Rule of Thumb: How Much Return Loss is Too Much?

　　It can be said that 99% of engineers are often confused by S parameters. When S parameters are used to define some specifications, often the definers themselves do not understand S parameters. This article will use empirical rules to tell you how to calculate return loss in a standardized way.

　　Each parameter in the S parameter matrix is ​​actually a comparison between the sinusoidal signal output from one port and the input of another port in the interconnection system. The reflection coefficient S11 is defined as the ratio of the energy reflected from port 1 to the incident signal at port 1, that is, the input return loss; the transmission coefficient S21 is defined as the ratio of the sinusoidal wave coming out of port 2 to the sinusoidal wave entering from port 1.

　　We know that the energy of a sine wave is the square of its amplitude. Based on this, for a network with very low loss, there is the following relationship between S11 and S21:

　　If you know the value of S11, for a lossless network, you can find the value of S21, of course, this is calculated based on the amplitude. For example, if the reflection coefficient S11 is 10%, then the transmission coefficient S21 will be 99.5%. A 10% reflection amplitude sounds like a lot, but in fact it has a negligible effect on the transmitted signal.

　　Usually, we describe S parameters in db. As the reflection coefficient increases in db, when will the transmission coefficient S21 be significantly affected? If S21 decreases by -0.5db, how much can S11 be reduced at most?

　　This is easy to estimate. We convert S11 into an amplitude value in dB, calculate the amplitude of S21, and convert it back to dB. The following figure shows the relationship between S11 and S21.

　　When S11 is -40db, it has almost no effect on S21; when S11 is -30db, it has little effect on S21; even when S11 is -20db, it has little effect on S21. As can be seen from the figure, only when S11 is as high as -15db can it slightly affect S21.

　　So how much S21 is considered too much? Let's assume that the impact on S21 is -0.5db. From the figure, we can see that only when S11 is -10db will it cause a -0.5db impact on S21, which is very surprising.

　　We noticed that when S11 is as high as -10db, that is, 30% of the signal is reflected, the transmission loss of S21 is -0.5db. Depending on how much transmission loss your system can accept, the threshold of S11 is about -10db to -15db, usually -13db.

　　This leads to the rule of thumb we mentioned earlier, which is a maximum S11 return loss value of -13db for interconnect structures and components.

　　If S11 is less than -13db, then we will not see the effect of reflection on the transmitted signal; but if S11 is greater than -13db, the effect on S21 will be reflected. For example, a connector with an S11 value of -20db will have no effect on the transmission system.

　　Now, answer the following questions:

　　1. If the return loss is -25db, does this have any impact on the transmission system?

　　2. The return loss S11 peak of a short transmission line is -15db. What is the impedance difference between the line and the port?