Chapter 5 Part 2. AC Bridges. Comparison Bridges. Capacitance. Measurements. Dr. Wael Salah

Transcription

1 Chater 5 Part 2 AC Bridge Comarion Bridge Caacitance Meaurement

2 5.5 AC - BIDGES AC - Bridge enable u to erform recie meaurement for the following : eactance (caacitance and inductance) meaurement. Determining the (Q-factor O D-factor). Frequency meaurement. Teting and analyzing of antenna and tranmiion line erformance 2

3 AC BIDGE The baic circuit of an ac bridge i exactly the ame a the Wheattone bridge circuit excet that imedance are ued intead of reitance, and the uly i an ac-ource. Alo, the null detector mut be an ac intrument. V Princile The bridge offet voltage can be found a: V V For balancing condition: (V=0) V Therefore,. = 2. For AC-bridge, the null-condition i only valid if V a and V b are equal in amlitude and alo ame in-hae. 2 V AC Structure 2 * Firt balance condition * 2 nd balance condition =amlitude in-hae

4 EXAMPLE : V A AND V B V a V a V a V b V b V b V a V b 0 V a - V b 0 V a - V b = 0 V a and V b are equal in amlitude but not in-hae. V a and V b are equal in-hae but not equal in amlitude. V a and V b are equal in amlitude and in-hae.

5 EXAMPLE 7 The imedance of the bridge arm are 2000 ; ; x unknown Determine the value of the unknown arm. V AC 2 5

6 Solution 7 The firt condition for balance require that x 2 ; x The econd condition for balance require that the um of the hae angle of ooite arm hould be equal x ; 0 ( x 2 ) Hence the unknown arm imedance x can be written a x (6. j76. 9) Where, x = x + j y = + j X x = r co φ = 87.5 co (-70) = 6. y = r in φ = 87.5 in (-70) =

7 CAPACITOS EQUIVALENT CICUITS Caacitor Equivalent Circuit: The equivalent circuit of a caacitor conit of a ure caacitance C and a reitance. Where, C rereent the actual caacitance value, and rereent the reitance of the dielectric or leakage reitance. Caacitor with a high-reitance dielectric are bet rereented by a erie C circuit, Caacitor with a low-reitance dielectric rereented by the arallel C circuit. The erie imedance i j wc S The arallel admittance i Y j wc C S P C P 7

8 D-FACTO OF A CAPACITO The quality of a caacitor can be exreed in term of it ower diiation. A very ure caacitor ha a high dielectric reitance (low leakage current) and virtually zero ower diiation. The diiation factor or D-factor i imly the ratio of the comonent reactance (at a given frequency) to the reitance meaurable at it terminal. For a arallel equivalent circuit D X wc S For a erie equivalent circuit D X wc C S P C P 8

9 INDUCTOS EQUIVALENT CICUITS Inductor Equivalent Circuit: The erie equivalent circuit rereent an inductor a a ure inductance L S, in erie with the reitance of it coil S. Thi erie equivalent circuit i normally the bet way to rereent an inductor, becaue the actual winding reitance i involved and thi i an imortant quantity. The arallel L equivalent circuit for an inductor can alo be ued. The erie imedance i The arallel admittance i Y jwl j wl S L S P L P 9

10 Q - FACTO OF AN INDUCTO The quality of an inductor can be defined in term of it ower diiation. An ideal inductor hould have zero winding reitance, and therefore zero ower diiated in the winding. The quality factor or Q-factor, of the inductor i the ratio of it inductive reactance to it reitance at the oerating frequency. For a erie equivalent circuit: For a arallel equivalent circuit : Q Q X X wl wl S L S P L P 0

11 5.6.. CAPACITANCE COMPAISON BIDGES i) Serie-eitance Caacitance Bridge (alo known a Similar-angle bridge) The unknown caacitance C S i rereented in erie with reitance S. A tandard adjutable reitance i connected in erie with C. To obtain a bridge balance, reitor and either C are adjuted alternately. 2 wc j wc j When the bridge i balanced: 2 ; ; wc j wc j The imedance are:

12 . CAPACITANCE BIDGES Then the equation i imlified a: j j wc wc After equating the real term for both ide, we get: S And by equating the Imaginary term both ide, we get: : j j wc wc C S C 2

13 EXAMPLE A erie reitance-caacitance bridge a hown below ha a 0.F tandard caacitor for C, and = 0k. Balance i achieved with 00Hz uly frequency when =25 and =.7k. Calculate the reitive and caacitive comonent of meaured caacitor and it diiation factor. SOLUTION C S C 0. 0k.7k 0.068F 2 C S G C S S k 0k D wc S S

14 II) PAALLEL-ESISTANCE CAPACITANCE BIDGE (ALSO KNOWN AS SIMILA-ANGLE BIDGE) In thi bridge the unknown caacitance i rereented by it arallel equivalent circuit; C in arallel with, and and are reitor. The bridge balance i achieved by adjutment of and C. The load imedance are: Y When the bridge i balanced: jwc jwc 2 ; ; Y jwc 2 jwc C V C 2 After equating the real & Imaginary term: P and C P C

15 EXECISE 6 Find the arallel equivalent circuit for C S and S value determined in Examle 8. Alo determine the comonent value of and required to balance the calculated C P and P value in a arallel reitance-caacitance bridge. Aume that remain at 0k and C at. 0.F 5

16 SOLUTION EXECISE 6 6

17 EXAMPLE A arallel-reitance caacitance bridge ha a tandard caacitance value of 0.F. Balance i achieved at a uly frequency of 00Hz when = 0k, =75k, and =.7k. Determine the reitive and caacitive comonent of the meaured caacitor and it diiation factor (D-factor). 7

18 Solution For the given arallel-reitance caacitance bridge, find, C and the D-factor :- C P C 0.F 0k.7k 0.068F 75k.7k P 55. k 0k The diiation factor i the D-factor D wc P P