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

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

Amplifiers

Amplifiers

Operational Amplifier

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)

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 manneri) Periodic = variation of magnitude repeats at

regular intervals in timeii) 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, fc

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, fc1 and high cutoff frequency, fc2, 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 = 1/2fc, = 2f- Phase shift, () = -tan-1 - Roll-off slope = 20 dB/decade- Cutoff frequency, fc(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/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]

Butterworth Filter Design

For other values, L = Li Rs / 2fc and C = Ci / (Rs 2fc)

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 / 2R2C2

Gain, K = R2 / R1

First-order, single-stage, high-pass Butterworth active filter:

fc = 1 / 2R1C1

Gain, K = R2 / R1

Magnitude ratio, M(f) = f/fc / [1 + (f/fc)2]1/2

Active bandpass filter – combining high- & low-pass filters:

Low cutoff, fc1 = 1 / 2R1C1

High cutoff, fc2 = 1 / 2R2C2

Grounds, Shielding & Connecting Wires Rules to keep noise levels low:1) Keep the connecting wires as short as

possible2) Keep signal wires away from noise

sources3) Use a wire shield and proper ground4) 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