MECH 373 Instrumentation and Measurements

1. MECH 373Instrumentation and Measurements Lecture 5 (Course Website: Access from your “My Concordia” portal) Measurement Systems with Electrical Signals (Chapter 3) • Electrical signal measurement systems • Signal conditioners Amplification Attenuation Filtering

2. Example 2 Determine which amplifier has the lower input loading error?

3. Example 2

4. Signal Attenuation • In some cases a measurement will result in a voltage output with an amplitude higher than the input range of the next component. The voltage must then be reduced to a suitable level, a process known as attenuation. • The simplest method is to use a voltage-dividing network as shown below: • The resulting output voltage is

5. Signal Attenuation • Dividing networks of this type have potential loading problems. • It will place a resistive load on the system that generates Vi, which will change Vi. • The problem can be avoided by having the sum of R1 and R2 be very high compared to the output impedance of the system generating Vi. • However, high value of R2 will lead to a problem when the output load is connected. • It may be desirable to feed the voltage divider output into a high-input impedance amplifier with unit gain to reduce output loading problems. • The use of large values of resistance in voltage dividers presents another problem. At high signal frequencies, the impedance due to small amounts of capacitance can be comparable to the divider resistances and can produce attenuation that is frequency dependent.

6. Signal Attenuation

9. PARAMETRIC ANALYSIS

10. Filter input output Outlines of Filter Design Filtering: Certain desirable features are retained Other undesirable features are suppressed

11. Signal Filter Analog Filter Digital Filter Element Type Frequency Band Passive Active Low-Pass Band-Pass All-Pass High-Pass Band-Reject Classification of Filters

12. Classification of Filters

13. Classification of Filters

14. Low-Pass Butterworth filter • Maximally flat in pass-band with constant gain • Gain = G = 1/√((1+f/fc)^2n). • n = order, fc = corner frequency. • f/fc >> 1.0; G = (fc/f)^n. • n = 1, double the frequency = half the gain, 2f = 0.5G – 6dB per octave. • e.g. n = 1, fc =1500Hz, • f1 = 15,000Hz – G1 = -20dB; • f2 = 30,000Hz, - G2 = -26dB. • Roll-off in stop-band – 6n dB per octave, e.g., n=8, 48db per octave. 14

15. Low-Pass Butterworth filter 15

16. Low-Pass Butterworth filter 16

17. Classification of Filters

18. Classification of Filters

19. Classification of Filters

20. Classification of Filters

21. Signal-To-Noise Ratio (S/N) Terminology in Filter Design • Bandwidth the range of frequencies of |G(jw)|>0.707 • Cutoff Frequency the end of pass-band frequency • Break-point of a filter the point with a gain of -3dB

22. R C Vout Vin RL Vout Vin w wp ws Passive Low-Pass Filter • The pass-band is from 0 to some frequency wp. • Its stop-band extends form some frequency ws, to infinity. • In practical circuit design, engineers often choose amplitude gain of 0.95 for passive RC filters:

23. C Vout R Vin Vout Vin w ws wp Passive High-Pass Filter • Its stop-band is form 0 to some frequency ws • The pass-band is from some frequency wp to infinity. • In practical circuit design, engineers choose amplitude gain of 0.95 for passive CR filters:

24. Example – Butterworth low pass filter Transducer signal – Amplitude =+/-10v, Frequency up to 20Hz. Superimposed on this signal – 60Hz noise with an amplitude of 0.2v – need to attenuate this noise signal to less than 5% of its value. Corner frequency fc = 30Hz. Calculate order of filter: G = Vo/Vi = 0.05 = 1/sqrt(1+(f/fc)^2n). f = 60Hz, fc = 30Hz. n = 4.32 say 5. 24