# Interpretation of scattering parameter

Currently I am (non-engineer) trying to understand the origin of measured scattering parameters with a vector network analyzer and a 2 port system. The second port is terminated with a matched load to force a2=0. I am observing the amplitudes of |S11| and |S21| to verify the optimal matching, and to exclude standing waves.

Since

|S21|= b2/a1
|S11|= a1/b1


I expect that with a1=100% of incident wave nearly everything is transmitted ~100% to the output port b2. So I would assume as best and maximum value for |S21| =1, rather smaller lets assume b2 being 80% |S21|= 80/100=0.8. This gives me a range from 1~0 for |S21|. The closer the value is to 1, the better is my transmission.

Now lets observe |S11| in case of a perfect match there should not by any reflected wave, a perfect match is leading to b1~0. Which brings me to be best measurable value of ~100 for |S11|. Since nothing is ideal lets assume b1=10%. Which shows me that |S11| can take values from 100~0. The higher the value the better is my transmission line matched.

In case of a standing wave I expect my |S11| being very good compared to other frequencies, however if |S21| is showing a poor transmission at that frequency with a value <1, it indicates that a standing wave probably is existing.

Am I right with my estimations so far?

Can I see more out of the |S21| and |S11| measurement than standing waves?

In reality I measure negative values for both parameters. |S21| is nearly showing a flat line close to -1 and |S11| has an average value of -15dB with a dip going down to -30 dB @1.5 GHz.

If I argue the following is that correct? I would like to say that this dip -30 dB @1.5 GHz is a very good matched frequency and not a standing wave, since I still see a |S21|-value ~-1 dB. A standing wave would show a value much "smaller" so something which is closer to "zero".

I am aware of the following conversion

Insertion loss = -20*Log|S21| in dB
Return loss    = -20*Log|S11| in dB


But I don't know what these formulas tell me. With |S21|=0.1 it gives an insertion loss of 20. Does this mean that 20% are not transmitted to b2?

With |S11|=15 it gives a return loss of -23. Does this mean that 23% are reflected or that 77% are reflected?

Maybe I am completely wrong, thank you for taking a look! =)

• How are you measuring S21 if your second port is terminated in a matched load? Sketch your setup. S parameters can also be low due to attenuation, not just standing waves. Show the trace obtained, engineers can often figure out what's going on from what the trace does as the frequency varies. Most of your if this, then that, seems quite garbled, I don't think you have the fundamentals of S parameter measurement properly understood yet, but attempting to correct you would be fruitless at the moment without a diagram of what you're doing. – Neil_UK Nov 20 '19 at 13:57
• Can you tell us what the device you are testing is? – Captainj2001 Nov 20 '19 at 14:12
• -23 dB is:[ -20dB -3dB], which is 1/100 the power * 1/2 the power, or 1/200 the power. The voltage ratio is the sqrt of the power ratio, or sqrt(2000. – analogsystemsrf Nov 20 '19 at 15:20

## 1 Answer

I am assuming that since you say you are observing the S-Parameters you have access to a Vector Network Analyzer (VNA) or at least a Scalar Network Analyzer (SNA).

Your musings about S-parameters are not all correct. There are several things you should be aware of. When you're using the "a" and "b" coefficient convention instead of voltage ratios $$\a_1\$$ is almost always assumed to be equal to 1.0. For a passive device $$\S_{11}\$$ and $$\S_{21}\$$ are always also related by conservation of energy, i.e., they are not independent: $$|S_{11}|^2 + |S_{21}|^2 = 1.0$$

This just states that all the power input to a passive 2-port device is either reflected or transmitted. This does not account for radiated power, or loss due to physical properties of your material / device.

You are also confounding the linear scale used in text-book derivations/descriptions of S-Parameters with the displayed values of your measured device, which is almost certainly in decibels (dB). We will address this in a few parts, along with other parts of your question.

Regarding your question about standing waves: in linear scale for $$\|S_{11}| = 1.0\$$ indicates that all the power is being reflected from the input and only standing waves exist on your transmission line. There is also another concept called the Reflection coefficient $$\\Gamma\$$ (which is equal to $$\S_{11}\$$ in many cases) from which you can calculate the Voltage Standing Wave Ratio (VSWR) of your device.

$$VSWR = \frac{1 + |\Gamma|}{1 -|\Gamma|}$$

Higher values calculated for VSWR indicate more standing waves (worse impedance matching) on your transmission line. All VNAs and most SNAs will be able to display this value as well. VSWR < 2.0 is typically a value that indicates impedance matching that is "good enough".

On to insertion loss and return loss. For passive devices both of these values in log scale will be negative. Logarithms are very useful in RF engineering because they are useful for amplifying variations that are very small in linear scale to values that are easy to discuss in log scale.

Insertion loss shows you how much power is lost when passing through your device from port 1 to port 2 (values closer to 0 dB are better).

Return loss shows how much power is reflected back to the source from port 1 of your device (values in the 10-30 dB range are typical for devices that are considered well matched). Every 10 dB is an order of magnitude (10x) in linear scale.

I think now that we have some background information established we can talk about your measurements.

In reality I measure negative values for both parameters. |S21| is nearly showing a flat line close to -1 and |S11| has an average value of -15dB with a dip going down to -30 dB @1.5 GHz.

This seems like a normal measurement for both $$\S_{21}\$$ and $$\S_{11}\$$ and that your device is best matched at 1.5 GHz. Lets translate -1 dB and -15 dB back to linear scale and talk about percentages since it seems you are more comfortable in linear scales.

$$|S_{21}|(lin.) = 10^{S_{21}(dB)/20} = 0.891$$ $$|S_{11}|(lin.) = 10^{S_{11}(dB)/20} = 0.178$$ $$|S_{11}|^2 + |S_{21}|^2 = 0.825$$

This indicates that 89.1% of the voltage wave is transmitted from port 1 to port 2 in of your device. 17.8% of the voltage wave is reflected. Equation 3 indicates that only 82.5% of the power input into your device is transmitted or reflected, this means that 17.5% is absorbed (lost as heat) or radiated into space.

Your last two inferences are incorrect, always make sure what type of scale you are working in. You can only consider percentages in linear scale, so if your network analyzer provides results in decibels you have to convert to linear scale to get percentages. Always annotate the units next to measurements so you don't get confused, this can be especially confusing when working with logarithmic scales because quantities (like S-Parameters) are unitless ratios, so always indicate that you're in log scale by putting dB next to your quantity.

• Captainj2001 You certainly deserve an upvote for that wonderfully clear answer.I hope the title of the question will bring all newbies to your answer. – analogsystemsrf Nov 20 '19 at 15:24
• Thank you very much Captainj2001, your explanations helped me a lot! – Jacccy Nov 21 '19 at 14:31