How to convert Inductor to series transmission line?

My objective is to understand the travelling wave amplifiers, but I am stuck on how to realize inductors in transmission lines.

But, I am basically stuck on how to convert a series inductor to a series tranmission line.

I tried this in ADS. I could replace the series inductor with a short-circuited transmission line, but it does not work with series connected line. This actually works (S11 and S22) are same, but the problem is the TLIN is short circuited. I want something in series (for travelling wave amplifier topology). I tried the following as well, but I got S22 as 50 ohms. If you could give any suggestions on how to realize inductors using series transmission line, it would help.

The substrate definitions are below: • What is the purpose of R1 in your new circuits? – The Photon Oct 28 '18 at 18:26
• @ThePhoton resistors just add the real part. It has no significance. – sundar Oct 29 '18 at 10:36

This [first replacement circuit] actually works (S11 and S22) are same, but the problem is the TLIN is short circuited.

Instead of connecting the stub end of the line directly to ground, connect it to ground through a capacitor. Make the capacitor value large enough and it will be essentially a short circuit at your operating frequency, but still keep the line from being shorted at DC, so it won't mess up the bias of your amplifier stages.

I tried the following [second replacement circuit] as well, but I got S22 as 50 ohms.

If you work in 50-ohm line, then a segment of higher-Z0 line will look inductive over some frequency band starting at DC (of course an inductor at DC is expected to have no effect).

The geometry of this line is probably not exactly the same as the geometry of the line needed to make a stub line appear inductive.

Since you haven't shared your substrate definition, or the inductance you're targeting, or the frequency band you're operating in, I can't say more about how you would implement this.

• Thanks very much. Is there any exact formula or relation to make the stub line inductive? I added the substrate definition as well. – sundar Oct 29 '18 at 10:38
• @sundar, based on the page you linked to, you're probably better off with a series line than a shunt line. But even so, if you adjust the line length so that Zin for the whole load has a positive imaginary part, that's an inductive termination. – The Photon Oct 29 '18 at 16:27
• Sorry for the confusion, I think my question is wrong, it has to be "how to convert inductance and capacitance to a transmission line (lossless)?" actually the Travelling wave amplifier has an inductance and capacitance at a node. Then that inductance and capacitance is converted to a transmission line (With no losses) using the simple relation Zo=sqrt(L/C). I was mislead by thinking that inductor has become a Transmission line. – sundar Oct 29 '18 at 17:44
• Should i delete this question? (since it is misleading?) – sundar Oct 29 '18 at 17:44