Toward a Simple Return Loss Bridge.

Wes Hayward, w7zoi, 27Feb2012, update 4March12

Abstract: The fundamental ideas used in the return loss bridge are reviewed. A simpledesign is then presented that covers the MF, HF, and VHF spectrum. This discussionsupplements that of section 7.7 of EMRFD.

Some Basics

An extremely handy tool for the home RF Lab is the return loss bridge, or RLB. Thisinstrument, usually intended for use in a 50 Ohm system, allows one to evaluate thequality of an impedance match. It is usually built as an accessory that is used with otherequipment. The RLB usually operates at small signal levels, so it is possible to examinethe input or output of small signal amplifiers, filters, or even receivers. The sameinstrument can be used for antenna impedance evaluation. Some basic schematicdiagrams are shown in Fig 1.

Fig. 1. Schematic diagrams that show the basic ideas and some variations of the ReturnLoss Bridge.

The concept for the return loss bridge evolves from Fig 1A, a traditional WheatstoneBridge. A battery is shown as the source, but the circuit can be used with an AC sourceand detector. This classic circuit uses an uncalibrated detector that serves as a nullindicator. An unknown resistance is attached to the circuit and the calibrated variableresistance is adjusted until no signal is seen in the detector. The two resistors on the leftside of this circuit, Fig 1A, are equal, so the unknown is equal to the calibrated resistancewhen there is a null response at the detector. It is not necessary that equal resistors beused on the left side of the bridge.

There are a seemingly unlimited number of bridge types. It's interesting to peruse theselections in Reference Data For Radio Engineers.

Figure 1B shows a radio frequency return loss bridge. The dominant departure from theclassic Wheatstone Bridge of Fig 1A is in the addition of transformer T. T is an isolationtransformer, also known as a common mode choke. The reader is urged to read theclassic paper by G. Guanella, "New Method of Impedance Matching in Radio FrequencyCircuits," Brown Boveri Review, September 1944, p327. This paper is widelyavailable on the web. The transformer connects the instrument at the Detector port,usually one with a 50 Ohm impedance, directly to the floating port at the other end of thetransformer. T isolates the floating port from ground, yet allows a differential signal toappear at the detector. The detector impedance appears at the floating port. Thesignal path is by way of the "differential mode" of the transformer while isolation isachieved from the common mode. The simplest versions of a RLB merely place abifilar winding on a ferrite toroid. The common mode inductance can be measured bytemporarily soldering the dotted ends of T to each other and the un-dotted ends to eachother to form a simple inductor with the usual single winding replaced by two parallelwires. The inductance is then the common mode value. The common modeinductance should be high enough to have a reactance of 5 times (or more) the bridgeimpedance (50 Ohms in these examples) at the lowest operating frequency for thecircuit. At the same time, the capacitance and resistance across the inductor should bothbe small enough that they do not present a low impedance common mode path betweenthe floating detector port and ground. The real subtlety of the circuit, and the genius ofthe Guanella work, is that T acts as a transmission line with regard to the differentialmode. Transformer modes are illustrated in Fig 2.

Fig. 2. Transformer Modes

Another difference between the classic Wheatstone circuit, Fig 1A, and the RF bridge of

Fig 1B is in the role of the detector. The Wheatstone detector is just a null indicator.However, a return loss bridge facilitates a measurement by using the information of thatappears at the detector port. Consider a normal measurement. An RF source isattached to the RF-In port and the Unknown-Load port is open circuited. The responseat Det, the detector port, is noted. An unknown is then attached and the response at Detis again noted. The ratio of the two, or the difference if logarithmic units such as dBmare being used, is the return loss, usually in dB. The characteristics of the instrument atDet. is a vital part of the overall measurement.

The RLB of Fig 1B differs from the Wheatstone in by using an external referenceimpedance. It is attached to the circuit in place of a simple internal resistor. This meansthat the reference contains all of the stray impedance elements that might appear with theunknown, including transmission lines. This external impedance is an option and is notrequired for all bridges.

Figure 1 shows two useful RLB refinements. Transformer T of Fig 1B has one windingconnected to ground at the Det port while the other end attaches to the detectorimpedance, typically 50 Ohms. This asymmetry is partially fixed by adding inductor L,shown in Fig 1C. Both the reference and the unknown ports now see an inductor toground. The added inductor is ideally an exact copy of transformer T, but wired as acommon mode element, as shown in Fig 2.

The quality of the transformer T was mentioned. Parasitic C and R come into play athigh frequency to compromise the high common mode impedance of a singletransformer. Fig 1D shows a topology where two Guanella transformers are cascaded.T1 of Fig 1D might be compromised with coupling around it at the high end of theinstrument frequency range. If T2 is constructed to have good performance at the highend, it may well correct the lower frequency difficulties.

The modifications shown in Fig 1C and 1D are common to many commercially builtinstruments, such as those found with some HP network analyzers.

Fig 3, The "String of Pearls Bridge."

A bridge variation shown in Fig 3 is sometimes called the SOP or "String of Pearls," sonamed because it resembles such jewelry. (This name was applied to the structure by acolleague, either W7PUA, or G4TXG.) Recall that T in Fig 1B formed a transmissionline to connect the detector to the floating port within the bridge. Hence, thetransmission line characteristic impedance is important. If it differs from the detectorimpedance, a transformed, frequency dependent impedance will appear at the floatingport. The transformer in the SOP is fabricated with a piece of coaxial cable that isloaded with ferrite beads. These might be toroids if the coax is large, but are more oftenferrite beads that have an inside diameter that will accommodate the coax cable. Thetransformer structure is duplicated and connected to emulate the inductor of Fig 1C. It isbest to use ferrite that fits tightly against the coax to effectively choke the flow of currenton the outside of the coax. A large enough collection of beads is added to have suitablelow frequency inductance. Most implementations of the SOP RLB use a mixture offerrite types, creating a transmission line version of Fig 1D.

Ferrite loaded coax cable structures have been around for a long time. For example seeC.G.Scntheimer, US Patent 3,492,569, "Bridge Circuit Network for Measurement ofReflection Coefficient." An excellent paper within the amateur literature is MichaelMartin, "Wideband Directional Coupler for VSWR Measurements in Receive Systems,"VHF Communications, Issue 3, 1983, pp153-162.

Measurements

There are two frequency dependent parameters that characterize the bridges that webuilt. The first is called directivity which is a measure of the bridge response when the"unknown load" is a perfect 50 Ohms. To measure directivity, a generator is attachedand set to the frequency of interest. The unknown port is open circuited and the power atthe detector port is noted. The "perfect" load is then attached and the new power isnoted. It will be (we hope) much lower than the calibration response from an open.The ratio of the two powers is the directivity. A good goal for directivity is 30 dB ormore. Directivity is a measure of how well the bridge does in measuring impedancesclose to 50 Ohms.

The second parameter of interest is the Open-Short ratio. This is a comparison betweenthe response with an open circuit and a short circuit applied to the unknown port. Bothcases represent very high reflection or high VSWR. A good bridge will have OS valuesof less than 1 dB. This is a measure of the bridge response to very poorly matchedimpedances, "on the edge of the unit circle."

Fig 4. Open, Short, and Load elements used for bridge evaluation.

Most of the bridges in our experiments used SMA connectors. This connector isconvenient for easily built evaluation fixtures. An ideal "open" was obtained bygrinding the center pin down with a Dremel tool as shown in Fig 4, left. The short wasbuilt with a small piece of metal with a center hole that was placed over the connector,followed by soldering everything to everything else. The "perfect" 50 Ohm load consistsof four 200 Ohm, 0.1 % 0805 SMT resistors soldered to a modified SMA header.Calibration with a set of references of this sort is referred to as OSL Calibration.

The difference between a clean "open" (left element of Fig 4.) and merely leaving theunknown port connected to nothing was no more than a 0.1 dB up to our measurementlimit of 500 MHz. But a small phase variation is easily detected when VNAmeasurements are done. The elements of Fig 4 were originally built to calibrate a bridgeused with an N2PK vector network analyzer. See N2PK.com.

A wide variety of measurement tools were used as the RF source and as the detector.More often than not, a simple signal generator was used, followed by enough of a 50Ohm pad to provide a clean source impedance. The usual detector was just an AnalogDevices AD8307 based power meter. It is important to keep the RF level at the powermeter below -10 dBm when operating above 400 MHz, for we discovered errors withhigher levels. In some cases we used a spectrum analyzer as the detector. In othercases the VNA was used as both the RF source and the detector. The VNA is the idealinstrument, but the N2PK design only operates to 60 MHz.

Once a bridge has been evaluated, it can be used for measurements. The measurementprocedure starts with an open circuit applied to the "unknown" port. The detectorresponse is noted. The unknown impedance is then attached and the detector response isagain noted. The ratio of the power levels is called the return loss. If the powers aremeasured in dBm, the difference is the return loss in dB, a positive value for passiveloads. Reflection coefficient (often signified by Gamma), return loss, and voltagestanding wave ration (VSWR) are all related. See http://w7zoi.net/retloss.pdf.

Experiments and Some Results

This report is not intended to be an exhaustive study. While all of the bridge circuitsmentioned above have been built, only limited data will be summarized here. The goal

is to present a design that will do a reasonable job from the bottom of the MF spectrumthrough the top of VHF. The device goals are D>30 dB and |OS|<1 dB.

In all of the bridges built, the resistors attached to the RF source were always SMT types,usually 1206. Some of the circuit boards will be seen in later photos. An externalreference on a coax connector was used for all of the bridges built.

The bridges presented in EMRFD often used a FT37-43 core. This was a poor choice.The core is something of a standard, and there is good reason for this: it works well formany of our applications. The -43 material is popular for wide band low impedancetransformers and for EMI suppression. But it is a lossy material and this loss willcompromise the performance as a bridge transformer. The -43 initial permeability isabout 850, low enough to make it difficult to obtain good low frequency performance.Remember that this bridge is an application where the impedance is often much differentthan 50 Ohms. We found that the Amidon "J" material with an initial permeability of5000 offered better bridge performance. The J material is similar to -75 material.

All transformers are wound with #32 enameled wire, twisted to about 7 full turns perinch. The windings are evenly spaced on the toroids to minimize turn to turncapacitance. Initial measurements showed this to be reasonable close to a 50 Ohmtransmission line, although optimization is definitely in order. The more common #28wire was tried, but did not work as well owing to added turn-to-turn capacitance with 10turns.

Fig 5. A comparison of three designs.

Figure 5 above shows measurements from 0.1 to 500 MHz for three simple bridges. Theblack and red curves use the circuit of Fig 1B, the classic RLB. The black curves showdirectivity and Open/Short results for a bridge using a single toroid as the transformerwhere T consists of 11 bifilar turns of #32 wire on a FT37-61 core. This is a materialwith high Q, but very low initial permeability of 125. The common mode inductance isonly about 5 uH, so it is not surprising that directivity is poor at low frequency.However, this very simple bridge provides good directivity up to 500 MHz. The bluetraces show the performance with 10 bifilar turns, also #32, on a FT37-J core. The highfrequency performance is not as good as the -61 core, but the performance is good from0.5 to over 100 MHz.

The red curves of Fig 5 illustrate a cascade of the two transformers described andmeasured individually. There is a significant improvement in both VHF directivity andO/S with the cascaded cores. Two of the bridges described by the red curves are shownbelow in Fig 6. Most of our work used the SMT versions, for we had the best referenceelements for OSL measurements. However, some have been built with BNCconnectors.

Fig 6. Photos show bridges with SMA and BNC connectors. The schematic is that ofFig 1D. The boards were designed to accommodate SMA connector on the board edge,but where then modified with a nibbling tool or file when walls were placed around thestructures. There was minimal performance difference between BNC and SMAbridges. The toroids are only supported by the windings. Other builders may want tocut a rectangular hole in the board that would accommodate the toroids. Some Siliconecaulking might then hold the core in place. Holes in the board with very small cable tiesthrough the toroid and the holes might also do well. The ground plane was removedunder the toroids in some cases, but with no observed results.

The next experiment addressed the effectiveness of adding the inductor of Fig 1C. Twobridges were evaluated. The first used 10 bifilar turns of #32 wire on a FT37-J core.Data for this bridge is shown in the red curves. Then an inductor, again 10 turns on aFT37-J core, was added. A DVM was used to determine which side of the bridge wasgrounded, revealing where the inductor should be added. The data is shown in Fig 7below with a photo in Fig 8. The extra inductance clearly helps the low frequencydirectivity.

Fig 7. Effect of adding an inductor to the simple bridge. See figures 1B and 1C. Thesemeasurements used a VNA sweep that stopped at 50 MHz. It is not clear if the finestructure at 50 MHz in the OS response is real or the result of a measurement anomaly.

Fig 8. Photo and schematic for the simple bridge with an added inductor.

A simple bridge suitable for duplication is described in the next measurement. It is builtwith the schematic and photo shown in Fig 8 above. Only 7 bifilar turns is used on eachof the FT37-J cores. It was reasoned that some low frequency performance could besacrificed for improve high frequency performance. The results are shown below in Fig9. These measurements used two manually tuned signal generators and an AD8307based power meter with digital readout. The power meter has a reading of -75 dBmwith no applied signal, the result of wideband circuit noise. This compromised thedirectivity readings. The actual directivity may be better than shown.

Fig 9. Directivity and Open/Short performance for the simple bridge of Fig 8, whichfeatures an added inductor. The design goal mentioned earlier was met except at 300MHz where directivity was only 28 dB.

The reference impedance for the bridge of Fig 8 is a coaxial element essentially identicalto the one that we use for directivity measurements. Indeed, most of the bridges wehave built emphasized this symmetry. This is probably not required at HF/VHF and a49.9 Ohm SMT resistor could be substituted, making the construction simpler andreducing cost. Experiments are definitely in order.

Conclusions and Other Experiments.

The simple bridge with a transformer on a J core with an added inductor is an easy bridgeto built, yet one that should satisfy the needs of most experimenters. But there are manyother bridges that can be considered. One obvious one is to add external inductance tothe bridges of Fig 6. This experiment was done and the low frequency directivityimmediately became excellent. However, the behavior between 300 and 500 MHz wascompromised. Further work is required.

An experiment that needs to done is to evaluate a simple bridge with a single transformeron a -61 core with a matching -61 shunt inductor. Cores somewhat larger than the 0.37inch OD size might be in order, for they would allow slightly more common modeinductance than achieved with a FT37-61 core shown in the black curves of Fig 5.

Bridges using the String-of-Pearls structure need to be investigated in more detail. Onecolleague (W7PUA) built one with excellent wide band performance, although he used aHP VNA to adjust it. Several SOP bridges have appeared on the web in recent times.Three url are suggested.

http://www.ve2azx.net/technical/RLBridges.pdfhttp://www.yagicad.com/Projects/RLBConv.htmhttp://www.yagicad.com/Projects/ARRLB.htmAnd how could we forget the wonderful work of Scotty who has built several bridges.See http://scottyspectrumanalyzer.com/

This RLB project has encompassed several years of sporadic experimentation andnumerous email discussions. I sincerely appreciate the interactions with N7FKI,W7PUA, G4TXG, and WA7TZY.