Lumped Matching via Smith

[robismyname]

lumped matching

Im following an example of how to design a lumped matching circuit to match 50 ohms in order to ensure minimum noise. The example starts of by implemeting a series inductor.

The example assumes that the data sheet or CAD yields a optimum noise match of 3 + j2.0 ; (normalised to 50-ohms).

If you look at part III page 1 of the article, I noticed that there is green admittance circle (G=0.2). I see how he got the G=0.2 circle. My problem is that underneath the smith chart diagram on page 1 he says that the distance between B and C gives the value of the inductor as shown in part 1.

So I then looked at part I page 10(bottom) he's saying to subtract .2 from .5 to get the reactance (XL) and then the value of L.

My question is since .2 is associated with an admittance circle and .5 is associated with a impedance circle how can you subtract an admittance circle from an impedance circe to obtain (XL) and L?

 

[biff44]

smith diagram noise matching

Don't believe everything you read on the internet. To get the inductance to go from the center to point A, you simply follow the constant reactance curve to the edge of the chart, read that reactance value, denormalize it, and use L=X/2πf.

I think the author was confusing lumped element inductors with a short circuited transmission line approximation of the lumped element inductor. In that case, it would be the wavelengths betweem point B and C.

I would highly recommend to never use single colored smith charts when doing impedance matching. Use the two colored ones, where both impedance and admittance charts are superimposed. It keeps your brain from hurting.

 

[biff44]

Sorry, the only one I had handy was one with 50 ohms in the center. It is better to use one with 1 ohm as the center.

Added after 13 minutes:

Here is a better one:
**broken link removed**