electric and electronic principles. circuit symbols

Electric and Electronic Principles

Circuit symbols

Circuit symbols

Transformer

Resistors

Diode

Op Amp

Earth

Transistor

LED

Thermistor

Definitions

EMFElectromotive "force" is not considered a

force, as force is measured in newtons, but a potential, or energy per unit of charge, measured in volts

PD Potential difference measured between two

points (eg across a component) if a measure of the energy of electric charge between the two points

Definitions

Current The flow of electric chargeResistance The resistance to currentCapacitorsStore charge in circuit

Simple circuit

The ammeter is in series with components in the circuit

The voltmeter is connected in parallel with the components in the circuit

Current in a series circuit

Current stays the same all the way round a series circuit

voltage in a series circuit

The voltage (pd) across the battery terminals is shared between all the components in the circuit

voltage in a series circuit

Current in a parallel circuit

The total current is shared by the components in a parallel circuit

Resistance

Electron drift

Resistance

The electrical resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor

Temperature coefficient of resistance

αΔT = ΔR/R₀

ΔR = αR₀ΔT

Question

Question A copper wire has a resistance of 400 Ω at

0o C1, Calculate the resistance at 30oC if the

temperature coefficient of copper is 0.0043/oC

superconductors

If mercury is cooled below 4.1 K, it loses all electric resistance

The critical temperature for superconductors is the temperature at which the electrical resistivity of a metal drops to zero. The transition is so sudden and complete that it appears to be a transition to a different phase of matter;. Several materials exhibit superconducting phase transitions at low temperatures.

The thermistors we normallyrefer to are NTC where the resistance increases when thetemperature decreases

PTC thermistor resistorsIncrease resistance with Increasing temperature

In the above test the open circuit The open circuit voltage was measured. The decade box was then set to a maximum and connected as the load. The resistance of the box was reduced so that the voltage across it decreased by 10% each time. From this information the load current and the power in the load was calculated for each voltage.Graphs of load voltage VL against load current IL and power in the load PL against load resistance RL were plotted.

Graph ofVL against IL

VL

VO/C

ILCalculating the gradient of the graph gives us the internal resistance of the source

PL

Graph ofPL against RL

RL

RL = RS

The peak (maximum power) is where the load resistance is equal to the internal resistance of the source

r

R

VL

VI

Using Kirchoff’s second Law The sum of all the PD’s around the circuit is equal to the e.m.f. of the source. If the load resistance is equal to the internal resistance then the PD across each must be the same. Thus VL must be half the e.m.f. of the cell

This means that maximum power is obtained when the load resistance is equal to the internal resistance. As was show in the experiment

The need for Maximum power transfer is when there is a high source impedance and power is scarce. This is contrasted to when power is abundant (i.e. low source impedance)and a constant voltage is available Power is inversely proportional to load resistance.That is the higher the load resistance the lower the power

Basic voltage divider circuit

V out = V in x R2/ R1 +R2

Internal or source resistance is always less thanthe lowest of R1 or R2 When measured in a half voltage test

This system is effectively a variable voltage divider

Capacitors

Capacitors

Capacitors

Capacitance is typified by a parallel plate arrangement and is defined in terms of charge storage:

Capacitors

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field

Capacitors

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in a conductor but only slightly shift from their average equilibrium positions causing dielectric polarization.

Capacitors

Capacitors

In an insulating material, the maximum electric field strength that it can withstand intrinsically without breaking down, i.e., without experiencing failure of its insulating properties. Field strength E = V/d

V = potential across the platesD = distance between the plates

Capacitors

In a test on a 1mm thickness of polymer, it is ruptured by an applied voltage of 20kV.

a) Calculate the dielectric strength of the material

b) Describe what happens in the material when the rupture occurs

c) Explain why a solid insulator with a hairline crack through it breaks down at a lower voltage than the rated voltage

Permittivity

The permittivity of a substance is a characteristic which describes how it affects any electric field set up in it. A high permittivity tends to reduce any electric field present. We can increase the capacitance of a capacitor by increasing the permittivity of the dielectric material.

Permittivity

The permittivity of free space (or a vacuum), e0, has a value of 8.9 × 10-12 F m-1.

The absolute permittivity ε of all other insulating materials is greater than ε0.

The ratio ε / ε0 is called relative permittivity of the material and is denoted by K (or εr).

K = ε / ε0 = Absolute permittivity of medium /

Absolute permittivity of air

Permittivity

Material

Vacuum

Relative permittivity, er

1 (by definition)

Air 1.0005

Polythene 2.35

Perspex 3.3

Mica 7

Water 80

Barium Titanate 1200

Permittivity

Capacitance is increased by the use of a dielectgric

Capacitors

Energy stored in a capacitor

The energy stored in a capacitor can be expressed as

W = 1/2 C V2 (1)

where

W = energy stored (Joules)

C = capacitance (Farad)

V = potential difference (Voltage)

Example question

A 2.0kV power supply unit has an internal 2.6μF capacitor connected across the output.

a) Calculate the charge storedb) Calculate the energy storedc) State how stored charge creates a

hazardd) Describe how the hazard may be

reduced

Variable capacitor

A variable capacitor is a capacitor whose capacitance may be intentionally and repeatedly changed mechanically or electronically

Variable capacitor

Types of variable capacitors

Mechanically controlled In mechanically controlled variable capacitors, the distance between the plates, or the amount of plate surface area which overlaps, can be changed

Variable capacitor

Electronically controlledThe thickness of the depletion layer of a

reverse-biased semiconductor diode varies with the DC voltage applied across the diode. Any diode exhibits this effect (including p/n junctions in transistors)

Their use is limited to low signal amplitudes

Variable capacitor

Transducers

In a capacitor microphone (commonly known as a condenser microphone), the diaphragm acts as one plate of a capacitor, and vibrations produce changes in the distance between the diaphragm and a fixed plate, changing the voltage maintained across the capacitor plates.

An air-spaced variable capacitor has semi-circular plates. Minimum capacitance is 20pF (at 0°)and maximum capacitance is 400pF when the shaft is rotated 180°.

a) Sketch a graph of capacitance against angle of rotation of the shaft

b) Calculate the capacitance when the shaft is rotated 90°

c) Calculate the maximum capacitance if a polymer film of relative permittivity 2.3 is placed inthe airspace between the plates

Capacitors in parallel

CT = C1 + C2 etc

Capacitors in series

1/CT = 1/C1 + 1/C2 + 1/C3 etc

Capacitor Charging

                                                                                                                                                                                                                                                                                                                                                                                                 current

Voltage

V max

Time

C = Q/V Q = CV

Q = CVmax (1 – e-t/RC)

I = (V/R) – e-t/RC

Discharging a Capacitor

RC 2RC 3RC

The Voltage, Current and Charge all follow the same kind of decay curve (exponential)V = Vmaxe-t/RC

Q = CVmaxe-t/RC

I = (Vmax/R)e-t/RCCR (capacitance x resistance) is the time constant. For each period of RC half decay will take place

time

Magnetism

Magnetism

Solenoid

Magnetic field strength equation in a coil H = (NI) / l

where: H = magnetic field strength (ampere per metre) I = current flowing through coil (amperes) N = number of turns in coil l = length of magnetic circuit

Magnetic Flux

The rate of flow of magnetic energy across or through a (real or imaginary) surface. The unit of flux is the Weber (Wb)

Magnetic Flux Density

A measure of the amount of magnetic flux in a unit area perpendicular to the direction of magnetic flow, or the amount of magnetism induced in a substance placed in the magnetic field.

The SI unit of magnetic flux density is the Tesla, (T).

One Tesla, (1T), is equivalent to one weber per square metre (1 Wb/ m2).

Magnetism

The relationship between magnetic field strength and magnetic flux density is:

B = H × µ

where µ is the magnetic permeability of the substance

Magnetism

Permeability Is a measure of how easily a magnetic field can set up in a material It is the ratio of the flux density of the magnetic field within the material to its field strength. µ =B/HPermeabilty of free space µo is 4Pi x10-7 H/m

Magnetism

Relative Permeablity µr

This is how much more permeable the material is compared to free space (a vacuum). The permeability of the material can be calculated by multiplying its relative permeability by the permeability of free space.

µ = µo x µr

Magnetism

The magnetomotive force in an inductor or electromagnet consisting of a coil of wire is given by:

F = NI where N is the number of turns of wire in the coil and I is the current in the wire. The equation for the magnetic flux in a magnetic circuit, sometimes known as Hopkinson's law, is:

F = ΦR

where Φ is the magnetic flux and is the reluctance of the magnetic circuit

Magnetism

The magnetic flux density , B, multiplied by the area swept out by a conductor, A, is called the magnetic flux, Φ.

Φ = BAUnits of flux: weber, Wb.

‘Hard’ and ‘soft’ magnetic materials

Hard magnets, such as steel, are magnetised, but afterwards take a lot of work to de-magnetise. They're good for making permanent magnets, for example.

Soft magnets are the opposite. With an example being iron, they are magnetised, but easily lost their magnetism, be it through vibration or any other means. These are best for things that only need to be magnetised at certain points, eg magnetic fuse/trip switch.

Retentivity – A measure of the residual flux density corresponding to the saturation induction of a magnetic material. In other words, it is a material's ability to retain a certain amount of residual magnetic field when the magnetizing force is removed after achieving saturation

Residual Magnetism or Residual Flux - the magnetic flux density that remains in a material when the magnetizing force is zero.

Coercive Force - The amount of reverse magnetic field which must be applied to a magnetic material to make the magnetic flux return to zero. (The value of H at point c on the hysteresis curve

Magnetism

Starting with the concept of molecular magnets in a magnetic material, explain

a) Relative permeability of a material

b) Loss of magnetisation in a ‘soft’ material

c) Magnetic saturation

Magnetism

a) Relative permeability of a material, molecular magnets align with applied field

b) Loss of magnetisation in a ‘soft’ material, molecular magnets take up random alignment

c) Magnetic saturation, molecular magnets all aligned in field direction

Right hand rule

Moving a conductor through a magnetic field can induce an emf. The faster the conductor moves through the field the greater the emf and hence the greater the current

N S

N S

Inducing a current in a coil

Pushing a magnet into a coil induces a current in the coil wire

Pulling the magnet out of the coil induces a current in the opposite direction

Inductors

If an Alternating Current is passed through the coil an alternating magnetic field is produced which in turn produces a back emf given by the equation E = -l dI/dtIn a purely inductive circuit the applied pd leads the current by 90o

An inductor which has zero resistance is called pure Inductance

This type of device is called and Inductor

Inductance of a Solenoid

This means that the inductance L of a solenoid is directly proportional to the

number of turns squared and the area.

It is inversely proportional to the length of the solenoid

It is also directly proportional to μo and μr

permiability of free space and relative permiability

An air-cored coil has 200 turns and an inductance of 1.5mH.

a) If the number of turns is increased to 400 calculate the new value of inductance

b) Calculate the value of inductance if the 200 turn coil is mounted on a toroidal ferrite core

of μr=270

c) Describe the effect on inductance of an air gap in the core

Inductors

a) L proportional to N2 L = 1.5 x (400/200)2 mH = 6.0 mH

b) L proportional to μr L = 1.5 x 270 mH = 405 mH

c) An air gap would reduce inductance depending on width.

Inductors

Energy stored in an inductor

Inductors

A relay coil has inductance of 1.2H, resistance of 400Ω and operates on 24V dc.

a) Calculate the coil current when the relay is closed

b) Calculate the energy stored in the coil when it is operated

c) Describe what happens to the energy stored when the coil current is switched off

d) State one method for suppressing the effect in b)

a) Operating current = V/R = 24/400 A = 60 mA

b) Energy stored = ½ LI2 = ½ x 1.3 x 0.0602 = 2.34 mJ

c)Back emf developed

d) Parallel diode

coil

Centre limb 50x40mm

Side limb 25 x 4 0mm

A low frequency inductor, the winding has 2000 turns and the length of magnetic circuit through the centre limb and side limb is 300mm. A current of 400mA creates a total flux in the centre limb of 0.92mWb DetermineA, The MmfB, Flux in the side limbC, Flux density in the centre limbD, The magnetic field strength H

A) Mmf = NI = 0.4 x 2000 Amp-Turns= 800 A-T

B) Flux in side limbs Flux = flux density x area so flux in side limbs is half that in the centre limb 0.92/2 mWb = 0.46 mWb = 460 μWb

C) Flux density in centre limb = Ф/A = 0.92 x 10-3 / 40 x 30 x 10-6 Wb/m2 = 0.77 Wb/m2 or Tesla

D) Magnetic field strength H = NI/length = 800/ 0.3 A-T/m = 2667 A-T/m

AC Theory

AC Theory

Peak value

Peak value

Peak to peakvalue

Currentor voltage

Time

Time period T

Frequency (f) = 1/T

Rotational vector representation

ωt

90o

180o

270o

360o

ωt = angle ( radians)

ω/t = angular velocity

Consider arrow rotating anticlockwise

AC Theory

Resultant waveform

V1

V2

Angular difference between V1 and V2 =40o

40o

V2 lags V1 by 40o

AC Theory

V1

V2

40o

Phasor diagram representing two alternating voltages V1 and V2. V2 lags V1 by 40o

AC Theory

V1

V2

Resultant voltage VR

Phasor of added voltages

AC Theory

When an AC circuit is purely resistive the current and voltage are in phase

R = V/I

AC Theory

V/IVoltage

Current

R

V

IV

Waveform and phase diagram for a purely resistive circuit. Voltage and current are in phase

t

AC Theory

In a purely capacitive circuit the current leads the voltage by 90o the opposition to the flow of alternating current is called the capacitive reactance Xc

Xc = V/I

AC Theory

currentvoltage

V/I

V

C

t

Waveform and phase diagram for a purely capacitive circuit. current leads voltage by 90o

I

V

AC Theory

In a purely inductive circuit the voltage leads the current by 90o. The opposition to the flow of alternating current is called inductive reactance

XL

XL = V/I

AC Theory

voltage

current

V/I

V

L

Waveform and phase diagram for a purely inductive circuit. Voltage leads current by 90o

t

I

V

Measures of AC

Value Description

Peak Maximum value in positive or negative half cycle

Peak to peak Difference between positive and negative peak

Root mean square (r.m.s.)

The value of direct current which would provide the same heating effect as the AC current. For a sine wave the value = 0.707 x maximum value

Average The average of the instantaneous measurement in one half cycle. For a sine wave the average value is 0.637 x maximum value

Instantaneous The value of the voltage or current at a particular time instant. If measured at the instant that the cycle polarity is changing the this value would be zero

Form factor This is the r.m.s. divided by the average value. For a sine wave the form factor is 1.11

Peak factor This is the maximum value divided by the r.m.s. value. For a sine wave the peak value is 1.41

Impedance (Z)

Electrical impedance is the measure of the opposition that a circuit presents to the passage of ac current

Z= V/I Total Reactance = XL – XC

Z = R + (XL – XC)

I rms = Vrms / + (XL – XC)2

Irms would be at a maximum when XL = XC

Fundamental frequency

XL = 2πfoL and XC = 1/2πfoC

fo = fundamental frequency

fo = 1

2πLC

Fundamental frequency

Irms

ffo

Low RHigh Q

High RLow Q

Q = quality factor

Fundamental frequency

V

VC

VL

VR (=V)

Conditions for resonance

LCR Circuits

The resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are 180 degrees apart in phase. The sharp minimum in impedance which occurs is useful in tuning applications. The sharpness of the minimum depends on the value of R and is characterized by the "Q" of the circuit

LCR Circuits

Phasor Diagram for a Series RLC Circuit

In a parallel (tank) LC circuit, this means infinite impedance at resonance as opposed to the series LC circuit, which has zero impedance at resonance:

Phasor Diagram for a Parallel RLC Circuit

ω = angular velocity in radians /sec

a radian is arc length / radius

A full circle is 2π radians

An angle can be referred to as ω t (ω x t)

1 revolution = 2π radians

360o = 2π radiansω = 2π/T (T = time period)

ω = 2πf (f = frequency)

Q = 2πfoL/R

LCR Series Resonsnce circuit

IVin

VL

VC

At resonance Vc lags Vin by 90o

At resonance VL leads Vin by 90o

At resonance Inductive reactance = Capacitive reactance XL = XC and would cancel each other out therefore impedance, Z is at a minimum and IRMS is at a maximum

Because the resistor, capacitor and inductor are in series, the cancelling out of the reactance leaves a minimum resistance in the circuit

Q factor means Quality or goodness

factorvoltage

magnification factor or sharpness of

tuning

LCR Parallel Resonance Circuit

LCR Parallel Resonance Circuit

Because the resistor, capacitor and inductor are in parallel, the cancelling out of the

reactance leaves a maximum resistance in the circuit

In a parallel resonance circuit the voltage output VP is in phase at resonance, Below

resonance VP leads Vin showing the reactance is Inductive (VL leads Vin )

Above resonance VP lags Vin showing that the reactance is Capacitive (VC lags Vin )

LCR Parallel Resonance Circuit

When the input is a square wave the tuned circuit acts as a bandpass filter selecting the fundamental frequency and filtering out harmonics

Radio Tuner

Frequency filters

Low pass filterBy definition, a low-pass filter is a circuit offering easy passage to low-frequency

signals and difficult passage to high-frequency signals.

High pass filterA High pass filter does the opposite

Low pass filter

Low pass filter

capacitive low-pass filter (one resistor, one capacitor),

the cut off frequency is given as:                                      fcut off = 1/2

Frequencies below the cut off frequency are allowed to pass

Low pass filter

For a half power cut off point, power out/ power in = 0.5

(Vout/ Vin for same current)

Log10 0.5 = -0.3 decibels (dB)

Half power = -0.3 decibels

Low Pass Filter frequency response plot

High pass filter

High pass filter

fcut off = 1/2

Capacitive high pass filter (one resistor, one capacitor),

the cutoff frequency is given as:

Frequencies above the cut off frequency are allowed to pass

High Pass Filter frequency response plot

.