Return loss, VSWR and S11. What is the difference? Antenna S-parameters physical sense.

Modern radio engineering is such a complex science that it has long been divided into several areas of knowledge, in which there are similar and even identical concepts that have completely different definitions. This leads to a lot of confusion. And if we take into account the fact that some concepts, for example the concept of “return loss,” have a definition completely opposite to their name, then this can quite strain the brain of not only a radio amateur, but also a specialist. What is the difference between such concepts as reflection coefficient, “return loss”, VSWR, S11? Wherefore, or rather why, are there so many similar concepts? Let's try to look into…

Let's start with the S-parameters. These parameters were introduced as universal ones for the analysis of any microwave circuits. Such a circuit can be analyzed by measuring the incident and reflected waves at its inputs/outputs. The binding between these waves is described by a wave scattering matrix or a matrix of S-parameters, which depend on frequency. In the general case, we have a multi-port network (for example, a microwave adder or a splitter), in which there may be several power sources and several loads. To simplify the calculations, all these sources and loads are replaced by one concept: “port”.

The “Port” is a completely abstract concept that can combine the properties of both load and source at the same time. For example, if this is an excitation port, then an incident wave emanates from it, but at the same time the reflected wave returning to this port is, as though, “scattered” there. As we already noted in the article about the WBME antenna, quite often abstract mathematical concepts are confused with real devices. The concept of an “excitation port” is another such example that should not be confused with the concept of a “source”, much less with an actual transmitter. The main difference between a “port” and a “source” is that the “source” is always an integral part of some closed circuit, and the “port” for a microwave device is a kind of gate, a “portal to the infinite universe.” An electromagnetic wave may come from (or go into) this universe, but it is not an integral part of the device. If you find it difficult to imagine the “microwave universe,” another way to think of the port is as a kind of virtual waveguide of infinite length.

In general, the number of elements of the S-scattering matrix is proportional to the square of the number of ports. In the classical multi-terminal circuit theory, which operates with a similar set of matrices, the device must have at least one input and one output with four terminals (4-pole network), to which the source and load are connected respectively. However, in microwave theory, there can be even one port, due to its unique properties. And terminals are not at all necessary for it. Where did you see the “terminals” on a hollow waveguide? Their role is played, roughly speaking, by a “hole” or, to put it mildly, by an “opening”.Why is the S-matrix called the scattering matrix? Where and what is dissipated? The easiest way to understand this is with a simple example of a microwave transmission line (take, for example, the hollow waveguide that is mentioned above). An electromagnetic wave enters this line through the excitation port: “port1”, and the net load is “port2”. It is desirable for us that all the energy coming from port1 goes to port2. This occurs in the particular case of a lossless line with full impedance matching with both ports. In the general case, the wave “scatters” along the propagation path, is reflected from the input of the line back to port1, and also it's attenuated while propagation along the line. Since it is possible that the characteristics of the device during the forward and reverse wave propagation can differ significantly, as for example in microwave transistors, for a complete accurate analysis, we need to review the reverse situation, when the wave propagates from port2 to port1. As a result, we have a matrix of four S-parameters. All these parameters have the complex number values, because any wave, in addition to amplitude, also has a phase, and operations with them are doing out using the vector analysis mathematical method. Vector network analyzers, which have recently become available to radio amateurs, measure just these S-parameters, and only then convert them into graphs that we can understand.

Parameter S11/S22 characterizes the reflection coefficient of the wave from the input of the microwave device and is equal to the ratio of the complex value of the reflected wave to the complex value of the incident wave. It is completely equivalent to the older concept of “reflection coefficient”, which came from the classical O.Heaviside's transmission lines theory, which has also a complex (vector) value and is denoted by the capital Greek letter “Г”. Only the wave is reflected here not from the “load”, but from the entrance to the “black box” (the role of which is played by the microwave device) back to the excitation port. And as we know, the modulus of this vector |Г_U| is definitely related to the concept of VSWR. The modulus of the parameter |S11|, only in decibel scale expression, in the theory of microwave devices is called “return loss”. After all, part of the wave did not reach the load, returned to the abstract “port” and disappeared there without a trace, “scattered in the infinite microwave universe.” In practice, this, of course, does not happen, so “return loss” is the same VSWR, only “side face view”, and has absolutely nothing to do with real energy loss. Another parameter “mismatch loss” is usually associated with power loss, but it's also not at all equivalent to the real energy loss to heating the conductors, we are accustomed to. This immediately becomes clear if we return to classical circuit theory and replace the notorious “port” with the understandable “source”. Yet, in actual fact, additional heat loss in the microwave transmission line caused by high VSWR is actually also present. However, this is not the mismatch loss.

It should be noted that the value of return loss, expressed by |S11| is always less than one (in decibel terms it is always negative), because the reflected power cannot exceed the incident power. Which is logical. However, in theory there has long been a concept with the same name RL: return loss, but it is defined “upside down”, as the ratio of incident power to reflected power, and in decibel terms the value of such “losses” is always positive. At that, with the VSWR tending to unity, such “return loss” tend to infinity. We have an ideal VSWR, but some obscure “losses” are just off the charts! This can cause a serious break in the pattern for anyone. In fact, this value characterizes the degree of attenuation of the reflected wave in comparison with the incident one, but what a loss/damage this is, damn it! More like profit. Such an outrageous discordance between the concept and its definition is even noted on Wikipedia, quote:

This definition of “return loss” with a large positive value is older, it was introduced at the dawn of the development of microwave radio engineering in the “tube” era. The first network analyzer from Hewlett Packard HP8410 appeared in 1967 with the advent of good semiconductors. At the same time, the use of S-parameters became popular. It is very difficult to abandon the old, so the term “return loss” migrated as the definition of S11, confusion arose, and disputes about whether S11 is “return loss” in the engineering community do not subside to this day. However, in decibel terms, they differ only in sign and many do not even pay attention to this collision.

Parameter S21/S12 (“transmission coefficient”) is the ratio of the complex value of the wave at the output of the device to the complex value of the wave at the input. Let us note once again for a better understanding that the complex value of a wave is a measure of its amplitude and phase, characterized by a two-dimensional complex number, or a two-dimensional mathematical concept of a vector. Parameter module |S21|, in the theory of microwave devices, is called “insertion loss”. In the case of our transmission line example, “insertion loss” is the actual thermal loss of the line. Everything came together here. The wave in this case was actually partially dissipated while propagation along the line, and its energy was converted into heat. But this doesn't always happen. For example, the same S-parameters describe the properties of microwave transistors. In this case, S21 is the transmission coefficient of the transistor, close in meaning to the h21 parameter: the gain coefficient, not loss.

In an antenna with one port, we are doing with only one parameter: S11 or, in other words, the good old reflection coefficient Г. By calculating it in the simulator or measuring it with a vector analyzer, we can clearly calculate the input impedance, bandwidth and VSWR of the antenna. There are already four S-parameters in a two-port MIMO antenna. Moreover, S21/S12 in this case characterize the cross-port isolation between MIMO ports. In general, in antenna technology, energy should go where it needs to, that is, be radiated into space, and not “scatter” anywhere. Therefore, the modulus of any S-parameter of the antenna must be minimal or, in decibel terms, as negative as possible.

The question posed in the title of the article can be answered unequivocally. There is no difference between the reflection coefficient and S11, as well as between VSWR and return loss. By and large, all these parameters describe one the same phenomenon. They can be converted into each other using the above formulas; the web is full of tables of direct interralation between them. For example, level -6 dB on the graph |S11| equivalent to VSWR≈3. There is no point in arguing which parameter is better/correct. Use the one you are used to.

As we see, radio engineering in a broad sense, due to its complexity, has been divided into a scrappy set of narrow disciplines. Engineers working in a particular discipline come up with a concept that is convenient for their work, without really thinking that it has long been invented somewhere in a related field. As a result, the same phenomenon in different disciplines is described by different terms, or completely different phenomena are called by the same term. We have to put up with this fact.

Related links:

• Return loss - Wikipedia;
• Mismatch loss - Wikipedia;
• Scattering parameters - Wikipedia;
• Return Loss: A Collision Between Two Worlds - Where did the different definitions of return losses come from, and why were they called that?
• Online calculator of the loss in a coaxial cable, taking into account mismatch loss and additional losses due to VSWR;