A 78 Ω lossless planar line was designed but did not meet a requirement. The fraction of the widths of strip (in %)should be added or removed to get the characteristic impedance of 75Ω is ___Correct answer is '4'. Can you explain this answer?

Question

Answer

Given Information:

A 78 Ω lossless planar line was designed, but it did not meet the requirement of having a characteristic impedance of 75 Ω.

Finding the Required Change:

We need to determine the fraction of the widths of the strip that should be added or removed to achieve the desired characteristic impedance of 75 Ω.

Characteristic Impedance:

The characteristic impedance of a planar line is determined by its physical dimensions, such as the width of the strip and the separation between the strip and the ground plane. The characteristic impedance can be calculated using the following formula:

Zc = (Z0/60) * sqrt((W+T)/(W-T))

Zc is the characteristic impedance

Z0 is the impedance of free space (approximately 377 Ω)

W is the width of the strip

T is the separation between the strip and the ground plane

Calculating the Required Change:

In the given problem, we have a characteristic impedance of 78 Ω, which is not the desired value of 75 Ω. We can set up the following equation to find the required change:

75 = (78/60) * sqrt((W+T)/(W-T))

Simplifying the equation:

75 * 60 = 78 * sqrt((W+T)/(W-T))

4500 = 78 * sqrt((W+T)/(W-T))

Squaring both sides:

(4500)^2 = (78)^2 * ((W+T)/(W-T))

Simplifying further:

20250000 = 6084 * ((W+T)/(W-T))

3330 = ((W+T)/(W-T))

Cross multiplying:

3330 * (W-T) = W+T

3330W - 3330T = W + T

3330W - W = 3330T + T

3329W = 3331T

W/T = 3331/3329

W/T ≈ 1.0006

Fractional Change:

The fractional change is the difference between the actual value and the desired value, divided by the actual value. In this case, the fractional change is:

(W/T - 1) * 100

(1.0006 - 1) * 100 ≈ 0.06%

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