ME411Engineering Measurement

& Instrumentation

Winter 2017 – Lecture 3

1

Current Measurement

• DC or AC current

• Use of a D’ Arsonval Meter - electric current carrying conductor passing through a magnetic field would create a force, F.

F = I l B

Where I = current

l = length of the conductor

B = magnetic field strength

• For N number of turns of conductor in a magnetic field, the torque is:

T = NIAB sin a

2

Voltage Measurement

• Can use d’ Arsonval meter with a known resistor in series (figure 6.6).

• Can use an oscilloscope.

• Can use a voltage divider circuit (figure 6.9), where

• Can use potentiometer circuit (figure 6.10)

3

Resistance Measurement

• Use d’ Arsonval meter with known input voltage, Ei, and known resistor, see Fig 6.11, 12.

4

Wheatstone bridge

Used for measuring very small resistance changes (in sensors). Can have one of the following set-up

• Balanced bridge (no current flow or null method, Ig). Then:

Under balanced conditions, the current through G is 0 and:

Source: Figliola and Beasley 5

Wheatstone bridge

• Deflection method (use of a voltmeter to determine current flow direction).

• Need a stable input voltage & an accurate way to measure voltage!

Source: Figliola and Beasley 6

Example – Problem 6-10

7

Signal Conditioning Analog Filters

Filters can be used to separate desired signals from unwanted interference or noise. They use the frequency response of a measuring system to alter the dynamic characteristics of a signal.

Filters can be classified as:

Low-pass eliminate high frequency components.

High-pass eliminate low frequency components.

Band-pass eliminate frequencies outside of a given range or band.

Notch eliminate frequencies in a given range or band.

8

Ideal Filters

9

As

and

The magnitude ratio can be written as:

Low-pass Butterworth Filter

)t(E)t(E)t(ERC ioo

RC

2/1221

1

ffM

M(f) is a function of input frequency, f.And the phase shift is:

f2tanf 1

Source: Figliola and Beasley 10

Low-pass Butterworth Filter (cont.)

• A filter is designed around its cut-off frequency, fc.

• Defined as the frequency at which the power is reduced by HALF. This is the same as the magnitude being reduced to:

• When the input frequency, f is at fc, the output will degrade by -3 dB.

• Also, at fc, = RC = 1/(2fc) for a single stage RC filter

dB3707.0log20fMlog20dB

707.02

1

11

Example 6.6Design a one-stage Butterworth RC Low-pass filter with a cutoff frequency of 100Hz.

12

0 100 200 300 400 500 600 700 800 900 1000-100

-50

0

Frequency (Hz)

Phase (

degre

es)

0 100 200 300 400 500 600 700 800 900 1000-60

-40

-20

0

Frequency (Hz)

Magnitude (

dB

)

A single-stage low-pass RC filter with fc = 100 Hz

cutoff = 100/1000;[b, a] = butter(1,cutoff);freqz(b,a,128,2000);

-3 dB at 100 Hz

For input frequency of 150 Hz, M(f) = 0.555, or -5.1 dB; and the phase shift is -56.3 deg.

13

Cascading Low-pass Filters using RC

For a cascading filter (i.e., additional elements added), the combined magnitude ratio and phase shift for k-stage filter are given by:

Source: Figliola and Beasley14

A 9-stage low-pass RC filter with fc

= 100 Hz

Note the magnitude range of this figure is different than that of the previous figure.

cutoff = 100/1000;[b, a] = butter(9,cutoff);freqz(b,a,128,2000);

For input frequency of 150 Hz, M(f) = 0.026, or -31.7dB.

0 100 200 300 400 500 600 700 800 900 1000-800

-600

-400

-200

0

Frequency (Hz)

Phase (

degre

es)

0 100 200 300 400 500 600 700 800 900 1000-600

-400

-200

0

200

Frequency (Hz)

Magnitude (

dB

)

15

Example Problem

A single stage low-pass RC filter with fc = 100 Hz is used to filter an analog signal. Determine the attenuation of the filtered analog signal at 10, 50, 75, and 200 Hz.

16

For a high-pass filter, use a CR circuit as shown. Then the magnitude ratio is given as:

High-pass Butterworth Filter

17

Cascading High-pass Filter

For a cascading filter (i.e., additional RC circuits used), the combined magnitude ratio and phase shift for k-stage filter are given by:

18

0 100 200 300 400 500 600 700 800 900 10000

50

100

Frequency (Hz)

Phase (

degre

es)

0 100 200 300 400 500 600 700 800 900 1000-30

-20

-10

0

Frequency (Hz)

Magnitude (

dB

)

A single-stage high-pass RC filter with fc = 100 Hz

cutoff = 100/1000;[b, a] = butter(1,cutoff,'high');freqz(b,a,128,2000);

-3 dB at 100 Hz

For input frequency of 50 Hz, M(f) = 0.555, or -7 dB; and the phase shift is 63.5 deg.

19

A 9-stage high-pass RC filter with fc

= 100 Hz

Note the magnitude range of this figure is different than that of the previous figure.

cutoff = 100/1000;[b, a] = butter(9,cutoff,’high’);freqz(b,a,128,2000);

For input frequency of 50 Hz, M(f) = 0.002, or -54.2dB. 0 100 200 300 400 500 600 700 800 900 1000

500

1000

1500

Frequency (Hz)

Phase (

degre

es)

0 100 200 300 400 500 600 700 800 900 1000-150

-100

-50

0

Frequency (Hz)

Magnitude (

dB

)

20

Comparison of different type of filters

Key Features of Low Pass Filter Types:

Bessel: linear phase shift, gradual roll offButterworth: Steeper roll off, nonlinear phase shiftChebyshev: Steep roll off, nonlinear phase shift, non-smooth pass band magnitude ratioElliptic: very steep roll off, nonlinear phase shift, non-smooth pass band magnitude ratio.

21

Active FiltersUse of op-amp, resistor, and capacitor in the arrangement as shown in Figure 6.33. (note: inverting circuit)

The low-pass cutoff frequency is:

The high-pass cutoff frequency is:

And the magnitude ratio is:

22

cCR2

1f

11

cCR2

1f

2/121

2

1 c

c

ff

ff

R

RfMK

22

Image credits

• All images from Figliola and Beasley, Mechanical Measurements 5th edition unless otherwise stated

23