HFE1104_Sevick.pdf
(
183 KB
)
Pobierz
From November 2004
High Frequency Electronics
Copyright © 2004, Summit Technical Media, LLC
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.
44
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.
46
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.
48
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.
Plik z chomika:
ei6kd
Inne pliki z tego folderu:
TS480_serv.pdf
(36720 KB)
counterpoise.pdf
(844 KB)
Contest Bandpass Filters.pdf
(142 KB)
Clean Up Your Signals 2 W3NQN.pdf
(135 KB)
Clean Up Your Signals W3NQN.pdf
(92 KB)
Inne foldery tego chomika:
Ekonomia
Galeria
Hobby żonki ;)
Prywatne
Przydatne programy
Zgłoś jeśli
naruszono regulamin