Measurements & Electrical Analog Devices (Part 2)

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

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

Amplifiers

Operational Amplifier

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)

Amplifiers

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

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

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)

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

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

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)

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

Signal Waveforms (2)

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

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

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

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

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)

Filters

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

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

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

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]

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

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

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

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

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

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

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

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

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