Flashcards
UA ECE 340 Electromagnetics Final Exam Concepts
Cards in this deck (35)
- 1Define a time domain traveling wave equation and directional conventionsy(x, t) = (A cos2πt/T − 2π x/λ + φ0)
y(x, t) = A cos(ωt − βx) - 2define the phase velocity formulaup = f λ
up = ω/β - 3define angular velocity and phase constant equationsω = 2πf
β = 2π/λ - 4define wave magnitude in lossy mediaA -> Ae−αx
- 5define the threshold for considering transmission line effectsl/λ < .01 -> Transmission effects may be ignored
- 6Define the propagation constant w.r.t. transmission linesγ = (R + jωL)(G + jωC) .
- 7define the attenuation constant and phase constant w.r.t. the propagation constantα = Re(γ )
β = Im(γ ) - 8define the characteristic impedance of a transmission lineZ0 = (R + jωL)/γ = sqrt[(R + jωL)/(G + jωC)]
- 9define lossless case considerationsR = G = 0 (evaluate γ to get below values)
α = 0
β =ω*sqrt(e_r)/c
up = c/sqrt(e_r) - 10Define dispersionA dispersive transmission line is one on which the wave
velocity is not constant as a function of the frequency f. Signals distort due to different frequency components traveling at different velocities - 11Define the Voltage Reflection CoefficientGamma = V0-/V0+
=-(I0-/I0+)
= (ZL − Z0)/(ZL + Z0) - 12Define Voltage Reflection Matched CaseZL = Z0, Gamma = 0 regardless of phase angle
- 13Define Voltage Reflection short and open cases|Gamma| = 1
Short: theta = +- 180
Open: theta = 0 - 14Define SWRS = |V|max/|V|min
= 1 + |Gamma |1 − |Gamma| - 15Smith Chart Circumference w.r.t wavlength2πr = .5 λ
- 16Smith Chart Vmax/min locationsVmax -> (.25λ) | <- Vmin (0λ)
<-Imax (0λ)| Imin-> (.25λ) - 17SWR LoadNormalize ZL/Z0
Find intersection between RL and XL - 18SWR Input ImpedanceGet SWR Load, move by λ to new point
denormalize Zin*Z0 - 19SWR AdmittanceGet SWR Input Impedance, go 180 degrees (.25λ)
new 'RL' is GL, and new 'XL' = YL
Denormalize - 20Define the Dot ProductScalar function returning overlap between a and b
A * B = ABcos(theta) - 21Define the Cross ProductVector function returning orthogonal equation
AxB = ˆnABsin(theta) - 22Mathematically Define Divergencediv E = ∂Ex/∂x + ∂Ey/∂y + ∂Ez/∂z
Dell * E - 23Define Divergence Conventions+div-> outward net flux (source)
-div ->inward net flux (sink) - 24Define the Divergence TheoremThe volume integral of the divergence of a filed field is equivalent to the surface of closed differential dot product of that same vector.
3d div integral - 2d closed dot integral
(link to Stoke's) - 25Mathematically define CurlCross product equation (usually given on formula sheets)
- 26Define Curl Conventions+ curl -> right hand rule convention prevails
- curl -> negate right hand orthogonal convention
Curl defines the amount of circulation perpendicular to two given vectors. - 27Stoke's TheoremThe surface integral of the curl of a vector is equivalent to the line integral of differential dot product of that same vector.
2d curl integral = 1d dot integral
Link to Divergence theorem - 28Define Gauss's Law for electric fields∇ ·D = ρv
divergence of the electric flux density is equal to the enclosed charge density - 29Define Faraday's Law∇ × E = −∂B/∂t
The curl of the electric field is equivalent to the opposing change in magnetic field. - 30Define Gauss's Law for magnetism∇ ·B = 0
The divergence of the magnetic field is always 0.
No magnetic monopoles exist, the thus, magnetic flux is always 0. - 31Define Ampere's Law∇ × H = J + ∂D/∂t.
The curl of the magnetic flux density is equivalent to the current density plus a change in electric flux density.
Rotating around a magnetic coil generates current. - 32Define Coulomb's LawE = ˆR*q/(4πR^2)
ˆR the unit vector pointing q->P
R the distance between them
e is permittivity - 33Prove the integral form of Gauss's Law for e field. (∇ ·D = ρv)Integrate both sides, apply divergence theorem to get
surface integral of D· ds = Q. - 34Define the relationship between V and eV21 = the definite integral from P1 to P2 of E*dl
E = −∇V. - 35Prove KVL from Maxwell'selectrostatic Faraday's
then use stokes 2d curl to 1d closed line.
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- Final Exam review of conceptual topics covered in ECE 340 at UofA
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- wyatt reid
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