Return Loss Bridges
RLBs can be used to measure antennas to see how close to 50 Ohm they are (what VSWR you can expect), they are also used to measure the input and output impedances of amplifiers, filters and other circuits.
A bridge made with half watt resistors cannot be used with a high power signal so you shouldn’t leave it in circuit when you want to actually use an antenna (you waste 75% of the transmitter power) so a SWR meter has some advantages over an RLB.
You can work out how an RLB works using transmission line theory or Ohm’s law, I prefer Ohm’s law.
A return loss bridge (RLB) is a simple 4 resistor bridge, with one of the resistors omitted - you put the device to be tested in its place. The abbreviation DUT is often used - the Device Under Test.
Two equal value resistors in series will divide the voltage across them
by two (provided little current is drawn away from their midpoint) If
the device to be tested is a 50 Ohm resistor then the voltage at point A
will be the same as the voltage at point B. The voltage between points A
and B will be zero
Applying a signal from a signal generator when the DUT is an accurate 50 Ohm load should give no reading(or a tiny reading near zero) at the detector output, everything is balanced and the voltage between A and B is zero.
Shorting the DUT terminals (or leaving them open/disconnected) gives a maximum voltage - the limit of what the bridge can generate. Attaching an actual DUT will give a voltage between the maximum limit and zero.
If the device is not 50 Ohms you can infer the impedance of the Device to be tested depending on how far away from the limit the detector sees. The limits when a real bridge has an output with the DUT left open or shorted, is a important reference and we divide it into the reading we get with the DUT connected. The open or short readings should be similar, within a dB or two. Use either, or halfway between them as the reference.
I say divide, but if the detector readings are in dBm we actually subtract the readings because dBms (or dBVs) are logarithmic numbers and you add or subtract logs to multiply or divide numbers. Don't worry about the theory, the practical things you need to use an RLB are straightforward. You take 3 or 4 readings and do a couple of subtractions.
A real detector output needs a Balun or choke to allow it to measure things with respect to ground. See the QST article at https://www.qsl.net/kl7jef/Build a Return Loss Bridge.pdf ; it is an excellent read and I reproduce some of its content here.
The two coils allow the measuring device to have one of its terminals at ground which is much more convenient that designing a differential input detector. You can also use a common mode choke, it acts to convert a balanced signal to an unbalanced one – as a Balun. You can make this with a large number of expensive ferrites or use a broadband ferrite transformer; the more expensive option works over a broader range of frequencies.
As I said above, we can convert voltages to dBV and subtract them instead of dividing the numbers – the answer is in dB. These are voltage ratios so you use 20 times the log of a voltage to get dBV. If your detector reads power in dBm directly, you can still subtract the two numbers and get dBs
In practice the zero point is never perfect, there is always some leakage, particularly as frequency increases so you should measure the (small) output when connected to a good 50 Ohm load. The difference in dB between the open or short case and the 50 ohm case is called the directivity of the bridge, how good it is. You cannot measure return losses greater than the directivity. Home-made RLBs might only have a directivity of 25 to 30 dB, commercial ones are higher 40db+ I got 35dB on my home-brew RLB using a single ferrite core (an FT50-43) at HF frequencies near 14MHz, I have yet to sweep it from 3.5 to 54MHz.
When you subtract your reference in dB(V or m) from the reading of something you want to test you get a negative number of dB because the reference is always bigger than the reading of your device under test. This number as a positive number of dB is the return loss and it represents the same thing as SWR but expressed in a different way. A table allows conversion. This is handy if your device under test is an antenna as we are used to SWR (technically we should say VSWR). We are used to having an antenna at VHF and above with an SWR of 1.5 or better, certainly better than 2:1. At HF an SWR of under 2:1 is ok and 3:1 will work for some transceivers if they have internal tuners or protection circuitry (that may reduce power a bit). Once you have SWRs getting below 1.2 or so then that is good enough, more accuracy is not needed. Just as well as the RLB can’t accurately measure really really good SWRs- expressed as return losses that are beyond the directivity; the limit of the RLB.
For example, if an open-circuit voltage of 1 volt drops to 0.1V with the device connected, the ratio also called the reflection coefficient, ρ, is 0.1 divided by 1 gives 0.1 and 20 times the log of (0.1) is -20 dB so we say the Return loss is 20dB and the table below gives us an SWR of 1.22:1 (from the Table). By the way ρ is the Greek letter rho and is conventionally used in equations – irrelevant to us if we just use the tables…
If your detector is a spectrum analyser you can take readings in dBm, if you get -10dBm when reading a short and -30dBm when taking a reading then the subtraction gives (-30) - (-10) which is -20, Return Loss is 20dB.
If your detector is a crude diode detector feeding a DVM then you need to take two readings, adjust your signal generator to give a high output when the device is connected, replace the device with an open or short and connect and adjust an attenuator between the signal generator output and the RLB until the diode detector has the same reading, the attenuation set is the return loss. The same trick works if you use a receiver with an S-Meter as the detector but switch off the AGC.
Note I like specifying Return Loss as a positive number of dB, a “LOSS” of 20dB is a reading of (-20)dB. However some people say the RL is -20 dB, including some manufacturers <sigh>. It is usually clear what is meant. Likewise it does not matter what reading you subtract from what as long as you write down the answer as a positive number of dB.
Antennas are easy to measure with an RLB although you obviously can’t leave the RLB in circuit when you connect up your transmitter so an SWR meter is handier, but an RLB can also measure coax loss, see the QST article listed above. You can also measure input and output impedances of amplifiers and other devices. You can see the passband of filters as it is the band of frequencies where the RL is high since this is when the input impedance is near 50 Ohms. Filters have much bigger or smaller impedances outside their passbands - they reflect the energy back and do not pass it. Unless it is a diplexor.
You can convert RL and SWR to an equivalent impedance using the formulae below, but of course a table is handier. I referenced the website https://www.yagicad.com/Bridge1.pdf for this;
The ratio of the voltages Vtest/Vopen is ρ (conventionally the greek letter rho), it will be less than 1.
So Return Loss RL = -20 Log10(ρ) You can also measure RL with a VNA, it is the same as S11 but with the sign changed S11 is usually a negative number of dB.
You can use the table above or below to convert S11 from a VNA to SWR but note the NanoVNA can do this for you using its display routines (not all VNAs do).
You can also rearrange the formula | ρ | = | (Z0-Zx)/(Z0+Zx) | to get Zx but again the table is easier.
Note all these measurements only work if the internal impedance of the signal generator and detector is 50 Ohms. If it varies a bit with frequency then you can use an attenuator between the generator and the RLB to bring its impedance nearer to 50 Ohms. Likewise if you are unsure of how good the 50 Ohm internal impedance of your detector is then you could add an attenuator between the RLB and it. The detector can be a spectrum analyser, a power meter, or just a simple diode detector feeding a DVM or even a receiver with an S-Meter but you must have accurate 50 Ohm internal impedances in your detector and signal source.
As mentioned in previous articles you can measure both input and output impedances (or return losses, or SWRs) at the input and output of amplifiers. Measuring Input Return Loss is straightforward as shown below. Remember to take a reading with the RLB device port shorted or open before connecting up the amplifier. The amplifier is the shaded triangle below. You are measuring the RL at a low power, if the amplifier is linear (class-A) then this is valid.
Measuring output return loss is a bit more complicated and risky although I haven’t blown up my SA yet! It is a theoretical risk, if you don’t check you will “probably” be all right… you force signals into the output. You MUST have a dummy load at the amplifier input, hopefully to ensure the amplifier itself is generating no output.
To test Output Return Loss you should first check that the amplifier is well behaved. Before connecting the RLB to the amplifier output, connect a dummy load to the output and a scope or a spectrum analyser (through a big attenuator) on the terminated output and check the amplifier has no output when its input is also terminated in a second dummy load. If there is instability in the amplifier it could be oscillating and generating its own spurious signal and outputting it despite having an actual input of zero.
Make sure the amplifier has a capacitor or transformer at the output so there is no superimposed DC on the output (do this any time you use a Spectrum Analyser although some have DC blocks provided, not all do).
You can use a RLB with low power resistors in these tests, even when testing higher power amplifiers. Once you move away from linear Class A amplifiers you are probably better testing SWR at rated output instead and adding a suitable inline SWR meter at the input of the amplifier – fed from a medium power driver amplifier which you should characterise (measure) first. I hope to experiment with an alternative load pull technique when I build higher power amplifiers that are not Class A; this involves using two dummy loads with slightly different values and solving simultaneous equations. I haven't seen this is any textbooks and it needs a detailed analysis of measurement errors. These may contrive to make the results too inaccurate if the two loads are too close together.
Once you have the return losses you can convert them to impedances and redesign or adjust matching networks as required. Note RLBs only give you the magnitude and not the phase differences of Zin or Zout. You want a magnitude of 50 Ohms in most designs. An RLB system is a SNA (Scalar Network Analyser) whereas a VNA is a Vector Network Analyser and can give you impedance as a complex number.
Practical Tests
Here are photographs of my homemade RLB and also a £10 ebay version. There is a similar version from the web at https://www.k8iqy.com/. He gives the schematic too – it comes from the EMRFD book that I so often quote. I used a FT50-43 with 13 bifilar windings of thin enamelled wire. It is fine between 3MHz and 50MHz (good to much higher actually but I am only building a 3 to 30MHz uBitx at present).
Here is my construction, I made a box out of PCB material, as small as practical. I also superglued a small square of PCB material to the floor of the box as a connection point.
I used pairs of 100 Ohm resistors connected in parallel to get 50 Ohm resistors, you could also use 51 Ohm resistors and accept a small inaccuracy.
I have soldered the remaining side and the lid on although I didn't see any difference in readings with the lid on or off.
All my readings were done at 13.035MHz but I have ordered a DDS signal generator and will make a sweep oscillator for my Spectrum analyser (My RSP1a SDR) and repeat for 3 to 50MHz (or higher). My Ferrite will be poor below 3MHz...
The Ebay version uses a common mode choke with lots of ferrites – better at higher frequencies
.jpg)
Note this needs R3, the third resistor added on the REF - reference port – you should add a 50 Ohm SMA dummy load – easily bought on EBAY. It needs to be very compact to work at 3GHz. You can use this RLB in 75 Ohm systems by using a 75 Ohm reference. You will also need a second dummy load to act as a load at the input or output of any amplifier you test, as per the diagrams above. You also need a shorted SMA and/or a open circuit SMA connector, though at HF you just leave the DUT unconnected, You take two readings and subtract them.
The version I bought from Ebay had a mistake in its wiring; the soldering was faulty, I had to add two wire links to parallel each pair of the 100 Ohm surface mount resistors. You can see them in the close-up above, I also re-soldered the top pads of one of the SMT resistors as there was almost no solder under the pads! Use the circuit diagram above and a simple Ohmmeter to confirm your connections. You should see 51 Ohms on J1 if only Rref is connected as R3 is floating and R2 is shorted by the balun. The resistance from J2 should be 100 Ohms since you are measuring through R3 and R1.
I then measured -14.5Bm with the DUT port open and -12.7dBm with it shorted, when I connected a 50 Ohm dummy load I got a reading of -51dBm, the open and short readings should be close to each other and using an average (which is not correct mathematically but it is handy) this gives about 38dB of directivity at 13MHz, this is very good, anything over 25dB is good enough, even 20dB is useful.
Hopefully you can see that RLBs are very simple devices, perhaps with less simple mathematics behind their use but be confident that using tables and ignoring the maths is easy. They only give the scalar value of return loss, the impedance is just in Ohms (if you convert the RL using the tables above) you do not get any phase information. There are two values of Ohms as well, above or below 50, you do not know which is the actual value, but as your aim is to adjust matching circuits or antenna lengths to get near 50 it doesn't matter which it is. The nanoVNA is better in this regard, but you can use the RLB to verify that the nanoVNA is giving viable readings. I like to have two ways of doing things!
Also worth knowing is that these RLBs have other uses; they can combine two signals and produce a single output where neither of the two signals interfere with each other. My two tone generator has one inside it.
Now to the results of testing the TIA amplifiers from the uBitx using both of these, a previous article showed the results of measuring S11 and S22 (S11 looking into the output port). I did these (too) quickly and so I have redone them here, I took more care that there were no loose connections and didn't touch anything during the tests.
I don’t have a tracking generator yet so I just took readings using one tone of my two-tone frequency generator (13.035MHz). You take a reading with the DUT port open or shorted and then a second reading with the amplifier connected to the DUT port and the dummy load connected to the other port of the amplifier. You subtract these two readings to get the return loss. You should also take a third reading with a dummy load connected and subtract this from the shorted or open readings as well, this is the biggest RL you can measure.
Result:
1. Measuring Zin of the TIA amplifier.
Using my homemade RLB, with a 20dB attenuator at the output of my signal generator and a -10dB attenuator on the input to my Spectrum analyser (SDRPlay's RSP1a) Gave readings of;
(i) DUT Port Open = -42dBm (ii) DUT Port Shorted = -42dBm
(iii) DUT Port to 50 Ohm gave -77dBm which is a directivity of 35dB ( i - iii)
(iv) DUT Port connected to input of TIA amp gave -68dBm so return loss is 26dB (iv - i )
This RL is bit low - in this test the amplifier is actually amplifying the test tone and I think this increases leakage which means the SA detector gives a reading higher than the true reading. Maybe I need a metal test bench or better shielding around the SA (the RSP1a SDR receiver). On the other hand 26dB is still a "good" value, good enough to not need matching circuitry...
Using the EBAY RLB gave slightly better readings and its directivity was better;
(i) DUT Port Open = -43dBm (ii) DUT Port Shorted = -43dBm
(iii) DUT Port to 50 Ohm gave -84dBm which is a directivity of 41dB ( i - iii)
(iv) DUT Port connected to input of TIA amp gave -74dBm so return loss is 31dB (iv - i )
2. Measuring Zout of the TIA amplifier. (Again with 20dB, not 6dB attenuation, and 10dB at the SA)
The homemade RLB gave a reading of -75dB which is a RL of 75-42 = 33dB
The EBAY RLB gave a reading of -74dB which is an RL of 74-43 = 31dB
The NanoVNA gave an S11 reading of -32dB, |z|=48.9 or a VSWR=1.05. If we were pedantic we could describe the S11 reading as an S22 reading as that is what you get when you look into the output port of a system under test
In summary all three methods are close enough, the lower input RL with the homemade bridge is probably due to leakage around the cables, but 26dB is still a very good Return loss and all these systems get better as the return loss gets worse. Also the TIA amplifier is working! time to get the VFOs going and then I am ready to make a uBitx - the receiver part.
Note, a few weeks after I first posted this, I gave a talk to my Radio Club, and have copied the slides to a further post here on RLBs, there is some duplication but I used the RLBs to measure coax cable loss. Look for a post on 12th October, 2022
