Measurements & Electrical Analog Devices (Part 2)

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 E0(t) = h{Ei(t)} • Simplest amplifier = linear scaling amplifier: h{Ei(t)} = GEi(t) • Have finite frequency response & limited input voltage range • Most widely used – solid-state operational amplifier

4. Amplifiers

5. Amplifiers Operational Amplifier

6. Amplifiers • High internal gain, A: E0 = A [Ei2(t) – Ei1(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, fc

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, fc1 and high cutoff frequency, fc2, 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fc,  = 2f • Phase shift,  () = -tan-1  • Roll-off slope = 20 dB/decade • Cutoff frequency, fc(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/fc)2k]1/2 • Phase shift,  (f) =  i (k) • Attenuation (dB) = 10 log [1 + (f/fc)2k] • Roll-off slope = 20 x k [dB/decade]

26. Butterworth Filter Design For other values, L = Li Rs/ 2fc and C = Ci / (Rs 2fc)

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R2C2 • Gain, K = R2 / R1

30. First-order, single-stage, high-pass Butterworth active filter: • fc = 1 / 2R1C1 • Gain, K = R2 / R1 • Magnitude ratio, M(f) = f/fc / [1 + (f/fc)2]1/2

31. Active bandpass filter – combining high- & low-pass filters: • Low cutoff, fc1 = 1 / 2R1C1 • High cutoff, fc2 = 1 / 2R2C2

32. Grounds, Shielding & Connecting Wires • Rules to keep noise levels low: • Keep the connecting wires as short as possible • Keep signal wires away from noise sources • Use a wire shield and proper ground • 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