# Length of Transmission Line & Characteristic Impedance

Just a simple Question for clarification: Does the physical length of transmission line affect its impedance?

We all understand that the height of dielectric (space between line and ground) affects the capacitance of transmission line and width of the line affects its inductance. But then why is it so important to keep the length of transmission lines (Microstriplines for example) a multiple of Lambda/4 or some other specific number when designing feed lines for antennas?

• Learn about antenna tuners. – analogsystemsrf Aug 3 '17 at 4:04

The height of a line (thickness of dielectric) affects both its capacitance and inductance. The width of a line affects both its capacitance and inductance. The length of a line affects only its delay, and its attenuation.

If a transmitter and an antenna are the same impedance, and connected by a line of that impedance, then the length of the line connecting them is irrelevant (except for ohmic losses causing attenuation).

However, often the transmitter isn't matched for some reason, power or efficiency, and the antenna may not be matched, perhaps for space, and the line between them is used for matching. In that case, the maximum matching effect can be achieved with a $\lambda/4$ or odd multiples of that length line. With a $\lambda/2$ line or multiples, no matching impedance transformation is achieved, regardless of the line impedance.

• So what i gather from this answer is that it might be more important to keep the feed line length as short as possible than to make it equivalent to odd numbered multiples of lambda/4, given that the source and load are matched flawlessly to feed line. – Curfue Aug 2 '17 at 11:09
• @Curfue Nothing is ever perfectly matched. In order to minimise accidental mismatches, keep the line as short as possible (<< $\lambda/4$), or to multiples of $\lambda/2$. Odd multiples of $\lambda/4$ will exacerbate any unintended mismatches. In practice, a mismatch has to be quite serious before it impacts transmission loss significantly, and any line length is usually OK when everything is intended to be matched. Attenuation in a long line mitigates against the exacerbating effect of $\lambda/4$. – Neil_UK Aug 2 '17 at 12:58

If you're talking about the characteristic impedance of a transmission line, Z0, then no, length does not affect the quantity. All variables are independent of the length of the transmission line:

• Z0 = sqrt((R+jωL)/(G+jωC))

where:

• R is resistance per unit length
• L is inductance per unit length
• G is conductance per unit length
• C is capacitance per unit length
• j is the imaginary unit
• ω is angular frequency

The reason the transmission line is capped at 1/4 λ of the highest frequency affecting the system is because of a resonant effect if a standing wave occurs (reflection from mismatched impedances). Source impedance is inversely proportional to load impedance at 1/4 λ, this means a voltage or current node (zero) will form at source and an antinode (maximum) will form at load end. The phase difference between voltage and current waves will affect where these node/antinode pairs occur along the transmission line.

I use these links as reference: http://www.ittc.ku.edu/~jstiles/723/handouts/Transmission_Line_Input_Impedance.pdf