The generalized constant A for a medium line has magnitude

Question

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Option A: Close to but less than 1

Explanation & Concepts:
For a medium transmission line represented by the nominal $\pi$ or nominal $T$ circuit model, the generalized constant $A$ is given by $A = 1 + \frac{YZ}{2}$. Since $Y$ (shunt admittance) and $Z$ (series impedance) are both positive complex numbers for a physical transmission line, the product $YZ$ results in a value such that $|A|$ remains slightly less than 1 due to the phase characteristics of the line parameters.

Working Principle: In a medium line, the shunt capacitance is lumped at the ends or center. The ABCD constants represent the relationship between sending and receiving end voltages and currents. Because $Y = j\omega C$ and $Z = R + j\omega L$, the term $1 + \frac{YZ}{2}$ involves subtracting a small positive real part from unity because $j^2 = -1$, resulting in a magnitude typically falling in the range $0.95

Key Formulas: $A = 1 + \frac{YZ}{2}$ — Generalized constant for medium transmission lines; $AD - BC = 1$ — Reciprocity condition for transmission networks

Key Points: Transmission lines are reciprocal networks, so $AD - BC = 1$.; For symmetric lines (medium line), $A = D$.; Short lines have $A=1$, while long lines have $|A|; The constant $A$ is a complex dimensionless number.

Advantages: Simplified analysis of voltage regulation; Facilitates cascade connection calculation

Disadvantages: Approximation error increases with line length; Neglects distributed parameter effects

Applications: Power system steady-state analysis; Calculation of voltage regulation and efficiency

Additional Info: For a short transmission line, $Z$ is very small, so $A \approx 1$.. For long lines, $A = \cosh(\gamma l)$, where $\gamma$ is the propagation constant.

Answer: A is correct — The generalized constant A for a medium transmission line is defined as $1 + \frac{YZ}{2}$, which results in a magnitude slightly less than unity.

Exam Tip: Remember that for all passive, linear, two-port reciprocal networks, the product $AD - BC = 1$ always holds; if the line is also symmetric, then $A = D$.

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Option B: Close to but greater than 1

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Option C: Nearly equal to the series impedance of line

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Option D: None of above

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