Design pi/2 artificial transmission line using lumped elements

Hi, I was reading the paper "Design Methodology for distributed Power Amplifier in Software -Defined Radio Applications" and came across
"Once the characteristic impedances values are fixed, design can be completed by synthesizing the pi/2 transmission lines using lumped components and embedding the devices". I know how to make a transmission line using lumped elements but how do we do it for particular length of the line? Does it mean we need to design an inductor and capacitor per unit length and distribute them until we have pi/2 electrical length?

I don't know how to make a transmission line using lumped elements.

Teach me how to make a transmission line using lumped elements.

Simply it is a phase shifter of pi/2.

I don't believe if you say that you don't know something. You are genius. I can make lossless line using lumped elements. Connect Inductor in series and Capacitor in shunt and repeat the combination that gives artifical transmission line.

I don't understand what do you mean by this

Look at ABCD parameters for lumped components and transmission line.

What he means is that you can only approximate a particular length of transmission line at a particular frequency by lumped components. Placing a length of transmission line only rotates your impedance on the Smith Chart and introduces a phase delay. And given full freedom in the choice of lumped components, you can match any (passive) load to another (passive) load. For example, one of the most common approximations of a lambda by 4 tline is a pi network but it works 'perfectly' only at one frequency.



pi/2 is the electric length I think.. Won't the phase shift be pi?



pi/2 is the electric length I think.. Won't the phase shift be pi?



Ignore the last part of the last message. I was thinking of something else when I typed that. Sorry about it. (somehow I misread pi by lambda)..

A lambda by 4 TLIne introduces a phase shift of pi/2. It also transforms your impedance as Zo^2/ZL where Zo is the characteristic impedance of the line and Zl is the load impedance,

Yes, your delay line from lumped components will have low pass characteristics. The more segments you use, the more it approximates the truely distributed LC of the line, for wider bandwidth.

It is not a transmission line.
https://www.edaboard.com/showthread.php?385727#4

A Transmission Line can be represented and modelled by R-L-C-G elements.
This page is available for everyone and the chapters can be downloaded.
http://eceweb1.rutgers.edu/~orfanidi/ewa/

Chapter 11-6 expresses this ..

These are not lumped components.

Rather https://www.edaboard.com/showthread.php?385427#2

If you want to see how increasing number of LC segments make a closer approximation to transmission line, check out this rather basic paper: https://ip.cadence.com/uploads/1012/...Final_0416-pdf