1. Measurements & Electrical Analog Devices (Part 2)

2. Introduction Analog Signal Conditioning: Amplifiers Analog Signal Conditioning: Filters Grounds, Shielding & Connecting Wires

3. Amplifiers Amplifier - device that scales the magnitude of an analog input signal according to E 0 (t) = h{E i (t)} Simplest amplifier = linear scaling amplifier: h{E i (t)} = GE i (t) Have finite frequency response & limited input voltage range Most widely used – solid-state operational amplifier

4. Amplifiers

5. Operational Amplifier

6. Amplifiers High internal gain, A: E 0 = A [E i2 (t) – E i1 (t)] A – flat at low frequencies, falls off rapidly at high frequencies but can overcome using external input and feedback resistors (control G)

7. Amplifiers

8. Filters Filter = used to remove undesirable frequency information from a dynamic signal Classified as low pass, high pass, bandpass and notch

9. An introduction to signal… Measurement system – takes input quantity / signal & transforms into measurable output quantity / signal Shape / form of signal = waveform Waveform – information on magnitude, amplitude, frequency

10. Definition of signal Signal = physical information about a measured variable being transmitted from one place to another (between a process and the measurement system, between the stages of a measurement system, or the output from a measurement system)

11. Classification of signals Signals – analog, discrete time, digital Analog signals = continuous in time

12. Classification of signals (2) Discrete time signals – information about the magnitude of signal is available only at discrete points in time Results from sampling of continuous variable at finite time intervals

13. Classification of signals (3) Digital signals – 1) exist at discrete values in time; 2) discrete magnitude determined by quantization (assigns single number to represent a range of magnitudes of continuous signal)

14. Signal Waveforms Static signal = does not vary with time Dynamic signal = time-dependent signal Deterministic signal = varies in time in predictable manner i) Periodic = variation of magnitude repeats at regular intervals in time ii) Aperiodic = do not repeat at regular intervals Nondeterministic = has no discernible pattern of repitition

15. Signal Waveforms (2)

16. Filters Low-pass filter: - Permits frequencies below a prescribed cut-off frequency to pass while blocking the passage of frequency information above the cut-off frequency, f c

17. Filters High-pass filter: - Permits only frequencies above the cutoff frequency to pass

18. Filters Bandpass filter: - Combines features of both low & high pass filters - Described by a low cutoff frequency, f c1 and high cutoff frequency, f c2, to define a band of frequencies that are permitted to pass through the filter

19. Filters Notch filter: - Permits passage of all frequencies except those within a narrow frequency band

20. Filters Passive filters – combinations of resistors, capacitors and inductors Active filters – incorporate operational amplifiers Important terms – roll-off (rate of transition where the magnitude ratio decreases relative to the frequency – dB/decade); phase shift (between input & output signal)

21. Filters

22. Butterworth Filter Design Characteristics – relatively flat magnitude ratio over its passband, moderately steep initial roll-off and acceptable phase response

23. Butterworth Filter Design For first-order RC filter system: - Magnitude ratio, M = 1 /  (1+ (  ) 2 ), where  = RC = 1/2  f c,  = 2  f - Phase shift,  (  ) = -tan -1  - Roll-off slope = 20 dB/decade - Cutoff frequency, f c (dB) = 20 log M(f) = -3dB

24. Butterworth Filter Design Roll-off slope can be improved by staging filters in series (cascading filters) – adding additional reactive elements (L / R)

25. Butterworth Filter Design For k-stage low-pass Butterworth filter: - Magnitude ratio, M = 1 / [1 + (f/f c ) 2k ] 1/2 - Phase shift,  (f) =   i (k) - Attenuation (dB) = 10 log [1 + (f/f c ) 2k ] - Roll-off slope = 20 x k [dB/decade]

26. Butterworth Filter Design For other values, L = L i R s / 2  f c and C = C i / (R s 2  f c )

27. High-pass Butterworth Filter (Li) HP = (1/Ci) LP and (Ci) HP = (1/Li) LP Magnitude ratio, M(f) = f/fc / [1 + (fc/f) 2k ] 1/2

28. Bessel Filter Design Sacrifices a flat gain over its passband with a gradual initial rolloff in exchange for a very linear phase shift

29. Active Filters Uses high frequency gain characteristics of op- amp to form an effective analog filter First order, single-stage, low-pass Butterworth filter: fc = 1 / 2  R 2 C 2 Gain, K = R 2 / R 1

30. First-order, single-stage, high-pass Butterworth active filter: fc = 1 / 2  R 1 C 1 Gain, K = R 2 / R 1 Magnitude ratio, M(f) = f/fc / [1 + (f/fc) 2 ] 1/2

31. Active bandpass filter – combining high- & low- pass filters: Low cutoff, fc 1 = 1 / 2  R 1 C 1 High cutoff, fc 2 = 1 / 2  R 2 C 2

32. Grounds, Shielding & Connecting Wires Rules to keep noise levels low: 1) Keep the connecting wires as short as possible 2) Keep signal wires away from noise sources 3) Use a wire shield and proper ground 4) Twist wire pairs along their lengths

33. Ground & Ground Loops Ground = a return path to earth Ground loops = caused by connecting a signal circuit to two / more grounds that are at different potentials Ensure a system has only one ground point

34. Shields & Connecting Wires Shield = a piece of metal foil or wire braid wrapped around the signal wires and connected to ground Different type of wires – single cable, flat cable, twisted pair of wires, coaxial cable, optical cable