Analyzing Reflection S-Parameters

We’ll be taking a look at analyzing reflection S-Parameters with respect to the S-Parameter matrix. The S-Parameter matrix consists of reflection and transmission coefficients where the main diagonal of the matrix consists of reflection coefficients and the rest of the matrix consists of transmission coefficients. This week, we’re going to learn how to quickly discern these reflection coefficient values in LogMag format (S11, S22, S33, … Snn).

These reflection coefficients are a measure of incident and reflected “power” waves. For a lot of analysis applications, these reflection coefficients are translated to logarithmic magnitude representations in decibels (dB). Logarithmic magnitude representations are great for observing small, meaningful differences in reflection coefficient values as the reflection coefficient technically varies in value from 0 to 1.

So, how do we lock in a rule of thumb for analyzing logarithmic magnitude representations of reflection coefficients? We’re also going to use the analogy of rolling 10000 marbles from one end of the room to the other. Here are three rules I constantly follow when analyzing return loss.

1. A value of -10dB corresponds to 90% of the power delivered from the source to the load with 10% of the power reflecting back towards the source. Roll 10000 marbles down and 1000 of them come back. This commonly is considered “decent”. Not terrible, but not that great either.

2. A value of -20dB corresponds to 99% of the power delivered from the source to the load with 1% of the power reflecting back towards the source. Roll 10000 marbles down and 100 marbles comes back. This is commonly considered as “good to great”.

3. A value of -40dB corresponds to 99.99% of the power delivered from the source to the load with 0.01% reflecting back towards the source. Roll 10000 marbles down and 1 comes back. This is commonly considered “excellent”.

These values are actually derived from what I refer to as the reflected power percentage equation. A picture of it is attached in the post along with a graph depicting power reflection percentage versus LogMag for the reflection coefficient.

Of course, how “good” the logarithmic magnitude of the reflection coefficient in the S-Parameter matrix is really dependent on the application or specifications of the design. Across the frequency band of interest some designs require -20dB, some require -10dB, and I’ve even seen some applications only require -5dB (yes, -5dB - wild). Regardless, you can use these three rules of thumb to gauge how much reflection is occurring in your circuit (with marbles!)