Electromagnetics Flashcards
electrostatic field
- results from static electric charge
- fields and forces determined by spatial relationships between charges
- relationships analyzed by vector analysis
net electric field
- superposition sum of all electric fields due to all sources
Coulomb Force Equation
- The force on a point charge, Q2 due to the electric field of another point charge. Q1
F2 = Q1 Q2 / (4 π ε ) ar 12
ar12 : a unit vector directed from point 1 to point 2
general force equation
The force on a test charge particle is
F= QE
E is the electric field exerting the force on the particle
the electric field exerting force may be
- point charge
- distributed charge field (sphere, line, sheet)
- sum of fields due to multiple sources
If medium is linear, net electric field is vector sum of fields due to all sources.
If field acts on distributed charge, force is integral of force over charge distribution
magnetic field strength, H
- measure of strength of magnetic field in free space
- independent of medium
- units are amperes per meter (A/m)
magnetic flux density, B
- includes magnetic response of material that field passes through
- dependent on medium
- units are teslas (T)
- in strongly magnetic material, B-field is greater than in free space
permeability, μ
- units are henrys per meter (H/m)
μ = μn μo
μr: relative permeability
μr approximately equals 1 –> unless currents can circulate in the material, in which case material is magnetic
μo is permeability of free space = 4 π x 10^-7 H/m
magnetic field lines
- imaginary lines drawn so that the direction of a line at any point is the direction of B at that point
- never terminate – each line eventually joins back on itself to form a loop
If an imaginary tube is bounded by B lines and end surfaces S1 and S2, the magnetic flux through S1 and S2 is the same
static magnetic field
- can change the direction of an electron
- does not perform work on the electron
changing magnetic field
- can perform work
- can induce voltage in a conductor, this causes electrons to move
static magnetic field
- can change the direction of an electron
- does not perform work on the electron
magnetic flux
analogous to electric flux
unit is the weber (Wb) Φ
magnetic poles
- exists only in pairs, called magnetic dipoles
- poles in pair have equal and opposite strength
- by convention, magnetic flux runs from north pole and south pole
ferromagnetic materials
examples: iron, nickel, cobalt
- divided into small “magnetic domains” (–> region with a magnetic material in which magnetization is in a uniform direction)
- within each domain, spin of atoms is aligned
- if material is unmagnetized, domains not aligned (no net magnetization)
- if placed in strong enough magnetic field, domains align (become magnetized)
hysteresis
- when magnetic field is applied to material, atoms migrate to domains that align with field, increasing magnetization of material
- if field is weak, process will reverse when field is removed (material returns to no net magnetization)
- if field is strong enough, magnetization persists when field is removed
- material become permanent magnet, retains magnetization until demagnetized by heat or magnetic field in opposite direction
magnetic field strength for an infinite wire
H = B/μ = IaΦ/ 2πr
- Magnetic field lines are circles around wire
For any point,
r is distance from center of wire to point
unit vector aΦ is cylindrical coordinate tangent to circle that intersects point
magnetic moment
fundamental concept behind rotating machines
- magnetic fields exert force on current in loop of wire
- forces in opposite sides of loop are in opposite directions
- results in a moment about the loop and a torque
del operator
- vector differential operator
- performs differentiation in three dimensions
- can be represented in polar, cylindrical, and other coordinates systems
- when applied to a scalar, the result is the gradient and it is the slope of the function in three dimensions
divergence
- dot product of the del operator with a vector
- results in a scalar quantity
- may be visualized as the flow out of or into a point in space
curl
- cross product of the del operator with a vector
- results in a vector quantity
- may be visualized as the “swirling” motion about a point in space in three dimensions
Maxwell’s equations
- show the electricity and magnetism aren’t different but are two aspects of the same thing
- a changing electric field induces a magnetic field
- a changing magnetic field induces an electric field
- electric field and magnetic field are perpendicular to each other
Gauss’s Law
The total electric flux passing out of an enclosing surface (the Gaussian surface, S) is proportional to the total charge within the surface
Lorentz force equation
- gives force on particle moving at velocity, v when both electric and magnetic fields are present
F= Q(E+v x B)
-electric and magnetic forces act independently on particle
propagation velocity, U, of electromagnetic wave
- depends on medium
- changes when passing into new medium (U and λ, f remains the same)
- in vacuum, equals speed of light, c
- can never be greater than c (and can be much less in some media)
electromagnetic compatibility (EMC)
- when a system functions properly in its intended electromagnetic environment and does not interfere with the proper operation of other systems
electromagnetic interference (EMI)
when effects interfere with proper operation, including
- radiated emissions
- conductive coupling
- capacitive coupling
- inductive/magnetic coupling
conducted noise
can be same or different on conductors
- -> When in phase on two conductors, coupling is called common-mode coupling or common-impedance coupling
- -> When out of phase on two conductors coupling is called differential mode coupling
capacitive coupling
- Any conductor in any circuit can serve as a capacitor
- When circuit is exposed to a varying electric field, a change in voltage will be induced which can cause current.
- Capacitors and similar components are very efficient at capacitive coupling
- Wires, resistors, and similar components are very inefficient at capacitive coupling
- Distance and orientation between source and victim circuit make a big difference in efficiency of coupling
inductive coupling (magnetic coupling)
- Any conductor in any circuit can serve as an inductor
- When circuit is exposed to a varying magnetic field, a change in current will be induced
- Inductors, transformers and similar components are very efficient at inductive coupling
- Wires, resistors, and similar components are very inefficient at inductive coupling
- Distance and orientation between source and victim circuit make a big difference in efficiency of coupling
electromagnetic compatibility (EMC) control
the practice of designing to
- mitigate damaging effects of electromagnetic interference
- reduce risks to acceptable levels
control process involves
- characterizing the threat
- setting standards for emission and susceptibility levels
- designing for compliance with standards
- testing for compliance with standards
EMC Control Plan
- may be required for complex or unusual piece of equipment
- summarizes how control process is to be applied
- specifies additional documents required
characterizing the threat
- usually based on statistical estimates using standardized disruptive electromagnetic interference (EMI) risk models
- estimates the probability of EMC but does not ensure EMC
- requires understanding of
- -> estimate of interference environment
- -> estimate of coupling path to victim
- -> vulnerability of victim to EMI environment
- -> significance of possible malfunction
setting standards for emission and susceptibility levels
- EMC standards are agreed to and published by several international organizations
- Where possible, other organizations adopt these standards with little to no change
- Engineers must comply with national or international standards for EMC design
- Some are required – engineers must comply by law
- Others are guidelines that giving helpful design criteria
designing for compliance with standards
- EMC design practice applies to both potential sources and to potential victims by breaking a coupling path
- Any circuit that is a source of electromagnetic energy coupling is also a potential victim
EMC design methods
- shielding and grounding
- emission suppression
- susceptibility hardening
- other general methods
EMC design methods often reduce both emissions and susceptibility
shielding and grounding
protect potential victim by
- reducing emissions
- diverting EMI away from victim by providing alternative, low-impedance path
Both shielding and grounding are used in most systems
techniques include:
- shielded housings
- shielded cables
- grounding schemes
shielded housings
- conductive enclosures around circuits that divert emissions to ground
- must allow access to components, so access may have radio frequency (RF) gasket to reduce interference leaking through joint
shielded cables
conductive wires surrounded by outer conductive layer that is grounded at one or both ends
grounding schemes
- design to specific to system
- an integrated circuit card assembly often includes a ground plane (flat area of copper foil connected to a ground point) to reduce interference
emission suppression
reducing source emissions
- Avoid unnecessary switching operations
- Make necessary switching as slow as technically possible to reduce transients
- Use spread spectrum method to avoid high peaks in spectral frequency
- Separate noisy circuits (those with a lot of switching activity) physically from rest of design, possibly with shielding in between
- Filter for harmonic frequencies
- Reduce energy available for emission by designing for operation at lower signal levels
susceptibility hardening
reducing susceptibility of circuits to EMI
- Uses fuses, trip switches, circuit breakers, or other methods of automatically disconnecting the circuit when a high-power EMI event occurs
- Use transient absorbers, which absorb part of the energy of large transients created by a large EMI event
- Design for operation at higher power with a higher signal level in order to reduce noise level in comparison
-decoupling (filtering)
–> RF chokes (type of inductor)
and/or RC elements used at critical points such as cable entries and high-speed switches
–> implemented between device and line with a line filter
- transmission line techniques for cable and wiring, such as
- -> balanced differential signal and return paths
- -> impedance matching
- avoiding circuits or mechanical structures that will act as antennas, such as
- -> loops of circulating current
- -> resonant mechanical structures
- -> unbalanced cable impedances
- -> poorly grounded shielding
testing for compliance with standards
- Radiated emissions are typically measured for radiated field strength, especially in systems intended to radiate.
- conducted emissions along cables and wiring may be measured where appropriate
- Inductive (magnetic) and capacitive (electric) field strengths are measured only if the device under test (DUT) is designed for a location near other electrical equipment
- Emissione levels of the DUT are typically measured across a wide band of frequencies (frequency domain) using a spectrum analyzer
characteristic impedance, Zo
the impedance of the transmission line with infinite length
- ratio of electrical to magnetic energy needed for wave to propagate in transmission line; depends on impedance of line
- for ideal line (no loss) Zo is real number (no imaginary component)
- for lossy line, Zo is complex
