# Confusion in parrallel and series of Transmission line

A transmission line terminals in two branches,each of length $\frac{\lambda}{4}$,as shown.The branches are terminated by $50 \Omega$ loads.The lines are lossless and have the characteristics impedances shown.Determine the impedance $Z_i$ as seen by the source.

My only confusion in this question is,the two right branches will be in series but i will not get the correct answer ,if i will do it by assuming them in series if i take that two branches in the parrallel i will get the correct answer. But i am not getting how that right two branches will becomes parrallel?

because only parrallel line i saw is this.can anyone help?

• I dont see how they would be in series? They are parallel! It seems like you haven't grasped the basic truth of transmission lines (namely, that they are transmission lines, and not simply two "perfect phase-free" cables as you learned them in first semester EE. Go back a few pages in your microwave engineering book and read what a transmission line is! – Marcus Müller Sep 9 '17 at 18:13
• @MarcusMüller sir i confused because of this,as this image line also saying its in parrallel and my question lines also is in parrellel s3.amazonaws.com/answer-board-image/… – Rohit Sep 9 '17 at 18:23
• You are right to be confused - the drawing shows them in series which would lead to an impedance at the feed of 6.25 ohms. The other blue drawing shows how you would draw lines connected in parallel. Series lines are quite possible and useful, an open stub has a special impedance characteristic, but in practice one has to be careful of radiation from the line. I've used them coiled up to prevent radiation. – tomnexus Sep 9 '17 at 19:14
• Its an illusion, not to scale, as the 50 ohm transmission lines would be closer together than the 100 ohm lines. But in actuality the transmission line is filled between the lines so a wider conductor track over a dielectric and ground plane yields a lower impedance. So these lines are fat tracks shown in parallel. These are not intend to be line and return schematics in series. – Tony Stewart Sunnyskyguy EE75 Sep 9 '17 at 20:23
• Is it possible that the diagram in the question represents a waveguide rather than a two-wire transmission line? In that case, the junction in the middle would effectively be a parallel connection rather than series. – Dave Tweed Sep 15 '17 at 12:08