HFE1104_Sevick.pdf

From November 2004 High Frequency Electronics

High Frequency Design

BROADBAND UNUNS

Design of Broadband

Ununs With Impedance

Ratios Less than 1:4

By Jerry Sevick

Bell Laboratories (Retired) and Consultant

T he first appearance

Broadband transformers

with impedance ratios less

than 1:4 are required for

solid-state power amplifiers

as well as signal dividing

and combining circuits

from HF to microwaves

of the broadband

transmission line

transformer occurred in

1944, in a paper pub-

lished by George Guan-

ella [1] in the Braun-

Boveri Review . In that

paper, he expounded the

principles of this broadband impedance

matching device and is considered the inven-

tor. His goal was to design a broadband balun

(balanced-to-unbalanced) for the HF band,

matching the balanced impedance of 960

ohms in a vacuum tube amplifier to the unbal-

anced impedance of a 60 ohm coaxial cable; a

16:1 ratio. Since he did not have the magnet-

ic materials of today he was unable to reach

his goal. Even today it is a formidable task.

Figure 1 shows Guanella’s approach for a

1:4 transmission line transformer, which is

generally considered to be a balun. With ter-

minal 2 grounded it becomes an unbalanced-

to-unbalanced (unun) transformer. As seen in

the figure, his technique uses two transmission

lines, connected in parallel on the input and in

series on the output side, the transmission

lines are coiled such that their common-mode

“choking” action provides input-to-output iso-

lation for the desired low frequency perfor-

mance. Since each transmission line sees one-

half of the load R L its optimum characteristic

impedance Z 0 should be R L / 2. Since Guanella

adds voltages that have equal delays through

the transmission lines, his technique is can be

considered to be a member of the “equal-delay

transformer” family. The method can be

expanded by connecting three transmission

lines in series parallel to obtain a ratio of 1:9,

Figure 1 · Schematic of Guanella’s 1:4

balun, showing the inputs in parallel and out-

puts in series. By grounding terminal 2, this

transformer acts as a broadband 1:4 unun.

four lines to obtain a 1:16 ratio, etc.

In 1959 Ruthroff [2] presented his classic

paper in the Proceedings of the IRE . In it he

employed two different versions of the balun

and unun (Figure 2). Figure 2A is his unun

and Figure 2B is his balun. As can been seen

his unun has a direct connection from the

input to the output. Since the transmission

lines are coiled forming chokes the transmis-

sion lines are literally raised by a voltage

equal to the input, resulting in a voltage twice

the input and hence a 1:4 ratio. The charac-

teristic impedance Z 0 of the transmission line

should be equal to one-half the load

impedance R L . This technique has been

described as a “bootstrap.” Clearly, it is a sim-

pler circuit than Guanella’s but does not have

the same high frequency response because it

adds a delayed voltage to a direct one. The

delay is excessive when the lines reach a sig-

nificant fraction of a wavelength. In many

cases, however, the transmission lines will be

short enough provide sufficient bandwidth for

the desired application.

High Frequency Electronics

High Frequency Design

BROADBAND UNUNS

Figure 3 · An equal-delay unun with an impedance

ratio of 2.25:1, using Guanella’s technique.

characteristic impedance of all four transmission lines

should be 75 ohms in a matched condition. If the genera-

tor impedance is 50 ohms then R L and the characteristic

impedances of the transmission lines should be reduced

by a factor of two.

By using a 1:16 Guanella transformer below the 1:1

unit, this configuration provides a ratio of 1:1.56. Again if

the generator is 100 ohms the 1:1 transformer sees 80

ohms and the bottom one 20 ohms. If the generator is 50

ohms then all characteristics impedances are 40 ohms.

The 1:1.56 ratio is important because it supports applica-

tions such as transforming between the common system

impedance of 50 and 75 ohms.

Figure 2 · Ruthroff’s 1:4 transformer as an unun (A) and

as a balun (B).

Guanella’s Technique for Ratios of Less Than 1:4

Figure 3 shows Guanella’s 1:1 balun combined with

his 1:4 balun. The voltages on the left side of the trans-

formers are in series and the currents in parallel on the

output. In this case, the left side has the higher

impedance. If the generator impedance was 100 ohms, the

output impedance ( R L ) should be 44.44 ohms and the

characteristic impedances of all three transmission lines

should be 67 ohms for a matched condition. If the genera-

tor impedance is 50 ohms then R L and the characteristic

impedances of the lines are reduced proportionately to

22.22 and 33 ohms respectively. In a matched condition,

this transformer should have a high frequency response

similar to a single transmission line. By grounding the

indicated terminals, it becomes a broadband unun.

Operation of this combination of transformers can be

described as follows: At the right side, the 1:1 and 1:4

transformers are connected in parallel to R L . Thus, the

voltage across the load, V L appears at both transformers.

At the left side, the same voltage appears at the 1:1 trans-

former, but the 1:4 transformer reduces the voltage by

one-half, or V L / 2. These voltages are connected in series,

so the input voltage ( V g ) is 1.5 V L , which corresponds to an

impedance transformation of R g / R L = 2.25.

In Figure 4, Guanella’s 1:9 transformer is used instead

of his 1:4. In this case, the voltages at the left side are V L

in series with V L / 3, so V g is 1.33 V L and R g / R L = 1.78. If

the generator is 100 ohms then the 1:1 transformer above

“sees” 75 ohms and the 1:9 transformer sees 25 ohms. The

Ruthroff’s Technique for Ratios of Less Than 1:4

Figure 5 shows a bootstrap circuit for a 1:2.25 unun. It

shows that there are three conductors with one of the con-

ductors in this case terminal 4 connected to the input

impedance. This is an extension of Ruthroff ’s basic “boot-

Figure 4 · An equal-delay unun with an impedance

ratio of 1.78:1.

High Frequency Electronics

High Frequency Design

BROADBAND UNUNS

Figure shows two versions, the one on the left is more use-

ful for matching 50 ohms to 75 ohms, while the one on the

right with the transposed winding is better suited to

match 50 ohms to about 33 ohms.

Concluding Remarks

In reviewing the history and theory of the transmis-

sion line transformers it can be seen that it they are ideal

for matching the lower impedance of today’s solid-state

amplifiers. With proper understanding and use of current

fabrication technologies, i.e. thin film, thick film and

molecular beam epitaxy (MBE), and with the equal delay

principles of Guanella, ununs (as well as baluns) with

ratios of less than 1:4 should be popular. For example, in

2-way combiner/splitter components, the 1:2 transmission

line transformer should be used. It is surprising that fair-

ly recent publications have shown the use of autotrans-

formers to match 25 ohms to 50 ohms! The transmission

line transformer is by far a broader bandwidth and lower

loss matching device.

As we have seen, the equal delay transformer basical-

ly has the same high frequency performance as a single

transmission line. The low frequency response is more

complicated since coiled transmission lines must be

wound on separate cores. This is where the bootstrap

approach has the advantage, since all the windings are

wound on the same core and therefore are in series-aiding

configuration. For very high frequency responses the

straight beaded transmission line has the advantage

since it does not have a self-resonance. Here is where the

equal delay transformer has the advantage since it does

not a have a direct connection from input to output like

that of the bootstrap transformer. The parasitic induc-

tance of the direct connection can limit the high frequen-

cy response in the bootstrap device. Experiments should

be performed on the equal-delay unun to see if a practical

1:2 ratio can be obtained.

Also it can be shown that the ununs described in this

paper can be constructed with coaxial cables

transmission lines. In the equal-delay case the

application is quite obvious. The use of coaxial

cable in the bootstrap case is not so obvious, and

is illustrated in Figure 7. Here we have

Ruthroff ’s application using two coaxial cables

resulting in a 1:2.25 ratio. The third conductor

in this case is the parallel connection of the two

outer braids of the coaxial cables. In this case

the top transmission line generally sees 1/3 of

the load and in the bottom transmission line

2/3. For a 50 ohm load the top transmission line

impedance should be 17 ohms and the bottom

transmission line 33 ohms. It has also been

found that the inner conductor of the top coaxi-

al conductor in Figure 7 can also be tapped

Figure 5 · Trifilar 1:2.25 bootstrap transformer, showing

how a tap can be used to obtain variable matching.

strap” technique as can be seen a direct voltage equal to

the input voltage is connected to terminal 4 which raises

the top transmission line by V 1 . Thus the output is equal

to (3/2) V 1 . It has been found experimentally that if the top

conductor is tapped at 0.8 of its length from the input that

the result is equally broadbanded and produces a 1:2

impedance ratio. This transformer also has advantages

over Ruthroff ’s unun since the low frequency model

shows that the three conductors are in series-aiding,

resulting in shorter transmission lines, also the delayed

voltage is only equal to half the direct voltage. Rather

large structures have shown to provide broad bandwidth

of the order 100 MHz [3]. By interposing winding 5/6

between the other two conductors this transformer can be

optimized at the 50 ohm level, otherwise it has better per-

formance operating at the 100 ohm level.

Using four conductors with the input connected to the

output of the third conductor this provides even a greater

bandwidth with a ratio of 1:1.78. By the application of five

conductors shown in Figure 6, an even greater bandwidth

can be provided with the important ratio of 1:1.56. The

Figure 6 · 5-winding 1:1.56 Bootstrap transformer connections:

(A) higher impedance, and (B) lower impedance.

High Frequency Electronics

High Frequency Design

BROADBAND UNUNS

Figure 7 · Connection diagram for Ruthroff’s bootstrap

application, using two coaxial cables to obtain the

impedance ratio of 1:2.25 or 1:2 with a tap winding.

yielding a broadband ratio of 1:2. Many examples of

transmission line transformers using coaxial cables are

found in the literature [3]. And finally it should be men-

tioned that equal-delay transformers should be investi-

gated with tapped windings and with windings sharing

the same magnetic medium.

References

1. G. Guanella, “Novel Matching Systems for High

Frequencies,” Braun-Boveri Review , Vol. 31, Sep 1994, pp.

327-329.

2. C. L. Ruthroff, “Some Broad-Band Transformers,”

Proc. IRE , Vol. 47, August 1959, pp. 1337-1342.

3. J. Sevick, Transmission Line Transformers , Noble

Publishing Corp., 4th Edition 2001.

Author Information

Jerry Sevick is retired from Bell Laboratories and

remains an occasional consultant and lecturer.

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