UA ECE 340 Electromagnetics Final Exam Concepts

wyatt reid
Flashcards by wyatt reid, updated 8 months ago More Less
wyatt reid
Created by wyatt reid 8 months ago
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Final Exam review of conceptual topics covered in ECE 340 at UofA

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Question Answer
Define a time domain traveling wave equation and directional conventions y(x, t) = (A cos2πt/T − 2π x/λ + φ0) y(x, t) = A cos(ωt − βx)
define the phase velocity formula up = f λ up = ω/β
define angular velocity and phase constant equations ω = 2πf β = 2π/λ
define wave magnitude in lossy media A -> Ae−αx
define the threshold for considering transmission line effects l/λ < .01 -> Transmission effects may be ignored
Define the propagation constant w.r.t. transmission lines γ = (R + jωL)(G + jωC) .
define the attenuation constant and phase constant w.r.t. the propagation constant α = Re(γ ) β = Im(γ )
define the characteristic impedance of a transmission line Z0 = (R + jωL)/γ = sqrt[(R + jωL)/(G + jωC)]
define lossless case considerations R = G = 0 (evaluate γ to get below values) α = 0 β =ω*sqrt(e_r)/c up = c/sqrt(e_r)
Define dispersion A 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
Define the Voltage Reflection Coefficient Gamma = V0-/V0+ =-(I0-/I0+) = (ZL − Z0)/(ZL + Z0)
Define Voltage Reflection Matched Case ZL = Z0, Gamma = 0 regardless of phase angle
Define Voltage Reflection short and open cases |Gamma| = 1 Short: theta = +- 180 Open: theta = 0
Define SWR S = |V|max/|V|min = 1 + |Gamma |1 − |Gamma|
Smith Chart Circumference w.r.t wavlength 2πr = .5 λ
Smith Chart Vmax/min locations Vmax -> (.25λ) | <- Vmin (0λ) <-Imax (0λ)| Imin-> (.25λ)
SWR Load Normalize ZL/Z0 Find intersection between RL and XL
SWR Input Impedance Get SWR Load, move by λ to new point denormalize Zin*Z0
SWR Admittance Get SWR Input Impedance, go 180 degrees (.25λ) new 'RL' is GL, and new 'XL' = YL Denormalize
Define the Dot Product Scalar function returning overlap between a and b A * B = ABcos(theta)
Define the Cross Product Vector function returning orthogonal equation AxB = ˆnABsin(theta)
Mathematically Define Divergence div E = ∂Ex/∂x + ∂Ey/∂y + ∂Ez/∂z Dell * E
Define Divergence Conventions +div-> outward net flux (source) -div ->inward net flux (sink)
Define the Divergence Theorem The 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)
Mathematically define Curl Cross product equation (usually given on formula sheets)
Define 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.
Stoke's Theorem The 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
Define Gauss's Law for electric fields ∇ ·D = ρv divergence of the electric flux density is equal to the enclosed charge density
Define Faraday's Law ∇ × E = −∂B/∂t The curl of the electric field is equivalent to the opposing change in magnetic field.
Define 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.
Define 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.
Define Coulomb's Law E = ˆR*q/(4πR^2) ˆR the unit vector pointing q->P R the distance between them e is permittivity
Prove 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.
Define the relationship between V and e V21 = the definite integral from P1 to P2 of E*dl E = −∇V.
Prove KVL from Maxwell's electrostatic Faraday's then use stokes 2d curl to 1d closed line.
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