AI HOC QUOC GIA THANH PHO HO CH MINHTRNG AI HOC BACH KHOA

Nguyen Ngoc Tan - Ngo Van Ky

KY THUAT OTAP 1O IEN

NHA XUAT BAN AI HOC QUOC GIATHANH PHO HO CH MINH - 2005

3

MUC LUC

Li m auChng 1KHAI NIEM VE O LNG1.1 ai lng o lng1.2 Chc nang va ac tnh cua thiet b o lng1.3 Chuan hoa trong o lng1.4 Chat lng cua o lng1.5 Nhng phan t trong thiet b o ien t1.6 Li ch thiet thc cua ien t trong o lng1.7 S chon la, tnh can than va cach dung thiet b o1.8 He thong o lngChng 2O IEN AP VA DONG IEN2.1 C cau ch th kim2.2 o dong mot chieu (DC) va xoay chieu (AC)2.3 o ien ap AC va DC2.4 o ien ap DC bang phng phap bien tr2.5 Von-ke ien t o ien ap DC2.6 Von-ke ien t o ien ap AC2.7 Ampe-ke ien t o dong AC va DCBai tapChng 3O IEN TR3.1 o ien tr bang Von-ke va Ampe-ke3.2 o ien tr dung phng phap o ien ap bang bien tr3.3 Mach o ien tr trong Ohm-ke3.4 Cau Wheatstone o ien tr3.5 Cau oi Kelvin3.6 o ien tr co tr so ln3.7 o ien tr at3.8 o ien tr trong V.O.M. ien tBai tapChng 4

7

9910111220212122

262635424852617071

82828484919496105111118

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O IEN DUNG, IEN CAM VA HO CAM4.1 Dung Von-ke, Ampe-ke o ien dung, ien cam va ho cam4.2 Dung cau o o ien dung va ien cam4.3 o ho camBai tapChng 5O CONG SUAT VA IEN NANG5.1 o cong suat mot chieu5.2 o cong suat xoay chieu mot pha5.3 o cong suat tai ba pha5.4 o cong suat phan khang cua tai5.5 o ien nang5.6 o he so cong suat5.7 Thiet b ch th ong bo hoa (Synchronoscope)5.8 Tan so keChng 6O AI LNG C HOC VAT THE RAN6.1 Cam bien v tr va s dch chuyen6.2 Cam bien ien tr bien dang6.3 Cam bien o toc o6.4 Cam bien o lc, trong lng6.5 Cam bien o ngau lc6.6 o gia toc, o rung va s va chamChng 7O NHIET O7.1 Thang o nhiet o7.2 o nhiet o bang ien tr7.3 o nhiet o bang cap nhiet ien7.4 Dung diod va transistor o nhiet o7.5 o nhiet o bang IC7.6 Dung cam bien thach anh o nhiet o

Chng 8O CAC AI LNG C HOC CHAT LONG

125125128139141

146146148155159162167171173

178178202207215221223

228228228234243246248

255

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8.1 o van toc chat long8.2 Lu lng ke8.3 o va do mc chat longChng 9O AI LNG QUANG9.1 Cac ac tnh rieng cua cam bien quang9.2 ien tr quang9.3 Diod quang9.4 Transistor quang9.5 Cam bien phat xa quangChng 10DAO ONG KY, TIA AM CC VA MAY GHI X-Y10.1 Ong phong ien t (CRT)10.2 Cac khoi chc nang trong dao ong ky10.3 Trnh bay tn hieu tren man anh cua dao ong ky10.4 Dao ong ky hai kenh10.5 Thanh o (Probe) cua dao ong ky10.6 Bo tao tre10.7 ng dung cua dao ong ky10.8 Von ke t ghi ket qua (Voltmeter Recorder)10.9 May ghi tren he truc X - Y (X - Y recorder)Phu lucTai lieu tham khao

255264269

273273276284291296

310310314317321323325327332333333343

6

7

Li m au

KY THUAT O c bien soan nham phuc vu cho mon hoc Ky thuat o(o lng ien va ien t - Electrical measurements and ElectronicInstrumentation) c bien soan thanh hai tap:KY THUAT O - TAP 1 - O IEN VA THIET B O IEN T C BANgom 10 chng.KY THUAT O - TAP 2 - O IEN T gom 5 chng.Trong tap 1 cac chng 1, 2, 3, 4, 5, 10, do thac s Nguyen Ngoc Tan biensoan: trnh bay nhng phan c ban ve o lng ien va o lng ien t.Nguyen ly hoat ong cua thiet b o gom bo ch th, mach o va phng phap ocua von-ke, ampe-ke, thiet b o ien tr, ien dung, ien cam, ien nang ke,cos-ke, tan so ke. Trong phan von-ke, ampe-ke, ohm-ke chung toi trnh baythem mach o ien t nham muc ch e sinh vien hieu ro nguyen ly o cua mayo ien thong thng chuyen sang nguyen ly may o ien t ngay nay angc s dung rong rai.Cac chng 6, 7, 8, 9 va bai tap chng 2, 3, 4 do thac s Ngo Van Ky biensoan: trnh bay nguyen ly hoat ong va ac tnh ky thuat cua cac cam bien ocac ai lng c, nhiet, quang, c hoc lu chat. ay la nhng cam bien c banchuyen oi ai lng khong ien sang cac ai lng ien c s dung trongcac thiet b o lng cong nghiep hien nay (industrial instrumentation) va tronghe thong o lng va ieu khien t ong.Cuon sach nay nham cung cap nhng kien thc c ban ve thiet b o lngcho sinh vien cac nganh ien - ien t - May tnh (Cong nghe Thong tin) cuacac trng ai hoc; ong thi cung giup ch cho sinh vien cac nganh khacmuon tm hieu ve thiet b o.

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Chung toi mong nhan c nhieu y kien ong gop cua quy ong nghiep,cac oc gia e lan tai ban cuon sach c hoan thien hn.Xin chan thanh cam n cac ban ong nghiep, Bo mon C s Ky thuat ien- Khoa ien - ien t, Trng ai hoc Bach khoa a giup va tao ieu kienthuan li cho chung toi hoan thanh quyen sach nay.a ch: Bo mon C s Ky thuat ien - Khoa ien - ien t, Trng aihoc Bach khoa - ai hoc Quoc gia TPHCM - 268 Ly Thng Kiet, Q10. T:(08) 8647685. Email: nntan@hcmut.edu.vnnvky@hcmut.edu.vnNguyen Ngoc Tan - Ngo Van Ky

9

Chng

1

KHAI NIEM VE O LNG

1.1 AI LNG O LNGTrong lnh vc o lng, da tren tnh chat c ban cua ai lng o,chung ta phan ra hai loai c ban.ai lng ienai lng khong ien (non electrical) la nhng ai lng vat ly, hoahoc, sinh hoc, y hoc, ... khong mang ac trng cua ai lng ien.Tuy thuoc vao tng tnh chat cu the cua ai lng o, chung ta at raphng phap va cach thc o e t o thiet ke va che tao thiet b o.1.1.1 ai lng ienc phan ra hai dang:ai lng ien tac ong (active)ai lng ien thu ong (passive).1- ai lng ien tac ongai lng ien ap, dong ien, cong suat la nhng ai lng mang nanglng ien. Khi o cac ai lng nay, ban than nang lng nay se cung capcho cac mach o. Trong trng hp nang lng qua ln, se c giam bt chophu hp vi mach o. V du nh phan ap, phan dong.Neu trong trng hp qua nho se khuech ai u ln cho mach o co thehoat ong c.

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CHNG 1

2- ai lng ien thu ongai lng ien tr, ien cam, ien dung, ho cam, ... cac ai lng naykhong mang nang lng cho nen phai cung cap ien ap hoac dong ien chocac ai lng nay khi a vao mach o.Trong trng hp ai lng nay ang la phan t trong mach ien anghoat ong, chung ta phai quan tam en cach thc o theo yeu cau. V du nhcach thc o nong ngha la o phan t nay trong khi mach ang hoat onghoac cach thc o nguoi khi phan t nay ang ngng hoat ong. moi cach thco se co phng phap o rieng.1.1.2 ai lng khong ienay la nhng ai lng hien hu trong i song cua chung ta (nhiet o, apsuat, trong lng, o am, o pH, nong o, toc o, gia toc ...).Trong he thong t ong hoa cong nghiep ngay nay, e o lng va ieukhien t ong hoa cac ai lng khong ien noi tren, chung ta can chuyen oicac ai lng noi tren sang ai lng ien bang nhng bo chuyen oi hoaccam bien hoan chnh, thuan li, chnh xac, tin cay hn trong lnh vc o lngva ieu khien t ong.1.2 CHC NANG VA AC TNH CUA THIET B O LNG1.2.1 Chc nang cua thiet b oHau het cac thiet b o co chc nang cung cap cho chung ta ket qua oc ai lng ang khao sat. Ket qua nay c ch th hoac c ghi lai trongsuot qua trnh o, hoac c dung e t ong ieu khien ai lng ang co.V du: trong he thong ieu khien nhiet o, may o nhiet o co nhiem vuo va ghi la ket qua o cua he thong ang hoat ong va giup cho he thong xly va ieu khien t ong theo thong so nhiet o.Noi chung thiet b o lng co chc nang quan trong la kiem tra s hoatong cua he thong t ong ieu khien, ngha la o lng qua trnh trong congnghiep (industrial process measurements). ay cung la mon hoc trong nganh tong hoa.1.2.2 ac tnh cua thiet b o lngVi nhieu cach thc o a dang khac nhau cho nhieu ai lng co nhngac tnh rieng biet, chung ta co the phan biet hai dang thiet b o phu thuocvao ac tnh mot cach tong quat.

KHAI NIEM VE O LNG

11

V du: e o o dan ien chung ta dung thiet b o dong ien thuan tuyien la micro ampe-ke hoac mili ampe-ke. Nhng neu chung ta dung thiet bo co s ket hp mach ien t e o o dan ien th phai bien oi dong ieno thanh ien ap o. Sau o mach o ien t o dong ien di dang ien ap.Nh vay gia thiet b o ien va thiet b o ien t co ac tnh khac nhau.Co loai thiet b o, ket qua c ch th bang kim ch th (thiet b o danganalog), co loai bang hien so (thiet b o dang digital). Hien nay loai sau angthong dung. ay cung la mot ac tnh phan biet cua thiet b o.Ngoai ra thiet b o lng con mang ac tnh cua mot thiet b ien t (neula thiet b o ien t) nh: tong tr nhap cao, o nhay cao, he so khuech aion nh va co o tin cay am bao cho ket qua o. Con co them chc nang,truyen va nhan tn hieu o lng t xa (telemetry). ay cung la mon hoc quantrong trong lnh vc o lng ieu khien t xa.1.3 CHUAN HOA TRONG O LNG1.3.1 Cap chuan hoaKhi s dung thiet b o lng, chung ta mong muon thiet b c chuanhoa (calibzate) khi c xuat xng ngha la a c chuan hoa vi thiet b olng chuan (standard). Viec chuan hoa thiet b o lng c xac nh theobon cap nh sau:Cap 1: Chuan quoc te (International standard) - cac thiet b o lng capchuan quoc te c thc hien nh chuan tai Trung tam o lng quoc te attai Paris (Phap), cac thiet b o lng chuan hoa cap 1 nay theo nh ky canh gia va kiem tra lai theo tr so o tuyet oi cua cac n v c ban vat lyc hoi ngh quoc te ve o lng gii thieu va chap nhan.Cap 2: Chuan quoc gia - cac thiet b o lng tai cac Vien nh chuanquoc gia cac quoc gia khac nhau tren the gii a c chuan hoa theo chuanquoc te va chung cung c chuan hoa tai cac vien nh chuan quoc gia.Cap 3: Chuan khu vc - trong mot quoc gia co the co nhieu trung tam nhchuan cho tng khu vc (standard zone center). Cac thiet b o lng tai cactrung tam nay ng nhien phai mang chuan quoc gia (National standard).Nhng thiet b o lng c nh chuan tai cac trung tam nh chuan nay semang chuan khu vc (zone standard).Cap 4: Chuan phong th nghiem - trong tng khu vc se co nhng phong thnghiem c cong nhan e chuan hoa cac thiet b c dung trong san xuatcong nghiep. Nh vay cac thiet b c chuan hoa tai cac phong th nghiem

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CHNG 1

nay se co chuan hoa cua phong th nghiem. Do o cac thiet b o lng khic san xuat ra c chuan hoa tai cap nao th se mang chat lng tieu chuano lng cua cap o.Con cac thiet b o lng tai cac trung tam o lng, vien nh chuanquoc gia phai c chuan hoa va mang tieu chuan cap cao hn. V du phongth nghiem phai trang b cac thiet b o lng co tieu chuan cua chuan vunghoac chuan quoc gia, con cac thiet b o lng tai vien nh chuan quoc gia thphai co chuan quoc te. Ngoai ra theo nh ky c at ra phai c kiem trava chuan hoa lai cac thiet b o lng.1.3.2 Cap chnh xac cua thiet b oSau khi c xuat xng che tao, thiet b o lng se c kiem nghiemchat lng, c chuan hoa theo cap tng ng nh a e cap tren va sec phong kiem nghiem nh cho cap chnh xac sau khi c xac nh sai so(nh nh ngha di ay) cho tng tam o cua thiet b. Do o khi s dung thietb o lng, chung ta nen quan tam en cap chnh xac cua thiet b o c ghitren may o hoac trong so tay ky thuat cua thiet b o. e t cap chnh xac naychung ta se anh gia c sai so cua ket qua o.V du: Mot von-ke co ghi cap chnh xac la 1, ngha la gii han sai so cuano cho tam o la 1%.1.4 CHAT LNG CUA O LNG1.4.1 ac tnh cua cach thc oS hieu biet ve ac tnh cua cach thc o rat can thiet cho phan ln viecchon la thiet b o thch hp cho cong viec o lng. No bao gom hai ac tnhc ban.ac tnh tnh (static)ac tnh ong (dynamic)

KHAI NIEM VE O LNG

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1.4.2 ac tnh tnh (static)Tong quat, ac tnh tnh cua thiet b o la ac tnh co c khi thiet b oc s dung o cac ai lng co ieu kien khong thay oi trong mot qua trnho. Tat ca cac ac tnh tnh cua cach thc o co c nh mot qua trnh nhchuan.Mot so ac tnh c dien ta nh sau:Mc o chnh xac (sai so)o phan giai: khoang chia nho nhat e thiet b o ap ng co nhayo sai biet cua tr so o c vi tr so tin cay cTr so o chap nhan c qua xac suat cua tr so o.1.4.3 nh ngha sai so trong o lngo lng la s so sanh ai lng cha biet (ai lng o) vi ai lngc chuan hoa (ai lng mau hoac ai lng chuan). Nh vay cong viec olng la noi thiet b o vao he thong c khao sat, ket qua o cac ai lngcan thiet thu c tren thiet b o.Trong thc te kho xac nh tr so thc cac ai lng o. V vay tr so oc cho bang thiet b o, c goi la tr so tin cay c (expected value). Batky ai lng o nao cung b anh hng bi nhieu thong so. Do o ket qua o tkhi phan anh ung tr so tin cay c. Cho nen co nhieu he so (factor) anhhng trong o lng lien quan en thiet b o. Ngoai ra co nhng he so khaclien quan en con ngi s dung thiet b o. Nh vay o chnh xac cua thiet bo c dien ta di hnh thc sai so.1.4.4 Cac loai sai soSai so tuyet oi: e = Yn Xn

e - sai so tuyet oi;

Yn - tr so tin cay c; Xn - tr so o c

Sai so tng oi (tnh theo %): er|

Yn X nYn

|100%

o chnh xac tng oi: A 1|

Yn X nYn

|

o chnh xac tnh theo %:

a = 100% er = (A100%)

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CHNG 1

V du: ien ap hai au ien tr co tr so tin cay c la 50V. Dung von-ke o c 49V.

Nh vay sai so tuyet oi:

e = 1V

Sai so tng oi:

er

1V50V

100% 2%

o chnh xac: A = 10,02 = 0,98, a = 98% = 100% 2%

Tnh chnh xac (precision): 1|

X n X nX n

|

X n - tr so trung bnh cua n lan o.

V du:

Xn = 97,

tr so o c

X n = 101,1 tr so trung bnh cua 10 lan o

Tnh chnh xac cua cach o: 1|

97 101,1101,1

| 96% 96%

Sai so chu quan: Mot cach tong quat sai so nay do loi lam cua ngi sdung thiet b o va phu thuoc vao viec oc sai ket qua, hoac ghi sai, hoac sdung sai khong ung theo qui trnh hoat ong.Sai so he thong (systematic error) phu thuoc vao thiet b o va ieu kienmoi trng.Sai so do thiet b o: cac phan t cua thiet b o, co sai so do cong ngheche tao, s lao hoa do s dung. Giam sai so nay can phai bao tr nh ky chothiet b o.Sai so do anh hng ieu kien moi trng: cu the nh nhiet o tang cao, apsuat tang, o am tang, ien trng hoac t trng tang eu anh hng en saiso cua thiet b o lng. Giam sai so nay bang cach gi sao cho ieu kien moitrng t thay oi hoac bo chnh (compensation) oi vi nhiet o va o am. Vadung bien phap bao ve chong anh hng tnh ien va t trng nhieu. Sai sohe thong chu anh hng khac nhau trang thai tnh va trang thai ong: trang thai tnh sai so he thong phu thuoc vao gii han cua thiet b ohoac do qui luat vat ly chi phoi s hoat ong cua no. trang thai ong sai so he thong do s khong ap ng theo toc o thayoi nhanh theo ai lng o.Sai so ngau nhien (random error): Ngoai s hien dien sai so do chu quantrong cach thc o va sai so he thong th con lai la sai so ngau nhien. Thongthng sai so ngau nhien c thu thap t mot so ln nhng anh hng nhieu

KHAI NIEM VE O LNG

15

c tnh toan trong o lng co o chnh xac cao. Sai so ngau nhien thngc phan tch bang phng phap thong ke.V du: gia s ien ap c o bang mot von-ke c oc cach khoang 1phut. Mac du von-ke hoat ong trong ieu kien moi trng khong thay oi,c chuan hoa trc khi o va ai lng ien ap o xem nh khong thay oi,th tr so oc cua von-ke van co thay oi chut t. S thay oi nay khong chieu chnh bi bat ky phng phap nh chuan nao khac, v do sai so ngaunhien gay ra.1.4.5 Cac nguon sai soThiet b o khong o c tr so chnh xac v nhng ly do sau:Khong nam vng nhng thong so o va ieu kien thiet keThiet ke nhieu khuyet iemThiet b o hoat ong khong on nhBao tr thiet b o kemDo ngi van hanh thiet b o khong ungDo nhng gii han cua thiet ke1.4.6 ac tnh ongMot so rat t thiet b o ap ng tc thi ngay vi ai lng o thay oi.Phan ln no ap ng cham hoac khong theo kp s thay oi cua ai lng o.S cham chap nay phu thuoc ac tnh cua thiet b o nh tnh quan tnh, nhietdung hoac ien dung... c the hien qua thi gian tre cua thiet b o. Do os hoat ong trang thai ong hoac trang thai giao thi cua thiet b o cungquan trong nh trang thai tnh.oi vi ai lng o co ba dang thay oi nh sau:Thay oi co dang ham bc theo thi gianThay oi co dang ham tuyen tnh theo thi gianThay oi co dang ham ieu hoa theo thi gian.ac tuyen ong cua thiet b oToc o ap ngo trung thcTnh treSai so ong.

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CHNG 1

ap ng ong bac zero (bac khong)Mot cach tong quat tn hieu o va tn hieu ra cua thiet b o c dien tatheo phng trnh sau ay:

an

n

n

an1

n1n1

K a1

dxodt

aoxo

bm

mm

bm1

m1m1

K b1

dxidt

boxo

xo - tn hieu ra cua thiet b o;

xI - tn hieu o

ao an - thong so cua he thong o gia s khong oibo bn - thong so cua he thong o gia s khong oi.Khi ao, bo khac khong ( 0) th cac gia tr a, b khac bang khong (= 0).Phng trnh vi phan con lai:

aoxo = boxI;

xo

boao

xi ;

K

boao

: o nhay tnh

Nh vay ay la trng hp ai lng vao va ai lng ra khong phuthuoc vao thi gian, la ieu kien ly tng cua trang thai ong. V du nh sthay oi v tr con chay cua bien tr tuyen tnh theo ai lng o.ap ng ong bac nhatKhi cac gia tr a1, b1, ao, bo khac khong ( 0), con cac gia tr con lai bang

khong (= 0): a1

dxodt

aoxo boxi .

Bat ky thiet b o nao thoa phng trnh nay c goi la thiet b bac nhat.Chia hai ve phng trnh tren cho ao ta co:

ao dt ao dt ao

x x

(D + 1)xo = Kxi

Vi: D =

dtdt

;

=

a1ao

: thi hang;

K

boao

: o nhay tnh

Thi hang co n v la thi gian, trong khi o o nhay tnh K co n vla n v cua tn hieu ra/tn hieu vao.Ham truyen hoat ong (transfer function) cua bat ky thiet b o bac nhat:

xoxi

KD 1

V du cu the cua thiet b o bac nhat la nhiet ke thuy ngan.d xodtd xodtd xidtd xidt xo i . Hoac: xo i ;a1 dxo bo dxo bo

KHAI NIEM VE O LNG

ap ng ong cua thiet b bac hai, c nh ngha theo phng trnh

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a2

2

2

a1

dxodt

aoxo bxi

Phng trnh tren c rut gon lai: (

D 22n

2

Dn

1)xo Kxi

vi:n

ao/a2 - tan so khong em t nhien, radian/thi gian

- t so em; =

a1aoa2

; K

boao

Bat ky thiet b o nao thoa phng trnh nay goi la thiet b o bac hai.Thong thng loai thiet b o bac nhat ch hoat ong o vi ai lngco nang lng.V du: loai can dung lo xo an hoi (lc ke) co nang lng la c nang,nhiet ke co nang lng la nhiet nang.Loai thiet b o bac hai co s trao oi gia hai dang nang lng.V du: nang lng tnh ien va t ien trong mach LC, cu the nh ch thc cau ien t ket hp vi mach khuech ai.1.4.7 Phan tch thong ke o lngS phan tch thong ke cac so lieu o rat quan trong, t o chung ta xacnh cac ket qua o khong chac chan (co sai so ln) sau cung. e cho s phantch thong ke co y ngha, phan ln so lieu o lng oi hoi sai so he thongphai nho so vi sai so ngau nhien.Khi o mot ai lng bat ky nao ma biet ket qua o phu thuoc vao nhieuyeu to, th nhng yeu to nay eu quan trong ca. Theo ieu kien ly tng, mco anh hng cua cac thong so phai c xac nh e cho viec o lng neuco sai so phai c giai thch va hieu c nguyen nhan gay ra sai so. Nhngs phan tch sai so khong c tach khoi so lieu a c co nh trong cac ketqua o lng.d xodto

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CHNG 1

Y ngha so hoc cua s o nhieu lan: hau het gia tr o chap nhan c vabien so o co y ngha so hoc cua thiet b o oc c nhieu lan o. S ganung tot nhat co the co khi so lan oc cua cung mot ai lng o phai ln. Yngha so hoc cua n lan o c xac nh cho bien so x c cho bang bieuthc:

x

x1 x2 ... xnn

trong o: x - tr trung bnh; xn - tr so x lan o th n; n - so lan o.o lech

o lech lan o th 1:o lech lan o th 2:

d1 x1 xd2 x2 x

...............................

o lech lan o th n:

dn xn x

V du: x1 = 50,1; x2 = 49,7; x3 = 49,6; x4 = 50,2

Y ngha so hoc:

x

50,1 49,7 49,6 50,2 199,64 4

o lech cua tng gia tr o:

d1 = 50,1 49,9 = 0,2;

d2 = 49,7 49,9 = -0,2

d3 = 49,6 49,9 = -0,3; d4 = 50,2 49,9 = 0,3Tong ai so cua cac o lech: dtot = 0,2 0,2 + 0,3 0,3 = 0Nh vay khi tong ai so cac o lech cua cac lan o so vi y ngha so hocx bang khong th khong co s phan tan cua cac ket qua o xung quanh x .o lech trung bnh: co the dung nh mot bieu thc cua tnh chnh xac cuathiet b o.o lech trung bnh cang nho th bieu thc o cang chnh xac.Bieu thc o lech trung bnh D c xac nh:

D

|d1 | |d2 |... |dn |n

V du: D cua cac tr so o cua v du trc|0,2| |0,2| |0,3| |0,3|4 49,9D

KHAI NIEM VE O LNG

19

o lech chuan (standard deviation): o lech chuan cua mot so lan o lacac gia tr o lech quanh gia tr trung bnh c xac nh nh sau:.

o lech chuan cho n lan o: [

2

n

]

(so lan o

n 30 ).Neu so lan o nho hn 30 lan (n VC diod D dan

70

CHNG 2

ien. VC = e(t) tu ien nap en ien the nh cua e(t) bang Em. Mach khuechai theo ien ap (he so khuech ai bang 1) co nhiem vu ngan cach tu C vingo ra cua mach o. Khoa S dung e xa ien cho tu C e chuan b cho chu trnh oke tiep. ien tr R1 co nhiem vu ngan khong cho mach khuech ai A1 dao ong khiien dung nap ien. Khuyet iem ln nhat cua mach o la s bao hoa cua A1khi e(t) < VC, bi v mach o khong co hoi tiep am. Hien tng nay lam apng tan so cua mach b gii han.Hnh 2.56b: Tn hieu trong mach o co cai tien hn so vi mach o trcla hoat ong vi tan so ln hn. Mach khuech ai A1 la mach khuech ai aodau. Khi e(t) vt qua tr so -VC, V1 tr nen am va D1 dan. S hoi tiep am tronghai mach khuech ai cho ien ap ra E = Em ien ap ri tren diod va ien apsai lech (do s khong oi xng) cua mach khuech ai A2 b loai bo. Khi e(t)giam V1 tang en tr so ngng dan cua diod D1 e cho s hoi tiep am qua R2lam cho diod D2 dan e tranh s bao hoa cua mach khuech ai A1. Tr so nhdng cua e(t) c ao dau va nap vao tu C. Nh vay khong co dong ien rnao qua diod D1 va tong tr vao cua A2 rat ln. Muon ao cc tnh E th aochieu diod D1 va D2.2.7 AMPE-KE IEN T O DONG AC VA DC2.7.1 o dong DCNguyen ly o dong DC trong ampe-ke ien t la chuyen dong ien oIo thanh ien ap o bang cach cho dong ien o Io qua ien tr RS theo macho nguyen ly sau (H.2.57).

AIo

IoB

RS

Vo

+

+Imax Rm

R1

A

B

Io

Io

I1

I2

I3

I4

RS1

RS2

RS3

RS4

MACHOIENAP DC

Hnh 2.57: Mach o dong DC

Hnh 2.58: Mach phan tam o dong ien

O IEN AP VA DONG IEN

71

Phan tam o dong ien bang cach thay oi ien tr (H.2.58).Tam o I4 >I3 >I3 >I2 >I1; cho nen tam o cang ln th ien tr RS canggiam.2.7.2 o dong ACNguyen ly o: e o dong AC th chung ta chuyen dong ien AC thanhien ap AC bang ien tr RS nh trong trng hp o dong DC. Sau o chuyenien ap o AC thanh ien ap DC bang nhng phng phap o ien ap AC nha noi phan tren.BAI TAP2.1. Mot ampe-ke dung c cau o t ien co ien tr c cau o R(m) = 99 va donglam lech toi a Imax = 0,1mA. ien tr shunt RS = 1. Tnh dong ien tong cong iqua ampe-ke trong cac trng hp:a) Kim lech toi a.b) 0,5Dm; (FSD = Imax, full scale deviation).c) 0,25Dm.

Hnh B.2.1Giai: a) Kim lech toi a Dmien ap hai au c cau o.Vm = Im Rm = 0,1mA 99 = 9,9mV

Is RS = Vm IS =

VmRS

9,9mV1

Dong tong cong: I = IS + I = 9,9mA + 0,1mA = 10mA.

b) 0,5 Dm:

Im = 0,50,1mA = 0,05mAVm = ImRm = 0,05mA 99 = 4,95mVVm 4,95mVRS 1I = IS + Im = 4,95mA + 0,05mA = 5mA 9,9mAI S 4,95mA

72

CHNG 2

c) 0,25 Dm: Im = 0,250,1mA = 0,025mAVm = ImRm = 0,025mA 99 = 2,475mVVm 2,475mVRS 1I = IS + Im = 2,475mA + 0,025mA = 2,5mA.2.2. Mot c cau o t ien co I = 100A, ien tr noi khung quayR = 1k. Tnh ien tr shunt mac vao c cau o e tr thanh mot ampe-ketng ng vi cac trng hp hnh B.2.1.a) Dm = 100 mA = tam o 1.b) Dm = 1A = tam o 2.Giai: a) tam o 100mA.Vm = ImRm = 100A 1k = 100mV

It = Is + Im Is = It

Im

= 100mA 100A = 99,9mA

RS

VmI S

100mV99,9mA

b) tam o 1A: Vm = ImRm = 100mV

Is = It Im = 1A 100A = 999,9mA; RS

VmI S

100mV999,9mA

2.3. Mot c cau o t ien co ba ien tr shunt c mac theo kieu shunt ayrton sdung lam ampe-ke. Ba ien tr co tr so: R1 = 0,05, R2 = 0,45; R3 = 4,5;Rm = 1k; Imax = 50A, co mach o nh hnh B.2.3. Tnh cac tr so tam o cuaampe-ke.

Giai: Khoa ien B:

Hnh B.2.3

Vs = ImaxRm = 50A1k = 50mV.

I S

VSR1 R2 R3

50mV0,05 0,45 4,5I o 2,475mV 1,001 0,10001 10mA

O IEN AP VA DONG IEN

It = Is + Im = 50A + 10mA = 10,05mA; I = 10mA.Khoa ien C:Vs = Im (Rm + R3) = 50A(1k + 4,5) 50mV.

73

I S

VS 50mV( R1 R2 ) (0,05 0,45)

I = 50A + 100mA = 100,05mA.I 100mA.Khoa ien D:V5 = Im(Rm + R3 +R2) = 50A(1k + 4,5 + 0,45) 50mV

I s

VSR1

50mV0,05

2.4. Mot c cau o t ien Imax = 100A, ien tr noi (day quan)Rm = 1K c s dung lam von-ke DC. Tnh ien tr tam o e von-ke coVtd = 100V. Tnh ien ap V hai au von-ke khi kim co o lech 0,75Dm;0,5Dm; va 0,25Dm (o lech toi a Dm).

Hnh B.2.4

Giai:

V = IM (RS + Rm)

RS

VI m

Rm

Khi:

V = Vtd = 100V IM = Imax = 100A

RS

100V100A

1k = 999k.

Tai o lech 0,75 (FSD) DmIm = 0,75 100A = 75AV = Im (RS + Rm) = 75A (999k + 1k) = 75VTai o lech 0,5 (FSD) Dm: Im = 50AV = 50A (999k + 1k) = 50V.Tai o lech 0,25 (FSD) Dm: Im = 25AV = 25A (999k + 1k) = 25V.2.5. Mot c cau o t ien co Imax = 50A; Rm = 1700 c s dung lam von-ke DC co tam o 10V, 50V, 100V. Tnh cac ien tr tam o theo hnh B.2.5a,b 100mA 1 A .I = 50A + 1A = 1,00005A 1A

74

nh sau:

Hnh B.2.5

CHNG 2

Giai: Theo hnh B.2.5a: Rm + R1

VI max

R1

VI max

Rm =

10V50A

1700 = 198, 3k

R2

R3

50V50A100V50A

1700 = 998,3k

1700 = 1,9983M

Theo hnh B.2.5b: Rm + R1

V1I max

R1

V1I max

Rm =

10V50A

1700 = 198, 3k, Rm + R1+ R2 =

V2I m

R2 =

V2I max

R1 Rm =

50V50A

198, 3k 1700 = 800k

Rm + R1 + R2 + R3 =

V3I max

R3 =

V3I m

R2 R1 Rm

= 100V 50A 800k 198; 3k 1700 = 1M2.6. Mot von-ke co tam o 5V, c mac vaomach, o ien ap hai au ien tr R2 nhhnh B.2.6.a) Tnh ien ap VR2 khi cha mac von-ke.

b) Tnh VR2 khi mac von-ke, co o nhay 20k/Vc) Tnh VR2 khi mac von-ke, co o nhay 200k/V.Giai: Cha mac von-ke:

Hnh B.2.6

O IEN AP VA DONG IEN

75

VR2 = E

R2R1 R2

= 12V

50k70k 50k

= 5V

Vi von-ke co o nhay 20k/VRv = 5V 20k/V = 100kRv // R2 = 100k // 50k = 33,3k

VR2 = E

RV // R2R1 RV // R2

12V

33,3k70k 33,3k

3,87V

Vi von-ke co o nhay 200k/VRv = 5V 200k/V = 1MRv // R2 = 1M // 50k = 47,62k

VR2 12V

47,62k70k 47,62k

4,86V

2.7. Mot c cau o t ien co IfS = 100A vaien tr c cau o Rm = 1k c s dung lamvon-ke AC co V tam o = 100V (RMS). Machchnh lu co dang cau s dung diod silicon nhhnh B.2.7, diod co VF(nh) = 0,7V.

a) Tnh ien tr noi tiep RS ?

Hnh B.2.7

b) Tnh o lech cua von-ke khi ien ap a vao von-ke la 75V va 50V(tr hieu dung RMS)c) Tnh o nhay cua von-ke. Tn hieu o la tn hieu xoay chieu dang sin.Giai: a) Tnh RS: ay la mach chnh lu toan ky nen ta co quan he:I P (tr dnh) I tb/0,637Vm (tr nh) 2 V (RMS: tr hieu dung).

C cau o co: Ifs = Itb = 100A

I P

100A0,637

157A

76

CHNG 2

Ta co: I m

1,414Vtd 2VFRS Rm

RS

1,414Vtd 2VFI P

Rm

=

(1,414 100V ) (2 0,7V )157A

1k 890,7k

Tnh o lech:

V = 75V.

I tb 0,637I m 0,637

1,414V 2VFRS Rm

0,637

(1,414 75V ) (2 0,7V )890,7k 1k

Itb = 75A = 3/4 o lech toi a. (Im: dong nh khi V = 75V)V = 50V.

Itb 0,637

(1,414 50V ) (2 0,7V )890,7k 1k

= 50A =

12

o lech toi a

Tnh o nhay:Im = 157A I(RMS) = 0,707Ip = 0,707 157A = 111A

Tong tr: R

100V111A

900,9k . o nhay =

900,9k100V

9,009k/V

2.8. Mot c cau o t ien co: IfS = 50A; Rm = 1700 ket hp vi mach chnhlu ban ky nh hnh B.2.8. Diod siliconD1 co tr gia dong ien thuan IF (nh)toi thieu la 100A. Khi ien ap o bang20% Vtam o, diod co VF = 0,7V. Von-keco Vtam o = 50V.

Hnh B.2.8b) Tnh o nhay cua von-ke trong hai trng hp: co D2 va khong co D2.Giai: a) Tnh RS va RSH ay s dung chnh lu ban ky nen ta co:Ip = Itb/(0,5 0,637): tr nh trong trng hp chnh lu ban ky.

C cau o co Ifs = Itb = 50A I m

50A0,5 0,637

157A (tr nh)

Khi V = 20% Vt, IF(nh) co tr gia 100A. Vay khi V= Vt, IF(nh) co trgia:

I F ( nh )

100%20%

100A 500Aa) Tnh Rs va RSH

O IEN AP VA DONG IEN

IF = Im + ISH ISH (nh) = IF Im = 500A 157A = 343AVp(nh) = ImRm = 157A 1700 = 266,9mV

77

RSH

Vm( nh )I SH ( nh )

266,9mV343A

778

I F ( nh )

VRS

RS

1,414Vt Vm( nh ) VFI F ( nh )

()1,414 50V 266,9mV 0,7V500A

=139,5k

b) Tnh o nhay.Co D2: trong ban ky dng, dong qua D1 co tr gia nh:IF(nh) = 500ATrong ban ky am, dong qua von-ke I(nh):

I ( nh )

1,414VtRS

1,414 50V139,5k

I(hieu dung) = 0,707500A = 353,5A (RMS)c

Tong tr: R

50V ( RM S)353,5A( RM S)

141,4k ;

o nhay

141,4k50V

2,8k/V

Khong co D2Trong ban ky dng: IF(nh) = 500A. Trong ban ky am: I = 0Trong chu ky cua tn hieu:I(hieu dung) = 0,5 IF(nh)vi I la dong ien mach chnh chay qua Rs trong ban ky dng.

2

I2T

T /20

( I F sint )2 dt

I F2 ( nh )4

I = 0,5 500A = 250A

Tong tr: R

50V250A

200k50V

2.9. Mot ampe-ke s dung c cau o t ien co cau chnh lu va bien dong nhhnh ve. Biet rang c cau o co Ifs = 1mA va Rm = 1700. Bien dong co Nth =1,414Vt m nh VF 500AI (hi eu dun g) 200k . o nhay 4k/V

78

CHNG 2

500; N s = 4. Diod co: VF(nh) = 0,7V; Rs = 20k. ampe-ke lech toi a khi dongs cap IP = 250 mA. Tnh tr gia RL.

Hnh B.2.9Giai: Chnh lu toan ky nen ta co:

I m (tr nh)

I tb 1mA0,637 0,637

ien ap Em hai au cuon th bien dong (tr nh):Em = Im(Rs + Rm) + 2VF = 1,57mA(20k + 1700) + 1,4V = 35,5V Es(tr hieu dung) = ( 0,70735,5V) = 25,1VDong lam lech toi a c cau o co tr hieu dung I:I = 1,11Itb = 1,11 1mA = 1,11mA

Ta co:

I th I s

N sN th

250mA

4500

2mA

Ith = Iqua c cau o + IL; 2mA = 1,11mA + IL25,1VI L 0,89mA2.10. Tnh ien ap hai au c cau o t ien (PMMC) co Rm = 850 va Ifs =100A khi kim lech toi a.S: 85mV.2.11. Tnh tr gia ien tr tam o cho c cau o t ien co Ifs = 200A, Rm = lkc s dung lam von-ke DC co Vt = 150V. 1,57mAIL = 2mA1,11mA = 0,89mA; RL ES 28,2k

O IEN AP VA DONG IEN

79

2.12. Tnh dong ien i qua c cau o t ien khi kim co o lech bang 1/2 o lechtoi a (FSD) biet rang c cau o co o nhay la 20 k/V.S: 25A.2.13. Tnh tr gia ien tr shunt e cho ampe-ke co: It = 1mA; Rm = 103 tr thanhampe-ke co It (Itam o) = 150mA.2.14. C cau o A co tam o t 0 en 10V va ien tr tam o la 18k, c cauo B co tam o t 0 en 300V va ien tr tam o la 298k, ca hai c cau oeu co ien tr day quan Rm = 2k. Hay cho biet c cau o nao co o nhayln hn.S: C cau A.2.15. Tnh dong ien chay qua c cau o A, B nh hnh B.2.15.

Hnh B.2.152.16. Tnh cac tr gia ien tr t R1 en R5 nh hnh B.2.16.

Hnh B.2.162.17. Tnh tr gia ien tr R1, R2, R3 hnh B.2.17.

Hnh B.2.17

80

CHNG 2

2.18. Tnh tr gia ien tr R1, R2, R3, R4 trong hnh B.2.18.

Hnh B.2.18S: R1 = 1; R2 = 9; R3 = 90; R4 = 900.2.19. Ta o ien ap hai au ien tr 6k trong mach nh hnh B.2.19 bangcach mac von-ke hai au ien tr nay, von-ke co o nhay 10k/V. Gia svon-ke co cac tam o 1V, 5V, 10V va 100V, hay cho biet tam o nhay nhat cothe s dung ma sai so gay ra do tai cua von-ke nho hn 3%.S: tam o 100V.

Hnh B.2.19

Hnh B.2.20

2.20. Trong mach o sau, von-ke A co o nhay 5k/V c noi gia X va Ych 15V tam o 30V. Von-ke B c noi gia X va Y ch 16, 13V tam o50V. Tnh o nhay cua von-ke B.2.21. Dong ien i qua c cau o co tr gia nh Ip = 150A. Tnh tr gia IDCneu c cau o dung mach chnh lu ban ky.2.22. Dong ien i qua c cau o t ien o c la 0,8mA. Tnh tr gia nhcua dong xoay chieu neu c cau o s dung mach chnh lu toan ky.2.23. Mot c cau o t ien co Ifs = 1mA va ien tr day quan Rm = 500 kethp vi mach chnh lu ban ky e tr thanh von-ke AC. Tnh o nhay AC vaDC, tnh ien tr tam o e von-ke co Vt = 30V.S: SAC = 450/V; SDC = 1 k/V; Rs = 13,3k.2.24. Mot c cau o t ien co Ifs = 200A va ien tr day quanRm = 500 c s dung lam von-ke AC bang cach dung mach chnh lu toan

O IEN AP VA DONG IEN

81

ky. Tnh ien tr tam o e von-ke co Vt = 50V.2.25. Tnh o nhay AC va DC va ien tr Rs trong mach o (H.B.2.25).

Hnh B.2.252.26. Mot von-ke AC o tr gia nh va mot von-ke AC o tr gia hieu dungc s dung e xac nh tn hieu nao co dang sin. Hay cho biet tn hieu naoco dang sin biet rang ket qua o co tr gia nh sau:

S: Tn hieu 2 va 3 co dang sin.2.27. Mot von-ke AC c dung e o ien ap hai au ien tr R2 nh hnhB.2.27. Biet rang von-ke dung c cau o t ien co Ifs = 100A, ien tr day quanRm = 1,5k, s dung mach chnh lu ban ky va co Vt = 10V. Hay cho biet trgia oc c tren von-ke.

Hnh B.2.27

Hnh B.2.28

2.28. Hai von-ke AC khac nhau c dung e o ien ap hai au ien tr R2nh hnh B.2.28. Von-ke A co o nhay AC la 10k/V va cap chnh xac la 2%va co Vt = 200V. Von-ke B co o nhay AC la 4k/V, cap chnh xac la 1,5%va Vt = 100V. Cho biet von-ke nao cho ta ket qua chnh xac hn.Tn hieu 1Tn hieu 2Tn hieu 3o tr gia nh-nh: 35,26Vo tr gia nh-nh 11,31Vo tr gia nh-nh 25,00Vo tr gia hieu dung: 12,00Vo tr gia hieu dung: 4,00Vo tr gia hieu dung: 8,83V

82

CHNG 3

O IEN TR

3.1 O IEN TR BANG VON-KE VA AMPE-KE

Chng

3

Hnh 3.1: a) Mach o RX;

b) Mach o RX

ay la phng phap xac nh phan t ien tr ang hoat ong (o nong)theo yeu cau. Co hai cach mac e o ien tr:Hnh 3.1a: Von-ke mac trc, ampe-ke mac sau (loi mac re dai). Khi oien tr can o RX c xac nh bi:

RX

VI

(3.1)

trong o: V - cho bi von-ke; I - cho bi ampe-ke.

Theo mach o:

V = Va + Vx

(3.2)

vi: Va - ien ap ri tren ampe-ke; Vx - ien ap ri tren RX.Ta thay co sai so trong viec xac nh RX do anh hng noi tr cua ampe-ke. Neu Ra (noi tr cua ampe-ke) rat nho so vi RX th VX > Va. Sai so do anhhng cua ampe-ke khong ang ke.Hnh 3.1b: Ampe-ke mac trc, von-ke mac sau (loi mac re ngan). ien trRX van c xac nh bi:

83

RX

VI

(3.3)

trong o: I = IX + IV - cho bi ampe-ke vi IV dong ien i qua von-ke.

Neu IV

IX tong tr vao cua von-ke rat ln so vi RX th sai so do anh

hng cua von-ke khong ang ke.V du 3.1: o ien tr r cua tu ien (RX) khihoat ong ien ap qui nh. Mach o cmac theo hnh 3.2. Von-ke co tam o 50Vva o nhay 20k/VDC c mac noi tiep vitu ien C can o. Kim ch th ien ap 10

von. Khi o ien ap ri tren tu ien.VC = VS V = 300V 10V

Hnh 3.2: o ien tr r RX

= 290VDong ien toi a Imax cua c cau ch th bang 50A (kim ch 10V)Vay ien tr r cua tu ien290V10AV du 3.2: Trong mach hnh 3.1a, von-ke co o nhay 10k/V ch 500 von vaampe-ke ch 0,5A co RA = 10. Von-ke at tam o 1000V. Xac nh ien trRX.

Giai: Theo von-ke va ampe-ke: RX

VI

500V0,5 A

Neu phan tch: V = VX + Va = (Ra + RX)I; Ra RX V /I 1000Suy ra tr so thc cua RX = 1000 10 = 990.Vay sai so do anh hng cua ampe-ke va von-ke:

101000

100% 1%

V du 3.3: Neu von-ke va ampe-ke c mac theo hnh 3.1b th von-ke vaampe-ke oc bao nhieu? Khi R = 990Giai: ien tr tng ng gia von-ke va RX.RV // RX = (10k/V1000V) // 990 = 989,9Von-ke ch th:

VX 500V

( RV // RX )Ra ( RV // RX )

500V

989,9999,9

= 495VRX 29 M egohm 1000

84

Ampe-ke ch th tr so:

CHNG 3

I I V I X

VXRV // RX

495V989,9

Do o hai v du 2 va 3 la neu o RX bang cach lay tr so oc cua von-kechia cho tr so oc cua ampe-ke th tr so oc cua v du 3 chnh xac hn v:RX V /I 495V /0,5 A 990 .Trong khi tr so o c v du 2: RX 500V /0,5 A 10003.2 O IEN TR DUNG PHNG PHAP O IEN AP BANGBIEN TRMach o c mac theo hnh 3.3.

Hnh 3.3: o ien ap bang phng phapbien tr suy ra RX theo RS

Nguon cung cap E tao ra dong ien I qua RX la VRX ien ap ri tren ien

tr mau VS:

VRX RX IVS RS I

VVS

VRX va VS c o bang phng phap bien tr.o ien tr bang phng phap so sanh nay khong phu thuoc vao dongien I cung cap cho mach o.3.3 MACH O IEN TR TRONG OHM-KETrong may o van nang (multimeter V.O.M) co phan o ien tr (ohm-ke). Trong trng hp dung ohm-ke e o ien tr th trang thai o la phan tien tr o (RX) khong co nang lng (o nguoi), mach o se la nguon nanglng rieng (nguon pin).3.3.1 Mach nguyen ly o ien trMach o c mac theo hnh 3.4. 0,5 A. Suy ra: RX S RX . R

O IEN TR

Hnh 3.4: a) Mach ohm-ke; b) Thang o khong tuyen tnh cua ohm-keay la mach ohm-ke kieu mac noi tiep, dong ien qua c cau ch th R1:

85

I m

EbRX R1 Rm

vi: R1 - ien tr chuan cua tam o; Rm - ien tr noi cua c cau.Khi RX 0; Im Imax (dong cc ai cua c cau ien t).

Khi RX;

Im Imax (khong co dong qua c cau).

V du 3.4: Eb = 1,5V; Imax = 100A; R1 + Rm = 15k.Xac nh ch th cua kim khi RX = 0 va s ch th tr so ien tr khi Im= 1/2 thang o; 1/4 thang o; 3/4 thang o.Giai: T phng trnh tren khi RX 0: I 1,5V /0 15k 100ATai tr so 1/2 thang o: I 100A/2 50AKhi o ien tr RX 1,5V (R1 + Rm) = 30 15 = 15k50AKhi dong Im = 1/4 thang o: Im = 25Aien tr RX c xac nh: RX 1,5V /25A 15k 45kTai dong Im = 3/4 thang o: Im = 75Aien tr RX 1,5V /75A 15k 5kNh vay gia tr thang o ien tr khong tuyen tnh theo dong ien I(H.3.4b).3.3.2 Mach o ien tr thc teTrong thc te nguon pin Eb co the thay oi. Khi RX0, Im qua c caukhong bang Imax, do o mach o co the mac them R2 (H.3.5) bien tr nay dunge chnh iem 0 cho mach o khi Eb thay oi. Nh vay trc khi o phaingan mach hai au AB, ieu chnh R2 e sao cho ohm-ke ch 0.

86

Hnh 3.5: Mach ohm-ke co chnh 0

CHNG 3

Theo mach tren ta co: Ib =

E BRX R1 R2 // Rm

Neu R2 // Rm

R1, th: I b

EbRx R1

Nh vay ien ap:

Vm = Ib(R2 // Rm)

Se co dong Im qua c cau ch th: I m

Rm Rm

.

Do o moi lan o cho RX0 ieu chnh R2 e co:

I m

Eb ( R2 // Rm )R1 Rm

I max

Sao cho khi Eb co s thay oi th s ch th RX se khong thay oi.V du 3.5: Eb = 1,5V; R1 = 15k; Rm = 1k; R2 = 1k; Imax = 50A. Xac nh tr so

oc cua RX khi Ib = Imax; Im=

12

I max ; Im =

34

I max

Giai: Tai Im = Imax = 50A; Vm = ImaxRm = 50A1k = 50mV.

Do o: I2 =

VmR2

50mV1k

50A . Nh vay dong: Ib = 100A.

Vay: RX + R1

EbI b

neu RX + R1

R2 // Rm

500.

#

1,5V100

15k . RX + 15k = 15k; RX = 0.

Khi Im =

12

max 25 ; Vm 25mV I2 = 25A.

Suy ra Ib = 50A. Vay RX + R1 #

1,5V50

; RX # 15kVm I b ( R2 // Rm )

O IEN TR

87

Tng t nh cach tnh tren. m

34

max 37,5.

Ib = Im + I2 = 37,5A + 37,5A = 75A.

RX R1

1,5V75

20k , RX = 5k.

V du 3.6: Trng hp Eb = 1,3V, tnh cac tr RX nh v du 1.Giai: Khi RX = 0 th Im = 50A (ieu chnh R2).

b

bR1 RX

1,3V0 15k

I 2 I b I m 86,67A 50A 36,67A

R2

Vm2

50 1k36,67A

tr ch th 1/2 thang o Im = 25A.

2

VmR2

25mV1,36k

RX R1

1,3V43,38

29,96k .

RX = 29,96k 15k = 14,96k # 15k.Giong nh tr so cua v du 1 khi Eb = 1,5V. tr ch th 3/4 thang o Im =37,5A.

2

37,5mV1,36k

27,57 , Ib = 37,5A + 27,57A = 65,07A.

RX R1

1,3V65,07

19,97k .

RX = 19,97k 15k = 4,97k # 5k.Ket qua o v du 2 va v du 1 gan giong nhau mac du Eb giam. V aieu chnh R2 e cho Im = Imax.Mach o ien tr vi nhieu tam o trong may o van nang (H.3.6).Khi thay oi tam o (X1 hoac X10 hoac X100...) dong ien qua c cauch th Im van bang nhau nhng tr so oc c tren thang o c nhan vi giatr tam o (H.3.7). 86,67. 1,36k 18,38 ; Ib = 25A + 18,38A = 43,38A

88

CHNG 3

Hnh 3.6a: Mat ngoai ohm-ke

Hnh 3.6b: Mach o ien tr co nhieu tam oV du 3.7: Khi RX = 24 (H.3.7a).

Hnh 3.7: Mach o cho tng tam o: a) Mach cho tam o X1

O IEN TR

b) Mach cho tam o X100; c) Mach cho tam o X10K

89

b

1,5V24 14 [10 // 16.685]

31,254mA .

m 31,254m

1010 16.685

= 18,72A (gia thang o)

Khi RX = 2400 (H.3.7b).

b

1,5V2400 1470 [1k // 15,695k]

0,311mA

Dong Im qua ong ho:

I mb

94015.695

0,311m 0,059 18,62

Neu thang o X1: Im = 18,72A tng ng RX = 24

vi:

Im =b

(10 // 16.685)10 16.685

#b

1010 16.685

1,5/[ RX 14 (10 // 16.685)] 5,989 104

RX (

1,5V 5,989 10433 106

) (14 10) = 27,2 24 = 3,2

Nh vay thang o cua ohm-ke khong tuyen tnh hoan toan, moi tam oeu phai chnh 0 .3.2.3 Nguyen ly o cua ohm-ke tuyen tnhThang o cua ohm-ke theo nguyen ly dong ien nh a e cap trenkhong tuyen tnh theo ien tr o. Do o trong cac mach o ohm-ke tuyen tnhtrong may o ien t ch th kim hoac ch th so, chung ta chuyen tr so o ientr RX sang ien ap o VX bang cach cung cap nguon dong ien I khong oi(bat chap tr so RX). VX = RX I. Sau o RX c o bi mach ien ap, VX tuyentnh theo RX.Nh vay: Khi RX 0, VX 0 Von.Khi RX, VX tien en gia tr ln nhat cua mach oV du: Mach o ien ap co ien ap ln nhat 1,5V th khi RX th VX1,5V.Nh vay neu von-ke co ien tr chnh may trc khi o, th phai chnhRX cho mach o. Khong chnh RX0 nh mach o dung nguyen lydong trong phan trc (chung ta se e cap trong phan may o ien t).3.2.4 o chnh xac cua ohm-ke

90

CHNG 3

Do mach ien tr khong tuyen tnh theo thang o, nen sai so tang nhieu khoang o phi tuyen. V vay khoang thang o co sai so cho phep trong khoangt 10 90% khoang hoat ong vi ieu kien chnh 0 cho moi tam o.Nh a noi phan trc khi ohm-ke ch th 1/2 thang o th ien tr RXbang noi tr cua mach ohm-ke. Neu 1/2 thang o cua s ch th dong ien cosai so 1% cua thang o ien tr dan en sai so la 2% ket qua o ien tr.

Khi: RX = R1 va I b

EbR1 RX

. T sai so 2% cua dong Ib ( 1/2 thang

o) se co sai so cho phan o ien tr la 2% cua (RX + R1)Gia s R1 co sai so khoang 1%, khi R = R1 th sai so tai RX (tai 1/2 thango) se la 2% (2 R1) = 4 %.V du 3.8: phan tch sai so cua ohm-ke khi kim ch th 0,8 thang o va 0,2thang o.Giai: 0,8 thang o:

I b 0,8max

bRX R1

Eb Eb0,8max 0,8Eb/R1

R10,8

V khi RX 0 (H.3.4):b

Eb EbR1 RX R1

.

Vay: RX = 1,25R1 R1 = 0,25R1; R1 = 4RX.Neu sai so cua thang o la 1 % cho s ch th cua kim th tai 0,8 thang o,sai so cua s ch th dong ien la 1,25% Imax. Nh vay sai so phan o ientr:RX (%) = 1,25% (4RX + RX) = 6,25% RX 0,2 thang o:

RX + R1 =

Eb0,2max

R10,2

Sai so cho toan khung thang o 1%, 0,2 thang o, sai so cho ch th laR4 RX R1# 5R1 ; RX = 4R15%. Sai so cho RX:RX 5%( X RX ) 6,25%

O IEN TR

91

Theo s phan tch sai so cua thang o ien tr tren, e o chnh xac hnnen chon tam o cho ien tr khoang 1/2 thang o, v tai o sai so cchng minh v du tren la 4%, trong khi o 0,2 thang o va 0,8 thang o saiso eu ln bang nhau va bang 6,25%.3.4 CAU WHEATSTONE O IEN TRe cho ien tr c chnh xac hn, chung ta dung cau Wheatstone e oien tr bang hai phng phapPhng phap can bangPhng phap khong can bang3.4.1 o ien tr dung cau Wheatstone can bangay la phng phap thng dung trong phong th nghiem v nhng uiem cua no.Nguyen ly cau WheatstoneCau Wheatstone c mac nh hnh 3.8.

Hnh 3.8: Cau Wheatstone o ien tr

Hnh 3.9: ien ke G

Khi cau Wheatstone can bang la dong ien qua ien ke G = 0:VP = VQ va VR = VSNeu dong I1 qua P va R, dong I2 qua Q va S.Khi o I1P = I2 > Q va I1R = I2S.

Suy ra:

R SP Q

hoac R

PQ

S .

Vi tr so P, Q, S biet chnh xac, ien tr R c xac nh. Ket qua o Rkhong phu thuoc vao nguon cung cap E. ay cung la u iem cua phep o. ochnh xac cua R phu thuoc vao o nhay cua ien ke G. o nhay cua ien keln dan en s can bang tot hn.

92

CHNG 3

Ngoai ra sai so cua ien tr P, Q, S cung anh hng cua sai so R.V du: Sai so cua S la 0,5%; P, Q la 1%. Th sai so cua R:R =S +R +Q = 2,5%.Vi bat ky R e ieu chnh cau Wheatstone can bang chung ta thngthay oi t so P/Q (tam o) va S la bien tr (hop ien tr) co gia tr thay oitng 0,1 (hoac tng 1,0) nh cac cau o Wheatstone trong cac phong thnghiem.V du: P/Q 1/10 ; S = 237,5. Khi cau can bang, do o R c xac nh:R = 23,75.3.4.2 o ien tr dung cau Wheatstone khong can bang

Hnh 3.9: Mach tng ng Thevenin cua cau Wheatstonea) ien ap ngo ra e h cua cau; b) ien tr r ngo rac) Mach Thevenin khi tai la rg cua ien keTrong cong nghiep, ngi ta thng dung nguyen ly cau Wheatstone khongcan bang ngha la nh ien ap ra (hoac dong ien ra) ngo ra cua cau e oien tr R hoac s thay oiR cua phan t o. Phng phap nay can nguon Ecung cap cho cau o c on nh, v ien ap ra co phu thuoc vao nguon E.Ngoai ra cung con phu thuoc vao o chnh xac cua cac phan t cauWheatstone. o nhay cua cau phu thuoc vao nguon cung cap E va noi tr cuabo ch th (hoac tong tr vao cua mach khuech ai neu ien ap ngo ra cuacau c a vao mach khuech ai).T mach cau o hnh 3.9, ien ke G c thao ra khoi cau o. ien ap ngo ra cua cau:

VR VS Eb[

R SR P Q S

]

Tong tr ngo ra cua cau c xac nh:r = [P // R] + [Q // S]Nh vay mach tng ng Thevenin cua cau c xac nh (H.3.9c). Do

O IEN TR

o dong ien Ig qua ien ke khi cau khong can bang:

93

I g

VR VSr rg

,

rg - noi tr cua ien ke G

V du 3.9: Xac nh s thay oi ien tr R nho nhat ma ien ke G phat hienc khi o nhay cua ien ke G = 1A/diV (diV: mot vach chia cua thang o).P = 3,5k; Q = 7k va S = 4k khi R = 2k va noi tr cua ien ke G: rg =2,5k; Eb = 10V.Giai: Theo bieu thc mach tng ng Thevenin:

VR VS = Ig (r + rg)3,5k 2k5,5k

7k 4k11k

3,82k

ma:

Khi Ig thay oi 1A th co s thay oi: VR VS.(VR VS) =Ig(r+rg) = 1A(3,82 + 2,5)k = 6,32mV]RR P S QNh vayRmin co c khi:(VR VS) = 6,32mV;Rmin (2+3,5)k6,32mV = 10 V ( )2kRmin 3,5k 7k 4k

Rmin 2k5,5k

4k 6,32mV11k 10V

Nh vay e choRmin cang nho th(VR VS ) cang ln, o nhay cangtang th Eb cang ln, nhng s tang Eb co han che. Do o, can phai khuechai(VR VS ) va tong tr Z i cua mach khuech ai phai ln ( r g c thaybi Z i cua mach khuech ai).3.4.3 Tam o ien tr cua cau Wheatstonee cho ien tr o bi cauWheatstone c chnh xac th gia tro cua no phai ln hn gia tr ien trtiep xuc va ien tr day noi. Nhmach hnh 3.10 do anh hng cua day

noi co ien tr noi gia R va S khi oien ke G c xem nh noi a hoacb a en ket qua o:

Hnh 3.10: ien tr day noigay ra sai so cauWheatstonevi: r = (P // R) + (Q // S) =(VR VS) = Eb[R R SRmin 2k 4k 6,32 106 362 5,5 103 3,476

94

CHNG 3

R

( S Y )PQ

hoac R

SPQ Y

Trong thc te ien tr R o c chnh xac co gia tr nho nhat vaokhoang 5. Nh vay e o nhng ien tr nho hn 1 ( 1/10 ;1/100 ; 1/1000 ) chung ta phai dung ky thuat o ac biet.Ngoai ra, cau Wheatstone cung c dung e o cac ien tr ln vai M(megohm) hoac vai tram M, phai dung cach thc o ac biet (se noi phansau). Nhng cung gii han tr 1012 ohm.3.5 CAU OI KELVINay la cau o ac biet c dung e o ien tr gia tr nho.

3.5.1 ien tr bon auNhng ien tr co gia tr nho nh ientr shunt can phai co au ien tr c xacnh chnh xac, e tranh sai so do s tiepxuc cua au ien tr vi day dan ien codong ien ln i qua. Do s xuat hien hieung nhiet ien co the co, cho nen ien trc che tao bon au (H.3.11), hai au dongien thng co be mat tiep xuc vi day danco dien tch ln; con hai au nho goi la authe (potential terminal) c noi vao ampe-

au dong

au theau dong

au theHnh 3.11: ien tr bonau

ke (miliampe-ke), gia tr ien tr c tnh hai au nay va khong co ien apri tren au the nay do hieu ng nhiet ien.3.5.2 Cau oi KenvinCau oi Kelvin c mac hnh 3.12. Trongcau o nay co ien ap ang ke ri tren ien tr Ycua oan day noi a, b. Neu t so cua phan tP/r p/R (P=p va R=r) th khi o sai so doien ap ri tren day dan Y se b loai bo.Phng trnh cau can bang nay phc taphn cau Wheatstone. Khi cau can bang th Vg =0:

dong i1 qua ien tr P va R;qua ien tr Q va S

dong I

Hnh 3.12: Cau oiKelvin o ien tr nho

dong i2 qua P va r;

dong

I

i2

O IEN TR

qua ien tr Y.Bi v khong co ien ap ri tren ien ke G cho nen:i1R = i2r + IS

95

Suy ra:Con co:

IS = i1R i2R = R(i1 i2r /R)i1P = IQ + Pi2, IQ = P (i1 pi2/P )

Chia:

I S R(i1 i2r /R)

;

Q PS R

. Neu p = P va r = R

Vay, vi ieu kien can bang cua cau va luon luon co p = P va r = R thphan t o Q c xac nh:

Q S

P pR r

Q khong phu thuoc vao ien tr day dan, Y, S la ien tr mau co sai sonho, P la hop ien tr thay oi co o chnh xac cao va o phan giai nho (cothe tng bc thay oi la 0,1 (hoac 1)), R la ien tr thay oi tam o chocau.

Hnh 3.13: Cau Kelvin vi ien tr Q, S co bon auCau o Kelvin thc te dung ien mau S co bon au nh hnh 3.13. V Qva S thng co ien tr nho t vai microohm (), vai m (miliohm) en 1cho nen dong I+i1 thng co tr so han che (vai ampe). V vay phai co bien trRb va ampe-ke theo doi. o chnh xac cua cau o Kelvin cung giong nh cauWheatstone (a c phan tch). oi vi nhng ien tr o Q co gia tr nho hn0,1 (microohm) o chnh xac se kem i nhieu.V du 3.10: Dung S = 1m; Q = 23,5; R = 1000 dong qua ampe-ke 5 ampe,nguon Eb = 6V th ien ke G ch 0. Nh vay:IQ P(i1 i2 p/P ) S

96

CHNG 3

Q

23,51000

1m 23,5 106

V du 3.11: Mot ien tr (bon au) co tr so khoang 0,15 c o bi cauKelvin. ien tr mau 0,1. Xac nh t so cho cau o R/P hoac r/p.Giai: Theo cong thc khi cau can bang.

Q S

P p Pr r R

R r 0,1 10P p 0,15 15

Nh vay tren cau o Kelvin chnh P = p = 15.R = r = 10 hoac P = p = 150 va R = r = 100.3.6 O IEN TR CO TR SO LNTrong phan nay chung ta e cap en phng phap o ien tr co gia trln (vao khoang vai megohm tr len) dung von-ke, microampe-ke, cauWheatstone va megohm-ke chuyen dung. Khi o ien tr co tr so rat ln nho ien tr cach ien cua vat lieu thong thng se co hai phan t ien tr.ien tr khoi (volume resistance).ien tr r be mat (surface leakage resistance).Hai phan t ien tr nay xem nh song song vi nhau, nh vay hai ientr co tr so co the so sanh c se anh hng ang ke en ien tr khoi cano cua vat lieu cach ien.3.6.1 Phng phap o ien tr ln dung von-ke va microampe-keCau o ien tr cach ien cua vo boc gia day dan trong va day dan benngoai (vo giap bang kim loai) cua day dan ien ong truc co vo boc giap(H.3.14). Khi dong ien i vao day dan th se co hai dong ien i qua microampe-ke, o la dong IV i qua lp cach ien cua vo boc, dong IS i qua be matcua day dan va lp cach ien. Cho nen ien tr song song gia lp cach ienva be mat [RV//RS] c xac nh bi von-ke va micro ampe-ke. Neu RS sosanh c vi RV th RS se anh hng rat ln en RV can o. e tranh anhhng cua RS bang cach loai bo dong IS qua microampe-ke, ngi ta thngdung day dan ien (khong co vo boc hoac vecni) quan quanh lp vo cach ienva noi trc microampe-ke. Nh vay dong ien IS i qua RS luc trc se i quaday dan nay (H.3.14b) do o anh hng cua RS vao RV b loai bo. Vong daydan nay c goi la vong day bao ve tranh ien tr r be mat RS. 0,1 0,15 . Suy ra S

O IEN TR

97

Hnh 3.14: o ien cach ien lp vo boca) Dong r be mat IS; b) Co vong day bao veV du 3.12: Mot cap day dan ien loai ong truc lp giap bang kim loai benngoai cung, ngan cach day dan ien ben trong bang lp cach ien. Neu machc mac noi nh hnh 3.14a th dong ien qua microampe-ke la 5A khi ienap th nghien la 10.000V. Neu mach c mac nh hnh 3.14b th dong ieno c la 1,5A. Xac nh ien tr khoi cach ien cua lp cach ien. Sau oxac nh ien tr r be mat hnh 3.14a.Giai: ien tr khoi cach ien:

RV

V

10 1031,5 106

Dong ien qua ien tr r be mat:IS = 5A IV = 5A 1,5A = 3,5A v IV + IS = 5A

RS

S

10 1033,5 106

Nh vay neu chung ta khong loai bo dong IS bang vong day dan bao ve th se9 9

Nho hn ba lan ien tr khoi cach ien that. 6,7 109 (ohm) 2,9 109 (ohm)o c ien tr: RS // RV = (2,9 // 6,7)10 = 2,0210 ohm

98

CHNG 3

Trong trng hp o ien tr cach ien cua mot mau cach ien be mat(H.3.15) khi o e loai bo dong ien r be mat ngi ta dung vong bao ve bangkim loai hnh vanh khan ben ngoai ban cc mat tren e o ien tr cach ien.

IL

A

Cao the

Chat cachien

V

IV

Vong baove

Hnh 3.15: o ien tr cach ien loai bo ien tr r be matTrong trng hp dung cau Wheatstone e o ien tr cach ien e loaibo ien tr r be mat, chung ta cung dung vong bao ve nh hnh 3.16a va cphan tch thanh mach tng ng (H.3.16b), ien tr b va c la hai ien tr r

be mat va be mat di cua vat lieu can o ien tr cach ien. V btr cua ien ke).

rg (ien

b // rg rg va c

S c // S S

Nh vay b va c khong anh hng en ien tr R la phan t o cua cau.

Hnh 3.16: a) Cau Wheatstone o ien tr cach ien be matb) Mach tng ng3.6.2 Megohm-ke chuyen dung

O IEN TR

99

Bo ch th thng dung cho megohm-ke (loai co ien) la t so ke t ien(H.3.17). C cau ch th nay gom co hai cuon day.Cuon day lech (deflecting coil).Cuon day kiem soat (control coil).

Hnh 3.17: Megohm-ke chuyen dungHai cuon day nay quan tren truc quay mang kim ch th. Momen quay T2= Kq2()I2 va T1 = Kq1()I1.Hai momen nay luon luon oi khang nhau va Kq1, Kq2 la ham so theo gocquay cua kim ch th e sao cho tai goci cua kim ch th ta co:

Tq1 = Kq1(i)I1 = Tq2 = Kq2(i)I2. Suy ra

12

K q2 (i )K q1 (i )

K (i )

Vay goc quayi cua kim ch th phu thuoc vao tr so dong ien I1 va I2(c cau ch th nay khong co tr ban au v khong co lo xo kiem soat hoac daytreo nh c cau ien t ma ch co truc quay do o khi khong co dong I1, I2 kimch th v tr bat ky).Theo mach cu the cua megohm-ke: Nguon E c cung cap bi may phatien quay tay (hoac nguon phat bang mach ien t dung pin nh cac may misau nay). Dong I1 qua cuon day kiem soat:

1

R1 r1

, R1 - ien tr chuan, r1 - ien tr noi cua khung quay kiem

soat dong I2 qua cuon day lech.

2

RX R2 r2

100

CHNG 3

RX - ien tr o; R2 - ien tr chuan; r2 - ien tr noi cua khung quay lech.Khi RX; I2 0: Dong ien I1 keo kim ch th lech toi a ve phatrai thang o co tr so.Khi RX 0; I2 I2max (cc ai)T so21 tr so cc ai kim ch th lech ve pha phai (tr so 0)Khi RX tr so bat ky khi o goc quayi.R1 r1 RX R2 r2

2 /( RX R2 r2 )

K (2 ) ;

RX R2 r2R1 r1

K (i )

Nh vay goc quayi phu thuoc vao tr so o RX.ac biet khi kim ch th gia thang o:

12

1 RX = R1 + r1 R2 r2

Neu: r2 = r1 RX = R1 R2.Nh vay thay oi tam o cho thang o bang cach thay oi tr so R2.Trong mach nay co au Guard e gan vao vong bao ve (guard ring) hoacday bao ve (guard wire) e loai bo ien tr r be mat (RS) khi o ien tr cachien3.6.3 ng dung o ien tr cach ien va cho day b cham atcua day ien liTong quat: Ngi ta thng o ien tr cach ien cua cac ng day taiien hoac phan phoi ien trong cong nghiep. V du theo tieu chuan thiet kemang ien, ien tr cach ien c th nghiem vi megohm-ke 1000V (hoac2000V), nguon ien ap cap cho megohm-ke. ien tr cach ien c o giahai au day dan ien vi nhau hoac tng day dan ien vi day trung tnh viieu kien day dan c thao ra khoi nguon ien li va tai (v du ien trcach ien qui nh toi thieu 1M).1va21 /( R1 r1 )

O IEN TR

101

o ien tr cach ien khi tat nguon ienTrc khi o, mach c ngat ra khoi nguon. ien tr cach ien cua daydan A so vi mass. Mot au cua day A c noi vao au L cua megohm-ke conau E cua megohm-ke c noi au mass cua day dan (day trung tnh cua hethong ien) (H.3.18). Nh vay ien tr c o la RA//(RAB + Rb). Neu RAB + Rbrat ln so vi RA th RA t sai so. Sau o lau Rb, Rc cua ba day dan c xacnh ien tr cach ien vi day trung tnh. Con ien tr cach ien gia hai dayA B c o RAB//[RA+RB]. Tng t nh vay ien tr cach ien cua day BCRBC//[RB+RC].

Hnh 3.18o ien tr cach ien dung M ke

Hnh 3.19Von ke V, V1 o ien tr cach ien

o ien tr cach ien trong trng hp co nguonTrong trng hp day dan co nguon cung cap. Khi o chung ta dung von-ke V o ien ap nguon cung cap, von-ke V1 lan lt o ien ap VA, VB cua dayA, day B so vi day trung tnh (H.3.19). Dong ien I1 qua RB.

1

RB RB [ RA // RV ]

vi: RA, RB - ien tr cach ien day dan A, B oi vi massRV - tong tr vao cua von-keTng t khi von-ke c mac gia day B la co dong I2 qua RA.

2

V VBRA

VRA ( RB // RV )

T hai phng trnh tren suy ra:V VA V

102

CHNG 3

RA = RV

V VA VBVB

; RB = RV

V VA VBVA

Neu nh RA

RB khi von-ke V1 c mac gia day A vi trung tnh, c

xem nh von-ke V1 mac noi tiep vi RB hai au von-ke V.

Do o:

RB = RV ( V 1)VA

Tng t nh vay neu RB

RV, th: RA = RV ( V 1)VB

Nh vay neu ien ap V cua li ien khong oi th ien ap o gia motcuon day dan ien vi trung tnh phu thuoc vao ien tr cach ien cua day danien th 2. Cho nen von-ke co the khac o theo ien tr cach ien.

Hnh 3.20Hai von-ke o ien tr cach ien

Hnh 3.21Ba von-ke o ien tr cach ien

T tren ta suy ra tr cach ien gia hai day dan ien co the o c bangcach mac nh hnh 3.20. Trong ieu kien bnh thng cua s cach ien, moivon-ke se cho ket qua ien ap nguon cung cap day dan.Bat ky s giam ien tr cach ien nao cua mot trong hai day dan, cungse lam giam cach o cua von-ke nay, trong khi von-ke con lai se tang tr solen.Trng hp ba day dan cua nguon ien ba pha, ien tr cach ien cua baday dan c ch th bi ba von-ke (H.3.21). Neu nh ien tr cach ien cuaday dan A giam xuong th von-ke VA giam, con VB, VC se co s gia tang tr so.

O IEN TR

103

Hnh 3.22: Von-ke c mac vi bien ap ooi vi nguon ien cung cap tren 1kV th cac von-ke c mac qua bienap ba pha o lng nh hnh 3.22. Bien ap ba pha dang nay khong thuan likhi hoat ong trong trnh trang xau xay ra la mot trong ba pha b cham at.Nh vay cuon s cap cua pha b cham at ngan mach, ien ap cac pha con laitang len lam chay cuon s cap cua bien ap cho nen phai co s bao ve cho phans cap cua bien ap.o ien tr oan day ien b cham massVan e quan trong la xac nh c v tr cua cap dan ien b cham masse mat thi gian va chi ph cho viec boc d ca oan day (neu loai capngam chon di at). Nhng h hong thng xay ra nh sau:Lp cach ien cua cap b beLp cach ien b giam o cach ien, co s phong ien lam honglp cach ien.

Hnh 3.23: Vong Murray o ien tr cham massPhng phap thng dung e xac nh v tr cham mass la vong thnghiem (test loop). Nhng phng phap nay u xac nh cho hong. Machthng dung la vong Murray va vong Varley. ay cung la mot ng dung cuacau Wheatstone (H.3.23). Khi cau Wheatstone can bang (ieu chnh R2 va thay

104

oi R1).

CHNG 3

R2R1

Ra Rb RXRX

. Suy ra: RX (R1 + R2) = R1 (Ra + Rb)

Vay RX

R1( Ra Rb )R1 R2

Neu oan day RX co chieu dai LX; Ra co chieu dai La; Rb co chieu dai Lb.Cac day co cung ien tr suat, La = Lb = L va cung thiet dien A:

A R1 R2 A A

L X R1 L L b

L X

R1R1 R2

2L '

V du 3.13: oan day cap co cham mass c xac nh bang vong Murray canbang khi R1 = 100 va R2 = 300. oan day A, B co chieu dai La = Lb = 5000m.Day cap dan ien ong chat va ong nhat.Giai: Chieu dai cho cap b cham massL X [ R1/( R1 R2 )]2L a (100/400) 2 5000m = 2500mhoac dung vong Varley.

Hnh 3.24: Vong VarleyMach ien mac theo hnh 3.24, cau Wheatstone co them ien tr R3. ayla phng phap xac nh them ien tr day cham at chnh xac nhat va sngan mach trong mot day cap co nhieu day dan ien. No c cai tien thchhp nhat t vong Murray. Gia s cho b cham mass tren day dan ien co ientr Ra. Noi hai au day dan. Sau o khoa S v tr a ieu chnh R3 e sao chocau can bang.

R2 Ra RbR1 R3

. Suy ra: Ra Rb

R3 R2R2

Nh vay ien tr day dan c xac nh. Sau o chuyen khoa S sang v[ a] ;

O IEN TR

105

tr b, ieu chnh en tr R3' sao cho cau (vong VARLEY) can bang. Chung taco:

R2R1

Ra ( Rb RX )RX R3'

; R2RX + R2 R3 = R1Ra + R1Rb R1RX

RX(R1 + R2) = R1 (Ra + Rb) R2 R3

Vay:

RX

R1 ( Ra Rb ) R2 R3R1 R2

V du 3.14: Trong mach hnh 3.24 R1 = 1k, R2 = 2k, chieu dai cua oan daycap La = Lb = 10Km, ien tr cua day cap 0,02/m. Khi khoa S a ieu chnhR3 =100 th cau can bang, con khi S b, R3 = 99 th cau can bang. Xacnh LX cho day cham mass.Giai: Khi khoa S a:

Ra Rb

Khi khoa S b:

R2 R3R1

2000 1001000

RX

R1 ( Ra Rb ) R2 R3'R1 R2

(1000 200) (2000 99)3000

0,67

Vay chieu dai: L X

0,670,02/m

335m

3.7 O IEN TR ATCoc o ien tr atThanh dan ien bang kim loai (thng bang ong) hoac nhieu thanh danien c ong xuong at, vung at can o ien tr, khi o chung ta co cocat. Sau o cac coc at nay c noi vao mach o bang nhng day dan ien.ien tr atien tr cua vung at can o tiep xuc vi coc at se c xac nh biien ap ri tren ien tr at khi co dong ien i qua no. Trong thc te ien trat phu thuoc vao ieu kien moi trng xung quanh (nhiet o, o am), thanhphan cua at.''' 200

106

CHNG 3

Khoang cach gia cac coc ate cho ien tr at cua cac coc at khong anh hng vi nhau (ngha lacac ien tr coc A la RA khong b anh hng bi vung at cua coc B co ientr at la RB). Ngi ta khao sat thc te nh hnh 3.25. Dong ien I i quavung at gia hai coc at se tao ra ien ap:VAC = RAI vi: RA - ien tr at cua coc A

VBC = RBI

RB - ien tr at cua coc B

Khi coc P c ong gia coc A va B bat ky v tr nao, th von ke giacoc AC co tr so thay oi theo ng bieu dien (H.3.25b). Nh vay ngoai phamvi 10m th ien ap VAC khong thay oi (cac iem ngoai 10m ang the). Nhvay hai coc at cach nhau 20m se co ien tr at khong anh hng len nhau.(Trong thc te hai coc cach nhau 10m en 20m co the xem nh hai coc atrieng biet).

Hnh 3.25: Khao sat ien tr at, va ien ap ritren ien tr at cung dong I i quaNguon ien ap cung cap cho mach oNguon tn hieu cung cap cho mach o la nguon tn hieu xoay chieu dangsin hoac xung vuong. Chung ta tranh dung nguon DC do anh hng cua iengiai se lam tang sai so o ien the ien cc. Neu dung ien li cua ien lcth phai dung bien ap cach ly tranh anh hng dong trung tnh (neu co do ienthe li mat oi xng) va coc at cua day trung tnh.3.7.2 Mach o ien tr atDung von-ke va ampe-kePhng phap trc tiepMach o c mac nh hnh 3.26.

O IEN TR

Coc A: coc o ien tr at RX; Coc P: coc phu o ien ap; Coc C: coc phu o dong ienHnh 3.26: Mach o ien tr at bang von-ke va ampe-keTheo mach tng ng cua ien tr at cua coc A, P, C (H.3.27)ien tr cho bi von-ke V:VAP = RX I + RPIVvi I = I + IV cho bi ampe-ke.

107

Neu: IV

I th I I. Do o: RX

VA

Hnh 3.27Mach tng ng cua ba cocA, P, C

Hnh 3.28Mach o ien tr at bang phngphap gian tiep

Vay ien tr c xac nh bi tr so oc cua von-ke va ampe-ke. Do oneu chung ta quan tam en sai so do von-ke va ien tr coc phu thuoc ien apth RX co sai so tng oi: R [ RB /( RB RV )]100%trong o: RB - ien tr at cua coc phu ien ap BRV - tong tr vao cua cua von-ke

Nh vay e sai so cang nho th RB

RV.

108

CHNG 3

Phng phap gian tiep: Trong trng hp nay o ien tr at tng coc nhhnh 3.28. Von-ke va ampe-ke co gia tr ien tr tng coc:

RA RP

V11

Sau o lan lt o ien ap cua hai coc BC va CA:

RP RC

V22

Tng t nh vay: RC RA

V33

Sau o t ba phng trnh nay chung ta xac nh RA, RB, RCTrong phng phap nay ca ba coc at (gom coc o va hai coc phu) euc xac nh, loai tr c anh hng sai so do ien tr coc phu gay ra nha e cap trong phng phap trc tiep.Dung cau Kohlrausch o ien tr atay la dang cau Wheatstone e oien tr cua dung dch co tnh chat iengiai bang hai ien cc, no cung cng dung e o ien tr at (H.3.29)ien tr RA+RB c xac nh khi caucan bang (giong nh phng phap giantiep dung von-ke va ampe-ke).

RA RB

R1R2

R3

Phng phap o ien tr at dungcau can bang co u iem la loai bo c

Hnh 3.29: o ien trbang cau o

dong ien tan chay qua vung at can o ien tr.May o chuyen dung e o ien tr atMay o dung t so ke t ien: mach o nguyen ly hnh 3.30.Dong ien I1 i qua cuon day I cua t so ke i qua vung at can o ientr. Dong ien I2 i qua cuon day 2 co t so phu thuoc vao ien ap ri tren coco va coc phu ien ap. ieu chnh bien tr RS, I2 thay oi. V VAP = (RS + r2)= RX I1. Suy ra I 2/1 RX /( RS r2 )

ieu chnh RS cho en khi:

I1 = I2 RX = RS +r2

O IEN TR

109

Nh vay vi RS tai tr so2/1 1 , se xac nh c RX khi r2 a biettrc.Trong thc te dong I1 qua t so ke la DC, con dong i1 chay qua vung ato la AC, do o co bo bien oi I1 (DC) sang i1 (AC) a vao coc o. Sau odong i1 (AC) chuyen sang I1 (DC) tr ve may phat G mot chieu bang bo chnhlu, con ien ap VAP (AC) c chnh lu sang ien ap VAP (DC) tao ra dongien I2 (DC).Nh vay trong cac may o co ien, dung may phat (quay tay) thng cotruc quay gan lien vi bo bien oi DC sang AC, hoac chnh lu t AC ve DCdung hien tng c ien.

RS

I1

I2

G

MRRS

MC

G

E1

I1A

E2P

I2B

I1

A

E1

E2P

I2B

a)

b)

Hnh 3.30: May o dung t so kea) Mach o nguyen ly; b) Mach o thc teMay o dung c cau ch th t ien (H.3.31): Mach o co hai v tr cua SW1(cong tac chuyen mach) la v tr C dung e chnh may, ien tr chuan RCthay the ien tr at can o. v tr M: Mach o hoat ong vi ien tr at can o. T nguon phatxoay chieu G tao ra dong ien I i qua ien tr RC (khi chnh may) hay qua RXkhi o ien tr at se tao ra ien ap: RCI1 hoac RXI1.ien ap nay c so sanh vi ien ap I2Ras vi I2 phu thuoc vao KII1,trong o KI la t so bien dong CT va Ras phu thuoc vao v tr S cua bien tr RV.Neu I2Ras khac RXI1 th V1 = I2Ras I1RX 0.Khi o V2 = KVV1 c chnh lu qua c cau ien t, kim ch th khac

110

CHNG 3

khong.Con chay S cua Rs c ieu chnh cho en khi V1 = 0, khi o kim ch thcua c cau ien t ch khong: I1RX = K1I1Ras

Do o:

RX = KIRas

Nh vay ien tr Ras xac nh ien tr at RX.

Hnh 3.31: Mach o cua may o ien tr atCT: Bien dong, VT: Bien ap

1- Coc phu ap; 2- Coc phu dong; 3- Coc at oHnh 3.32: S o khoi may o Hnh 3.33: Cach ong cocMach o ien tr at co s ket hp vi mach ien t dung c cau t ien:

O IEN TR

111

S o khoi cua may o (H.3.32). Nguon tn hieu xung vuong tan so 500 Hzc tao ra nh mach dao ong dung transistor, co dong cung cap cho ien trat can o vao khoang t 1020mA. Mach so sanh tach song ong bo (dungphng phap tach song ong bo), co nhiem vu va chnh lu va so sanh haiien ap xoay chieu.EX = RX I va ES0 = RS0 KI I

ieu chnh con chay e cho G ch 0 RX

1n

RS0 . Vi (KI =

1n

).

Cach ong coc at e o cho nhng may o ien tr at sau nay (loai ient): Ba coc at E (coc o); P (coc ien ap); C (coc dong ien) c noi vaomay o theo hnh 3.33. Khoang cach gia cac coc la t 5 en 10m. V tr caccoc tao ra mot goc ln hn 100o. Khoang cach EC, EP can phai ln hn caccoc trong trng hp ong thang hang.Cach o ba ien ap ri tren coc at (H.3.34)Co nhng may o ien tr at co phan o ien the ri tren coc at 1 vicoc at 2, khi o bo ch th tren may o cho biet ien ap ri tren hai coc. Vdu, o ien ap ri tren coc at c xem la coc an toan cua tai vi coc trungtnh cua li ien (H.3.34).

1- Coc phu ap (Coc trung tnh); 2- Coc at oHnh 3.34: o ien ap ri tren coc atNeu ket qua o c ien ap di 10V th kha nang an toan chap nhanc va khi o chung ta co the o ien tr at cua coc at an toan cho tai.Trong trng hp ien ap tren ln hn 10V th viec o ien tr at cua coc atb anh hng va kha nang an toan phai lu y do co s hien dien cua dong r vas hien hu cua dong trung tnh do s mat can bang cua li ien.3.8 O IEN TR TRONG V.O.M. IEN T3.8.1 Nguyen ly

112

CHNG 3

e o c ien tr trong may o ien t, ngi ta cung chuyen ailng ien tr sang ai lng ien ap, sau o a vao mach o ien ap cuavon-ke ien t. Mach o ien tr co hai dang:Noi tiepMac re.3.8.2 Mach o ien tr dang noi tiepMach o c mac nh hnh 3.35Mach o tren co nam tam o1 10 100 1k 10k. Ngha latr so oc c nhan vi he so nhan cua tam o. V du: tam100 tr so oc trenmat ch th la 36 th ket qua o cua RX = 3600.Mach thay oi tam o gom co cac ien tr chuan noi tiep vi RX, cacien tr chuan nay la loai ien tr chnh xac, sai so nho hn 1%. Tam o ientr cang ln th ien tr chuan moi tam o cang tang. Dong ien cua moi tamo giam tng ng (tam o tang 10 th dong ien giam 10).Khi RX = 0 (noi tac hai au AB), Vo = 0VKhi RX (hai au AB e h), Vo # 1,5VV tong tr vao cua mach o ien ap DC rat ln so vi ien tr chuan cua tamo, cho nen ien ap ri tren ien tr chuan khong ang ke trong trng hpAB e h.

Hnh 3.35: Mach o ien tr dang noi tiepTrng hp RX bat ky vi tam o tng ng co ien tr chuan R1.Chung ta co:

Vo E

RXRX R1

O IEN TR

113

Hnh 3.36: Thang o ien trV du 3.15: tam o 1k ien tr o co tr so RX = 1k. Khi o Vo co trso nh nhau.

Vo 1,5V

1k1k 1k

0,75V

Nh vay kim ch th se ch so 1 gia thang o.

Neu RX = 0,5K th:Vo 1,5V

0,5k1k 0,5k

0,5V

Nh vay kim ch th ch so 0,5 1/3 thang o. Neu RX = 2k th:2k1k 2kNh vay kim ch th so 2 2/3 thang o. Vay thang o ien tr trongtrng hp nay khong tuyen tnh.3.8.3 Mach o ien tr dang mac reMach o c mac theo hnh 3.37. Trong mach o nay:Khi RX = 0, khi o Vo = 0V

Khi RX th

Vo E

R2R1 R2

Khi RX co tr so bat ky.

Vo E

Theo bieu thc nay khi:

E

RX R2RX R2 R1 ( R2 RX )

RX ( R1 // R2 )

R1 R2R1 R2

th Vo

12

E

R2R1 R2

Khi o kim ch th 1/2 thang oVo 1,5V 1V R2 // RXR1 [ R2 // RX ]

114

Hnh 3.37Mach o ien tr dang mac re

CHNG 3

Hnh 3.38Mach o ien tr loai mac re

V du 3.16: Co mach o ien tr sau ay:C cau ch th co: Imax = 50A, Rm = 2k, E = 1,5VKhi RX = 10 tam 1.. RX = 100 tam 10Th I M1/2 I max xac nh R1, R2.Giai: Mach tng ng Thevenin cho mach o (H.3.39).

Et E

R2R1 R2

Rt = [R1 // R2]V mach o co mach khuech ai he

so khuech ai bang 1 cho nen:Vi = Vo, khi RX th:Vi (Vo)max = RmImax.(Vi)max = (Vo)max = 100mV

Hnh 3.39Mach tng ng Thevenin

Do o khi: RX = 10

R1 R2R1 R2

(1)

Th:

Vo = Vi = 50mV =

1 12 2

E

R2R1 R2

(2)

T phng trnh (1) va (2) ta co:100mV 1E 15Et( R R )( R RR2 1 2 1 2 )

O IEN TR

Suy ra:

R1R2 = 10(R1 + R2) = 1015R2R1 = 150 va R2 = 150/14 10,7 .

115

Trong trng hp RX = 100 ( tam 10). Th R1 R2/( R1 R2 ) 100

Suy ra

R1 R2 = 100(R1 + R2) = 10015R2

R1 = 1500 va R2 = 107,14Vay mach o co the ve lai nh tren co hai tam o (H.3.40).

Hnh 3.40: Mach o ien tr co hai tam o3.8.4 Mach o dong ien dung nguon dong khong oiTrong cac mach o ien tr tren tadung nguon ap khong oi, nhng ien ap oc chuyen t ai lng ien tr co dongien i qua thay oi theo ien tr o, cho nenien ap o nay a vao mach o khong tuyentnh theo ien tr RX, dan en thang o khongeu. e cho ien ap o tuyen tnh theo ien

tr RX, ngi ta s dung nguon dong ienkhong oi khi RX thay oi: Vo = IRX

Hnh 3.41: Mach o nguyenly nguon dong khong

Trong trng hp nay RXVo tr so ln nhat cua tam o ien apRX 0 th Vo = 0VMach o ien tr tuyen tnh (linear ohmmeter) thng c dung trongmay o a dung ien t ch th so (digital multimeter).Mach co nguon dong khong oi dung transistor (BJT)

116

CHNG 3

Nguon dong ien khong oi cung cap cho ien tr RX la dong IC cua Q1, R1,R2 ien tr phan cc cho cc nen Q1 theo ien ap cua mach a cho.Nh vay ien tr RE co ien ap 5V khong oi. Gia s, ieu chnh RE e cho IC= 1mA. Khi o ien tr RX = 5k th Vo = 5k1mA = 5V (tr so ln nhat cuatam o).Khi o ien tr ln hn 5k th phai chuyen tam o bang cach thay oinguon dong IC.V du: thay oi RE e cho dong IC = 0,1mA, khi o ien tr o c en50k.Neu khong muon thay oi dong I (hoac khong the cho IC qua nho khi RXtang len ln) th thay oi tam o ien ap tng ng vi ien tr RX.

Hnh 3.42Mach o ien tr tuyen tnh

Hnh 3.43Mach o dung nguon dong khong oi

O IEN TR

117

Dung nguon dong khong oi bang Op-AmpTheo ac tnh mach khuech ai dung Op-Amp: Vo( RX /R)E . Chung taxem nh dong I khong oi: I E/R ; Vo = IRX. Khi RX thay oi th Vo thay oituyen tnh theo RX.V du: E = +3V; R = 3k. Xac nh Vo theo RX.Ta co: Vo = IRX, vi: I E /R 3/3k 1mAVay Vo = RX (1mA)V du: RX = 100 Vo = 100mV. Neu Vo co tr so bao hoa 5V (ac tnhOp-Amp) th khi o RX = 5k la ln nhat. Vay muon thay oi tam o th thayoi R e co s thay oi I (nguon dong) tng ng vi moi tam o.Mach o cu the dung nguon dong on nh nh s ieu khien cua machkhuech ai Op-Amp. D1, D2, D3, D4 la loai 1N4154.

R1 = 330;

R2 = 3,3 k ;

R3 = 33 k ;

R4 = 330 k

RS = 2,2M; R6 = 1M (ien tr tam o).

Hnh 3.44: Mach o ien tr tuyen tnh dung Op-Amp

118

CHNG 3

R = 10k: ien tr chnh tr so ln nhat cho mach o ien trRZ = 10k: ien tr chnh 0 cho mach oQ1, Q2 (BC107): transistor co he so khuech ai lnQ3 (BC309C): transistor tao nguon dong ien cho mach o ien tr.S hoat ong cua mach o: Mach co hai Op-Amp 741.Op-Amp(1): Co nhiem vu ket hp vi Q3 tao ra dong ien IC3 cua Q3c on nh khong b thay oi iem phan cc do nhiet o cua moi trng vacua ban than transistor Q3.Op-Amp(2): Dung lam mach o ien tr, mach nay co he so khuech aibang 1.Qui trnh chnh Op-Amp ke: Trc het cho RX = 0 e chnh v tr 0 chothang o (co the chnh tr so) moi lan thay oi tam o eu phai chnh tr soln nhat cho thang o e tranh sai so phi tuyen do ien tr tam o gay ra.BAI TAP3.1. Mot ohm-ke loai noi tiep co mach o (H.B.3.1). Nguon Eb = 1,5V, c cauo co Ifs = 100A. ien tr R1 + Rm = 15k.a) Tnh dong ien chay qua c cau o khi Rx = 0b) Tnh tr gia Rx e cho kim ch th co o lech bang 1/2 FSD, 1/4 FSD va3/4 FSD (FSD: o lech toi a thang o).

Hnh B.3.1

O IEN TR

Giai:

119

a) I m

EbRx R1 Rm

1,5V0 15k

b)

o lech bang 1/2 FSD:100A2

Rx R1 Rm

EbI m

Rx

EbI m

1,5V50A

o lech bang 1/4 FSD:100A 1,5V4 25A

o lech bang 3/4 FSD:Im = 0,75100A = 75A; Rx

1,5V75A

15k 5k

3.2. Mot ohm-ke co mach o (H.B.3.2).Biet: Eb = 1,5V; R1 = 15k; Rm = 50; R2 =50, c cau o co Ifs = 50A.Tnh tr gia Rx khi kim ch th co olech toi a: (FSD); 1/2 FSD va 3/4 FSD.Giai: Kim lech toi a (FSD):

Im

= 50A;

Vm

=

ImRm =

Hnh B.3.2

50A50 = 2,5mV

I 2

VmR2

2,5mV50

Dong ien mach chnh: Ib = I2 + Im = 50A + 50A = 100A.

Rx R1

EbI b

1,5V100A

Rx = (Rx + R1) R1 = 15k 15k = 0Kim lech 1/2 FSD:

Im = 25A; Vm = 25A50 = 1,25mV; I 2

Ib = 25A + 25A = 50A

1,25mV50

25A

Rx R1

1,5V50A

30k ; Rx = 30k 15k = 15k 100A (FSD) 50A (v c cau o tuyen tnh).I m ( R1 Rm ) 15k 15k 25A ; Rx 15k 45kI m 50A 15k

120

Kim lech 3/4 FSD:Im = 0,75 50A = 37,5A; Vm = 37,5A50 = 1,875mV

CHNG 3

I 2

1,875mV50

37,5A ; Ib = 37,5A + 37,5A = 75A.

Rx R1

1,5V75A

20k Rx 20k 15k 5k

3.3. Mot Ohm-ke co mach o bai 2. Co nguon Eb giam xuong ch con 1,3V.Tnh tr gia mi cua R2? Tnh lai cac tr gia Rx tng ng vi o lech cua kim:1/2 FSD, 3/4 FSD.

Giai: Khi Rx = 0; I b

EbRx R1

1,3V0 15k

Im = 50A (FSD); I2 = Ib Im = 86,67A 50A = 36,67A

Vm = ImRm = 50A50 = 2,5mV; R2

VmI 2

2,5mV36,67A

Kim co o lech 1/2 FSD:Im = 25A; Vm = 25A50 = 1,25mV

I 2

VmR2

1,25mV68,18

Ib = Im + I2 = 25A + 18,33A = 43,33A

Rx R1

VmI b

1,3V43,33A

Kim co o lech 3/4 FSD:Im = 0,7550A = 37,5A; Vm = 37,5A50 = 1,875mV

I 2

1,875mV68,18

27,5A ;

Ib = 37,5A + 27,5A = 65A

Rx R1

VmI b

1,3V65A

3.4. Tnh dong ien chay qua c cau o va o lech cua kim ch th cua ohm-keco mach o nh hnh ve khi ta s dung tam o R1 trong hai trng hp: a) Rx= 0 va b) Rx = 24. 86,67A 68,18 18,33A 30k Rx = 30k 15k = 15k 20k Rx = 20k 15k = 5k

O IEN TR

121

Hnh B.3.4Giai: Mach tng ng cua ohm-ke khi ta s dung tam o R1 trong haitrng hp Rx = 0 va Rx = 24 nh sau:

Khi Rx = 0: I b

1,5V14 [10 //(9,99k 2,875k 3,82k)]

I b

1,5V14 (10 // 16,685k)

62,516mA .

Dong Im chay qua c cau o:

I m 62,516mA

1010 16,685k

Im = 37,5A = Ifs: kim lech toi a.Khi Rx = 24:

I b

1,5V24 14(10 //16,685k

31,254mA

I m 31,254mA

1010 16,685k

18,72A: kim lech 1/2 FSD

3.5. Tnh dong ien chay qua c cau o va o lech cua kim ch th cua Ohm-keco mach o nh bai 4, khi ta s dung tam o R100 va R 10K trong trnghp Rx = 0.

122

CHNG 3

Hnh B.3.5Giai: Mach tng ng cua ohm-ke khi ta s dung tam o R100 va Rx = 0.

I b

1,5V1470 [1k //(9k 2,875k 3,82k)]

1,5V1470 (1k // 15,695k)

622,38A

I m 622,38A

1k1k 15,695k

37,5A I fs : kim ch th lech toi a.

Mach tng ng cua ohm-ke khi ta s dung tam o R10k va Rx =0.

I b

15V236k [10 k //(2, 875 k 3, 82 k)]

15V236k10k // 6,695k

62,5A

I M 62,5A

10k10k 6,695k

37,5A I fs : kim ch th lech toi a.

3.6. Ta o ien tr bang cach dung phng phap V va A c mac re dai.Ampe-ke ch 0,5A, von-ke ch 500V. Ampe-ke co Ra= 10, von-ke s dungtam o 1000V va co o nhay la 10k/V. Tnh tr giaR.Giai: E + EA = 500V; I = 0,5A

Ra R

E E AI

500V0,5 A

R = 1000 Ra = 1000 10 = 990

Hnh B.3.6

3.7. Cac ampe-ke, von-ke va ien tr R bai 6c mac re ngan. Hay tnh o ch cua von-ke vaampe-ke (nguon cung cap van la 500V)

Hnh B.3.7 1000

O IEN TR

Giai: Noi tr cua von-ke:Rv = 1000V10k/V = 10M.RV // R = 10M // 990 = 989,9

123

o ch cua von-ke: E

500V ( RV // R)Ra ( Rv // R)

5000V 989,910 989,9

o ch cua ampe-ke I I V

ERV // R

495V989,9

3.8. Mot Ohm-ke noi tiep co ien tr R1 = 50k

c cau o co Ifs = 75 A va

RM 100 . ien tr mac shunt R2 300 , nguon cung cap E = 5V. Hay chobiet tr gia ien tr Rx o c tng ng vi o lech cua kim: 0,25%; 50%;75%; va 100%FSD.3.9. Mot Ohm-ke noi tiep co cac thanh phan sau: nguon cung cap Eb 3V ,ien tr noi tiep R1 30k , ien tr shunt R2 50 , c cau o coIfs 50A , ien tr c cau o Rm 50. Cho biet tr gia Rx o c tngng vi o lech: 1/4 FSD, 1/2FSD va FSD.3.10. Hay ve mach o cho ohm-ke noi tiep co nhieu tam o. Hay giai thch shoat ong cua mach.3.11. Gia s ohm-ke bai 3.9 co Eb giam xuong con 2,5V, hay xac nh trgia mi R2 can phai ieu chnh, va nh the tnh lai cac tr gia Rx tng ngvi o lech: 1/2FSD va 3/4FSD.3.12. Ta o Rx bang cach dung phng phap von-ke + ampe-ke co cach mac redai. Ampe-ke co noi tr Rx 10 , von-ke co o nhay 10k/V . Ampe-ke vavon-ke co cap chnh xac la 1%. Tnh tr gia that cua Rx khi ampe-ke ch 0,5A tam o 1A, va von-ke ch 500V tam o 1000V.3.13. Ta o Rx bang phng phap von-ke + ampe-ke co cach mac re ngan.Ampe-ke co Ra 0,1 , von-ke s dung tam o 5V, co o nhay 10k/V . Khivon-ke ch 5V, ampe-ke ch 0,6mA tam o 1mA.a) Tnh tr gia o c Rx .b) Tnh tr gia that Rx neu von-ke va ampe-ke co cap chnh xac 1%.3.14. Hay tnh R 3 e cau Wheatstone co the o c Rx trong khoang t:1 en 100k bang phng phap can bang. 495V 0,5 A .

124

Hnh B.3.14

Hnh B.3.15

CHNG 3

3.15. Tnh dong ien I g i qua ien ke (H.B.3.15).3.16. Neu ien ke hnh B3.16 co o nhay Sg 10mm/A , hay xac nh olech cua ien ke?

Hnh B.3.163.17. Cho mach o nh hnh B.3.17. Xac nh Eo theo Eb va phan t cau otrong cac trng hp sau:

a) R1 RR; R2 R3 R4 R ( Rb) R1 R3 RR; R2 R4 R ( R

R)R)

c) R1 R3 RR; R2 R4 RR ( R

Hnh B.3.17

R)

O IEN DUNG, IEN CAM VA HO CAM

Chng

125

4

O IEN DUNG, IEN CAM VAHO CAM

4.1 DUNG VON-KE, AMPE-KE O IEN DUNG, IEN CAMVA HO CAM4.1.1 o ien dungMach o c mac theo hnh 4.1. Tong tr cua ien dung CX c xacnh bi von-ke va ampe-ke (neu s hao mat do ien moi cua tu ien khongang ke).

Z CX

V 1I CX

; Suy ra: CX

IV

Hnh 4.1: Mach o CX dung von-ke vaampe-ke

Hnh 4.2: Mach o CX, RX dung von-ke,ampe-ke va watt-ke

Nguon tn hieu cung cap cho mach o phai la nguon tn hieu hnh sin, coo meo dang nho (hoa tan c xem khong ang ke). Bien o va tan so cuatn hieu phai on nh (khong thay oi). Neu tn hieu co song hai (hoa tan) baccao th se tao ra sai so ang ke cho ket qua o. Trong trng hp mach odung them watt-ke (H.4.2), ien tr r RX cua ien dung CX c xac nh bibieu thc sau: RX = P/I2

126

Tong tr cua ien dung: Z V /I RX2 (1/CX)2Va ien dung can o: CX 1/ Z 2 RX22

Do o: CX

2

2

S hao mat cong suat do ien dung cho bi:

P VI cos I 2

1CX

2

: goc mat cua ien dung. Neu goc mat nho: tg sin = PCX/I2.S chnh xac cua phng phap o nay co the bang hoac ln hn phngphap o trc. Phng phap dung watt-ke khong chnh xac khi xac nh nhngien dung co goc mat nho. e o goc mat c chnh xac, ngi ta thngdung phng phap cau o (e cap phan sau).4.1.2 o ien cam

Hnh 4.3: Mach o LX, RX dung von-keva ampe-ke

Hnh 4.4: Mach o LX, RX dung von-ke,ampe-ke va watt-ke

Mach o ien cam LX c mac nh hnh 4.3. Tong tr cua ien cam LX

c xac nh: Z

va ien cam:

VI

2

vi: Z - c xac nh bi von-ke va ampe-ke; RX - c xac nh trc.Trong trng hp dung them watt-ke nh hnh 4.4 cuon day co ien cam

LX c xac nh: L X

1

2

2

vi P la cong suat ton hao cua cuon day c xac nh bi watt-ke .T ba bieu thc tren ta suy ra: CX 1/[ V 2/I 2 ( P/I ) ]V 2 P 2sin , (v ) RX L X2LX = 1 Z 2 RX 2V 2 P 2

O IEN DUNG, IEN CAM VA HO CAM

4.1.3 o he so ho cam M

Hnh 4.5: Mach o M dung von-ke vaampe-ke

127

Hnh 4.6: o M cua hai cuon day macnoi tiep (quan cung chieu)

Theo mach o hnh 4.5, he so ho cam M gia hai cuon day c xac nhbi: M = V /I ; V va I cho bi von-ke va ampe-ke.Ngoai ra chung ta cung biet: M n1n2/Rn1, n2: so vong day quan vao cuon day 1 va 2. R: t tr cua mach tTrong trng hp hai cuon day c mac noi tiep vi nhau tren cungmach t, co cung chieu quan (cc tnh cua cuon day c nh tren hnh 4.6),th tong so ien cam cua hai cuon day c xac nh: La = L1 + L2 + 2MDo o La c xac nh bi tong tr Za cho bi von-ke va ampe-ke:

L a

1

Z 2 ( R1 R2 )2 vi Za - tong tr cua hai cuon day.

Trong trng hp hai cuon dayc mac noi tiep vi nhau tren cungmach t co chieu quan ngc nhau(cc tnh cua cuon day c nh trenhnh 4.7, khi o tong so ien cam cuahai cuon day c xac nh.

Lb = L1 + L2 2Mva Lb cung c xac nh bi tong trZb cho bi von-ke va ampe-ke theobieu thc:

Hnh 4.7: o M cua hai cuon daymac noi tiep (quan ngc

La

1

Z b2 ( R1 R2 )2a

128

CHNG 4

T hai gia tr cua La, Lb co the suy ra he so ho cam M nh sau:La Lb = 4M Hoac M = ( L a Lb )/44.1.4 o ien dung va ien cam trong may o a dung (V.O.M)Co mot so may V.O.M ngoai chc nang o ien ap, dong ien, ien tr,con co chc nang o ien dung hoac ien cam. Vi khoang tam o cho iendung, ien cam han che. Mach o cung dung nguyen ly o tong tr, nhng trso nay c chuyen sang nhng ai lng xoay chieu, c ch th tren thango, theo gia tr (n v mH hoacF) cua ien dung hoac ien cam. Theo macho nguyen ly hnh 4.8.

Hnh 4.8: o CX va LX bang V.O.MeS: nguon tn hieu a biet c bien o va tan so (co trong may o V.O.M).Bo ch th G bao gom mach chnh lu dong xoay chieu vi c cau ien t.Dong ien I (tr hieu dung) qua G phu thuoc vao tr so CX hoac LX. Khi ES(tr hieu dung) va = 2f (tan so cua tn hieu eS) a c xac nh va on nhth ta co I = ESCX hoac I = ES/LX.4.2 DUNG CAU O O IEN DUNG VA IEN CAM4.2.1 Cau Wheatstone xoay chieue n gian ta coi cau o AC c cau tao giong nh cau o Wheatstonemot chieu (cau o DC). Cac phan t cua cau la ien tr, ien dung hoac iencam. Nguon cung cap la tn hieu sin (o meo dang nho), tan so am tan(khoang 1kHz hoac tan so ien li). Phng phap o dung cho cau o ACgiong nh cau o DC. oi vi phng phap can bang hoac khong can bang,chung ta ch e cap en phng phap can bang cho cau o AC.ieu kien can bang cho cau o ACTheo mach o cua cau o AC (H.4.9):Z1 . Z3 = Z2 . Z4T phng trnh nay ta co s can bang theo

Hnh 4.9Cau Wheatstone AC

O IEN DUNG, IEN CAM VA HO CAM

129

ieu kien:Can bang suat: Z1 Z 3 Z 2 Z 4Can bang pha: Z1 Z 3 Z 2 Z 4Neu khai trien so phc cua phng trnh can bang, ta co:Can bang phan thc: Re[Z1Z3] = Re[Z2Z4]Can bang phan ao: Im[Z1Z3] = Im[Z2Z4]Thiet b ch th s can bang cua cau o ACTai nghe (earphone hoac headphone): gia thanh re, tng oi nhay, cdung pho bien co kha nang phan biet c s can bang cua cau mot cachtng oi chnh xac. Tuy nhien con phu thuoc vao o thnh tai cua ngi lamth nghiem.

Hnh 4.10: Cac thiet ke ch th can banga) Tai nghe; b) ien ke ACc) ien ke AC co khuech ai; d) Dao ong ky tia am ccVon-ke ien t hoac ien ke AC: ien ke DC/ ket hp vi mach chnh luhoac bo bien oi AC/DC chung ta co ien ke AC. Muon tang o nhay cho cauAC chung ta them mach khuech ai cho ien ke AC (H.4.10). Thiet b naychnh xac hn va khach quan hn so vi tai nghe. Ngoai ra con co the co nhieutam o nhay khac nhau thay oi theo ien ap khong can bang cua cau.Dao ong ky tia am cc: Theo ieu kien thuan li cua phong th nghiem,neu co c dao ong ky, chung ta cung co the dung e kiem tra s can bangcua cau mot cach chnh xac hn vi moi tn hieu tan so bat ky cung cap chocau.Cac phan t mau (ien tr mau, ien cam mau, tu ien mau) dung trong cauACien tr mau

130

CHNG 4

Hnh 4.11: a) Mach tng ng cua ien tr tan so caob) Kieu quan so vong thuan nghch ke can bang nhauc) Kieu quan Curtis va Groveroi vi phan t ien tr hoat ong tn hieu xoay chieu, gia tr ien trthng ln hn trong trng hp hoat ong vi dong ien DC. Hieu ng ngoaimat cua day dan (skin effect) phu thuoc vao tan so tn hieu, thiet dien day danva ien tr suat. tan so am thanh (1kHz) hieu ng nay khong ang ke khiday co ien tr suat ln va thiet dien nho c s dung. oi vi tn hieu ACco tan so cao i qua ien tr mach tng ng cua ien tr co dang machtng ng nh hnh 4.11a. e giam c ien cam ky sinh ngi ta quan sovong thuan nghch ke can nhau. Tuy nhien e anh hng cua tu ien ky sinhgiam ngi ta quan day dan theo kieu Curtis va Grover, khi ien tr co gia trln ngi ta quan tren ba mong theo kieu an ro.Tu ien: Trong thc te dong ien I qua tu ien khong lech pha 900 oi viien ap ri tren tu ien v co ton hao ben trong tu ien. Ton hao nay do ienmoi trong tu ien co ien tr r (khong cach ien hoan toan). Do o machtng ng cua tu ien c dien ta theo hnh 4.12. Neu goi la goc mat cuaien dung do ton hao cong suat tren ien dung, th ta co:2Neu nho, cong suat hao mat tren ien dung P = VI. Cac tu ien maudung trong cau o xoay chieu c che tao bang cac ien moi co ton hao rat t(o cach ien tot), goc mat co nh khong phu thuoc vao tan so tn hieu vanhiet o cua moi trng. Co nhieu loai tuy theo khoang tr so tu ien can sdung.P = VI cos = VI sin, vi

O IEN DUNG, IEN CAM VA HO CAM

131

Hnh 4.12: a) Mach tng ng cua ien dung khi lnb) nho; c) Gian o vect V-ITu ien co ien moi la khong kh: Tr so ien dung rat nho khoang vaitram pF, goc mat nho khong e bui hay am.Tu ien mica: ien moi la vat lieu mica co ien dung t vai pF4

Tu ien bang Polystyrene: Co ac tnh khong phu thuoc vao tan so nhnganh hng v nhiet o rat ln, ch s dung di 70oC, co goc mat nho, co thetch nho hn tu ien mica neu co cung tr so.Ngoai ra, trong cong nghiep chung ta thng gap tu ien giay. ien moila giay tam dung dch cach ien, thng co tr so ln nhng goc mat cung ln.Cuon day: Co ien cam L, ien tr R cua day quan va co mach tngng tan so cao nh hnh 4.13 con ien dung ky sinh gia cac vong dayquan cua cuon day khong ang ke tan so tn hieu am tan, nhng c quantam en tan so cao.

Hnh 4.13: a) Mach tng ng cua cuon day khi Q nhob) tan so cao; c) Khi Q lnCac ien cam mau c che tao di dang ong day co kch thc xacnh chnh xac. Cac ien cam mau thay oi c nh hai ong day ghep noitiep va phan thay oi c la loi cua cuon day. Tr so ien cam thay oi cphu thuoc vao v tr cua loi.(picofarad) en 0,1F (microfarad), goc mat nho (khoang 10rad).

132

CHNG 4

4.2.2 Cau o n gian o ien dung va ien camCau o ien dung: Mach o c mac theo hnh 4.14.Z1: la tu ien mau C1 (co the thay oi c tr so)Z2: tu ien can o CXZ3, Z4: la nhng ien tr mau thay oi c hoac la nhng hop ien trthay oi.Khi cau can bang D ch 0.

Z1 Z4 = Z2 Z3;

1 1j CX j C1

R4 ; Suy ra: CX

R3R4

C1

Vi gia tr cau o CX bat ky, chung ta ieu chnh t so R3 R4 va C1 (neu latu ien mau thay oi c) cho cau can bang e xac nh CX.

Hnh 4.14Cau o CX n gian

Hnh 4.15Cau o LX n gian

Cau o ien cam cuon day: Mach o c theo hnh 4.15Z1: cuon day mau L1; Z2: cuon day do LXR3, R4: la ien tr mau (hop ien tr) thay oi c.Khi cau o at c ieu kien can bang:Z2R4 = Z1R3; jLXR4 = jLR3; L X ( R3/R4 )LTrong hai cau o n gian tren chung ta ch xac nh thuan tuy gia tr CXva LX. Khong xac nh s hao mat tren ien dung cung nh tren ien cam cano.4.2.3 Cau pho quat (universal bridge) o ien dung va ien camHe so hao mat cua ien dung: Trong thc te mach tng ng cua iendung co hai dang tuy theo s hao mat cua ien dung. Do o chat lng cuaien dung c anh gia qua he so D cua ien dung (D factor).R3

O IEN DUNG, IEN CAM VA HO CAM

133

Trng hp ien dung co hao mat nho: tr so D nho mach tng ngbao gom [CX + RX] (H.4.16).He so D c xac nh bang bieu thc: Re Z X / Im( Z X ) D tg

Nh vay vi ZX = RX +

1jCX

; D

RX(1/)CX

RX CX

Theo bieu thc tren D thng co gia tr nho (D0,1).

Hnh 4.16: Mach tng ng cua C, LTrng hp ien dung co hao mat ln, he so D ln. Mach tng ngcua ien dung [CX//RX].

Tong tr Z cua ien dung co dang:

1 1Z X RX

j CX

He so D c xac nh: D

1/RXCX

1RX CX

;

(D 0,1: D ln).

He so Q cua cuon day: Pham chat cua cuon day co ien cam LX c xacnh bang he so Q. Neu cuon day co s hao mat nho (ien tr cua cuon daynho) th co mach tng ng RX noi tiep LX co he so Q cua cuon day la:

Q

phan ao Z Xphan thc Z X

, (ngc lai vi he so cua ien dung)

Q*

L XRX

(tr so nho) , (Q 10: Q nho).

Neu cuon day co s hao mat ln (ien tr cua cuon day ln) th mach

tng ng (RX // LX):

1 1 1Z X RX j RX

Q

1/ L X1/RX

RXL X

(tr so ln);

(Q 10: Q ln).

Tuy theo gia tr cua D (ien dung ky sinh), Q (ien cam) ln hn hoacnho se co mach cau o pho quat cho tng loai.Cau pho quat o ien dung: Cau pho quat o ien dung gom co hai loaiien dung co he so D ln va nho (H.4.47).

134

CHNG 4

Hnh 4.17: Cau pho quat o ien dung: a) Cau Sauty; b) Cau NernstTrong mach cau [RX + CX].

Khi cau can bang:

R3 R4

Can bang phan thc: RX R1( R4/R3 )Can bang phan ao: 1/CXR4 = 1/C1R3; RX ( R3/R4 )C1T ket qua o c CX, RX chung ta xac nh c he so D cho iendung:

DCX RX

R4 R3

R

Cho nen cau o pho quat cho chung ta gia tr D khi, R1, C1 c xacnh.V du 4.1: C1 = 0,1F; R3 = 10k. ieu chnh: R1 = 125; R4 = 14,7k th cau canbang xac nh CX, RX, D biet rang tan so tn hieu so cung cap cho cau f = 100Hz.Giai: Theo ieu kien can bang cua cau:

CX

R3R4

C1

10k14,7k

0,1F ; CX = 0,068F

RX

R3R4

14,7k10k

He so D =CXRX = 2100Hz0,068F183,8 = 0,008R1 j /C1 RX j /C3C1 1 =C1R1R3 R4R1 125 183,3

O IEN DUNG, IEN CAM VA HO CAM

135

Trong phng phap o CX dung cau pho quat dang nay. Tr so o CX, RXkhong phu thuoc vao tan so cua tn hieu. Con trong mach cau o ien dung[C1//R1], C1, R1 cung c chuyen sang dang [C1//R1] khi cau can bang danen:

Z1Z4 = Z2Z3;

Z3(1/Z1) = Z4(1/Z2)

R3(1/R1 + j

C1)R4(1/RX + j