx
C3 Rx
אא ٢٦٧א א
אא
- ١٠٥ -
אF٥ J٣٦WE
( ) ( )3C32Cxx1 XjRRXjRR −=− F٥ J٤٥E
אאאW
3C232Cx1x1 XRjRRXRjRR −=− F٥ J٤٦E
א،אאאאW 32x1 RRRR = F٥ J٤٧E
W
1
32x R
RRR = F٥ J٤٨E
אא،אאאW 3C2Cx1 XRjXRj −=− F٥ J٤٩E
W 3C2Cx1 XRXR = F٥ J٥٠E
W
1
3C2Cx R
XRX = F٥ J٥١E
W
31
2
x CRR
C1
ω=
ω F٥ J٥٢E
W
2
31x R
CRC = F٥ J٥٣E
אא ٢٦٧א א
אא
- ١٠٦ -
F٥ J٨E
אאאאא2 kHzאאא،אאW
Ω= k10R1،Ω= k50R 2،Ω= k100R 3&F100C3 µ= אאאאאאאאK
א אF٥ J٤٨Eאאאא،W
Ω=Ω
Ω×Ω== k500
k10k100k50
RRR
R1
32x
אF٥ J٥٣Eאאאא،W
F20k50
F100k10R
CRC
2
31x µ=
Ωµ×Ω
==
٥ J٣ J٣Maxwell Bridge אאאאK
KאאאאאאF٥ J١٧E،אאאאאW
F٥ J١٧EאK
d
R3
Rx
Lx
R2
a.c source
C1
R1
אא ٢٦٧א א
אא
- ١٠٧ -
F١E אZ1W
1
11
1
1
11
11
1
CjCR
CjR
CjR
CjR
Z
ω−ω
ω−
=
ω−
⎟⎟⎠
⎞⎜⎜⎝
⎛ω
−
= F٥ J٥٤E
11
11
11
CjR1
1jCR
jRZ
ω+=
−ω−
= F٥ J٥٥E
F٢E אZ2W 22 RZ = F٥ J٥٦E
F٣E אZ3W 33 RZ = F٥ J٥٧E
F٤E אZ4W
Lxx4 XjRZ += F٥ J٥٨E
אF٥ J٣٦WE
( ) 32Lxx
11
RRXjRCj
R1
1=+
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
ω+ F٥ J٥٩E
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛ω+=+ 132
1
32Lxx CRRj
RRR
XjR F٥ J٦٠E
אאאאW
1
32x R
RRR = F٥ J٦١E
אאאאW
132Lx CRRjXj ω= F٥ J٦٢E
אא ٢٦٧א א
אא
- ١٠٨ -
W
132Lx CRRX ω= F٥ J٦٣E
W
132x CRRL = F٥ J٦٤E
F٥ J٩E אא،אאאאW
Ω= k470R1،F01.0C1 µ=،Ω= k1.5R 2&Ω= k100R 3 אאאאK
א אF٥ J٦١EאF٥ J٦٤EאאW
WאRxW
Ω=Ω
Ω×Ω== k085.1
k470k100k1.5
RRR
R1
32x
WאאאLxW H1.5F01.0k100k1.5CRRL 132x =µ×Ω×Ω==
אא ٢٦٧א א
אא
- ١٠٩ -
אא
F١E אRxאאFאאאEא،W R1 = 400 Ω،R2 = 5 kΩ،R3 = 2 kΩ
F٢E FאאאEאRxא،אאW
R1 = 10 kΩ،R2 = 60 kΩ،R3 = 18.5 kΩ
F٣E FאאאEאRxא،אאW R1 = 5 kΩ،R2 = 40 kΩ،R3 = 10 Ω
A B G
R1 = 400 Ω R2 = 5 kΩ
R3 = 2 kΩ Rx
E
A B G
R1 = 10 kΩ R2 = 60 kΩ
R3 = 16.5 kΩ Rx
E
אא ٢٦٧א א
אא
- ١١٠ -
F٤E אאR3אאאא1א Ω100 kΩK
F٥E אאאא،אאאאאאאאאאK
F٦E אאא،אאאRxא،W Ig=13.6 µA, Vth= 24 mV
A B G
R1 = 5 kΩ R2 = 40 kΩ
R3 = 10 Ω Rx
E
A B G
R1 = 1 kΩ R2 = 10 kΩ
R3 Rx
E
A B G
R1 = 1 kΩ R2 = 1 kΩ
R3=1 kΩ R4=1050 Ω
E=3 V
אא ٢٦٧א א
אא
- ١١١ -
F٧E אאאאא10 mm/µAאאא،K
F٨E אRxא،אאאאW
Ra=1200 Ω, Ra=1600Rb, R1=800Rb & R1=1.25R2
A B G
R1 = 1 kΩ R2 = 1 kΩ
R3=5 kΩ Rx
E=3 V
Rg=100 Ω
A B G
R1 = 500 Ω R2 = 500 Ω
R3 = 1 kΩ R4 = 1010 Ω
E=3 V
Rg = 500 Ω
E A B G
R1 R2
R3 Rx
Ra
Rb Rlc
אא ٢٦٧א א
אא
- ١١٢ -
F٩E אא،אאKאa0.1 Ω/30mאb0.005 Ω/30mא،
אLxאא،Laא Lb אאאK
F١٠E אאא،אאאZxא
(R, L or C) K
F١١E אאאאאא،אZxא،W
°−∠Ω=°−∠Ω=°∠Ω= 20100Z,40300Z,0400Z 321
\
R1=100 Ω R2=500
A B E= 6 V G La
Lb
L
A B d
R1 = 200Ω R2 = 200Ω
R3 = 500Ω Zx
E = 6 C2 = 5 µF
C3 = 0.2 µF
F=1 kHz
אא ٢٦٧א א
אא
- ١١٣ -
F١٢E א،אאאאאאRx, CxK
F١٣E א،אאאאאאRx, Cxא،W °−∠Ω=°∠Ω=°∠Ω= 501000Z,015000Z,02000Z 321
b c a.c
detector
Z1 Z2
Z3 Zx
E= 6 V f = 1 k HZ
a
d
d
R1= 1.65 kΩ R2= 15.3 kΩ
R3= 2.5 kΩ
Cx
C3= 10 µF Rx
E = 6 V f = 1 kHZ
d
Z1 Z2
Z3
Cx Rx
E = 6 V f = 1 kHZ
אא ٢٦٧א א
אא
- ١١٤ -
F١٤E אאא،אאאאLx, RxK
F١٥E אאא،אאאאLx, Rxא،
W °∠Ω=°∠Ω=°−∠Ω= 01000Z,0100Z,758.153Z 321
d
R3=1 kΩ
Rx
Lx
R2=100 Ω
E = 6 V f = 1 kHZ
C1=1 µF
R1=600 Ω
d
Z3
Rx
Lx
Z2
E = 6 V f = 1 kHZ
Z1
אאאאאא
א
א
א
٦
אא ٢٦٧ א
אאא
- ١١٥ -
אאWאאאאאאאאאK
אאאאWאאW • אאאאאK • אאאאK • אאאאאK
אאאWאאאאא١٠٠K٪
אאWK
אאW
• אאK • אKאK
אאWאאאאK
אא ٢٦٧ א
אאא
- ١١٦ -
٦ J١ Introduction אאאא
אאאאא…KK אאא،אא
אאאאאאKא
אאאאאK
٦ J٢ General concepts ٦ J٢ J١ אא
אאא،אאאW
F١E אא F٢E אאאאK
אאאאאאא،F٦ J١KE
F٦ J١EאK
א جهاز قياس آهربائي
אא ٢٦٧ א
אאא
- ١١٧ -
٦ J٢ J٢ אאClassification of sensors and transducers אא،אא،א،א،K
٦ J٢ J٣ אאאSelection of sensors and transducers אאאאאאא
אאW F١E אWאאאאK F٢E אWאא
K F٣E אאWאא
אK F٤E אאאWאאאא
אK F٥E Wאאא
אK F٦E אאאאא
אאאאאאK F٧E אאאWא
אאאK F٨E אאWאאא
אא،אאאאאאאK
אאאאאאאאאאאאאאK
אא ٢٦٧ א
אאא
- ١١٨ -
٦ J٣ אאאאאBasic types of special instruments ٦ J٣ J١ אאאResistive position instrument
אאאאאאאאאאאאKאאאאא
אאאאK אאאאאא
אאאאא
אא،F٦ J٢EK
F٦ J٢EאאאK
אאאאאאאאאאF٦ J٣EKאW
אאאWA.B
W
منزلق
א
B A
אא ٢٦٧ א
אאא
- ١١٩ -
F٦ J٣Eאאאאאא
אאאW
21
T
RRVI+
= F٦ J١E
2O RIV = F٦ J٢E
21
2
21
2
T
O
RRR
)RR(IIR
VV
+=
+= F٦ J٣E
אאאאVOאאאאABK
A
W
R1
R2
VT
B
VO
אא ٢٦٧ א
אאא
- ١٢٠ -
F٦ J١E F٦ J٤Eא3 inches،א
5 kΩ،אאאVT = 5 Vא0.9" BKאאVOK
F٦ J٤EאאאF٦ J١KE
אWאF٦ J٣WE
21
2
T
O
RRR
VV
+=
Ω=×= 1500 5000 39.0 R 2
50001500
VV
T
O =
volts 5.1 50001500 5
50001500 VV TO =×=×=
5 kΩ
5 V
3 "
W
منزلق
B A
0.9 " A
W
R1
R2
VT = 5 V
B
VO
אא ٢٦٧ א
אאא
- ١٢١ -
٦ J٣ J٢ אStrain guage transducer
אאאאאאאאאK
אאאאאאK אF٦ J٥E
אאאאאאאK
F٦ J٥EאK
אאאאאאFאE،אאא،
،אאאW
aLR ρ= F٦ J٤E
W RWאא ρWאאאא LWא aWא
אW
אא
א
אא
אא ٢٦٧ א
אאא
- ١٢٢ -
F١E אאFKE F٢E אאK
אאאL∆אאאLאG،W
LLG ∆
= F٦ J٥E
אאאאאK אאאאאאא،אא،אא
אKW
LLRR
K∆∆
= F٦ J٦E
אאא1K אאאאFאW(Stress
א(Strain)א(Modulus of Elasticity (E))،אאאW
GSE = F٦ J٧E
W EWא SWא GWא
אSאW
AFS = F٦ J٨E
W FWאkg AWאm2
אא ٢٦٧ א
אאא
- ١٢٣ -
אkg/m2،אG،אEאSWkg/m2K
אאאאאK،אKאא،א
אFEאK
F٦ J٢E א2K =א
6101G −×=אאאא،Ω= 130R 0אאא،R∆K א
אF٦ J٦EאW
60
101130R
GRR
LLRR
2K−×
Ω∆=
∆=
∆∆
==
Ωµ=×××=∆ − 2601011302R 6
F٦ J٣E אאm02.0m4.0א،kg33000،
א210 m/kg102E ×=אא،L∆K א
אAW
( ) 2422
m1014.302.044
dA −×=×π
=π
=
אF٦ J٧EאEW
LALF
LLAF
GSE
∆××
=∆
==
mm1.2m101.21021014.3m4.0kg33000
EALFL 3
104 =×=×××
×=
××
=∆∴ −−
אא ٢٦٧ א
אאא
- ١٢٤ -
אאאאא،אא(Transducer)،
אK
אאא אאאאFא
E،אאאאא،Vo،אF٦ J٦KE
F٦ J٦EאK
אאאאאאא،אאאאKאא
אאאאא،אאא،،אאאKא
אאאא،K אאאאאאאא
אF٦ J٧KEאאאאאאאFHאEאאא،FאאאEאא
אא،אאא
oV
אR4 =
R1 R2
R3
E
אא ٢٦٧ א
אאא
- ١٢٥ -
אא،אאאאאאאאאא،K
F٦ J٧EאאאאאK
٦ J٣ J٣ אאInductive instrumentations אאאאא
אאאאKאאאאאאKאאאK
٦ J٣ J٣ J١ אאא(Tachometer) F٦ J٨Eאאאאאא
אא
E oV
R4
R1 R2
R3
אא
אא
אא ٢٦٧ א
אאא
- ١٢٦ -
א(10 mV/r.p.m)،(Voltmeter)אאאאאאא،א
K
F٦ J٨Eאאא
א،אאאאאאא
F٦אאא J٩KE
F٦ J٩EאאאK
אאFאEאאאאאאאא
אאK
South Pole
North Pole
אאאא
S
N
אא ٢٦٧ א
אאא
- ١٢٧ -
אא،אאאאאאאאאW
Pf120n = F٦ J٩E
W nWאא(r.p.m.) fWאcycle/sec = Hertz PWאאא
٦ J٣ J٣ J٢ אאאא Electro-magnetic transducer
אאאאאאאאאאאא
אאא،אאאאאאא،
F٦ J١٠Eאאא،אא،אאא
אא VK
F٦ J١٠Eאאאא
N S
V
B
אא ٢٦٧ א
אאא
- ١٢٨ -
אאאאאW VLBE = F٦ J١٠E
W EWאאאאאאאא(volts) BWאאא(Tesla = Weber/m2) VWאL(m/sec)
אאא،אאאאאאאאאא
אאF1 foot/secEאא0.5 siemens/mKאאא،אא
אאאאאאאK
F٦ J٤E ،אD=1.25 cm אא،
אB = 0.2 Tesla א،E = 25 mVאא،VK א
F٦ J١٠EW VLBE =
אVW
sec/m101025.12.0
1025LB
EV2
3=
××
×==
−
−
٦ J٣ J٤ אאCapacitive instrumentations
אאאCאאאאF٦ J١١EאW
)Farads(d
kAC 0ε
= F٦ J١١E
אא ٢٦٧ א
אאא
- ١٢٩ -
F٦ J١١EאאאאK
W CWאאאא(Farad) kWאאא AWאאא(m2) dWאאא(m)
ε0WאאאאPermittivityאאL،)m/Farad10854.8( 12
0−×=ε
אאאאאאאאאאאאאK
אאאK
٦ J٣ J٤ J١ אאאאRotational movement transducer אא
אאאF٦ J١٢KEאאאאאא
אK
F٦ J١٢EאאאאK
א א
A d
אא ٢٦٧ א
אאא
- ١٣٠ -
٦ J٣ J٤ J٢ אאאLinear movement transducer אאא
אאאאאF٦ J١٣KEאאאאאאאא
אK
F٦ J١٣EאאאK
٦ J٣ J٤ J٣ אPressure transducer אא
אאאF٦ J١٤KEאאאאאאKא
אאאאאאאאאאd0אאdאא،K
F٦ J١٤EאK d0
d1 א
א א
א א
אא ٢٦٧ א
אאא
- ١٣١ -
F٦ J٥E א،אאW
• אאא=× − 23 m105 • אא=× − m101 3
א אF٦ J١١EאאאW
)Farads(d
kAC 0ε
=
F1025.44m101
)m/F10854.8()m105()1(C 12
3
1223−
−
−−
×=×
××=
pF25.44C =
٦ J٣ J٥ אFאאEPiezoelectric Transducer אאאFאאquartzRochelle saltE
אא،،אKאאאאא
אF٦ J١٥KE
F٦ J١٥EאK
א
א
א
אא
א
אא ٢٦٧ א
אאא
- ١٣٢ -
אאאאאאאאאK
٦ J٣ J٦ אא
אאאאאW FE אאאResistance thermometerK FE אאאThermo CoupleK FE אאאThermistorK
אאאK
٦ J٣ J٦ J١ אאא אאאאאא
אאאאW F٦ J١٢E [ ]t1RR 0 ∆α+=
W R Wאאtא
R0W אאFC20 °E t∆Wאאאאאא
αWאאא אאאאאαאא
אאאKאאR∆אאאאאאF٦ J١٦KE
אא ٢٦٧ א
אאא
- ١٣٣ -
F٦ J١٦EאאאK
٦ J٣ J٦ J٢ אאאThermo-couple אאאא
،אKאאאאאאאאאאK
אאCopperאConstantanא،א(mV)،אא
אאאאא،אאאK אאאOperational Amplifierא
،אאאאF٦ J١٧KE
F٦ J١٧EאאאK
oV
אאR4 =
R1 R2
R3
E
FE
H
J
א
אא ٢٦٧ א
אאא
- ١٣٤ -
אאאאאאאאאW
mV)TT(k)TT(cE 22
2121 −+−= F٦ J١٣E
W E W אאאאK ckW אאאא
T1 W אאאFאאEאFאE T2 W אאאFאאאEאFאE
F٦ J٦E
אאאאא،אאא21075.3אc −×=א5105.4k −×=אאא
אאאK א
אאאWC100T1 °=אאWC0T2 °=KאF٦ J١٣EאאאאאאאW
mV)TT(k)TT(cE 22
2121 −+−=
mV2.4)0100(105.4)0100(1075.3E 2252 =−×+−×= −−
٦ J٣ J٦ J٣ אאאThermistor
אאאאאאאKאאאאאאאאאKאא
אאאאאKF٦ J١٨EאאאאאאאK
אא ٢٦٧ א
אאא
- ١٣٥ -
1
10
100
1000
10000
100000
1000000
-100 100 300 500درجة الحرارة (درجة مئوية)
وم) (أمةقاوالم
F٦ J١٨EאאאאאאאK
אאאאאאא
אאאאאאאאאΩ5.0ΩM75KF٦ J١٩EאאאK
F٦ J١٩Eאאא ٦ J٣ J٧ Photo – Electric Transducers
אאאאW
אא ٢٦٧ א
אאא
- ١٣٦ -
٦ J٣ J٧ J١ אא אאא،אא
אאא(Cathode)אאKאאאאאא
(Photo Cathode)(Anode)(Electrodes)(Dynodes)אא،א
F٦ J٢٠KE
F٦ J٢٠EאאאK
אאאאאFEאאא
אא،אאאאFאאEאאF100µA1mAKE
الضوء الساقط
0
+100
+200
+300
+400 V
+500
+600
+700 V
آاثود
أنود
אא ٢٦٧ א
אאא
- ١٣٧ -
٦ J٣ J٧ J٢ א אאאא،אא
אאKאאאאאFאF٦ J٢١EEא،
אאאFאEאאאFאEא،
אאK
F٦ J٢١EאאאאאK
F٦אאאאא J٢٢Eא،
אא،אאאא،אאאK
F٦ J٢٢EאאאאאK
V
א
אא ٢٦٧ א
אאא
- ١٣٨ -
F٦ J٢٣EאאאאאאאK
10
100
1000
10000
100000
1000000
1 10 100 1000(ft-c) اإلضاءة
م) ( أو
ة خلية الوممقا
F٦ J٢٣Eאאאאא
٦ J٣ J٧ J٣ א אאאאאFEא
אKאאFאאKE
אא ٢٦٧ א
אאא
- ١٣٩ -
אא א
F١E אאK F٢E ؟אאא F٣E אאאאK F٤E אK F٥E אאאאאאK F٦E אאאאאאאאK F٧E אK F٨E אאאאK F٩E אאאאK F١٠E אאK F١١E אאאK F١٢E אאאאK F١٣E אאאאאK F١٤E אאאK F١٥E אאאאK
אא ٢٦٧ א
אאא
- ١٤٠ -
א F١E א1א inchFE
אא10א Vאאא،XאאאאW FE Vo =3 V FE Vo=5 V FE Vo=8 V
F٢E אאאא،אא5 inchesאאא،10 Vא،אאאאאאW
FE Vo = 2 V FE Vo = 4 V FE Vo = 6 V F٣E אk = 4א،אאא
KאאאאR0 = 100 Ω،אG =
2×10-5אאאא،K F٤E אk = 4،Kא
א10א inches10.2 inchesאאא،אאKאאאאאR0 =120 Ωא،
אאK F٥E אאאאאאR0 =120 Ω،
אk = 12אאא،א1%K
B A W
X منزلق
10 V
1 "
A
W R1
R2 VT
אא ٢٦٧ א
אאא
- ١٤١ -
F٦E אאאאאאR0 = 250 Ω،∆R = 0.15 ΩאG=1.5×10-4،
אאkK F٧E אא،A=4×10-3 m2אא،
d=5×10-4 mאאאאא،W FE אאאאא(k = 1000) FE אאאא(k = 4)
F٨E אאאאאאא،אW
FE אאאאאK FE אאאאK FE אאkאאK
F٩E א0.02 m א،א0.1א Tesla א،0.5 m/sec Kא
אאאאאK F١٠E א0.02 m א،
אא0.5 Tesla ،אאאאא0.03 V KאאK
F١١E ،אאאאאאאT1=80°C،0.05א mV/°Cא5105k −×=אאאK
F١٢E א،אאאאאאאא2104c −×=א5105k −×=אא
אאאאK
א٢٦٧ אא א
- ١٤٢ -
אא(References)
[1] "Electronic Instruments And Measurements."
Larry D. Jones, A. Foster Chin. Prentice-Hall, Inc. A Division of Simon & Schuster Englewood Cliffs, New Jersey, 1991.
[2] "Electrical Measurements and Calibration: Fundamentals and Applications." Lawrence M. Thompson Instrumentation System & Paperback – June 1994.
[3] "The Measurements, Instrumentation and Sensors Handbook." J. G. Webster Spring -Verlag Berlin and Heidelberg GmbH & Co. KG Hardcover- December 1998.
[4] "Sensors for Measurement and Control." Peter Elgar Longman Paperback – 19 January 1998.
٢٦٧ אא א
א אאא١ ........................................................................................................................................ א
١ J١ ......................................................................................................................................................... ٣
١ J٢ ................................................................................................................................................. ٣
١ J٣אאא ..................................................................................................................... ٤
١ J٣ J١אאא ............................................................................................ ٤
١ J٤אא ......................................................................................................................... ٦
١ J٥אא١١ ........................................................................................................... א
١ J٦א١٥ ........................................................................................................................................... א
١ J٧אא ......................................................................................................................... ١٦
١ J٨אאאא١٧ ................................................................................................................ א
אא ........................................................................................................................................ ١٨
אאא٢١ .................................................................................................................................... א ٢ J١ ....................................................................................................................................................... ٢٠ ٢ J٢אאא.................................................................................................................. ٢٠ ٢ J٢ J١אאא ............................................................................................................ ٢٠ ٢ J٢ J٢אאא .................................................................................................... ٢١ ٢ J٢ J٣אאאאאאא٢١ ................................................................................. א ٢ J٢ J٣ J١אאאאאאא ............................................................................. ٢٠ ٢ J٢ J٣ J١ J١אא ........................................................................................................................ ٢٣ ٢ J٢ J٣ J١ J٢אאאאא ................................................................. ٢٧ ٢ J٢ J٣ J٢אאאאאא٢٨ ............................................................................ א ٢ J٢ J٣ J٢ J١אאאאא ................................................................. ٣٢ ٢ J٢ J٣ J٣אאאא٣٣ ........................................................................... א ٢ J٢ J٤אאאאאאא٣٥ ................................................................................. א ٢ J٢ J٤ J١אאאאא ........................................................................... ٣٥ ٢ J٢ J٤ J٢אאאאא ........................................................................... ٤١
אא ...................................................................................................................................... ٤٥ אאאא .................................................................................................................................... ٥٧
٣ J١ ...................................................................................................................................................... ٥٨
٣ J٢אא ............................................................................................................................... ٥٩ ٣ J٢ J١אאאאאא ....................................................................................................... ٥٩
٣ J٢ J٢אאאאא ...................................................................................................... ٥٩
٢٦٧ אא א
٣ J٣אאא ................................................................................................................ ٦٦
אא ..................................................................................................................................... ٦٩
אאאא٧١ .................................................................................................................................... א
٤ J١ .................................................................................................................................................... ٧٢
٤ J٢אאא٧٢ .......................................................................................................................... א
٤ J٣אאא٧٥ ...................................................................................................................... א ٤ J٣ J١אאאאא٧٥ ................................................................................................. א
٤ J٣ J٢אאא ......................................................................................................................... ٧٥
٤ J٣ J٣א ......................................................................................................................... ٧٠ ٤ J٣ J٤א .................................................................................................................................... ٧١
אאא ...................................................................................................................................... ٨١
אאאא ................................................................................................ >אאK
٥ J١ ....................................................................................................................................................... ٨٤
٥ J٢אאאאא٨٤ .............................................................................................................. א ٥ J٢ J١ ...................................................................................................................................... ٨٤
٥ J٢ J١ J١אא .................................................................................................................... ٨٤ ٥ J٢ J٢ ........................................................................................................................................... ٨٤
٥ J٢ J٢ J١א٨٥ .............................................................................................................................. א
٥ J٢ J٣אאאאאא٨٦ ................................................................................................................... א ٥ J٢ J٤אאאא٨٧ ................................................................................................. א
٥ J٢ J٥אאא .............................................................................................................. ٨٧ ٥ J٢ J٥ J١אא .................................................................................................................................... ٨٧
٥ J٣אאאאא٩٨ ............................................................................................................... א ٥ J٣ J١א ....................................................................................................................... ٩٨
٥ J٣ J٢אא٩٨ ............................................................................................................................. א
٥ J٣ J٣ ..................................................................................................................................... ٩٨
אא .................................................................................................................................... ١٠٩
אאאא ................................................................................................ >אאK
٦ J١ ............................................................................................................................................. J١١٦ J
٦ J٢ ...................................................................................................................................... J١١٦ J
٦ J٢ J١אא ................................................................................................................ J١١٦ J
٦ J٢ J٢אא .............................................................................................................. J١١٧ J
٦ J٢ J٣אאא ................................................................................................................ J١١٧ J
٦ J٣אאאאא ........................................................................................................ J١١٨ J
٢٦٧ אא א
٦ J٣ J١אאא ................................................................................................................ J١١٨ J
٦ J٣ J٢א .............................................................................................................................. ١١٣
٦ J٣ J٣אא .............................................................................................................................. ١١٧
٦ J٣ J٣ J١אאא ...................................................................................................................... ١١٧
٦ J٣ J٣ J٢אאא١١٧ ...................................................................................... א
٦ J٣ J٤אא ............................................................................................................................. ١٢٠
٦ J٣ J٤ J١אאאא ..................................................................................................................... ١٢١
٦ J٣ J٤ J٢אאא ....................................................................................................................... ١٢١
٦ J٣ J٤ J٣١٢٢ ................................................................................................................................ א
٦ J٣ J٥א........................................................................................................................ ١٢٣
٦ J٣ J٦אא ............................................................................................................................... ١٢٤
٦ J٣ J٦ J١אאא .......................................................................................................... ١٢٤
٦ J٣ J٦ J٢אא١٢٥ ............................................................................................................................. א
٦ J٣ J٦ J٣אא١٢٦ ............................................................................................................................. א
٦ J٣ J٧ .......................................................................................................................... ١٢٧
٦ J٣ J٧ J١אא ..................................................................................................... ١٢٧
٦ J٣ J٧ J٢א .................................................................................................... ١٢٨
٦ J٣ J٧ J٣א ..................................................................................................... ١٣٠
אא .......................................................................................................................... J١٣٩ J
אא .................................................................................................................................................... J١٤٢ J
