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



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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)



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match_at_50 = rf.wr10.match()

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



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match_at_50

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



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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



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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



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match_at_50 = rf.wr10.match()
match_at_50.renormalize(50j)
match_at_50.plot_s_smith(**kw)

Complex Impedances



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



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