Lodestone Wireless has worked on an Electromagnetic technical writing project. Topics Covered:
1.1) Electrostatics & Magnetostatics
The study of stationary electric charges, stationary magnetic dipoles, and the study of moving electric charges without acceleration otherwise known as steady currents. It is also the study of their corresponding stationary electric & magnetic fields.
Traditional engineering and science texts sadly never explain the connection between electrostatic theory and the practical real world situation of steady currents in circuits. This is done by explaining in detail how current moves through a wire.
Electric Charges, Coulombs Law and the concept of Electric Fields are introduced. Also, analysis of how electric field strength varies with distance from a point charge, and from a dipole.
Because no magnetic charge exists, we have to start our analysis of magnetostatics further into the conceptual and abstract stage than we did with electrostatics. The concept of the Magnetic Field (more correctly known as the B-Field) is introduced.
2.1) GAUSS'S LAW FOR ELECTRIC FIELDS - MAXWELL'S 1st EQUATION
Gauss's Law for Electric Fields is introduced early on as it is needed to prove three important properties of electrostatics:
1) Charge is found only on the surface of a charged conductor, not in the interior.
2) The electric field inside a charged conductor in static equilibrium is zero.
3) The field of a uniformly charged hollow sphere is zero inside but appears point like from the outside.
Which leads to 4)
4) Hollow sphere with a test charge inside creates an internal electric field, there is no electric field inside the conductor material, charge will appear on the inner surface, and charge on the outer surface will distribute itself independently of the position of the test charge.
This leads to the idea of electrostatic shielding:
5) Electrostatic Shielding from an internal electric field.
6) Electrostatic Shielding from an external electric field.
7) Electrostatic Shielding from a charged cage.
Gauss's Law for Electric Fields introduces the concept of Electric Flux.
In essence it states that electric monopoles exist, and these electric monopoles (aka electric charges) "generate" electric fields which consequently results in an electric flux.
Gauss's Law for Electric Fields is an equation which is very convenient for finding the electric fields around an object which has a symmetrical charge distribution.
As an example, it's shown, how using Gauss's Law for Electric Fields we can find interesting facts about Electric Fields (Magnitude and Vector Direction) inside and around the following:
- Conducting Hollow Sphere with a Charge (Gauss's Law shows that there is no Electric Field inside the sphere - Faraday Cage)
- Conducting Solid Sphere with a Charge.
- Uniformly Charged Plane of Infinite Size (Gauss's Law shows the Electric Fields only exist perpendicular to the plate).
- Two charged plates (Gauss's Law shows there are no electric fields outside the plates, and between the field is very intense).
2.1.2) Gauss Surface
Explanation of the Gauss Shape and its Gauss Surface and how they are used to solve for the Electric Field.
1.1.1) Polarisation (aka Induction)
This idea is very important in circuit analysis. Polarisation of wires and components is what creates the surface charge gradients which in turn create the electric fields which drive current around the circuit.
The following are introduced:
- Definition of polarisation.
- Induced Dipole
- Permanent Dipole
- Polarised Insulator
- Polarised Conductor
- Equilibrium in a conductor.
- Steady State Current in a conductor.
1.1.2) Charged Conductor
A metal structure can be both charged and polarised simultaneously. The effects can be superimposed on each other linearly. A fixed net charge on a circuit has no effect on the circuit and the circuit will perform just as if there was no net fixed charge.
1.1.4) Electric Field and Surface Charge Feedback in a Circuit with Steady State Current
The electric fields in a section of wire in your circuit are constantly adapting at close to the speed of light to equalise the current into and out of the section. This is because of a feedback mechanism which is an interplay between the surface charge on the wire (which are arranging themselves automatically) and the electric field in the wire.
This feedback mechanism also forces the current to follow the wire if you start to bend or twist it.
1.1.5) Electric Field and Surface Charge Feedback in an Isolated Metal Block
Feedback also occurs when you apply Electric Fields to an isolated metal block. Surface charges arrange themselves so that the electric field in the metal is zero.
1.1.6) Electrostatic Shielding
- Effect of electric field on a metal sheet not earthed.
- Effect of electric field on a metal sheet that is earthed
1.1.6.1) The Faraday Cage
The Faraday Cage is made of metal gauze or is a metal box, that is enclosed on all sides. It can be of any shape (sphere, boxed etc..) but it must be enclosed on all sides:
1.1.6.1.2) The Faraday Cage - Not Earthed
- Effect of external electric field source on contents of a screened cage.
- Effect of internal electric field source on devices external to a screened box.
1.1.6.1.3) The Faraday Cage - Earthed
- Effect of external electric field source on contents of a screened cage.
- Effect of internal electric field source on devices external to a screened box.
1.1.6.1.4) The Faraday Cage - Grounded
- Explanation of how shielding works in circuits that have no earth.
1.1.6.1.5) The Faraday Cage and Electromagnetic Waves
The Faraday Cage will also shield against Electromagnetic Waves but the mechanism is different as the waves are being reflected off the surface. This can be proved using Maxwell's equations and applying boundary conditions.
1.1.7) Electromotive Force (EMF) and Potential Difference (v)
Introduced are: Electrostatic Potential Energy (U), Electric Potential (V), Equipotential Surfaces, Electric Potential Difference (v) and Electromotive Force (EMF)
Electromotive Force and Potential Difference are the only two types of voltage required for a circuit analysis. There is also Electric Potential which is absolute, but circuits function in a relativistic way.
Voltage is not fundamental unit, but a product of two units: Joules per Coulomb. So why is voltage such a useful concept in circuit analysis ? The EMF (measured in voltage) from a battery or dynamo has the handy property of remaining approximately constant when under different current loads. This makes calculations on a circuit extremely convenient.
1.1.8) Electric Fields in Wires
This section discusses in detail why and how a current moves through a wire.
You might be surprised to learn that electrons are not pushed through a wire by the battery, as visualised using the classic water model.
In classic electronics, a water model is used. The battery is viewed as a water pump, and the wires and circuits are viewed as connecting pipes. The water represents the electric current which is pushed through the system by the water pump. Although the classic water model is extremely useful it is not an accurate description of the how the current moves through the wire. It is a common misconception that electrons are pushed into the connecting wires to the battery, and these electrons then push onto other electrons creating a current.
The truth is that electrons within a wire are not pushing onto other electrons creating the current.
To understand the true mechanism for current transportation in the circuit requires rethinking the role of the battery, examining charge distribution within the wire and on the surface of the wire, and the electric fields generated as the result of the charge distribution.
The discussion leads to the following conclusions:
Fact 1: Electric Fields are internal to the wire are parallel to the wire, no matter how bendy it is.
Fact 2: Electric Charges creating the internal electric field cannot be inside the conductor.
Fact 3: Charges can only reside on the boundary surfaces of two different conductors, or of a conductor and an insulator. The topic of charges residing on the boundary surfaces of two different conductors is of great interest in understanding semiconductor device operation.
Fact 4: The job of the battery is to maintain the distribution of free charges along the surface of the wire.
Fact 5: The gradient of the surface charge along the wire distributes itself automatically to create the internal electric field.
1.1.9) Quasi-Static Analysis
Quasi-Static analysis is the term used when an electrostatic analysis is done on a time varying circuit problem. This is extremely common in electronic engineering.
Nearly all real world electric charges, magnetic dipoles, electric fields and magnetic fields vary to some extent with time, but for many problems an electrostatic analysis gives accurate results. This is true when:
i) Time variation is slow so the fields may be considered stationary.
ii) When the elements are small compared to the wavelength.
iii) Transmission Lines
It must be remembered when using a quasi-static analysis that time varying fields may give rise to other phenomena, primarily a travelling electromagnetic wave. However, the underlying principles & effects demonstrated in the static condition are seen in time varying scenarios. The static analysis is easy to analyse and visualise and intuitively extend to time varying problems.
1.2) Electrodynamics
The study of time varying electric charges and time varying magnetic dipoles, and the study of time varying electric and magnetic fields.
2) MAXWELL'S FOUR EQUATIONS
2.1) GAUSS'S LAW FOR ELECTRIC FIELDS
This was described earlier.
2.2) GAUSS'S LAW FOR MAGNETIC FIELDS
Gauss's Law for Magnetic Fields introduces the concept of Magnetic Flux.
In essence, it states that magnetic monopoles (aka magnetic charges) do not exist, only magnetic dipoles, and these magnetic dipoles generate magnetic fields which consequently result in a magnetic flux, and on any closed surface as much magnetic flux flows in as out.
For calculating the Magnetic Field (B-Field), it is not at all useful in the same way as Gauss's Law for Electric Fields is. The Biot-Savart Law is much more helpful in finding the Magnetic Field around an object.
2.3) FARADAYS LAW OF INDUCTION
Introduction to concept of electromagnetic induction where a changing magnetic field causes a current in a wire. A profound discovery which has dramatically changed our society.
In essence, it states a changing electric field circulates arounds a changing magnetic field.
Specifically, Faradays Law allows us to find the Electric Field in a wire due to a changing Magnetic Flux.
2.4) AMPERES LAW plus Maxwell's Displacement Current
The Capacitor Paradox focussed Maxwell's mind on this equation. When the current is changing, the magnetic field around the capacitor plates is the same as the magnetic field around the wires feeding it even though no current is flowing between the plates. However, there is a changing electric field between the plates. Maxwell reasoned therefore that a changing Electric Flux might give rise to a Magnetic Field.
In essence, it states a magnetic field circulates around a current and/or a changing electric field.
2.4.1) Prediction of Electromagnetic Waves
Together, Amperes Law plus Maxwell's Displacement Current and Faradays Law of Induction predict the existence of electromagnetic waves. A changing electric field produces a changing magnetic field, and a changing magnetic field produces a changing electric field and so on.... an interaction that constitutes a propagating electromagnetic wave.
5) OSCILLATIONS AND WAVES
The following are introduced:
- The Wave Equation
- Travelling Waves
- Standing Waves.
- Resonance
- Boundary and Boundary Conditions (Open and Closed)
- Modes in 1D, 2D and 3D structures.
6) ELECTROMAGNETIC WAVE INCIDENT ON A REFLECTIVE SURFACE
- Electromagnetic Waves incident upon a perfect conductor.
Boundary conditions are applied to Maxwells equations to examine what is happening on surface of conductor.
- Standing Wave of an EM Wave.
7) TRANSMISSION LINES
Transmission Lines transfer power from one location to another.
TWO CONDUCTOR TRANSMISSION LINES
- Twin Lead
- Coaxial
- Microstrip
SINGLE CONDUCTOR TRANSMISSION LINES
- Waveguides
8) RESONANT CAVITIES
9) ANTENNA THEORY
An antenna is a passive device which launches electromagnetic waves into the atmosphere. Maxwell said that an accelerating charge (i.e. oscillating current) produces an electromagnetic wave. Therefore it is the current in the antenna which produces the electromagnetic wave.
- Near Fields
Near Fields are electric and magnetic fields that are detected close to the antenna. These are not radiated Electromagnetic Waves but the Quasi-Static Electric and Magnetic Fields. The near fields are not the source of the transmission of the electromagnetic waves but simply store electric and magnetic energy. These near fields determine the input reactance at the terminals of the antenna and are therefore mostly of interest for determining the input impedance of the antenna.
- Input Impedance
The ratio of the voltage to the current at the antenna input is the input impedance of the antenna.
- Radiation Efficiency of Antenna
For many antennas radiation efficiency is nearly 100% if the antenna is comparable to a wavelength in size. For electrically small antennas however, radiation efficiency can be extremely small.
- Efficiency of Matching Circuit Feeding Antenna
The matching circuit between the feeding transmission line and the antenna input terminals will create losses. And although matching in theory can improve the efficiency of power transferred into the antenna, there can be significant losses in the matching circuit, sometimes the losses can be greater than the theoretical improvement in efficiency.