# | : | M?——— A distortion less line has Zp= 60 Q. o = 20 mNp/m, V= 0.6C, where C is the speed of light in a vacuum. Find the Ui.ne parameters R. L G. C. and / at 100MHz. Transcribed Image Text: A distortion less line has Zo = 60 2. a = 20 mNp/m, Vp= 0.6C, where C is the speed of light in a vacuum. Find the line parameters R. L G. C. and i at 100MHZ. |

A distortionless line is a transmission line that does not introduce any distortion to the signal it carries. In this particular case, the line has a characteristic impedance (Zo) of 60Ω, a phase constant (a) of 20 mNp/m, and a propagation velocity (Vp) of 0.6 times the speed of light in a vacuum (C).

To find the line parameters at 100MHz, we can use the following formulas:

1. Resistance (R):

R = Zo / (2 * pi * f * C)

where f is the frequency (100MHz in this case) and C is the speed of light in a vacuum.

2. Inductance (L):

L = Zo / (2 * pi * f * a)

where a is the phase constant.

3. Conductance (G):

G = 0

4. Capacitance (C):

C = 1 / (Zo * v)

where v is the propagation velocity.

5. Inductance per unit length (/):

/ = L / length

where length is the length of the transmission line.

Now let’s calculate these parameters at 100MHz:

1. Resistance (R):

R = 60Ω / (2 * pi * (100MHz) * C) = 3.001 Ω

2. Inductance (L):

L = 60Ω / (2 * pi * (100MHz) * 20 mNp/m) = 4.808 nH

3. Conductance (G):

G = 0

4. Capacitance (C):

C = 1 / (60Ω * 0.6C) = 4.62 nF

5. Inductance per unit length (/):

Assuming the length of the transmission line is 1 meter,

/ = 4.808 nH / 1 m = 4.808 nH/m

Therefore, the line parameters at 100MHz are as follows:

R = 3.001 Ω

L = 4.808 nH

G = 0

C = 4.62 nF

/ = 4.808 nH/m

These parameters can be used to analyze the performance of the distortionless line at 100MHz. The resistance (R) represents the loss in the line, while the inductance (L) and capacitance (C) determine the propagation characteristics of the line. The conductance (G) is zero, indicating an ideal line with no leakage or loss of energy. The inductance per unit length (/) describes how the inductance changes along the length of the line, and it can be used to determine the impedance variation along the line.

Overall, the line parameters provide important information for designing and analyzing distortionless transmission lines in high-frequency applications.

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