Nidhi > Em > Lecture_4_xe38emb-c

4. CONVERTERS OF ELECTRICAL QUANTITIES, MEASUREMENT OF FREQUENCY Adding and subtracting converters (using OAs, using transformers) Electronic integrator: basic principle and derivation of output voltage Measurement of frequency: frequency standards, direct measurement using oscilloscope, counters (direct measurement of f , measurement of T, averaging, possibility of false reading) electronic analog frequency meters,

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Converters for measurement of sum and difference I1

R

I2

R

U1

IN

R

U2 UN

I

I

+

R2 U 0 = − R2 I = − R

i =1

U0

adder of currents

N

∑U

+

U0

adder of voltages

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R

R2

N

i

U 0 = − RI = − R ∑ I i i =1

2

I1

R U1

R

Io

R U1 U2

UB

Uo

+ U0 R

UA

U2

U0=k1U1+k2U2

Differential amplifier

a)

U1 − U B U0 −U B =− ; R R

U1 −

U2 U = −U 0 + 2 2 2

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I2

U2 UB =UA = 2

⇒ U 0 = U 2 − U1

I0=k1I1+k2I2 b)

a) voltage measuring transformers used for adding voltages b) current measuring transformers used for adding currents

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Electronic integrator (inverting) iC i1

C

u1 du = − iC = − C R dt

i1 =

R -

u1

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+

u2

u 2 (t1 ) =

t1

t1

1 1 i ( t ) d t = u1 (t ) dt C ∫ ∫ C0 RC 0

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MEASUREMENT OF FREQUENCY Frequency standards Note: frequency and time are mutually bounded physical quantities 1s is defined in SI-system as time of n-periods of radiation…… Basic (primary) standard – cesium resonator (stability up to 10-14/year) Secondary standards: temperature-controlled quartz-crystal oscillators (stability up to 109 /rok)

Frequency measurement using oscilloscope Comparison method in X-Y regime for rational ratio of frequencies (Lissajous patterns) Direct measurement using oscilloscope: fx = 1/T (low accuracy)

Electronic analog frequency meter u1 u1

u3

MKO

U0

u3

u2 t

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u2

TO

t

T0

u

Tx

t

1 U0 = Tx

TX

T

1 0 ∫0 u3 dt = Tx ∫0 U P dt =

= U PT0 f x = kf x 5

Digital frequency meters – counters Direct measurement of frequency SC

ID + A

G

fx TN

f0 CO

D

COUNTER(N )

fx =

N TN

DECOD.ER+ DISPLAY

Estimating uncertainty by direct frequency measurement Type B standard uncertainty of fX:

u fX =

(∆ f

) ( 2

/

X

3 + ∆f X

3

)

2

∆/fX = 1/TN is counter resolution in regime of direct frequency measurement δ fO N δ fO ∆f X = = fX , δfO frequency instability of quartz-crystal oscillator fO, 100 TN 100 causing error in gate opening time TN, N = number of pulses counted in TN.

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indirect frequency measurement - measurement of period time Tx fN

SC

ID + PA

COUNTER(N)

G

CO

f0

N fN

Tx =

Tx D

Tx

DEKODER + DISPLAY

Estimating uncertainty of period-time measurement Type B standard uncertainty:

uTX =

(∆ T /

X

) ( 2

3 + ∆TX

)

2

3 + 2u K

2

∆/TX = 1/fN counter resolution in regime of period measurement ∆TX =

δ fO 100

TN N =

δ fO 100

TX ,

Limits of fluctuations of comparison level

δfO is frequency instability of quartz crystal oscillator fO in %, TN period time of standard frequency, N is number of pulses counted in TX,

TMIN

uK is standard deviation of comparison level

TMAX

variations caused by noise.

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Estimating uncertainty by measurement of T using averaging Note: Averaging here means measuring the time of n periods (n = 10k) and shifting decimal point in display by k positions to the left. (it is NOT statistical processing as by estimating type A uncertainty!). Component ∆/TX (given by resolution) decreases n-times, since resolution corresponds to the value of 1/nfN. (After decimal point shifting, the weight of the last display position is n-times lower than by measurement of 1 period.) Component ∆TX (given by relative instability of oscillator frequency f0) is not influenced by averaging, since

∆TX =

δ f0

100

TX

n δ f0 = TX n 100

Component uk is constant, but by shifting the decimal point by k positions its value decreases n-times. Resulting type B uncertainty by measurement of period Tx using averaging is therefore:

uTX =

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(∆ T /

X

(n

3 ) + (∆T 2

X

3 ) + 2(u 2

2 / n ) k

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Possible false reading by measurements using counter input signal

Setting incorrect comparison level may lead to gross errors comp. level SC output

of measurement. Preliminary

rough

measurement

of

frequency

using

oscilloscope is therefore highly recommended.

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Measurement of revolutions and flow Output signal of induction sensors (by revolutions measurement) or from flow sensor is measured by counter. u

u

N

permanent. magnet

t mg. soft material

1 revolution u

u t

Note: Induction sensors do not work properly by low revolutions; more complicated sensors should be used in this case (Wiegand sensor).

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