A Better Antenna Balun

Which balun to use? The hybrid balun promises advantages over both voltage and current baluns.

By Andrew Roos, ZS1AN

aluns that are situated be- is effective only if the load impedance Fig 1. Although ZW is shown on only tween an antenna tuning unit is well balanced with respect to one of the transformer windings, its Band a non-resonant antenna ground. effects are felt equally on both wind- may be subjected to high-impedance, I then introduce a new design: the ings due to the coupling action of the highly reactive or unbalanced loads “hybrid” balun, which overcomes these “ideal transformer,” which can be that can prevent the balun from func- limitations of the voltage and current expressed by two rules: tioning effectively. baluns. It can operate with much 1. The currents in the two windings In this article, I apply the analyti- higher load impedances than can cur- of the “ideal transformer” are equal cal model of the transmission-line rent baluns and with unbalanced load and opposite. transformer developed by Roy impedances that voltage baluns could 2. VAC = VBD = (I1 – I2) ZW Lewallen1 to analyze the performance not drive effectively. The article con- The model assumes that the length of the 1:1 current balun and the 4:1 cludes by describing a simple test I of the transmission line used to con- voltage balun in this application. The conducted to confirm that the hybrid struct the TLT is short in terms of analysis shows that the current balun balun operates as predicted. wavelength, so transmission line ef- operates effectively only for small load fects can be ignored. Although this as- impedances, while the voltage balun Lewallen’s Model of a 1:1 Trans- sumption holds for the lower part of mission-Line Transformer 1 the HF region, some transmission- Notes appear on page 34. Lewallen models the 1:1 transmis- line effects do come into play at higher sion-line transformer (TLT) as an frequencies. PO Box 350, Newlands ideal 1:1 transformer with a “wind- The use of this model does not im-

7725, South Africa ing impedance,” ZW, in parallel with ply that TLTs operate like conven- [email protected] one of the windings,2 as shown in tional transformers. The ideal

Sep/Oct 2005 29 1:1 transformer is simply a modeling The 4:1 Voltage Balun I2 = VS / Z2 convenience, and the resulting model We can use the same model to ana- We can calculate Witt’s measure of applies to any device that exhibits lyze the performance of the Ruthroff’s imbalance: common-mode impedance, irrespec- 4:1 voltage balun shown in Fig 3. Once tive of its operating principle. IMB = 2 |I – I | / |I + I | again, Z1 and Z2 represent the load. 1 2 1 2 According to Lewallen’s model, the = 2 |Z – Z | / |Z + Z | (Eq 4) The 1:1 Current Balun 2 1 2 1 voltages across the two windings of the Fig 2 shows the schematic of transmission-line transformer (TLT) The degree to which the currents Guanella’s 1:1 “current” balun. Z and 1 are equal, and both equal VS, so are balanced depends only on the bal- Z represent the load. The junction ance of the load impedances with re- 2 I = V / Z between Z1 and Z2 is grounded to rep- 1 S 1 spect to ground. In order to keep resent the (typically capacitive) cou- and IMB ≤ 0.1, the impedances must be pling of the antenna system to ground. The load is balanced with respect to ground when Z1 = Z2. The principle limitation of this balun is that it can only maintain balance between the currents flowing into I 1 C the load, I1 and I2, for relatively low A load impedances. The ability to maintain the correct current balance in the I 2 I 1 load is of course the reason for using B D a balun in the first place, so the extent to which a balun maintains this balance is the primary measure of its I -I Z W effectiveness. In the case of the 1:1 cur- 1 2 rent balun, Lewallen shows that qx0509-roos01 I / I = (Z + Z ) / Z (Eq 1) 1 2 2 W W Fig 1—Lewallen’s model of the 1:1 TLT.

Where ZW is the “winding impedance” (common-mode impedance) of the balun. We can use this to calculate the measure of imbalance pro- posed by Witt3 as: I 1 V S

IMB = 2 |(I1 – I2) / (I1 + I2)|

= 2 |(I1 – I1 (Z2 + ZW)/ ZW) / (I1 + I1 (Z2 Z 1

+ ZW)/ ZW)|

= 2 |Z2| / |(Z2 + 2 ZW)| (Eq 2) (Note that |X| means the magnitude of complex variable X.) If IMB is Z 2 small, then |ZW| >> Z2. So as a good approximation, I 2

IMB = |Z2| / |ZW| (Eq 3) Although Witt does not suggest an qx0509-roos02 acceptable maximum figure for IMB, 0.1 seems a reasonable value since Fig 2—A schematic of Guanella’s 1:1 current balun. this means that the magnitude of the common-mode (unbalanced) current flowing in the antenna is one-tenth the magnitude of the differential-mode I 1 (balanced) current. To prevent IMB from exceeding 0.1 we require that |Z | ≤ 0.1 |Z |. This limits the use- 2 W Z 1 fulness of the current balun. Charles V S Rauch4 measured the common-mode impedance of several commercially V manufactured current baluns using a S network analyzer and found that most V had a common-mode impedance of less S Z 2 Ω than 1 k at 15 MHz, giving a maxi- I 2 mum acceptable value of |Z2| of less than 100 Ω. For balanced loads, this means that the baluns tested by qx0509-roos03 Rauch would be effective only for load impedances under 200 Ω. Fig 3—A schematic of Ruthroff’s 4:1 voltage balun.

30 Sep/Oct 2005 within about 10% of each other. through ferrite beads as suggested by tain balance and can operate effec- Imbalance does not impose any con- Walt Maxwell8 for the choke, Rauch’s tively and efficiently at much higher straint on the maximum impedance measurements (see Note 4) show that impedance levels than could a current a voltage balun can drive. This is de- beaded coax chokes have a large re- balun. In turn, the choke presents a termined by efficiency considerations sistive component to their common- balanced load impedance to the volt- and is usually greater than the mag- mode impedance. Equation 13 shows age balun preceding it, despite any nitude of the winding inductance, so that this will increase the choke’s imbalances in the antenna system, the voltage balun can drive balanced power dissipation and reduce the ef- allowing the hybrid balun to drive loads at least five times larger than ficiency of the balun. The voltage unbalanced loads more effectively can a current balun with the same balun found on many ATUs can be than could the voltage balun alone. winding impedance. converted to a hybrid balun by sim- Let VC be the common-mode volt- Unfortunately, supposedly ply adding a common-mode choke age across the choke windings as balanced antennas may present un- after the balun, without need for shown in Fig 5. Since VC also appears balanced loads due to the presence modification to the ATU or balun. across the winding impedance ZW in of nearby conductors or asymmetry Although the common-mode choke Lewallen’s model, and the current in the antenna installation imposed appears identical to the 1:1 current flowing through the winding imped- by site constraints. Kevin Schmidt5 balun, the term “common-mode choke” ance is the common-mode current describes one such case: is preferred, as it is driven by the bal- I1 – I2, “One of my antennas is a ‘dipole’ anced voltage at the output of the volt- VC = (I1 – I2) ZW (Eq 5) about 60 feet on a leg running around age balun, instead of having one side the outside of my 1-story house. It is fed grounded. This means the voltage The voltages at the input side of the Ω by about 30 feet of 300 TV twinlead. across the windings is no longer the choke are VS and –VS, so The legs of the ‘dipole’ are not straight, full source voltage V , but only a por- S I = (V – V ) / Z (Eq 6) and it isn’t symmetric about the feed 1 S C 1 tion of VS that depends on the degree point, since the shack is at a corner of of imbalance of the load. Consequently, and the house.” the common-mode choke does not suf- I = (V + V ) / Z (Eq 7) He measured the differential and fer from the limitation of the current 2 S C 2 common-mode impedances of the an- balun—that |Z2| must be less than Substituting Equations 6 and 7 into tenna at 3.52 MHz using professional one tenth of |ZW| in order to main- Equation 5 and solving for VC, instruments and obtained the results shown in Fig 4.6 If this antenna were driven by a voltage balun, IMB would be 0.22. This shows that the inherent Z = 191 + 358j balance of amateur antennas cannot 1 Z 2 = -33 + 176j be assumed, so antenna tuner baluns must be able to drive unbalanced loads effectively. Fig 4—The The Hybrid Balun Z = 887 + 622j impedances of 3 Schmidt’s dipole. The preceding sections have shown that the current balun is limited by its inability to maintain current balance when driving all but low-impedance loads, while the voltage balun qx0509-roos04 cannot maintain current balance in unbalanced loads. Since the mainte- nance of current balance in the load is the principle purpose of a balun, these limitations warrant a search for Voltage Balun Common-Mode Choke “a better balun.” This section de- V scribes and analyses the “hybrid C balun,” which consists of a voltage I balun followed by a common-mode 1 choke. The circuit shown in Fig 5 uses a 4:1 voltage balun, but a 1:1 voltage Z 1 balun would work equally well and V S the analysis is identical. The hybrid balun requires two separate transmission-line trans- V S formers. The TLT for the voltage balun V C is best realized using a bifilar wind- V S Z 2 ing on a toroidal ferrite or powdered- I iron core. The “hardy” balun designs 2 offered by Dr Sevick7 would be excellent in this application. I also rec- ommend this approach for the com- qx0509-roos05 mon-mode choke. Although one could use a length of coaxial cable threaded Fig 5—A schematic of the 4:1 hybrid balun.

Sep/Oct 2005 31 2 VC = VS ZW (Z2 – Z1) / (Z1 Z2 + ZW Z1 + given in Eq 8 and canceling |VS| maintain the current balance in the ZW Z2) gives load. If the load is perfectly bal- (Eq 8) anced, the choke dissipates no P / P = |Z (Z – Z ) / (Z Z + Z Z We can substitute this value into C V W 2 1 1 2 W 1 power. In the worst case, when Z or 2 1 equations 6 and 7 to obtain + ZW Z2)| (Eq 15) Z2 is zero (a completely unbalanced When |Z | is small compared to load), IMB = 2, and the choke dissi- I1 = VS (Z2 + 2 ZW) / (Z1 Z2 + Z1 ZW + Z2 W |Z Z |, this approaches zero, so the pates the same power as the volt- ZW) 1 2 (Eq 9) efficiency of the hybrid balun is the age balun. Such an extreme case is and same as that of the voltage balun. unlikely, however, and under normal When |Z | is large compared to |Z conditions (with IMB < 1) the choke I = V (Z + 2 Z ) / (Z Z + Z Z + Z W 1 2 S 1 W 1 2 1 W 2 Z |, it approaches dissipates less than one quarter of Z ) 2 W the power dissipated by the voltage (Eq 10) P / P = |(Z – Z ) / (Z + Z )|2 So Witt’s measure of imbalance is C V 2 1 1 2 balun, so the overall efficiency of the (Eq 16) hybrid balun is only slightly less IMB = 2 |(I – I ) / (I + I )| 1 2 1 2 Substituting the value of IMB for than that of a voltage balun driving = 2 |(Z – Z ) / (Z + Z + 4 Z )| 2 1 1 2 W the voltage balun given in Eq 4, a balanced load (which, incidentally, is the same as that of a current (Eq 11) 2 PC / PV = 1/4 IMB (Eq 17) balun driving a balanced load, since Comparing this to Eq 4, which in both cases the voltage across the So when |ZW| is large, the addi- gives IMB for the voltage balun, we tional power lost in the common- TLT windings is one half of the volt- see that the additional term in the mode choke is proportional to the age across the load). denominator reduces the imbalance square of the imbalance that would by a factor of have existed in the load if it was Comparison of Balun Performance IMB / IMB = |1 + 4 Z / (Z + Z )| driven by the voltage balun alone. V H W 1 2 This suggests the interpretation The chart in Fig 6 shows the regions (Eq 12) that the power dissipated by the in which the different baluns will op- choke depends on the amount of erate effectively for purely resistive Where IMBV and IMBH are the im- work the choke has to do in order to loads. R and R , the resistive (real) balance measures for the voltage 1 2 balun and the hybrid balun, respec- tively, with the same loads. 1 Efficiency of the Hybrid Balun Efficiency is as important as balance for antenna tuner baluns. The 0.9 power loss in a TLT can be derived from Lewallen’s model by noting that the power loss in each winding is the 0.8 dot product of the voltage across the winding, VW, and the current flowing 0.7 in the winding, so the total power loss in both windings is: 0.6 PLOSS= VW · I1 + VW · (–I2)

= VW (I1 – I2) 0.5 R2 = VW (VW / ZW) = Re (V (V / Z )*) W* W W 0.4 2 = Re(|VW| / ZW*) = |V |2 Re(Z ) / |Z |2 (Eq 13) W W W 0.3 Where “X*” means the complex con- jugate of “X” and “Re(X)” means the real component of “X.” This interest- 0.2 ing result shows that the power dissipation in the TLT is proportional to the square of the voltage across the 0.1 TLT windings. So for the hybrid balun (refer to Fig 5) if the winding imped- 0 ances of the two TLTs are the same, 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 the relationship between P , the power C R1 dissipated in the common-mode choke and PV, the power dissipated in the voltage balun is given by Current (upper bound) Voltage (lower bound) Voltage (upper bound) Hybrid (lower bound) Hybrid (upper bound) 2 2 PC / PV = |VC| / |VS| (Eq 14)

Substituting the formula for VC Fig 6—Effective operating regions of the current, voltage and hybrid baluns.

32 Sep/Oct 2005 components of Z1 and Z2, are shown on the X and Y axes. The plot lines represent the upper and lower bounds of the regions in which each of the baluns will maintain a load imbalance (IMB) not exceeding 0.1. The chart is normal- ized for |ZW| = 1. The horizontal line near the bottom of the chart is the upper bound of the current balun’s operating region, showing that the current balun is effective when R2 < 0.1 |ZW|, irrespective of the value of R1. (Although the current balun is able to drive high- impedance loads that are situated near the X-axis, this not terribly use- → ful since the limiting case as R2 / R1 0 is an unbalanced load being driven by an unbalanced source, so no balun is required.) The two lines that meet at the origin represent the upper and lower bounds of the region in which the voltage balun can maintain IMB ≤ 0.1. The voltage balun is effective for much larger load impedances than the current balun, but only when the load is well balanced (a perfectly balanced load would be situated on a 45° line passing through the origin). The Fig 7—The prototype hybrid balun. angled lines that intersect the X and Y axes at the value 0.2 are the lower and upper bounds of the region in which the hybrid balun is effective. The hybrid balun is effective for higher load impedances than the current balun (excluding loads situated near the X axis), and for a greater degree of load asymmetry than the voltage 5.0 balun. Although the chart displays only purely resistive loads, similar results are obtained for load impedances that 4.0 include both resistance and reactance. Any load that has a small resistive component combined with a large reactive component, however, may cause inefficiency and excessive heat- 3.0 ing in all balun types. If you have a load like this, you need to transform SWR the load impedance, either by using a balanced tuner or by adjusting the length of the transmission line be- 2.0 tween the balun and the antenna. Practical Testing It would require more sophisticated test equipment than I have to directly 1.0 measure the current balance achieved by the different types of balun. Fortu- nately, the input impedance of the voltage balun approximately equals the 0.0 value of Z1 in parallel with Z2. This 0 20 40 60 80 100 120 140 160 180 200 provides a good indication of load-bal- R1 (ohms) ance quality. That indication is the extent to which the input impedance QX0509-Roos08 Voltage Balun Hybrid Balun of the balun approaches the value ex- pected for a perfectly balanced load. For the 4:1 balun, this is one quarter Fig 8—SWR measured at the balun input for different ground-tap positions.

Sep/Oct 2005 33 of the total load impedance. design, but were simply what I had baluns used in antenna tuners may To measure this I connected 10, on hand. With these cores, 10 turns be required to drive loads that do not 20 Ω precision resistors in series to on each core gives a common-mode meet these requirements, neither the make a 200 Ω dummy load. A 12-posi- impedance of 500 Ω or higher from current balun nor the voltage balun tion switch allows the load to be 3.5 MHz to 21 MHz, while 8 turns per is perfectly suited to this application. grounded on either side, at any of the core is recommended to cover 7 MHz I introduced a new design, the nine junctions between resistors, or to to 30 MHz. “hybrid” balun, and showed that it can be left floating. I constructed a volt- Fig 8 plots the measured SWR maintain current balance while driv- age balun using 10 bifilar turns of against the value of R1 (the resistive ing a wider range of loads than either #14 AWG Thermoleze enameled cop- component of Z1). The total load im- the current or the voltage balun, in- 9 Ω per wire on an Amidon FT-240-61 to- pedance (R1 + R2) is always 200 . With cluding high-impedance and unbal- roidal core, connected it to the dummy the voltage balun, the SWR rises rap- anced loads. The hybrid balun is easy load and measured the SWR at the idly as the earth tap is moved away to construct and may be retrofitted to input of the balun when the load was from the center of the load, indicating many existing antenna tuners with- grounded at each position. I then that the currents flowing in the load out the need for any internal modifi- added a common-mode choke consist- are not balanced. With the hybrid cations. Although it is not perfect, I ing of 10 bifilar turns of #14 AWG balun, the SWR remains virtually flat, believe that the hybrid design is “a wire with a central crossover on an indicating that the load currents are better antenna-tuner balun.” FT-114-61 toroidal core to make a hy- properly balanced, irrespective of Notes brid balun and repeated the SWR whether the load impedance is bal- 1R. Lewallen, W7EL, 1995, “The 1:1 Current measurements. All measurements anced with respect to ground. Balun,” which is available at eznec.com/ were performed at 3.50 MHz. Fig 7 At frequencies above 7 MHz, the misc/ibalun.txteznec.com/pub/ shows the prototype, upside-down, SWR measured at the input to the ibalun.txt. Lewallen describes it as a with the base removed. The cores used hybrid balun increases, although it model of the 1:1 current balun, but it is are not an optimum or recommended remains constant as the balance of the relevant to all applications of the 1:1 TLT. 2 load with respect to ground is ZW is a complex variable with a real com- changed. This does not indicate a ponent representing resistance and an problem with the balun; it occurs sim- imaginary component representing reactance. Complex variables are typeset here ply because the bifilar winding of the in bold face. The Binary Clock common-mode choke acts as a trans- 3F. Witt, AI1H, “Evaluation of Antenna Tun- mission line with a characteristic im- ers and Baluns—An Update,” QEX, Sep/ pedance of approximately 50 Ω, which Oct 2003, p 13. transforms the load impedance of 4C. Rauch, W8JI, “Balun Test,” available at 200 Ω to a somewhat lower resistive www.w8ji.com/Baluns/balun_test.htm. value, with an additional reactive 5,6K. Schmidt, W9CF, “Putting a Balun and component. This could be avoided by a Tuner Together,” available at fermi.la. using a transmission line with a char- asu.edu/w9cf/articles/balun. Schmidt Ω gives the measurements in terms of the acteristic impedance of about 100 common-mode, differential-mode and un- So simple, yet no one to wind the voltage balun, and one balanced impedances. I calculated Z , Z with an impedance of about 200 Ω to 1 2 figures out what it is until and Z3 using the formulae he gives. wind the common-mode choke. Sevick 7J. Sevick, W2FMI, Understanding, Building you explain to them how suggests covering the #14 AWG and Using Baluns and Ununs, CQ Com- to read binary code. Thermoleze wires with 15-mil-wall munications, 2003, chapter 9. Then they are amazed Teflon tubing to obtain a characteris- 8W. Maxwell, W2DU, “Some Aspects of the Ω Balun Problem,” QST, Mar 1983, p 38. at what a great clock it is tic impedance close to 100 . He sug- 9 gests “tinned #16 AWG wire... covered Amidon Associates: www.amidoncorp. and how easy it is to com. with Teflon tubing and further sepa- 10J. Sevick, W2FMI, Understanding, Build- read the binary code. 10 rated by two Teflon tubes” for a char- ing and Using Baluns and Ununs, CQ A great gift and perfect acteristic impedance of about 190 Ω. Communications (2003), pp 59 and 81. for the techie. The clock Conclusion Andrew Roos has been a radio ama- includes a dimmer teur since 2001. He has a Bachelor switch and real binary I used Lewallen’s model of the of Arts with Honors degree from as well as BCD. transmission-line transformer to ana- Rhodes University and is the tech- lyze the performance of the 1:1 cur- nical director and principal systems rent balun and the 4:1 voltage balun. architect of a software development For instructions on how to The analysis showed that the current company in Cape Town, South Af- read the clock and or balun can only maintain the proper rica. He is a past chairman of to purchase, visit us at: current balance in a load when the the Cape Town Amateur Radio Cen- load impedance is relatively low, while ter, regularly teaches classes for www.realnerds.com the voltage balun can only maintain the Radio Amateurs’s examination, balance when the load is itself well and recently initiated a project to Clock pricing balanced with respect to ground. Since introduce Amateur Radio to school starts at $18.75. current balance is the reason for us- children from underprivileged ing a balun in the first place, and the communities.

34 Sep/Oct 2005