Nidhi > Em > Lecture_5_xe38emb-c

5. MEASUREMENT OF PHASE DIFFERENCE, MEASUREMENT OF CURRENT AND VOLTAG Measurement of phase difference using oscilloscope or counter, other methods of measuring ϕ (overview) Measurement of voltage and current: standards, reference and calibration sources (including principle of pulse-width modulation) measurement of DC voltage: overview of methods according to voltage level, principle of compensation method (where it is used), measurement of very low voltages, influence of input voltage offset of actual OA, automatically nulled amplifier, chopper-stabilized amplifier (principles) measurement of DC current: overview of methods according to current level, methods of measurement of heavy currents measurement of AC voltages and currents: overview of instruments, which quantity they measure, measurement of AC currents (overview, broad-band shunts), AC-DC current comparators

38EMC – P5

1

Measurement of phase difference Using oscilloscope: a) in X-Y regime

A

u1 (t)

Y

X

u2 (t)

B

ϕ = arcsin

A A′ = arcsin B B′

A´ B´

b) using dual-channel oscilloscope in time domain x1 (t)

x1 t0

t

x2 (t)

ϕ=

ϕ t

38EMC – P5

ϕ = ω t0 = 2π f t0 = 360 t0 T

2π t0 T

(rad )

(0 )

x2

2

Electronic phase-meters Principle: u1

u SC

u´1

u"1

MFF

t uϕ

u u"2

BFF u2 SC

u´2

u"1

u1

u2 t

MFF

u"2

uϕ

Evaluation of ϕ:

0

Up t0

T

t

a) analogue – measurement of mean value t

t ϕ 1 1 0 = ∫ uϕ (t ) dt = ∫ U P dt = U P 0 = U P = cϕ T 0 T 0 T 2π T

U 0 ,ϕ

b) counter:

ϕ=

2π t0 T

(rad )

ϕ=

360 t0 T

(0 )

(measurement of t0, T + calculation)

38EMC – P5

3

Digital phase-meter f u1

x 360 kD

fG

G uϕ

MFF

SC

COUNTER

t0 N = t0 f G = t0 k N f = 360k D = k Dϕ T

BFF u2

MFF

SC

Other possibilities of measurement of ϕ: - vectorvoltmeter (1st signal as reference, 2nd as Ux) - by power measurements, cosϕ=P/S - sampling method times t1, t2, t3 found by linear interpolation

u t1

t3 t2

38EMC – P5

t

t 2′ − t1′ ϕ = 2π t3′ − t1′

4

MEASUREMENT OF VOLTAGE AND CURRENT Standards, reference and calibration sources Basic unit in SI – electrical current (1 A) – realization: electrodynamic balance (primary standard) Secondary standards – standards of voltage (U=IR) Weston standard cell (known temperature dependence of U, high Ri, sensitive to shock) Josephson phenomenon

UN

Supercod. wire

h = nf 0 2e

2e = 483,59790 THz / V h

I

Supercond. strips

UN

U

R3

+

Temperature compensated Zener diodes (defined current proud + thermostat) R2 Ur R1

Temperature compen. 38EMC – P5 Zener diode

Reference sources – integrated circuits

Ur = UZD (R1+R2) / R1 5

Voltage calibrators (accurate DACs using pulse-width modulation)

RVS

Ur

U0 = Ur LP

SC

U0

TA X = Ur TN N

where CO

fN

u

CC

Ur

U0 TA TN

t

TA =

X N , TN = fN fN

X = number to be converted into voltage N = range of converter

MEASUREMENT OF DC VOLTAGE 10 mV ÷ 1000 V Ri > 10 MΩ/V 10 mV ÷ 1 V 0,1 mV ÷ 10 mV < 1 mV > 1000 V

PMMC voltmeters, Ri = 1 ÷ 50 kΩ/V direct-coupled measuring amplifiers ∗ direct-coupled measuring amplifiers ∗ automatically nulled amplifiers modulation amplifiers voltage dividers

at their output: PMMC meter, or ADC (for a DV typ. 200mV, 10 MΩ/V).

∗

see lecture 3 – influence of voltage offset taken into account

38EMC – P5

6

Principle of compensating method IIV

UX = Uk ⇒ IIV = 0 ⇒ Rvst = ∞

IV

Using UX

Uk

- compensating ADCs - compensating recorders

Automatically nulled amplifier _

MA

MA – main amplifier AA auxiliary amplifier

+

+ B A

Position A: AA is nulled by feedback, nulling voltage is stored on CA

CB

+

AA

B A

B

A

38EMC – P5

Position B: AA is compensated by voltage on CA. Input offset of MA is amplified by AA and taken to compensating input of MA – offset of MA is so compensated

CA

7

Chopper-stabilized amplifier

f RF ux

u3

u2

u1

~

C

ux

u

u1

u4

CF

C

u4

u2 t

t

38EMC – P5

t

u3

8

MEASUREMENT OF DC CURRENT 10 µA ÷ 1000 A

PMMC systems, PMMC systems with rectifiers , or shunt with an ADC, converter with preamplifier (voltage drop typically 50 ÷200 mV usually measurement of voltage on high-ohm using micro voltmeter with chopper-stabilized amplifier (voltage drops) without voltage drop – current-to-voltage converter using OA (see lecture 3, input bias currents must be taken into account) too high power on shunt resistors, magnetic sensors are used:

< 10 µA < 10 mA >1000 A

I2 Ix

N +

R

U2

Ix = N

U2 R

Hall probes

38EMC – P5

9

MEASUREMENT OF AC VOLTAGE 1. Measurement of rectified mean, calibrated in RMS value for sinusoid - PMMC with rectifier 2 ÷ 1000 V (50 Hz ÷ 5 kHz) - low-cost DMMs (from cca 10 mV, to cca 100 kHz)

INPUT DIVIDER

!

AC AMPLIFIER

OPERATIONAL RECTIFIER

FILTER+ADC P

ČV

analogue LF voltmeter

- < 1 mV - lock-in amplifier (see phase-sensitive rectifier – lecture 3) or selective mikrovoltmeter (only required frequency is measured). Selective voltmeters are usually based on heterodyne principle. PREAMPLIFIER

OSCILLÁTOR

38EMC – P5

IF AMPL.

MIXER

f0

OPERATIONAL RECTIFIER

FILTER +ADC

If

10

2. MEASUREMENT OF RMS VALUE - iron-vane (moving-iron), electrodynamic, PMMC with thermocouple 10 ÷ 1000 V ATTENTION: frequency limitation - < 10 V electronic RMS converters (TRUE RMS to DC converter)

most frequently the „implicit“ converter (e.g. IO AD 637) – see lecture 8

38EMC – P5

11

MEASUREMENT OF AC CURRENT - RMS value directly – iron-vane ammeter (1 mA ÷ 10 A) – voltage drops also on selfinductance of coil, limited frequency band (cca to 1 kHz) for harmonic waveform PMMC with rectifier – shunt – high power loss (see lecture 2) - digital multimeters (ammeters) – measure voltage on low-inductance (coaxial) shunt – voltage drops 10 (20) mV or 100 (200) mV, usable to hundreds of kHz. conducting material Ix UB ceramic cylinder layer of resistive material

- current measurement with galvanic isolation – Hall-probe converters and MCTs 38EMC – P5

12

Comparators of AC and DC currents ~ Ix

1

R 1. Ix → UP → IBI = 0

BI

=IN

~ Ux

2

Ut

=UN 1

UP

2. IN → IN → IBI 0 3. IN = IX RMS

2

note: e.g. comparator Fluke 792A, errors of comparison lower than 0,001 %

38EMC – P5

13