A_Better_Antenna_Balun_ZS1AN.pdf

A Better

Antenna-Tuner Balun

Which balun to use? The hybrid balun promises

advantages over both voltage and current baluns.

By Andrew Roos, ZS1AN

B aluns that are situated be-

is effective only if the load impedance

is well balanced with respect to

ground.

I then introduce a new design: the

“hybrid” balun, which overcomes these

limitations of the voltage and current

baluns. It can operate with much

higher load impedances than can cur-

rent baluns and with unbalanced load

impedances that voltage baluns could

not drive effectively. The article con-

cludes by describing a simple test I

conducted to confirm that the hybrid

balun operates as predicted.

Fig 1. Although Z W is shown on only

one of the transformer windings, its

effects are felt equally on both wind-

ings due to the coupling action of the

“ideal transformer,” which can be

expressed by two rules:

1. The currents in the two windings

of the “ideal transformer” are equal

and opposite.

2. V AC = V BD = ( I 1 – I 2 ) Z W

The model assumes that the length

of the transmission line used to con-

struct the TLT is short in terms of

wavelength, so transmission line ef-

fects can be ignored. Although this as-

sumption holds for the lower part of

the HF region, some transmission-

line effects do come into play at higher

frequencies.

The use of this model does not im-

ply that TLTs operate like conven-

tional transformers. The ideal

tween an antenna tuning unit

and a non-resonant antenna

may be subjected to high-impedance,

highly reactive or unbalanced loads

that can prevent the balun from func-

tioning effectively.

In this article, I apply the analyti-

cal model of the transmission-line

transformer developed by Roy

Lewallen 1 to analyze the performance

of the 1:1 current balun and the 4:1

voltage balun in this application. The

analysis shows that the current balun

operates effectively only for small load

impedances, while the voltage balun

Lewallen’s Model of a 1:1 Trans-

mission-Line Transformer

Lewallen models the 1:1 transmis-

sion-line transformer (TLT) as an

ideal 1:1 transformer with a “wind-

ing impedance,” Z W , in parallel with

one of the windings, 2 as shown in

1 Notes appear on page 34.

PO Box 350, Newlands

7725, South Africa

zs1an@qsl.net

Sep/Oct 2005 29

1:1 transformer is simply a modeling

convenience, and the resulting model

applies to any device that exhibits

common-mode impedance, irrespec-

tive of its operating principle.

I 2 = V S / Z 2

We can calculate Witt’s measure of

imbalance:

IMB = 2 | I 1 – I 2 | / | I 1 + I 2 |

= 2 | Z 2 – Z 1 | / | Z 2 + Z 1 |

The 4:1 Voltage Balun

We can use the same model to ana-

lyze the performance of the Ruthroff ’s

4:1 voltage balun shown in Fig 3. Once

again, Z 1 and Z 2 represent the load.

According to Lewallen’s model, the

voltages across the two windings of the

transmission-line transformer (TLT)

are equal, and both equal V S , so

I 1 = V S / Z 1

and

(Eq 4)

The 1:1 Current Balun

Fig 2 shows the schematic of

Guanella’s 1:1 “current” balun. Z 1 and

Z 2 represent the load. The junction

between Z 1 and Z 2 is grounded to rep-

resent the (typically capacitive) cou-

pling of the antenna system to ground.

The load is balanced with respect to

ground when Z 1 = Z 2 .

The principle limitation of this

balun is that it can only maintain bal-

ance between the currents flowing into

the load, I 1 and I 2 , for relatively low

load impedances. The ability to main-

tain the correct current balance in the

load is of course the reason for using

a balun in the first place, so the

extent to which a balun maintains this

balance is the primary measure of its

effectiveness. In the case of the 1:1 cur-

rent balun, Lewallen shows that

I 1 / I 2 = ( Z 2 + Z W ) / Z W (Eq 1)

Where Z W is the “winding imped-

ance” (common-mode impedance) of

the balun. We can use this to calcu-

late the measure of imbalance pro-

posed by Witt 3 as:

IMB = 2 |( I 1 – I 2 ) / ( I 1 + I 2 )|

= 2 |( I 1 – I 1 ( Z 2 + Z W )/ Z W ) / ( I 1 + I 1 ( Z 2

+ Z W )/ Z W )|

= 2 | Z 2 | / |( Z 2 + 2 Z W )| (Eq 2)

(Note that | X | means the magni-

tude of complex variable X .) If IMB is

small, then | Z W | >> Z 2 . So as a good

approximation,

IMB = | Z 2 | / | Z W | (Eq 3)

Although Witt does not suggest an

acceptable maximum figure for IMB,

0.1 seems a reasonable value since

this means that the magnitude of the

common-mode (unbalanced) current

flowing in the antenna is one-tenth the

magnitude of the differential-mode

(balanced) current. To prevent IMB

from exceeding 0.1 we require that

| Z 2 |

The degree to which the currents

are balanced depends only on the bal-

ance of the load impedances with re-

spect to ground. In order to keep

IMB

≤

0.1, the impedances must be

I 1

I 2

Z W

I 1 -I 2

qx0509-roos01

Fig 1—Lewallen’s model of the 1:1 TLT.

I 1

V S

Z 1

Z 2

I 2

qx0509-roos02

Fig 2—A schematic of Guanella’s 1:1 current balun.

I 1

0.1 | Z W |. This limits the use-

fulness of the current balun. Charles

Rauch 4 measured the common-mode

impedance of several commercially

manufactured current baluns using a

network analyzer and found that most

had a common-mode impedance of less

than 1 k

≤

Z 1

V S

Z 2

at 15 MHz, giving a maxi-

mum acceptable value of | Z 2 | of less

than 100

I 2

. For balanced loads, this

means that the baluns tested by

Rauch would be effective only for load

impedances under 200

qx0509-roos03

Fig 3—A schematic of Ruthroff’s 4:1 voltage balun.

30 Sep/Oct 2005

within about 10% of each other.

Imbalance does not impose any con-

straint on the maximum impedance

a voltage balun can drive. This is de-

termined by efficiency considerations

and is usually greater than the mag-

nitude of the winding inductance, so

the voltage balun can drive balanced

loads at least five times larger than

can a current balun with the same

winding impedance.

Unfortunately, supposedly

balanced antennas may present un-

balanced loads due to the presence

of nearby conductors or asymmetry

in the antenna installation imposed

by site constraints. Kevin Schmidt 5

describes one such case:

“One of my antennas is a ‘dipole’

about 60 feet on a leg running around

the outside of my 1-story house. It is fed

by about 30 feet of 300

through ferrite beads as suggested by

Walt Maxwell 8 for the choke, Rauch’s

measurements (see Note 4) show that

beaded coax chokes have a large re-

sistive component to their common-

mode impedance. Equation 13 shows

that this will increase the choke’s

power dissipation and reduce the ef-

ficiency of the balun. The voltage

balun found on many ATUs can be

converted to a hybrid balun by sim-

ply adding a common-mode choke

after the balun, without need for

modification to the ATU or balun.

Although the common-mode choke

appears identical to the 1:1 current

balun, the term “common-mode choke”

is preferred, as it is driven by the bal-

anced voltage at the output of the volt-

age balun, instead of having one side

grounded. This means the voltage

across the windings is no longer the

full source voltage V S , but only a por-

tion of V S that depends on the degree

of imbalance of the load. Consequently,

the common-mode choke does not suf-

fer from the limitation of the current

balun—that | Z 2 | must be less than

one tenth of | Z W | in order to main-

tain balance and can operate effec-

tively and efficiently at much higher

impedance levels than could a current

balun. In turn, the choke presents a

balanced load impedance to the volt-

age balun preceding it, despite any

imbalances in the antenna system,

allowing the hybrid balun to drive

unbalanced loads more effectively

than could the voltage balun alone.

Let V C be the common-mode volt-

age across the choke windings as

shown in Fig 5. Since V C also appears

across the winding impedance Z W in

Lewallen’s model, and the current

flowing through the winding imped-

ance is the common-mode current

I 1 – I 2 ,

V C = ( I 1 – I 2 ) Z W (Eq 5)

The voltages at the input side of the

choke are V S and – V S , so

I 1 = ( V S – V C ) / Z 1

TV twinlead.

The legs of the ‘dipole’ are not straight,

and it isn’t symmetric about the feed

point, since the shack is at a corner of

the house.”

He measured the differential and

common-mode impedances of the an-

tenna at 3.52 MHz using professional

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

balance of amateur antennas cannot

be assumed, so antenna tuner baluns

must be able to drive unbalanced loads

effectively.

(Eq 6)

and

I 2 = ( V S + V C ) / Z 2 (Eq 7)

Substituting Equations 6 and 7 into

Equation 5 and solving for V C ,

Z 1 = 191 + 358j

Z 2 = -33 + 176j

Fig 4—The

impedances of

Schmidt’s dipole.

The Hybrid Balun

The preceding sections have shown

that the current balun is limited by

its inability to maintain current bal-

ance when driving all but low-imped-

ance loads, while the voltage balun

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

“a better balun.” This section de-

scribes and analyses the “hybrid

balun,” which consists of a voltage

balun followed by a common-mode

choke. The circuit shown in Fig 5 uses

a 4:1 voltage balun, but a 1:1 voltage

balun would work equally well and

the analysis is identical.

The hybrid balun requires two

separate transmission-line trans-

formers. The TLT for the voltage balun

is best realized using a bifilar wind-

ing on a toroidal ferrite or powdered-

iron core. The “hardy” balun designs

offered by Dr Sevick 7 would be

excellent in this application. I also rec-

ommend this approach for the com-

mon-mode choke. Although one could

use a length of coaxial cable threaded

Z 3 = 887 + 622j

qx0509-roos04

Voltage Balun

Common-Mode Choke

V C

I 1

Z 1

V S

V C

V S

Z 2

I 2

qx0509-roos05

Fig 5—A schematic of the 4:1 hybrid balun.

Sep/Oct 2005 31

V C = V S Z W ( Z 2 – Z 1 ) / ( Z 1 Z 2 + Z W Z 1 +

Z W Z 2 )

given in Eq 8 and canceling | V S | 2

gives

P C / P V = | Z W ( Z 2 – Z 1 ) / ( Z 1 Z 2 + Z W Z 1

+ Z W Z 2 )| 2

maintain the current balance in the

load. If the load is perfectly bal-

anced, the choke dissipates no

power. In the worst case, when Z 1 or

Z 2 is zero (a completely unbalanced

load), IMB = 2, and the choke dissi-

pates the same power as the volt-

age balun. Such an extreme case is

unlikely, however, and under normal

conditions (with IMB < 1) the choke

dissipates less than one quarter of

the power dissipated by the voltage

balun, so the overall efficiency of the

hybrid balun is only slightly less

than that of a voltage balun driving

a balanced load (which, incidentally,

is the same as that of a current

balun driving a balanced load, since

in both cases the voltage across the

TLT windings is one half of the volt-

age across the load).

(Eq 8)

We can substitute this value into

equations 6 and 7 to obtain

I 1 = V S ( Z 2 + 2 Z W ) / ( Z 1 Z 2 + Z 1 Z W + Z 2

Z W )

(Eq 15)

When | Z W | is small compared to

| Z 1 Z 2 |, this approaches zero, so the

efficiency of the hybrid balun is the

same as that of the voltage balun.

When | Z W | is large compared to | Z 1

Z 2 |, it approaches

P C / P V = |( Z 2 – Z 1 ) / ( Z 1 + Z 2 )| 2

(Eq 16)

Substituting the value of IMB for

the voltage balun given in Eq 4,

P C / P V = 1/4 IMB 2

(Eq 9)

and

I 2 = V S ( Z 1 + 2 Z W ) / ( Z 1 Z 2 + Z 1 Z W + Z 2

Z W )

(Eq 10)

So Witt’s measure of imbalance is

IMB = 2 |( I 1 – I 2 ) / ( I 1 + I 2 )|

= 2 |( Z 2 – Z 1 ) / ( Z 1 + Z 2 + 4 Z W )|

(Eq 11)

Comparing this to Eq 4, which

gives IMB for the voltage balun, we

see that the additional term in the

denominator reduces the imbalance

by a factor of

IMB V / IMB H = |1 + 4 Z W / ( Z 1 + Z 2 )|

(Eq 17)

So when | Z W | is large, the addi-

tional power lost in the common-

mode choke is proportional to the

square of the imbalance that would

have existed in the load if it was

driven by the voltage balun alone.

This suggests the interpretation

that the power dissipated by the

choke depends on the amount of

work the choke has to do in order to

Comparison of Balun

Performance

The chart in Fig 6 shows the regions

in which the different baluns will op-

erate effectively for purely resistive

loads. R 1 and R 2 , the resistive (real)

(Eq 12)

Where IMB V and IMB H are the im-

balance measures for the voltage

balun and the hybrid balun, respec-

tively, with the same loads.

Efficiency of the Hybrid Balun

Efficiency is as important as bal-

ance for antenna tuner baluns. The

power loss in a TLT can be derived

from Lewallen’s model by noting that

the power loss in each winding is the

dot product of the voltage across the

winding, V W , and the current flowing

in the winding, so the total power loss

in both windings is:

P LOSS = V W · I 1 + V W · (– I 2 )

= V W ( I 1 – I 2 )

= V W ( V W / Z W )

= R e ( V W* ( V W / Z W )*)

= R e(| V W | 2 / Z W *)

= | V W | 2 R e( Z W ) / | Z W | 2 (Eq 13)

Where “ X *” means the complex con-

jugate of “ X ” and “Re( X )” means the

real component of “ X .” This interest-

ing result shows that the power dissi-

pation in the TLT is proportional to

the square of the voltage across the

TLT windings. So for the hybrid balun

(refer to Fig 5) if the winding imped-

ances of the two TLTs are the same,

the relationship between P C , the power

dissipated in the common-mode choke

and P V , the power dissipated in the

voltage balun is given by

P C / P V = | V C | 2 / | V S | 2

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Current (upper bound)

Voltage (lower bound)

Voltage (upper bound)

Hybrid (lower bound)

Hybrid (upper bound)

(Eq 14)

Substituting the formula for V C

Fig 6—Effective operating regions of the current, voltage and hybrid baluns.

32 Sep/Oct 2005

components of Z 1 and Z 2 , are shown

on the X and Y axes. The plot lines rep-

resent 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 | Z W | = 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 ef-

fective when R 2 < 0.1 | Z W |, irrespec-

tive of the value of R 1 . (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 R 2 / R 1

→

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

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

balun.

Although the chart displays only

purely resistive loads, similar results

are obtained for load impedances that

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-

ing in all balun types. If you have a

load like this, you need to transform

the load impedance, either by using a

balanced tuner or by adjusting the

length of the transmission line be-

tween the balun and the antenna.

Fig 7—The prototype hybrid balun.

5.0

4.0

3.0

2.0

Practical Testing

It would require more sophisticated

test equipment than I have to directly

measure the current balance achieved

by the different types of balun. Fortu-

nately, the input impedance of the volt-

age balun approximately equals the

value of Z 1 in parallel with Z 2 . This

provides a good indication of load-bal-

ance quality. That indication is the

extent to which the input impedance

of the balun approaches the value ex-

pected for a perfectly balanced load.

For the 4:1 balun, this is one quarter

1.0

0.0

100

120

140

160

180

200

R1 (ohms)

QX0509-Roos08

Voltage Balun

Hybrid Balun

Fig 8—SWR measured at the balun input for different ground-tap positions.

Sep/Oct 2005 33

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