instrumentation and measurements

instrumentation and measurements lectures

define measurement

is an experimental process that produces a value that can reasonably be attributed to a quantitative property of a phenomenon, body, or substance.

define measurement uncertainty

is a parameter, associated with the result of a measurement, that characterises the dispersion of the values that could reasonably be attributed to the measurand.

what are types of mean

geometric, harmonic, weighted, trimmed

define precision

the repeatability or reproducibility of measurements under unchanged conditions

define accuracy

the degree of closeness of measurements of a quantity to that quantity's true value.

what are the steps of finding geometric mean

1.Multiply all values together to get their product.2 Find the nth root of the product (n is the number of values).

how to find the harmonic mean

dividing the number of observations, or entries in the series, by the reciprocal of each number.

what are the steps of finding the weighted mean

1) Calculate the weighted value of each data point by multiplying each data point value by its weight.2) Sum the weighted values by adding the weighted value of each data point.3) Divide the sum by the sum of the weights for each data point.

how to find the trimmed mean

Calculate the number of data points to be trimmed from both ends

how to find the standard deviation

find the mean (average) of the values. Then, for each value, subtract the mean and square the result. Sum up all these squared differences, divide by the number of data points (for population standard deviation) or by the number of data points minus 1 (for sample standard deviation), and finally, take the square root of the result. 

how to find the confidence interval

adding and subtracting a margin of error from the sample mean

how to find the margin of error

margin of error = critical value * standard deviation/square root N

what is a waveform

physical quantity changing over time

what is signal

information-bearing function

what is noise

can be a random component signal that interferes with an information-bearing signal.

what is drift signal

can be considered noise, and in time-series modelling can be considered “trend”.

what are common properties of signals

Amplitude • Frequency • Frequency spectrum • Bandwidth (BW) • Phase • Period To (temporal period, if periodic in time) ; To = 1/f • Wavelength λ (spatial period, for traveling waves) ; λ = V(Speed)/f. • Power spectral density (if periodic or random) • Energy spectral density (if non-periodic)

what is a sinusoid signal

a fundamental signal in nature caused by oscillatory motion

what are basic properties of gamma rays

• Have the highest energy in the electromagnetic spectrum. • Produced in nuclear reactions and radioactive decay. • Their high frequency corresponds to shorter wavelengths, making them highly penetrating

what is frequency modulated

frequency f changes with time. Used in communications for improving signal transmission

what is bandwidth

A system can only pass a specific range or band of frequencies

what does bandwidth determine

the number and types of signals that can be processed

what is fourier transform

It is a transformation of a time signal x(t) to the frequency domain to get its spectrum X(f) that reveals its frequency content.

what is electric current

the amount of charge q that crosses a section over a unit of time

how dose current flow

from higher to lower potential

what is potential difference

The voltage difference (v) between 2 points is the work (W) [in Joule] needed to move a unit charge (1 C) from one point to another.

what is a resistor

a passive electric device that opposes current flow and consumes energy (in the form of voltage drop, 𝑣) that is proportional to the current

what is a resistor behaviour at high frequencies

practical resistors may exhibit a series inductance and a small parallel capacitance; in addition to noise

what is KCL

The algebraic sum of all currents meeting at a node is zero.

what is KVL

The algebraic sum of all voltages around a closed loop is zero.

what is a capacitor

a device that stores electric energy by accumulating electric charges on two closely-separated conducting surfaces (metal plates) insulated from each other by a non-conductive material called dielectric

what is capacitance

the capability of a device to store electrical energy, defined as ratio of charge |𝑞𝑜| on each conductor to the voltage 𝑣𝑜 between them, measured in Farad:

what is the behviour of capcitors

When the capacitor is uncharged, it behaves as a short-circuit (S/C) when DC voltage is applied at 𝑡 = 0 (it has zero impedance, i.e., 𝑋𝑐 = 0), until it is fully-charged, then it becomes Open-circuit (O/C)

what is reactance

Capacitor also opposes the current flow but in a frequency-dependent scaling since the current follows a time-derivative of voltage:

how are inductors made

Inductors are made by winding a conducting wire around a core material of high magnetic permeability

what do inductors do

Inductors store electric energy in their magnetic field when an electric current flows through them

what is the role of inductors in a circuit

When electric current flows through a coil, it generates magnetic field surrounding the coil. The ratio of the generated magnetic flux to the generating current is the inductance L, measured in Henry (H): 𝐿 = ΦΤ𝐼.

what is inductance dependent on

The inductance 𝐿 is dependent on the geometry of the coil: its length 𝑙, cross-sectional area 𝐴, number of turns N, and permittivity of free-space 𝜇𝑜 and core 𝜇𝑟 .

what happens when a circuit includes Inductors (𝐿) and/or Capacitors (C) in addition to Resistors (𝑅)

the total opposition to the current flow is called “impedance” , symbolized usually as “𝑍”; which is a complex-valued quantity including the effect of “real-valued” 𝑅 and “imaginary-valued” reactance 𝑋.

what is a transiet model (RLC)

Transient signals in RLC circuits happen when a sudden DV voltage is applied to the circuit. This can be important to test the step response of the system. • Solution of such models requires methods of differential equations.

how is RC discharge solved

Capacitor Discharge into a resistor; assume an initial charge on the capacitor that gives initial voltage of 𝑉𝑜 . • Applying Kirchhoff’s Voltage Law (KVL) for 𝑡 ≥ 0 • we have: 𝑣𝑅 + 𝑣𝑐 = 0 → 𝑣𝑐 = −𝑣

what is superposition theorem

If 2 independent sources are acting simultaneously, the final effect will be the sum of individual contributions

what is voltmeter

an instrument that can measure the electric potential difference (voltage) between two points; hence it should be connected in parallel

what is an ammeters

The Ammeter is an instrument that can measure the electric current; hence it should be connected in series

why were opAmp developed

to perform mathematical operations

what are the 2 golden rules of OpAmps

No current flows in or out of the input • The OpAmp tried to keep the inputs the same voltage

affect of an OpAmp buffer in relation to the golden rules

No current flows in or out of the input (Why? HUGE impedance between input channels) • The OpAmp tried to keep the inputs the same voltage (applies only to closed loops)

affect of an OpAmp negative feedback (relation to golden rules)

No current flows in or out of the input (Why? HUGE impedance between input channels) • The OpAmp tried to keep the inputs the same voltage (applies only to closed loops)

affect of an OpAmp inverting amplifier (relation to golden rules)

No current flows in or out of the input (Why? HUGE impedance between input channels) • The OpAmp tried to keep the inputs the same voltage (applies only to closed loops)

what is a schmitt trigger

ST is a comparator (hysteresis or loop) Converts analog to digital (1 bit)

whats the use of a Resistive Temperature Detector (RTD)

used to measure small temperature changes: ∆𝑇 ∝ ∆𝑅 Small changes; Linear relation

what is a thermistor

semiconductor sensor whose resistance is dependent on temperature; can measure large temperature change using resistor via Steinhart–Hart eqn: (1Τ𝑇) ∝ 𝑎 + 𝑏 ∙ ln 𝑅 + 𝑐 ∙ [ln 𝑅 ] 3 (nonlinear)

what is a photoresistor

Measure change in illuminance 𝐸 (not change in light intensity)

what are the applications of a photoresistor

Streetlights that turn on at dusk •Automatic brightness control in mobile phones •Solar garden lights •Light meters in photography

what is strain gauge

measure strain 𝜖 on an object using change in electrical resistance

what is the potentiometer for voltage measurement

An analog sensor that changes resistance → voltage changes

what are the to types of potentiometers

Rotary pot: Shaft rotates to vary resistance. • Linear (slide) pot: Shaft moves in a straight line

what is the relationship between resitivity and temperature

The resistivity of a metal increases as temperature increases

how dose a strain gauge work

When a conductor is stretched or compressed, its resistance changes

resistance behaviour for strain gauges

Stretched → longer & thinner → resistance increases Compressed → shorter & thicker → resistance decreases

what is a gauge factor

Relates strain to change in resistance:

real world applications of a strain gage

•Structural health monitoring (bridges, airplanes) •Force sensors in robotics •Pressure and load cells •Biomedical (e.g., prosthetic force sensors)

what is a resistance to voltage (R/V) converter

It is a sensor that converts the change in resistance 𝑅𝐿 to a change in voltage

R/V converter - offset and sensitivity

To reduce DC offset, choose a large 𝑘. • For small changes : 𝑥 ≪ 1 → 𝑣 ≈ 1/𝑘+1 , 𝜂 = 0 (Sensitivity (𝜂))

(R/V) Converter - sensitivity equation

Output Voltage 𝑣 = (1 + 𝑥)Τ(𝑘 + 1 + 𝑥) • Sensitivity (rate of change ): 𝜂 = 𝜕𝑣 /𝜕𝑥 = 𝑘+1+𝑥 −(1+𝑥) /(𝑘+1+𝑥) 2 = 𝑘 /(𝑘+1+𝑥) 2 [Non-Linear]

(R/V) Converter - key observations

• For fixed 𝒌: 𝜂 decreases as 𝑥 increases. • For fixed 𝒙: 𝜂 is concave (down).

(R/V) Converter - maximise sensitivity

We should find 𝑘 for best (max) sensitivity. Hence, for best operation: choose 𝑅 near to expected 𝑅𝐿 .

whats the use of a constant current source

used to pass a fixed current through an unknown resistor

use of LDR

Light Dependent Resistor (LDR) can be used to measure illuminance 𝐸

what is Magnetoresistivity

the property of a material to change its electrical resistance 𝑅 when a magnetic field is applied.

what is Anisotropic magnetoresistance

𝑅 depends on angle between direction of electric current and direction of magnetization

what are the applications of Magneto-resistive sensors

• used for angle sensing • measuring Earth's magnetic field • measuring electric current

how is the direction of a magnetic field measured

using wheatstone bridge

brief outline of capacitive sensors

Angle Measurement using Capacitance Goniometer. Such a sensor can be worn in biomedical applications to measure joint angles. If the capacitor plates are designed as two annular half-discs with one rotating, the capacitance 𝑐 will be angle-dependent.

what is a inductive sensor

Changes in Inductance can be used to measure or detect position changes (e.g., in medical applications), magnetic properties or detect nearby metal objects.

when and how dose inductance change

Inductance changes when a metal is approaching the coil. The magnetic field of the coil 𝐵 induces “Eddy current” in the metal, which in turn produces a magnetic field 𝐵𝑒 that interferes with 𝐵 and changes its magnitude 𝐵 or direction 𝜃; hence, 𝐿 will change.

how can inductance be measured

Inductance can be measured by measuring the value of 𝑋𝐿 using Wheatstone Bridge; or by measuring the frequency change ∆𝑓 of the oscillator.

what are changes in inductance dependent on

Distance from the metallic object and the direction of approaching the sensor. • Type of metal (iron, copper, alloys).

what are eddy currents

• Eddy currents are induced by motion of a conductor in magnetic field. • They flow in closed loops within conductor, in planes perpendicular to the magnetic field.

what is the hall effect

When a current flows into a conductor and a magnetic field is applied normal to direction of current, a potential difference (voltage) will be induced on the conductor; its direction is normal (perpendicular) to both the current and magnetic field.

why dose hall voltage need amplification

as it is weak

what is the application of the hall effect

In many smart phones, the leather cover (case) can turn on/off the screen when the case is open/closed. • The phone is equipped with a Hall sensor; while the cover has a built-in magnet. • When the case is closed, its magnet is close to the Hall sensor, which produces a voltage to shut down.

what the purpose of a schmitt trigger with hall sensor

To prevent random ON/OFF under minor cover flips

what is hall voltage proportional to

the strength of the magnetic field 𝐵 [Tesla=T = Vs/m2 ].

what can hall voltage be used for

It can be used to detect and measure the strength of magnetic fields.

what is temperature sensing based on

changes in some physical properties caused by temperature change

what is a thermocouple

a two-terminal metallic structure consisting of two different metal wires joined at one end

whats the difference between thermocouples and RTD’s

TC’s are a temperature sensors, but with much higher temperature ranges than RTD or Thermistors

what are thermocouples based on

TC is based on Seebeck Effect: A conductor between two points generates a voltage when it is subjected to a temperature difference ∆𝑇 between the two points

what is a thermocouple voltage function

TC voltage function, called E(T), is tabulated as a function of temperature (T) for each TC; called characteristic function of TC; and it is non-linear

what are pitot tube’s used for

measuring the velocity of flow of a liquid, usually applied to measure the speed of an aircraft.

how do pitot tubes work in aircrafts

it uses the differential pressure system by flowing air into a tube pointing directly into the air flow. The tube contains incompressible fluid (e.g., water), hence, the pressure difference ∆𝑝 (created by air movement) can be measured using the displacement of tube-fluid.

what is piexoelectric effect

If a force is applied to a segment of piezoelectric material, then an electrical charge will appear on the surfaces of the segment.

what is the Inverse Piezoelectric effect

orient dipolar crystals with an electric charge, creating stress in the crystal.

piezoelectric and voltage

Piezoelectric devices generate their own voltage, without need for external power source.

when do piexoelectric sensors work

Piezoelectric sensors work only under time-varying signals (e.g., force). They do not work under static conditions

how dose the charge to voltage converter work (piezoelectric sensors)

a piezoelectric sensor generates a charge, which can be used to create an input current to OpAmp to charge a feedback capacitor and have an output voltage 𝑣𝑜. This circuit is called charge amplifier.

what is strain

Strain is the relative change in length ∆𝐿 to the original length 𝐿𝑜: 𝜖 = ∆𝐿 𝐿𝑜 . It is a material property.

what is stress

ratio of internal resistive force (against the deformation) to the area: 𝜎 = 𝑓 𝐴 (internal pressure).

what is tensile (axial) strain

Strain in the direction of the stress