Bridge Circuits. DR. GYURCSEK ISTVÁN Classic Electrical Measurements 3
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1 DR. GYURCSEK ISTVÁN Classic Electrical Measurements 3 Bridge Circuits Sources and additional materials (recommended) q I. Gyurcsek: Fundamentals of Electrical Measurements, PTE MIK 2018 (manuscript) q S. Tumanski: Principles of electrical measurement, CRC Press ISBN q Máté J.: Méréstechnika 1. PTE PMMIK, ERFP-DD2001-HU-B-01 q 1 gyurcsek.istvan@mik.pte.hu
2 q Overview of Bridge Circuits q Null Type (Balanced) Bridges DC Impedance Bridges AC Impedance Bridges Transformer Bridges q Deflection Type (Unbalanced) Bridges q Alternatives (Anderson Loop) 2 gyurcsek.istvan@mik.pte.hu
3 Types of Bridge Circuits Sir Charles Wheatstone ( ) q Wheatstone type bridges q Thomson type (double) bridges q Bridged T-circuits q Current Comparators q Electronic bridges q Anderson loops 3 gyurcsek.istvan@mik.pte.hu
4 Bridge Circuits in General q Bridge circuits à most accurate devices for R, Z to U converters q Nowadays à replacing by more effective methods Two types! "#$ = & ' & ( & * & + & ' + & * & + + & ( + & '& * & & + + & ( + &! -! "#$ = +& ( "#$ & & ' + & * "#$ & ' & ( & * & + & ' + & * + & + + & ( + &. ' + & + & * + & - ( & "#$ 4 gyurcsek.istvan@mik.pte.hu
5 Condition of Balance q When Z out à! "#$ = & ' & ( & * & + & ' + & * & + + & ( + & '& * & & + + & ( + &! -! "#$ = +& ( & "#$ & ' + & * "#$ & ' & ( & * & + & ' + & * & + + & (! -! "#$ = & ' & ( & * & + & ' + & * + & + + & ( + & / ' + & + & * + & -! "#$ = ( & "#$ & ' & ( & * & + & ' + & * + & + + & ( / - q Universal condition of balanced bridge (U out =0) à & ' & ( & * & + = 0 & ' & ( = & * & + Complex impedances Split up to magnitude / phase conditions Notices (1) condition is U 0, Z out indept; (2) irrelevant linearity of IND; (3) source and indicator can be exchanged 5 gyurcsek.istvan@mik.pte.hu
6 Specific Bridge Circuit Specific bridge with 2 resistors Balance condition Z 1 and Z 4 different nature (inductive vs. capacitive) Balance condition Z 1 and Z 2 same nature (inductive or capacitive) 6 gyurcsek.istvan@mik.pte.hu
7 Sensitivity and Gear Sensitivity of bridge (S) q U out /U 0 relative value in % caused by 1% unbalance % Gear of bridge (m) ( hídáttétel )!" = & % ' 7 gyurcsek.istvan@mik.pte.hu
8 Calculating Sensitivity 1 q Z 1 + ΔZ 1 à U 2 + ΔU 2 à!" #$% =!" ) q Z out = à unloaded voltage dividers! Z out =, )!" #$% =!" ) =!" *, - +, ), ), - +, - +, ) out q for infinit small ΔZ 1 /Z 1 ( all linear in small ) 0 0!" #$% = /!" ), /, - -!" #$% = /, )!" /, - *, - +, ), - =!", ) *, - +, ) ), - 8 gyurcsek.istvan@mik.pte.hu
9 Calculating Sensitivity 2!9 :;< = >? B!9 + (num-denom Z out =? =!9? B +? B B devided and shorten w. m Evaluation?? B!9 :;< A? 1 + q Exchange of GEN and IND à no affect on balance BUT affect on S A 1 +!" B, =!9 E :;< F 9! A? F? 1 +!" B out q S=S MAX when q In case of!" = 1!" = " (%&'(), -./ = q In cas of!" = 2 3 " (4"'546'%7), -./ = 1 2 q Complex gear causes better sensitivity! 9 gyurcsek.istvan@mik.pte.hu
10 Operation Modes q Balanced (NULL TYPE) circuit! "#$ = 0 ( ) = ( * = ( + (, ( - q Unbalanced (DEFLECTION TYPE) circuit First step à! "#$ = 0 Second step à! "#$ =. ( ) ( )! 0 (S = sensitivity coefficient) 10 gyurcsek.istvan@mik.pte.hu
11 q Overview of Bridge Circuits q Null Type (Balanced) Bridges DC Impedance Bridges AC Impedance Bridges Transformer Bridges q Deflection Type (Unbalanced) Bridges q Alternatives (Anderson Loop) 11 gyurcsek.istvan@mik.pte.hu
12 DC Wheatstone Bridge q Range à R3 /R4 set in sequence: , etc. q Balancing à R 2 adjusting resistor! " =! $ =! %! &! ' q Uncertainty REMINDER: upper limit of uncertainty % ( (*) / =, -.$ % 2-3 % (% "4 (! " = (! % % + (! & % + (! ' % q Resolution à smallest 6R 2 causing 67 indication 12 gyurcsek.istvan@mik.pte.hu
13 Measuring Small Resistances 1 Additional uncertainty q Contact resistances (reduced by better connections) q Thermoelectric voltages (reduced by two step (+/-) supply voltage, average) q Resistances of wires (reduced by three-wire or four-wire connections) Three-wire connection! "! # + % =! '! ( + %! #! " =! '! ( + %! '! "! ' =! "! #! " =! '! ( (%,-./.012,3) 13 gyurcsek.istvan@mik.pte.hu
14 Measuring Small Resistances 2 Four-wire connection (Thomson Kelvin bridge) Condition of balance! %! " =! $ + (! %! ) &! ) %! &! &! &! ) ) % +! & Two of terms q r should be small (short wire with large diameter) q Mechanical coupling of the resistors, because! %! ) & =! ) %! &! % )! =! & ) %! & 14 gyurcsek.istvan@mik.pte.hu
15 Coffee Break?
16 q Overview of Bridge Circuits q Null Type (Balanced) Bridges DC Impedance Bridges AC Impedance Bridges Transformer Bridges q Deflection Type (Unbalanced) Bridges q Alternatives (Anderson Loop) 16 gyurcsek.istvan@mik.pte.hu
17 Recall AC Behavior 1 Inductor R t à resistance of the coil C p à parasitic C reduced to terminal points (HF only!) L à inductance (non-linear in case of iron-core). R v àhysteresis loss, eddy current loss [! " =! " (%) ]. Q à quality factor Low freq. - R v, C p neglible à Q=X/R t High(er) freq. - R t, C p neglible àr v /X Result of both effects - Q à max value! Resistor q Parasitic capacitance and inductance at HF, AC q Resistance measurement recommenden at DC 17 gyurcsek.istvan@mik.pte.hu
18 Recall AC Behavior 2 Capacitor R d à dielectric loss R sz à insulation loss L s à parasitic inductance (high freq.) δ à loss angle Loss-tangent (tan δ) reciprocal of Q (inductance) Low freq.- R d neglible à tan δ = X/R SZ High freq. - R sz neglible à tan δ = R d /X Result of both effects - tan δ à min value 18 gyurcsek.istvan@mik.pte.hu
19 The AC Bridge Circuits AC bridge more complicated than DC bridge q Balance condition à split to magnitude and phase conditions à two adjusting elements necessary q Parasitic capacitances (stray capacitances, earth capacitance,... ) (szórt kapacitások...) Shielding Wagner GND system Wagner GND system q Balance Bridge 1 (sw = 1) (Z 1 Z 2 Z 5 Z 6) q Balance Bridge 2 (sw = 2) (Z 1 Z 2 Z 3 Z 4) q Recursive repeat q a-b-e à GND potential q No affect of capacitances 19 gyurcsek.istvan@mik.pte.hu
20 Wien Bridge Circuit! " =! $ % & % ' 1 + * $! $ $ % $ $ % " = % ' 1 + * $! $ $ % $ $ * $ % $ % &! $ $ q Frequency dept. conditions à seldom used in measurement q Used in oscillators à FREQ determination (Wien-Robinson) * $ 1 = % +! + % $! $ 20 gyurcsek.istvan@mik.pte.hu
21 Maxwell Wien Bridge L X q Balance conditions! " = $ % $ & ' ( $ " = $ % $ & $ ( ) = *! + $ + 21 gyurcsek.istvan@mik.pte.hu
22 Measuring Mutual Inductance,- $ + $ =! $,. +!,- & $&,.,- $ + & =! &$,. +!,- & &,.! $& =! &$ = ( + =! $ +! & ±2(,-,. q Coils à same directions (L I ) q Coils à opposite directions (L II )! " =! $ +! & + 2(! "" =! $ +! & 2( ( =! "! "" 4 22 gyurcsek.istvan@mik.pte.hu
23 The de Sauty-Wien Bridge! " =! $ % & % ' % " = % $ % ' % & tan + =,% "! " tan + =,% $! $ 23 gyurcsek.istvan@mik.pte.hu
24 Schering Bridge Circuit q High voltage and cable testing! " =! $ % & % ' % " = % '! &! $ tan + =,% "! " tan + =,% &! & 24 gyurcsek.istvan@mik.pte.hu
25 Universal RLC Bridge RLC bridge circuits, composed from the same elements (R 2 R 3 R 4 C w ). Balance condition Balance conditions Balance conditions! " =! $! %! & ' " =! $! % ( ),! " =! $! %! & ( " = ( )! &! $,! " =! $! %! & q Uncertainties (for this example). +!, = +! $ $ + +! % $ + +! & $, +', = +! $ $ + +! % $ + +( ) $, +(, = +( ) $ + +! %& $ + +! $ $ 25 gyurcsek.istvan@mik.pte.hu
26 q Overview of Bridge Circuits q Null Type (Balanced) Bridges DC Impedance Bridges AC Impedance Bridges Transformer Bridges q Deflection Type (Unbalanced) Bridges q Alternatives (Anderson Loop) 26 gyurcsek.istvan@mik.pte.hu
27 Transformer Bridges Balancing process q Change of impedance OR q Inserting additional source! " =! $ % & % $ q 2nd transformer à current comparator for null indicator! "! $ = % & % $ = ' & ' ( ) " ) $ = ' & ' ( * & * ( 27 gyurcsek.istvan@mik.pte.hu
28 Measuring Capacitance Balance condition / 2! " = / 3! -. + / 4! -1 + ' = + 0 / - / " / 3 / 2 & ' = & 0 / " / - / 2 / 4 / 4 tan 8 = / 3 *& 0 + 0! " = $ " 1 & ' + )*+ ' ;! -. = $ " / - / " )*+ 0 ;! -1 = $ " / - / " 1 & 0 28 gyurcsek.istvan@mik.pte.hu
29 Transformer vs. Impedance Bridges Advantages of Transformer Bidges q Easy to balance (change # of turns) q Parasitic capacitors are shunts (no affect on conditions) q Better sensitivity q Minimal stray field (construction!) Drawbacks q Difficult transformer constructions q Expensive 29 gyurcsek.istvan@mik.pte.hu
30 q Overview of Bridge Circuits q Null Type (Balanced) Bridges DC Impedance Bridges AC Impedance Bridges Transformer Bridges q Deflection Type (Unbalanced) Bridges q Alternatives (Anderson Loop) 30 gyurcsek.istvan@mik.pte.hu
31 Unbalanced Bridges Used as Transducers, converting change of resistance (impedance) à output voltage! "#$ = &! ' ) * ) *' = &! ' + ) * = ) *' ± ) * = ) *' 1 ± + Two kind of symmetry in design q Symm in output diagninal q Symm in source diagonal 31 gyurcsek.istvan@mik.pte.hu
32 Transfer Func. of Unbalanced Bridge ) *+, = ) *+, = -. - / / ) $ -. - / / 4 $ Non-linear characteristics!! " =! "$ ±! " =! "$ 1 ± ( calc ) *+, 5 )$ = ( ( ) *+, 6 5 4$ =! $" ( ( 32 gyurcsek.istvan@mik.pte.hu
33 Linearization Method q Bridge automatically balanced à uses small (linear) part of the transfer characteristic q Very small output à additional amplifier is necessary.! "#$ =! ' ) 2)! "#$ =! ' ) 2) 1 + ) - ). 33 gyurcsek.istvan@mik.pte.hu
34 DC Bridge with Differential Sensors " #$%! "& = 2) 1 + ),.,. " #$% )! /& = 0 1& 1 + ). " #$%! "& = 1 2. " #$% 2! /& = 0 1& (1) diff. Sensors à linear! (more or less) S-factor calcultion (high R LOAD & neglicht. nonlinearity) q Single sensor q Differential sensors 3 3 ) 1 + ), 2) 1 + ), (2) diff. sensors à two times more sensitive 34 gyurcsek.istvan@mik.pte.hu
35 AC Bridge with Differential Sensors %!" = & = % & ( ) *+& % ' % ' ( ) *+' = % & ( ) * +&,+' - = " ( ) *. % ' - = 2!" 1 +!" ' - = 2" 1 + 2" cos 6 + " ' q Largest sensitivity ß m = 1, q Larger sensitivity ß phase bw. Z 1 Z 2 is larger AC bridge is more sensitive than DC bridge! 35 gyurcsek.istvan@mik.pte.hu
36 q Overview of Bridge Circuits q Null Type (Balanced) Bridges DC Impedance Bridges AC Impedance Bridges Transformer Bridges q Deflection Type (Unbalanced) Bridges q Alternatives (Anderson Loop) 36 gyurcsek.istvan@mik.pte.hu
37 Alternatives for Bridges Differential amplifier = alternative for bridge circuit q Wheatstone bridge à 150+ years old (Wheatstone 1843) q Substituted by diff. amplifier (R à U converter) Similar solution: Anderson loop (NASA patent, 1994) q Similar performances (as bridge) q Compensation of the offset voltage (zero output signal for!r= 0) q Linear conversion q Compensation of interferences (i.e. changes of ext. temperature) (next slide) 37 gyurcsek.istvan@mik.pte.hu
38 Anderson Loop (Examples)! "#$ = & ' ( * Advantages (to Wheatstone bridge) q Several sensors possible q Output of each sensor! +! -./ = & ' ( * q Difference of outputs (like bridge)! +! 0 = & ' ( * + * 0 38 gyurcsek.istvan@mik.pte.hu
39 Questions
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