Podcast
Questions and Answers
What type of fallacy occurs when a series of increasingly superficial and unacceptable consequences is drawn from an initial premise?
What type of fallacy occurs when a series of increasingly superficial and unacceptable consequences is drawn from an initial premise?
Slippery Slope
"If we ban computer shops, then students will not be able to do research. And if they do not have tools for research, these students will fail their subjects." This is an example of which fallacy?
"If we ban computer shops, then students will not be able to do research. And if they do not have tools for research, these students will fail their subjects." This is an example of which fallacy?
- Complex Question
- Slippery Slope (correct)
- Appeal to Pity
- Appeal to Force
Which fallacy involves asking a question that contains a controversial or unjustified assumption (e.g., a presumption of guilt)?
Which fallacy involves asking a question that contains a controversial or unjustified assumption (e.g., a presumption of guilt)?
Complex Question
What type of fallacy is demonstrated by the question "Have you stopped cheating on exams?"
What type of fallacy is demonstrated by the question "Have you stopped cheating on exams?"
What fallacy is committed when force, coercion, or a threat of force is used in place of a reason in an attempt to justify a conclusion?
What fallacy is committed when force, coercion, or a threat of force is used in place of a reason in an attempt to justify a conclusion?
"If you do not admit that evolution is not real, we will isolate you from the group." This statement exemplifies which fallacy?
"If you do not admit that evolution is not real, we will isolate you from the group." This statement exemplifies which fallacy?
Identify the fallacy where someone tries to win support for an argument or idea by exploiting their opponent's feelings of pity or guilt.
Identify the fallacy where someone tries to win support for an argument or idea by exploiting their opponent's feelings of pity or guilt.
What fallacy is used in the statement: "Please do not fire me for being absent all month; I have a sick mother and a special child to support."
What fallacy is used in the statement: "Please do not fire me for being absent all month; I have a sick mother and a special child to support."
Match the fallacy type with its description.
Match the fallacy type with its description.
Flashcards
Slippery Slope
Slippery Slope
A fallacy where a series of increasingly superficial and unacceptable consequences is drawn.
Complex Question
Complex Question
A fallacy where two or more points are combined into one question, expecting a single answer when one point may be acceptable and the other is not.
Appeal to Force
Appeal to Force
A fallacy where a threat, instead of reasoning, is used to support an argument.
Appeal to Pity
Appeal to Pity
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Study Notes
Antenna Arrays Introduction
- An array consists of a set of N antennas.
- The total field is the vector sum of the fields radiated by individual antennas.
- Properly phasing array elements allows for constructive addition of fields in the desired direction and destructive interference elsewhere.
- Arrays increase gain and directivity.
- Array factor refers to the radiation pattern of isotropic elements.
- Overall array pattern is the product of the array factor and element pattern.
Two-Element Array: General Case
- Consider two antennas separated by distance d.
- Total electric field at point P is E = E1 + E2 = E0 (e-jkr1)/r1 + E0 (e-jkr2)/r2 ejβ, where β is the phase excitation.
- In the far field, r1 ≈ r and r2 ≈ r - dcos(θ).
- Electric field simplifies to E = E0 (e-jkr)/r [1 + ej(kdcosθ + β)].
- Array factor is AF = 1 + ej(kdcosθ + β).
- Absolute value of array factor is |AF| = |1 + ej(kdcosθ + β)| = 2|cos((kdcosθ + β)/2)|.
Two-Element Array: Special Cases
- Broadside Array (β = 0): |AF| = 2|cos((kdcosθ)/2)|, with maximum radiation at θ = π/2.
- End-Fire Array (β = -kd): |AF| = 2|cos((kd(cosθ - 1))/2)|, with maximum radiation at θ = 0.
- End-Fire Array with Increased Directivity (β = -kd + π/2): |AF| = 2|cos((kdcosθ - kd + π/2)/2)|, with maximum radiation at θ = 0.
- Phased Array: Adjusting phase β steers maximum radiation to a desired angle.
N-Element Array: Uniform Amplitude and Spacing
- $N$ antennas are placed along the z axis with uniform spacing d and excitation phase β.
- Array factor is AF = Σn=1N ej(n-1)(kdcosθ + β).
- Simplified array factor is |AF| = |sin((N/2)(kdcosθ + β)) / sin((1/2)(kdcosθ + β))|.
- Maxima occur when kdcosθ + β = 0, ±2π, ±4π,...
- Broadside array with β = 0 has max radiation at θ = cos-1(± 2nπ/kd), n = 0, 1, 2,..., with maximum radiation at θ = π/2.
- End-fire array with β = -kd has max radiation at θ = cos-1(1 ± 2nπ/kd), n = 0, 1, 2,..., with maximum radiation at θ = 0.
- Nulls occur when kdcosθ + β = ± 2nπ/N, n = 1, 2, 3,...
N-Element Array: HPBW, FNBW, and Directivity
- Half-power beamwidth (HPBW) is approximated as HPBW ≈ (2sin-1(0.443λ/d)) / (Ncosθ0), where θ0 is the angle of maximum radiation.
- First null beamwidth (FNBW) is approximated as FNBW ≈ (2sin-1(λ/d)) / (Ncosθ0).
- Directivity is approximated as D ≈ (4πUmax) / Prad = (2Nd) / λ.
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