2. ANALOG MEASURING INSTRUMENTS
permanent magnet moving coil meters: principle, deflecting torque, connection of PMMC
voltmeter and ammeter – PMMC meters with rectifier (basic connection, what it measures,
frequency dependence)
iron-vane meters: principle, measured value, V-meter, A-meter measured value
electrodynamic meters: principle, measured value, W-meter, measured value
AE2BEM38B – L2
1
ANALOG MEASURING INSTRUMENTS
X  F (T d )  
X – measured quantity; F (M P ) – deflecting force (deflecting torque);
 - angular deflection
kd
kd


f
(
X
)


X
T d = k d ·f(X); T r = - k r ·; T d + T r = 0; 
; 
kr
kr
 - angle;  - deflection in scale divisions
PMMC METER
F = B·l·I  MP = 2B·l·r·N·I
permanent magnet
l
moving
coil
Fixed cylinder
from ferromg.
material
AE2BEM38B – L2
r

pole
pieces
B
Basic range:
10 A - 100 mA
Coil resistance:
10  - 1 k
Usage:
- DC PMMC ammeters and
voltmeters;
- AC PMMC ammeters and
voltmeters (with rectifiers)
2
PMMC AMMETER
a) single-range meter
I
I = I m + I b = U m /R m + U m/R b
Im
Ib
U
Rb
Rm

Um
Rb 
Um
I  I m 
b) several-ranges meter
Ayrton shunt:
NO! I m
I
I
R1
R2
R3
I1
I2
I3
Im
R1
R ADC
R2
Rm
U
Um
ADC
U ADC
R3
(Voltage drops on
resistors of switch are
added to voltage drop on
shunt)
AE2BEM38B – L2
U m = (R 1 + R 2 + R 3 )(I 1 - I m)
U m + R 1 I m = (R 2 + R 3 )(I 2 - I m)
U m + (R 1 + R 2 )I m = R 3 (I 3 - I m)
Note:
DMMs use the same
range-changing
principle
3
PMMC VOLTMETER
U = I m (R p + R m )
Rp
U
Rm
Um
RV

U
Rp 
 Rm
Im
Resistance usually given as R i v (/V) –
related to the range!
AE2BEM38B – L2
R1
R2
R AČP
AČP
U AČP
Note: A voltage divider is usually
used by DMMs for voltage range
changing
4
PMMC METER WITH RECTIFIER
i(t)
u(t)
i r2 (t)
IDEAL FULLWAVE
RECTIFIER
u r2 (t)
i(t)
R2
FILTER
ADC
i r2 (t)
I sa
t
t
I RM
1T
1T
  ir 2 (t )dt   i (t ) dt
T0
T0
 Meter measures rectified mean (RM), it is however calibrated in RMS values for
sinusoidal waveform.
 RMS value cannot be found from meter reading for non-sinusoidal waveform!
 Rectified mean value can be found by dividing meter reading by the form-factor for the
sinusoidal waveform (i.e. by 1,11)
AE2BEM38B – L2
5
PMMC METER WITH RECTIFIER
V-meter: I
A-meter:I
R1
RS
U
U
RM
Actual passive rectifier:
partial linearization by series resistor
R m 2R d
2R d +R m
I
Rp
2R d +R m +R p
RS
R2
RM
Electronic (digital) meters:
linearization of rectifier using
operational amplifier
(see lecture 3)
Frequency dependence:
- of amplifier
- of input divider (parasitic
capacitances of resistors)
U
- of Ayrton shunt (parasitic
inductances of resistors)
Frequency dependence:
- parasitic capacitances of series resistors (V-meter)
- (parasitic inductances of resistors (A-meter))
AE2BEM38B – L2
6
PMMC METER WITH THERMOCOUPLE
U t , measured by PMMC (milli)voltmeter,
mV
It is proportional to difference of θ a θ 0
Temperature θ, of the heating wire,
Is proportional to the square of the heating current
Ut

PMMC meter with thermocouple measures the RMS value
θ0
I
Rt
Advantages: low frequency dependence,
Measures correctly also by large crest-factor values.
θ
Disadvantage: Low accuracy, low overloading capacity.
IRON-VANE (FERROMAGNETIC, MOVING IRON) INSTRUMENT
Principle:
I
B
Ferromg.
core
AE2BEM38B – L2
F
F~B2
B~I
2
Td = kd I ;
1T
1T 2
2
Td   td (t )dt kd  i (t )dt  kd I RMS
T0
T0
Basic range: 10 mA to 100 A
Range changing of A-meter:
- coil taps
- series-parallel connection of
equivalent coil sections
7
Practical construction:
ferromagnetic
axis
pointer
needle
Movable segment
Fixed segment
coil
coil
pointer
coil
air
damping
axis
Iron-vane voltmeter:
RS
RV = RS + Rm
I
Range changing: R S
R m, L m
U
I
U
RV2   2 L2m Strong frequency dependence
(used almost exclusively for 50 or 60 Hz)
AE2BEM38B – L2
8
ELECTRODYNAMIC INSTRUMENT
Used as wattmeter
MOVABLE COIL - current I 2
POINTER
B
F ~ B I2
B ~ I1
FIXED
COIL - 2
SECTIONS
- current I 1
T d = k d I 1 I 2 ; I1 = I CC , I 2 = U VC / R VC
For AC waveforms:
AXIS
1T
1T
1 1T
P
Td   t d dt k d  i1i2 dt  k d
 iCC u VC dt  k d
T0
T0
RVC T 0
RVC
(For harmonic waveforms: M P ~ U I cos)
Frequency dependence:
Range changing:
Finding constant:
Td  k d
U VC
I 1 cos(     )
2
2
2
R VC   L VC
Voltage ranges – series resistor
Current ranges – series-parallel connection of equivalent coil sections
U I
P = k W 
Only in spec. cases
k W  N N ( cos  N )
 max
AE2BEM38B – L2
for cos = 0,1 or 0,2.
9