Everything You Should Know About Return Loss Measurements Using a Directional Coupler

Figure 5a : Phase response of a transmission line of 10 cm with a velocity of propagation of 2x10⁸

Figure 5b : Group delay of the transmission line from figure 5a

Figure 5c : Phase response of a 1-st order Butterworth LPF with W₀ set to 0.5 GHz

Figure 5d : Group delay of the LPF from figure 5c

2.5 Return Loss and Impedance Measurements

The reflection coefficient is often expressed as the return loss (RL) in dB:

RL(dB) = - 10 Log (|Γ|²) = -20 Log (|Γ|)    (4)

and, consequently

|Γ| = 10^{(-RL / 20)}    (5)

The minus sign is introduced to get a positive number that expresses a loss. The return loss is a convenient parameter to use when the value of Γ becomes small. Note, that in this conversion to return loss all phase information is lost. Therefore, the return loss parameter RL can only be used to express the mismatch of R_L to Z₀.

2.6 Adding VSWR to the Mix

Another much used way to indicate the amount of impedance mismatch between Z_L and Z₀ is the Voltage Standing Wave Ratio or VSWR for short. First, we will explain what the physical meaning of VSWR actually is and then take a look at the relations between VSWR, Return Loss (RL) and Γ.

2.6.1. The Physical Phenomenon VSWR

Again, we take a look at a wave that propagates through a transmission line which is terminated with a matched load as in Figure 4. So, there will be no energy reflected into the line. If we would observe how this wave propagates along the line, we would see that its maximum (peak) amplitude values move along the line in the direction of propagation (Animation 1). Also, at every point along the line, the amplitude of the wave is the same.

Please note that the x-axis in the animations and pictures in this paragraph represent the distance along the transmission line and not time! If you would look at some fixed point along the line you would see the amplitude at this point developing as a sinusoidal function of time. As can be observed when looking X=0.

Now we terminate the line with some impedance not equal to Z₀. In this case, some energy of the wave will get reflected into the line,  represented by the blue trace. This wave will interfere with the forward traveling wave (red trace) causing amplitude maxima and minima at the places along the line where the waves will add and subtract, due to their phase differences (black trace) as demonstrated in animation 2. The ratio between these maxima and minima is called the Voltage Standing Wave Ratio (figure 6).

VSWR = V_max / V_min (6)

Finally, we look at the example in which the line is not terminated at all. Now, all energy is reflected, causing maxima that are double in amplitude and minima that are equals to zero (due to total cancellation). In this situation, the VSWR approaches infinity. If we would observe the direction in which these maxima and minima travel, we would discover that they are not moving (black trace). Hence the name standing wave (animation 3).

If we go back to the first case of the transmission line with a matched termination, we can now understand that the VSWR is equal to one because there is no difference in amplitude along the line.

VSWR can be measured by probing the amplitude of the wave at several points along a transmission line and, in this way, find its maximum and minimum values. From there, the ratio is easily calculated. Also, phase information can be retrieved from the position where the minima and maxima appear along the line. However, this type of measurement is, in most cases, very impractical and cumbersome. Therefore, in practice VSWR is derived by measuring the reflection coefficient which caused the VSWR phenomenon in the first place.

2.6.2. VSWR, Γ and Return Loss (RL)

From the previous section we know that VSWR is a measure of the impedance mismatch as indicated by the magnitude of the reflection coefficient Γ. In paragraph 2.3 we already learned that the Return Loss (RL) is derived from |Γ| too. So, both VSWR and Return Loss can be used to describe |Γ|. They can also be converted into each other by the following equations:

VSWR = (1 + |Γ|) / (1 - |Γ|)                    (7)

|Γ| = (VSWR - 1) / (VSWR + 1)                (8)

and, also:

RL(dB) = -20 Log (|Γ|) = -20 Log [ (VSWR - 1) / (VSWR + 1) ]      (9)      using (4) and (8)

VSWR = (1 + 10^{(-RL / 20)}) / (1 - 10^{(-RL / 20)})                                (10)    using (7) and (5)

It can be helpful to look at Table 1, where we collected some common values of |Γ|, RL and VSWR to see how they are related. VSWR values are not very convenient when |Γ| gets smaller than 0.1. Return Loss expresses the complete range conveniently due to its logarithmic character. VSWR is often specified as a ratio. E.g. 1.2:1 instead of 1.2.

2.7 Putting It All Together

There are a lot of applications where reflections caused by an impedance mismatch are the main concern. The mismatch can be calculated by measuring the magnitude of the reflection. That is the first class of measurements we might encounter. It uses relatively simple measurement techniques because there is no need to measure phase information as well.

The second class of reflection coefficient measurements also measure the phase change. Besides measuring the mismatch relative to Z₀, we can now also calculate the impedance (both the real and imaginary parts) at the discontinuity. This technique is more complex because phase information has to be captured too.

VSWR measurements are seldom what its name suggests. Usually, VSWR is calculated from a reflection measurement instead of being measured directly.

So, it all boils down to measuring reflections. The device that is used for this task is the directional coupler, the subject of our next topic.

3. Measuring Reflections with a Directional Coupler

There are two fundamentally different ways to measure reflections. The first one is to measure the reflection in the time domain using a TDR (Time-Domain Reflectometer) and the second one is to measure it in the frequency domain using a VNA (Vector Network Analyzer) or SA (Spectrum Analyzer). The first method leads to results as visualized in Figure 7. The advantage of measuring in the time domain is that you can easily track the signal as it propagates through the system and, thus, separate the effect of the different discontinuities that the signal encounters during its journey.

When measuring in the frequency domain, we use the (to an RF engineer) well-known S_XX-parameters and Smith Charts views to present the impedance mismatch over frequency.

Note that both views represent the same information and, indeed, the frequency domain information can be transformed to the time domain and vice versa using FFT techniques. Modern TDRs and VNAs support this kind of functionality.

The advantage of a VNA or SA over TDR equipment is that they have a much lower noise floor and better dynamic range, due to their operating principle based on a narrow bandwidth sweep through the spectrum. The VNA can also add to this mix its high measurement accuracy thanks to its error correction procedures.

For these reasons, the majority of VSWR, Return Loss (RL) and S_XX parameters measurements are done in the frequency domain using a VNA- or SA- based test setup.

At the heart of a reflection measurements in the frequency domain is the directional coupler. VNAs usually have them built in, while reflection measurements with an SA always use an external coupler.

3.1 What is a Directional Coupler?

From our perspective, a directional coupler is a three port device (Figure 8) which passes a test signal from Port 1 to the DUT at Port 2 (S₂₁) and measures the signal that gets reflected at the DUT back at Port 3. Note, that the latter is attenuated by S₃₂. Therefore, the received signal at Port 3 is attenuated by an amount of (S₂₁ + S₃₂). When we compensate for this attenuation (by some calibration procedure) we can measure the reflected signal right away.

There is a catch however. In general, our three-port device will also pass the signal at Port 1 to Port 3 (S₃₁). This can render our measurement quite useless if the signal due to S₃₁ is strong enough to interfere with our measurement. The weaker the reflected signal, the bigger this problem will be. Also, the two signals that arrive at Port 3 add as vectors. Which will cause peaks and zeros where they are in- and out- of phase. So, we want to have a device with a S₃₁ as close to 0 as possible.

Because we want a small S₃₁ we call this parameters the isolation of the device. The difference between the reflected signal intensity (S₂₁ + S₃₂) and the interfering signal due to S₃₁, is called the directivity D:

D = S₂₁ + S_{32 -} S₃₁        (11)

The directivity has a strong effect on the accuracy of the measurement.

3.2 How to Measure Reflection with a Directional Coupler?

A typical return loss measurement setup is shown in Video 1. It consist of a Spectrum Analyzer (SA), a directional coupler, the DUT and cables to interconnect the components used. It may not be clearly visible from the picture, but the measurement cables are high-quality, semi-rigid cables. It is not a good idea to save on the quality of measurement cables when measuring into the GHz range. Before the setup can be used, it should be configured according to steps similar to the ones shown in Video 1. The video shows how to use a Siglent SSA 3032X spectrum analyzer while using a Gquipment SPLT-HY1-1-1000-A directional coupler.

The necessary configuration steps can be summarized as:

- Configure the SA for the frequency of interest and enable the tracking generator. The output of the tracking generator is used as the measurement sources and is connected to Port 1 of the directional coupler.

- Eliminate the effect of S₂₁ + S₃₂  in the SA reading. We do this by using an open termination at Port 2 so that all energy is reflected. So, what you see at the SA is just the effect of S₂₁ + S₃₂ alone. Now, use the normalization function of the SA so that this trace is seen as the 0dB level.

- Evaluate the directivity of the coupler to get a feel of the accuracy we can expect from this measurement setup. After the normalization step, connect a perfect 50-Ohm termination at Port 2. Now, there will be no energy reflected back. So, we only see the level created by S₃₁ minus (S₂₁ + S32) because that is the level at which the SA is normalized to. Put in other words, we are looking at the directivity right away. Easy! (Figure 9).

If the coupler has a high S₂₁ + S₃₂  (that is, a high insertion loss and low coupling) the measured signals can get quite weak. So care must be taken to keep the noise floor of the SA low. This can be achieved by using a higher tracking generator level, a pre-amplifier and lowering the Resolution Bandwidth.

3.3 Measurement Errors and How to Prevent Them

There are three phenomena that have an important influence on the accuracy of a return loss measurement with a directional coupler and an SA. We will look at all of them in succession.

3.3.1 Changes in the Plane of Reference at Port 2

From Paragraph 2.4, we learned that the shear length of a transmission line changes the impedance seen at the near-end of the line. This means that one should not create any distance between Port 2 and the DUT. The plane of reference can only be moved if a VNA is used that can compensate for the effect by de-embedding the device (e.g. using the port-extension feature).

Figure 10 shows what happens if the plane of reference is moved by creating some distance between the DUT and Port 2 in a typical setup which uses an SA. The effect of extra line length is related to the wave length of interest, so at high frequencies there is much less additional length needed to disturb the measurement! In the example, the frequency span is from 1MHz to 1 GHz.

3.3.2 Adherence to 50 Ohms of the Coupler's Port Itself

The port at which the DUT is connected should be as close to Z₀ as is possible. If it is not very close to the reference impedance of 50 Ohms, we are measuring against a faulty reference impedance. For example, if Port 2 has an impedance of 60 ohms and the DUT is 50 Ohms, we will measure an impedance mismatch with in this case is a return loss of 20.8 dB.

Therefore, a good quality directional coupler must possess very well matched ports too. In Figure 11 you will find a plot of the return loss of Port 2 and its impact on impedance mismatch, based on equation (14).

RL(dB) = -20 Log (|Γ|) = -20 Log[ |Z_L- Z₀| / (Z_L + Z₀) ]               (12)

We rewrite (12) as:

10^{(-RL / 20)} = [ |Z_L- Z₀| / (Z_L + Z₀) ]                                            (13)

Z_L = Z₀ (1 + 10^{(-RL / 20)}) / (1 - 10^{(-RL / 20)})                                  (14)

with Z₀ = 50 Ohms.

3.3.3 Measurement Error caused by the Finite Directivity of the Coupler

Finally: a coupler with a (very) high directivity is necessary if you want to take accurate measurements on a DUT with a low return loss. In this situation, the directivity quickly becomes the limiting factor. Again, we assume the use of an SA. A VNA uses error-correction procedures to greatly enhance the accuracy and (by the way) already has its couplers built in. So, we don't pay attention to that solution in this section. Although the underlying principles of coupler directivity and the impact on accuracy are the same.

Understanding the effect of directivity on accuracy starts by realizing that in the coupler the reflected signal with a level set by (S₂₁ + S₃₂) and the signal from Port 1 (set by S₃₁) both meet at Port 3 where they add up as vectors. That is the signal we observe at the SA. For the sake of this discussion, we denote the signal set by (S₂₁ + S₃₂ ) as the reflection signal R, and we call the signal created by S₃₁ the isolation leakage signal L, both of which are vector quantities.

If the signal strength from R is much larger than the isolation leakage signal L, the addition of R+L will closely follow R and the SA will display an accurate measurement. When R gets lower (DUT with a better return loss) and reaches the level of L, the result of R+L will have peaks and zeros because of their phase differences. When R gets much lower than L, we will only see L at the SA and no information of R will be revealed. See Figure 12 for a visualization of the effects.

We can also plot the maximum error as a function of the return loss for a given directivity. Then we can generate a chart by plotting this error function for different values of the directivity and use it to estimate the directivity that is necessary to make a measurement for some target return loss of the DUT. With a specified maximum error.

The chart in Figure 13 is generated by calculating the maximum errors which occur when R and L are in phase (the upper half of curves) and when they are 180 degrees out of phase (the lower part of the chart). Note that the curves at the lower half of the chart run much deeper, because in this area the two vectors can actually cancel out. The chart is rendered for 7 distinct directivities, ranging from 10 to 40 dB in steps of 5 dB.

When we examine the chart, we will discover that in order to get at a reasonable accuracy the directivity of the coupler used should be quite high. For example, if we want to be able to measure a return loss of 20 dB with an accuracy of 3 dB, we already need a coupler with a directivity of approximately 35 dB. If we demand a maximum error of 1 dB, the directivity must be higher than 40 dB.

Examples of broadband directional couplers with a high directivity are:

• Gqguipment, DIRCPL-6-1-1000-B, frequency range from 1MHz to 1 Ghz with a insertion loss and coupling of 6 dB.
• Gqguipment, DIRCPL-10-1-1000-B, frequency range from 1MHz to 1 Ghz, with 4 dB insertion loss and 10 dB coupling.

Fortunately, there also exists a whole range of return loss measurements that don't need very high accuracy. We will look at some of them in the section about Applications.

3.4 How to Evaluate a Directional Coupler?

There is a lot to tell about the relevant parameters of a directional coupler. The way they are designed has a great influence on their parameters. So, some insights into the design can help you to choose the right coupler for the job. There is already an article that covers a broad range of 3-port devices and its operating principles, including directional couplers.

4. Applications

Return loss measurements have many applications. In this section we will take a closer look at them.

4.1. To Optimize Power Transfer

If a transmission line is not well matched with its load, it will reflect energy back into the line with less power transferred to the load as a result. An example of this situation is a power amplifier that is connected to an antenna which is not well matched to the characteristic impedance of the feed line. If the match is really bad, the amount of power reflected back into the amplifier can even destroy the amplifier circuit. Most power amplifier therefore measure the amount of reflected energy and switch off if too much energy is reflected.

To prevent such failure, the antenna’s match to the characteristic impedance is verified with a return loss measurement (Figure 14). Often, the return loss reading is expressed as a Voltage Standing Wave Ratio (VSWR). A VSWR of 1:2 or lower is, in general, considered safe. This is equivalent to a return loss of 9.54 dB. The example antenna in Figure 11 has an excellent match at 948MHz with a return loss of around 20 dB.

4.2 Minimizing Amplitude Variations

In Section 2 we learned that reflections also lead to amplitude variations in a transmission line as a function of both distance and frequency. In most applications this is not very desirable. The most fundamental way to remedy this is to create a situation in which all impedances are well matched. But this is not always possible. For example, many RF mixers have ports that are not well matched to Z₀. A common solution for these kinds of problems is to add some attenuation in the line. The effect of an attenuator is that it will attenuate the incident wave and when it gets reflected the wave will be attenuated a second time. Because Return Loss (RL) is nothing more than a ratio between reflected and incident power, the RL will improve with twice the attenuation used (Figure 15).

Note that, because a long coax cable attenuates too, a VSWR measurement of an antenna at the near end of the antenna feed line will give you a better VSWR reading then when you took the measurement at the antenna port itself!

To minimize the effect of amplitude ripple, measurement cables are often connected to an SA by using attenuators to improve the RL at the SA ports. In these cases the attenuator must itself possess a very low VSWR, to not create a new source of impedance mismatch. The set-up shown in the pictures also uses two high quality 6 dB attenuators at the input and output port of the SA to improve the flatness of the frequency response of the measurement system itself.

Figure 16 demonstrates the effect of attenuation on the RL of an DUT that consist of nothing more than a not terminated coax cable.

This DUT will reflect all its energy, so we expect a return loss of 0 dB. However, there is a ripple caused by the length of the cable (as explained in Section 3.3.1). If we put a 3 dB attenuator at the end of the coax (also not terminated!), RL improves by 6 dB. The same happens with an attenuator of 6 dB which creates a RL improvement of 12 dB.

4.3 Antenna Tuning

If we want to transmit RF power to air, we need an antenna. The function of the antenna is to radiate the RF energy it is fed with. It turns out that an antenna possesses a frequency dependent complex impedance at its (from our perspective) input port. Antenna tuning facilitates the power transfer from the RF amplifier to the antenna system. Note the resemblance with Paragraph 4.1.

Counter to common belief, a tuned antenna is not a necessary condition for an antenna to radiate RF energy. It merely assists in the aforementioned power transfer between antenna driver and the antenna itself.

The port of a tuned antenna will have a real impedance, meaning that the voltage across and the current flowing into the port are in phase. If the antenna is operated at a frequency in which the antenna is not resonant (or mistuned) the impedance will have a large inductive or capacitive component. Voltage and current are not in phase anymore. Energy fed to the antenna will be stored in its near field and gets returned to the antenna port. So, in this situation, the return loss of the antenna system will be very bad indeed.

All this means that we can evaluate an antenna match by measuring its impedance mismatch to Z₀ By measuring the return loss of the antenna. A non-resonant antenna system in general has a large imaginary impedance component. We can see in Figure 2 (the green and red lines) that in this case all energy will be reflected as (|Γ| reaches 1. At the resonant parts of the antenna spectrum, there will be much less energy reflected (much smaller |Γ|). So, the expected return loss plot of an antenna system will be approaching 0 dB return loss with valleys (high return loss) where it is resonant (Figure 17).

A common procedure is to tune an antenna to the desired operating frequency. A real-time return loss measurement with an SA and directional coupler assist in this procedure greatly. In this demonstration the antenna is tuned by cutting its wire to the appropriate length.

4.4 Impedance Measurement

If you want to measure impedance (instead of a mismatch to Z₀) you should use a properly calibrated VNA. Due to the limitations inherent to the transformation from Γ to impedance (as visualized in Section 2) it is not possible to accurately measure impedance values that are much bigger or smaller then Z₀. If a larger impedance range must be covered then return loss measurement-based equipment is not a good fit.

The main advantage of the VNA for impedance measurement is not its impedance range or precision but its extended frequency range well into the tens of GHz if needed!

4.5 Filter Measurements

Return loss measurements can reveal some interesting properties of filters that otherwise could stay unnoticed. It is best illustrated with an example of two filters with rather similar insertion loss characteristics, but very different return loss figures. Filters with low return loss figures in their stop band(s) will reflect almost all energy back to its source. A well-known example where this could be problematic is a mixer which IF port is directly followed by some band pass filter because most mixers don't behave well when RF energy is reflected at its IF port. This situation can be solved by inserting a buffer amplifier with a matched input or by using a diplexer which has acceptable return loss figures over a broad range of operating frequencies.

In Figure 18 the same idea is shown for a notch filter. Both implementations reject frequencies around 5 MHz but differ substantially in their return loss plots.

Figure 18a,b : Notch filter - insertion loss and return loss. Return loss is nearly 0 dB at 5Mhz

Figure 18c, d : Diplexer insertion and return loss. Return loss is around 20 dB at 5Mhz

5. Conclusion

In this article we looked at the phenomenon of return loss measurement both from a theoretical and practical viewpoint. We discovered that reflections play an important role in transmission lines and that they can tell us a lot about impedance mismatches and discontinuities. Reflections are measured with the help of a directional coupler. To make accurate measurements with an a-priori known error margin, the directivity of the coupler is one of the critical factors to consider.

However, the best way to really understand how it all works is to start experimenting by yourselves. So, get into the lab and start playing!