# Renormalizing S-parameters¶

This example demonstrates how to use skrf to renormalize a Network’s s-parameters to new port impedances. Although trivial, this example creates a matched load in 50ohms and then re-normalizes to a 25ohm environment, producing a reflection coefficient of 1/3.

## Ok lets do it¶

In :

import skrf as rf
%matplotlib inline
from pylab import *
rf.stylely()

# this is just for plotting junk
kw = dict(draw_labels=True, marker = 'o', markersize = 10)


Create a one-port ideal match Network, (using the premade media class wr10 as a dummy)

In :

match_at_50 = rf.wr10.match()


Note that the z0 for this Network defaults to a constant 50ohm

In :

match_at_50

Out:

1-Port Network: '',  75.0-110.0 GHz, 1001 pts, z0=[50.+0.j]


Plotting its reflection coefficient on the smith chart, shows its a match

In :

match_at_50.plot_s_smith(**kw) Now, renormalize the port impedance from 50 -> 25, thus the previous 50ohm load now produces a reflection coefficient of

$\Gamma^{'} = \frac{50-25}{50+25} = \frac{25}{75} = .333$

Plotting the renormalized response on the Smith Chart

In :

match_at_50.renormalize(25)
match_at_50.plot_s_smith(**kw) You could also renormalize to a complex port impedance if you’re crazy

In :

match_at_50 = rf.wr10.match()
match_at_50.renormalize(50j)
match_at_50.plot_s_smith(**kw) ## Complex Impedances¶

In :

minusj_at_50 = rf.wr10.load(-1j, z0 = 50)
minusj_at_50.renormalize(20+20j)
minusj_at_50.plot_s_smith(r=2,**kw) In :

Zl= 1j
z0_imag,z0_real  = mgrid[-1:1:101j,-1:1:101j]
z0 = z0_real + 1j*z0_imag
s = (Zl+z0)/(Zl-z0)

/home/docs/checkouts/readthedocs.org/user_builds/scikit-rf/conda/stable/lib/python3.5/site-packages/ipykernel_launcher.py:4: RuntimeWarning: divide by zero encountered in true_divide
after removing the cwd from sys.path.
/home/docs/checkouts/readthedocs.org/user_builds/scikit-rf/conda/stable/lib/python3.5/site-packages/ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in true_divide
after removing the cwd from sys.path.