electrical length vs physical length | difference between electrical length and physical length

This page compares electrical length vs physical length and mentions difference between electrical length and physical length.

The concept of physical length and electrical length is very useful in the RF and microwave circuit design. It is required to calculate physical length for different degrees of electrical length for dielectric substrate. Though the calculation is done using the RF calculators. Following equations are behind the calculations.

Electrical length

The electrical length of a cable can be expressed in degrees of phase shift. These units are used with smith chart required to do impedance matching.

To find electrical length, dielectric material properties are needed. First full wavelength(λ) for 360 degrees is determined using equations mentioned below.
λ = (1/frequency)*(Vf*3x108) ... Equation-1
Where, velocity of propagation (Vf) = 1/(εr)0.5

(Phase shift in degrees/360)*λ = cable physical length ... Equation-2
Here Phase shift in degrees is the electrical length.
λ = c/frequency,
c= 3 x 108 m/sec.

physical length

Let us calculate physical length of following data:
• electrical length= 45 degrees
• Frequency=500 MHz
• PTFE dielectric with Vf = 0.69

➨Physical length of cable = 5.137 cm

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