Electronic – Wideband Impedance Matching

A Smith Chart is not so much an attenuator design aid
as a means of evaluating and adjusting a design.

So - see attenuator articles below and then Smith chart articles.

Carbon resistors may be carbon film or carbon composition?

• Carbon film are not suitable for UHF work as they are formed by cutting a spiral track in a carbon film cylinder, so have very substantial inductance.

• Carbon composition have a solid carbon body and may be suitable for UHF work depending on other factors.

UHF Attenuators:

RF attenuator basic tutorial

Attenuator design tutorial - looks good.

Interest - Commercial products

Wikipedia

What is a Smith Chart?

Wikipedia gives a better than average concise summary:
From here

• The Smith chart, invented by Phillip H. Smith (1905–1987),1[2] is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits.[3] Use of the Smith chart utility has grown steadily over the years and it is still widely used today, not only as a problem solving aid, but as a graphical demonstrator of how many RF parameters behave at one or more frequencies, an alternative to using tabular information. The Smith chart can be used to represent many parameters including impedances, admittances, reflection coefficients, scattering parameters, noise figure circles, constant gain contours and regions for unconditional stability, including mechanical vibrations analysis.[4][5] The Smith chart is most frequently used at or within the unity radius region. However, the remainder is still mathematically relevant, being used, for example, in oscillator design and stability analysis.[6]

Somewhat gentle introduction - 27 page powerpoint intro - still gets deep quite quickly BUT a Smith Chart can be very very useful with almost no maths or numerics involved.

Superb Smith Chart resource - essentially an index of indexes - breaks subject up into sections and provides many references for each.

Another good list of references

Smith Chart tutorial from Maxim - reasonable "dense" but looks understandable.

You'll understand this once you've read it :-)

Free software based Smith Chart

Freeware Smith Chart software

Sim Smith - Java based

Many Smith Chart related pages

Your use of the smith chart is correct, but your numbers are a little off due to the wavelength you used (6.5mm).

In stripline, the fields are completely contained inside the substrate. The fields are partially in air around a microstrip line, resulting in an effective permittivity which is lower than the relative permittivity of the substrate. Wavelength can be calculated using the effective permittivity or the delay (Tpd). Both are available from your impedance calculator. Er effective is 3.0635. Tpd is 5.8e-9 s/m.

\$ Wavelength = \frac{c}{\sqrt{E_{r}} \cdot f} = \frac{1}{T_{pd} \cdot f} \$
\$ Wavelength(w/ E_{r}) = \frac{c}{\sqrt{E_{r}} \cdot f} = 6.5 mm \$
\$ Wavelength(w/ E_{eff}) = \frac{c}{\sqrt{E_{eff}} \cdot f} = 7.1 mm \$
\$ Wavelength(w/ T_{pd}) = \frac{1}{T_{pd} \cdot f} = 7.1 mm \$

The difference between 6.5mm and 7.1mm may seem small, but check out the difference in return loss.

\$ Z_{out}(\Lambda:6.5mm) = 33-j24 \Omega \$ >>>> \$ ORL=9dB \$
\$ Z_{out}(\Lambda:7.1mm) = 46-j14 \Omega \$ >>>> \$ ORL=16dB \$

For a sanity check, match from the load to the conjugate of the generator. In other words, start at a load of \$50\Omega\$ and go towards the chip. You'll end up around \$20.8+j20.2\Omega\$. This is typical for most output stages, since they're usually low resistance and capacitive.

Your method of matching will provide a decent ballpark, but I'd like to point out a few important sources of error.

1. Tx & Txx are intended to be 100ohm differential signals. The small spacing between them produces an additional shunt capacitance. You need to include the extra capacitance, or use a coupled line model.
2. The datasheet doesn't say how they measured the Tx/Txx load impedances. Did they measure at the PCB output port and try to de-embed everything up to the chip? I'm skeptical of the accuracy without knowing where they came from. Additionally, I think these are the impedances looking into the Tx/Txx ports. I would call the load impedance the conjugate of the printed values, or the impedance presented to the Tx/Txx ports. It's all unclear.
3. The package pad (footprint) will have a different impact on a different board stackup.
4. I don't see anything to cancel mismatch from the launchers. The launchers will perform differently on a different board stackup.

The matching network they used is simple and probably low loss. I guess you could call it a stepped-impedance match. I don't know. It's a plus to avoid shunt components or stubs, and the high Q resonances they might produce.