Transcript
9. MEASURING CONVERTERS OF ELECTRICAL QUANTITIES - 2 Converters for measurement of sum and difference (using OAs, using transformers) Electronic integrator: basic principle and derivation of output voltage Converters of RMS value to DC voltage Converters of product value to DC voltage (multipliers) Controlled (phase sensitive) rectifiers, measurement of voltage vectors
AE2B38EMB, L9
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Converters for measurement of sum and difference I1
R
I2
R
U1
R
R2 IN
R
U2 UN
I
I
+
+ U0
U0
voltages adder
R2 U 0 R2 I R
currents adder
N
U i 1
N
i
U 0 RI R I i i 1
(input voltages in voltage adder might be weighted by different R values) AE2B38EMB, L9
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I1
R U1
R
Io
R U1 U
UB
Uo
+ U0 R
UA
U2
U 0 =k 1 U 1 +k 2 U 2
Difference amplifier
a)
U1 U B U0 U B ; R R
U1
U2 U U 0 2 2 2
AE2B38EMB, L9
I2
U2 UB UA 2
U 0 U 2 U1
I 0 =k 1 I 1 +k 2 I 2 b)
a) voltage measuring transformers used for adding voltages b) current measuring transformers used for adding currents (k 1 = k 2 = 1) 3
Electronic integrator (inverting) i i1
C
u1 du 2 iC C i1 dt R
R +
u1
u2
u 2 (t1 )
t1
t1
1 1 i ( t ) d t u1 (t ) dt C C0 RC 0
True RMS to DC converters 10 V electronic RMS value converters (used in DVM and DMM)
most used: implicit-computing converter (e.g. IO AD 637)
u x (t) u2/U zv
u1
U FB
AE2B38EMB, L9
LP
U 10
VF
U FB =U 1
1T 1 T u x2 U 10 u1dt dt U F T0 T 0 U FB T
1 U u x2 dt T 0 2 F
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Squaring circuit/divider could be based on logarithm and exponential function circuits:
u x2 exp( 2 ln u x ln U FB ) U FB Thermal RMS converters (using feedback) – based on physical definition of RMS
OA2
OA1 +
+
R R
U2
R T2
R T1 TC1
TC2
0,01% in the band 20 Hz to 50 kHz 2% to 5% in the band 10 MHz to 100 MHz
AE2B38EMB, L9
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Converters for measurement of product (multipliers) Multiplier log-antilog) |u 1 |
Function ln defined for positive argument only
ln|u 1 | + ln|u 2 | = ln|u 1 .u 2 | ln x
AC voltages cannot be directly multiplied
ln|u 1 | ex
+ |u 2 | ln x
ln|u 2 |
u 3 =exp(ln|u 1 u 2 |)=|u 1 u 2
Solutions: - superposition of a DC component - using auxiliary circuits for polarity indication and control of output
Typical parameters: f : tens of kHz; ~ 0.2 – 0.5 % Variable resistance or variable transconductance multiplier Realization: UP - voltage control resistance – linearized unipolar transistor in series with VCCS
u1
i 1 =k 1 u 1
- differential amplifier with bipolar transistors with voltage-controlled emitters current source Typical parameters: f : tens of kHz to tens of MHz; ~ 0.2 - 2 % AE2B38EMB, L9
u2
R=k 2 u 2
u3 = R i1 = k2 u2 k1 u1 = = k u 1 .u 2 6
Power to DC voltage converter using pulse-width pulse-height multiplier
u2
UA converter
u1
amplitude modulator
U1 T1 - T2
UA k
UA T1
T2
T1 - T2 = k1u1
U SS k
UA = k2u2
U DC
filter – low pass (LP)
U 2 (T1 T2 ) T1 T2
1 T1 T2
T1 T2
u1u2 dt
0
Typical parameters: f : units of kHz; ~ 0,1 – 0,5 % Hall multiplier
i1
Use: Electronic (static) W-h meters
i2 B
Typical parameters: f : units of kHz; ~ 1 - 2 %
u H = k.i 2 .B = k i 1 i 2 uH AE2B38EMB, L9
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Controlled (phase sensitive) rectifiers
R
R
u2
R
u1
+
u1
UC
UC
CC
u2
CC
U c – rectangular pulse train with magnitude 1
1 sin k t k ´1 k u 1 t U m sin t u c t
4
k odd
u 2 t u 1 t u c t
AE2B38EMB, L9
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4 1 u2 t U m cos t t cos t t 2 2 t
uC
u1
u2
u 20
4 1 cos t k t cos t k t Um 2 k 3 1 k t 1 k t 2 u2 t U m cos AC components u 20 AC comp.
Notes to derivation
2
U m U RM
sin sin
1 cos cos 2
(U RM U RMS !)
AE2B38EMB, L9
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Measuring voltage phasor using controlled rectifier-VECTORVOLTMETER After filtering out the AC components using a LP filter the DC component u 2,0 at the c.r. output is proportional to the real part of the phasor. After shifting the control voltage by 900 (/2), this DC component u 2,90 corresponds to imaginary part of the u0 measured phasor. UX
(u 90 ) FILTER
CR
U
(LP)
ur
u 2,0
uR,0 (uR,90 )
SC
0
ux
o
90
o
2
o
SC
u0 u 2,0 u R,90
ReU x
U m cos
2 2
u 2 , 90
ur
u R,0
Ur 90
2
2
U RMS cos U m sin
2 2
U RMS sin
u 90 ImU x AE2B38EMB, L9
Ux
u 2,90 10
