ME411 Engineering Measurement & Instrumentation. Winter 2017 Lecture 3

Transcription

1 ME411 Engineering Measurement & Instrumentation Winter 2017 Lecture 3 1

2 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

3 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

4 Resistance Measurement Use d Arsonval meter with known input voltage, E i, and known resistor, see Fig 6.11, 12. 4

5 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, I g ). Then: Under balanced conditions, the current through G is 0 and: Source: Figliola and Beasley 5

6 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

7 Example Problem

8 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 High-pass Band-pass Notch eliminate high frequency components. eliminate low frequency components. eliminate frequencies outside of a given range or band. eliminate frequencies in a given range or band. 8

9 Ideal Filters 9

10 Low-pass Butterworth Filter As and RCE o RC (t) E o (t) E i (t) The magnitude ratio can be written as: M f f 1/ 2 M(f) is a function of input frequency, f. And the phase shift is: f tan 1 2f Source: Figliola and Beasley 10

11 Low-pass Butterworth Filter (cont.) A filter is designed around its cut-off frequency, f c. Defined as the frequency at which the power is reduced by HALF. This is the same as the magnitude being reduced to: db log M f log db When the input frequency, f is at f c, the output will degrade by -3 db. Also, at f c, = RC = 1/(2f c ) for a single stage RC filter 11

12 Example 6.6 Design a one-stage Butterworth RC Low-pass filter with a cutoff frequency of 100Hz. 12

13 A single-stage low-pass RC filter with f c = 100 Hz cutoff = 100/1000; [b, a] = butter(1,cutoff); freqz(b,a,128,2000); -3 db at 100 Hz Magnitude (db) Frequency (Hz) 0 For input frequency of 150 Hz, M(f) = 0.555, or -5.1 db; and the phase shift is deg. Phase (degrees) Frequency (Hz) 13

14 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 Beasley 14

15 A 9-stage low-pass RC filter with f c = 100 Hz 200 cutoff = 100/1000; [b, a] = butter(9,cutoff); freqz(b,a,128,2000); Note the magnitude range of this figure is different than that of the previous figure. For input frequency of 150 Hz, M(f) = 0.026, or -31.7dB. Magnitude (db) Phase (degrees) Frequency (Hz) Frequency (Hz) 15

16 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

17 High-pass Butterworth Filter For a high-pass filter, use a CR circuit as shown. Then the magnitude ratio is given as: 17

18 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

19 A single-stage high-pass RC filter with f c = 100 Hz cutoff = 100/1000; [b, a] = butter(1,cutoff,'high'); freqz(b,a,128,2000); -3 db at 100 Hz Magnitude (db) Frequency (Hz) 100 For input frequency of 50 Hz, M(f) = 0.555, or -7 db; and the phase shift is 63.5 deg. Phase (degrees) Frequency (Hz) 19

20 A 9-stage high-pass RC filter with f c = 100 Hz cutoff = 100/1000; [b, a] = butter(9,cutoff, high ); freqz(b,a,128,2000); Magnitude (db) Note the magnitude range of this figure is different than that of the previous figure. Phase (degrees) Frequency (Hz) For input frequency of 50 Hz, 500 M(f) = 0.002, or -54.2dB Frequency (Hz) 20

21 Comparison of different type of filters Key Features of Low Pass Filter Types: Bessel: linear phase shift, gradual roll off Butterworth: Steeper roll off, nonlinear phase shift Chebyshev: Steep roll off, nonlinear phase shift, non-smooth pass band magnitude ratio Elliptic: very steep roll off, nonlinear phase shift, non-smooth pass band magnitude ratio. 21

22 Active Filters Use of op-amp, resistor, and capacitor in the arrangement as shown in Figure (note: inverting circuit) The low-pass cutoff frequency is: 1 f c 2R C The high-pass cutoff frequency is: And the magnitude ratio is: f c 2 1 2R 1 2 C 1 K R 2 f f M f 2 R 1 c 2 1/ 1 f fc 22

23 Image credits All images from Figliola and Beasley, Mechanical Measurements 5 th edition unless otherwise stated 23