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17901885

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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