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For distortion less transmission line

$RL = GC$

$RC = GL$

$RG = LC$

$RLGC = 0$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option B

$RC = GL$

Quick Summary:

A transmission line is considered distortionless if the attenuation constant is independent of frequency and the phase velocity is constant for all frequencies. This occurs when the transmission line parameters satisfy the condition $RC = GL$ , which ensures that the signal maintains its waveform shape during propagation.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$\gamma = \sqrt{(R + j\omega L)(G + j\omega C)}$ — General propagation constant

$RC = GL$ — Distortionless condition

$\alpha = \sqrt{RG}$ — Attenuation constant (frequency independent)

$\beta = \omega\sqrt{LC}$ — Phase constant

⚙️ Working Principle

The propagation constant is defined as $\gamma = \sqrt{(R + j\omega L)(G + j\omega C)}$ . For distortionless lines, the ratio of the series impedance to the shunt admittance must be equal to the ratio of resistance to conductance, i.e., $\frac{R}{L} = \frac{G}{C}$ . This condition simplifies the expression for $\gamma$ such that $\alpha = \sqrt{RG}$ (frequency independent) and $\beta = \omega\sqrt{LC}$ (linear phase shift).

📌 Key Points

▸
Distortionless lines eliminate both frequency and phase distortion.
▸
The attenuation constant $\alpha$ remains constant with respect to frequency.
▸
The phase velocity $v_p = \frac{1}{\sqrt{LC}}$ becomes independent of frequency.
▸
These lines are theoretically ideal but practically difficult to achieve for all frequencies.

✅ Advantages

▸
Preserves the waveform shape of the signal
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Constant time delay for all signal components

❌ Disadvantages / Limitations

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Hard to implement in practice as it requires specific R, L, G, C values
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Often requires artificial loading (loading coils)

🛠️ Applications / Uses

▸
Long distance telegraphy
▸
High-speed data communication lines

📄 Additional Information

▸
The condition $RC = GL$ implies that the time constants of the series and shunt branches are identical.
▸
Option A (RL=GC) is incorrect as it represents an incorrect algebraic arrangement of parameters.

📊 Diagram / Illustration

✅

B is correct — A transmission line is distortionless if the ratio of its series resistance to inductance equals the ratio of its shunt conductance to capacitance, expressed as $RC = GL$ .

Core Concepts Used

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Transmission Line Theory Distortionless Lines Propagation Constant

💡 EXAM TIP

Remember that for a lossless line ( $R=0, G=0$ ), the distortionless condition is automatically satisfied, which is a specific case of the general $RC=GL$ condition.

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