How to simulate and or calculate complex impedance of LC circuit

Let's say I have a matching network made up of inductors and capacitors like this. How would I go about simulating to get the complex impedance of this circuit at my frequency of interest. Something in the form 20+15j for example, or I guess even a Smith chart (I'm trying to relearn those). Can I do it in spice? Should I do it by hand or maybe I need something fancier like an RF simulator?

simulate this circuit – Schematic created using CircuitLab

• It's up to you. If you like math, do all the math by hand in the s-domain. It's not bad; the circuit is fundamentally a voltage divider with impedances. However, if you don't like math, throw it in the Spice flavour of your choice. Commented Feb 3, 2016 at 6:32
• @uint128_t I think the Laplace domain does the math model , but it will end up in terms of s , may be he need to transform the Laplace function to Fourier function as he is asking in terms of 'jw' , Commented Feb 3, 2016 at 10:37

Smith invented his chart to do this stuff before computers were powerful or ubiquitous enough to run simulators.

Whereas a simulator will show you what a circuit will do at a given frequency with given load and source impedances, it won't help you imagine what a circuit will do if you change the load slightly. More importantly it won't help you guess what type of component you should add to bring the response to where you want it. A simulator certainly will not offer to add components for you.

The thought process when gazing at a Smith Chart will often be 'my locus is here and it needs to be there, so I need a sniff of series C'.

Ideally, you'll learn the graphical approach on a Smith Chart, confirm it on a simulator, and check a few points with a calculator for a fully rounded understanding.

That will put you head and shoulders above what most students do today which is whack everything into a simulator and hope.

However, knowing how to use a simulator is way better than not.

I'd probably start with putting a simpler circuit into a simulator, that had a Smith Chart display for the results, understanding what it showed you, then building the complexity up to what you have drawn.

You could do worse than to search for the original Smith publications where he describes how to use his chart. Very readable.