HFE0105_Sevick(1).pdf

From January 2005 High Frequency Electronics

High Frequency Design

MAGNETIC MATERIALS

Magnetic Materials for

Broadband Transmission

Line Transformers

By Jerry Sevick

Bell Laboratories (Retired) and Consultant

Ferrite and iron pow-

der magnetic materials

were developed to sup-

port a wide range of com-

ponents, including induc-

tors, EMI suppressors,

conventional transform-

ers and transmission line

transformers (TLTs). This

article deals with trans-

mission line transformers, presenting the

observations and conclusions of the author,

reached after extensive experimental research

into the behavior and performance of these

devices in broadband applications.

The author’s series of

articles on broadband

transmission line transform-

ers (TLTs) concludes with

these notes on magnetic

materials and the proper-

ties that are important for

best performance

Figure 1 · The three transformers used in

comparing the performance of the auto-

transformer and the transmission line trans-

former. At the top left is an autotransformer;

at the top right is the transmission line trans-

former, while at the bottom is a transmission

line transformer without a ferrite core. All

transformers had a total of 10 turns.

Background

In 1944 George Guanella [1] published the

first paper on the broadband transmission

line transformer. His technique was to connect

transmission lines in parallel on the low side

and in series on the high side. His transfor-

mation ratios were 1: n 2 where n is 1:4. His

goal was to develop a balun (balanced-to-

unbalanced transformer) to match the inter-

nal impedance of a push-pull vacuum tube

amplifier with impedance of 960 ohms to the

unbalance load of 60 ohms of a coaxial cable.

Since Guanella did not have the magnetic

materials of today, his air wound transmission

lines could not satisfy his goal. Even with the

current materials it would still be a very diffi-

cult task.

Fifteen years later Clyde Ruthroff [2] pub-

lished his classic paper on the TLT. He not

only produced a 1:4 balun but also a 1:4 unun

(unbalanced-to-unbalanced transformer), each

using a single transmission line. For the unun

the bottom of the transmission line was con-

nected directly to the input, thus raising it by

the input voltage. Coiling the transmission

lines isolates the input and output, allowing

for low frequency operation. The output con-

sists of a direct voltage in series with a

delayed voltage. This technique has been

described as a “bootstrap.” His balun was

achieved by connecting the transmission line

as a phase inverter. The load then was con-

nected directly to the input voltage and to the

end of the transmission line. Ruthroff ’s 1:4

unun was a successful design for amplifiers

using transistors, which have low impedance

and ferrite cores, which were then available.

High Frequency Electronics

High Frequency Design

MAGNETIC MATERIALS

Figure 2 · Measurements taken on the three trans-

formers in Figure 1 when matched at 12.5:50 ohms.

Note that the transmission line transformer is superior to

the autotransformer both in efficiency and bandwidth.

Also notice the limited bandwidth without a core.

Figure 3 · Loss and bandwidth performance of 4:1

transformers operating at the 50:12.5 ohm level. Note

the shift in frequency range when materials of different

permeability are used.

Figure 3 shows the comparison of K5 and Q1 ferrite

cores operating at a 50:12.5 ohm using Ruthroff ’s 1:4

design. These are in turn compared to an autotransformer

using the Q1 core. As can be seen, the autotransformer is

vastly inferior and the TLTs have similar efficiencies at

this impedance level. Also the K5 transformer has a bet-

ter low frequency response because of the higher perme-

ability of this material.

Figure 4 includes a comparison of the two cores used

in Figure 3, but at the higher impedance level of a 200:50

ohm ratio. A similar transformer using a Q2 core is also

shown in the figure. The Q2 core shows that at a higher

impedance level a higher bulk resistivity is required for

optimum efficiency. Results for a fourth transformer

using a powdered iron core (E material) are also included.

Since this material has much lower permeability than the

ferrite materials, its low frequency response suffers

accordingly.

These amplifiers were used in the emerging digital sys-

tems of the time, namely high speed PCM (pulse code

modulation).

It can be said that the broadband TLT favors low

impedance matching as will be shown. Higher

impedances cannot use higher permeabilities because

they tend to have higher losses. On the other hand lower

impedances not only benefit from lower reactive require-

ments but also by use of higher permeabilities. The next

section will show the general relationship between per-

meability and loss.

Magnetic Materials

An investigation on the short vertical antennae in the

40-meter amateur radio band [3] led to an interesting

conclusion. A 6-foot high, “top-hat” loaded vertical over a

lossless image plane (100 radials) presented an

impedance at resonance of only 3 ohms. After much

searching it was found that two 1:4 Ruthroth-style ununs,

connected in series, provided a match to a 50 ohm cable.

The resulting 1:16 impedance ratio efficiently trans-

formed the 3 ohms of the short vertical radial to 50 ohms.

The first experiment performed for understanding

these broadbrand devices was the comparison of a TLT

with an autotransformer, and with a TLT without a mag-

netic core. Figure 1 shows the three transformers. Since

all have the same number of turns, the transformers on

the top look the same while the one with the missing core

is obvious. Figure 2 shows the results of this experiment.

As can be seen, the autotransformer performs very poor-

ly compared to the TLT, and the core is very important for

low frequency response. The rest of this paper will review

results obtained for various magnetic materials.

Figure 4 · Loss vs frequency of four 4:1 transformers at

the 200:50 ohm level.

High Frequency Electronics

High Frequency Design

MAGNETIC MATERIALS

following conclusions:

1) Since very little flux occurs in

the cores in the passband, the losses

are basically due to the potential dif-

ference along the lengths of the

transmission lines. The losses are

due to the voltages and are therefore

dielectric in nature. As was seen, the

highest bulk resistivity yields the

highest efficiency.

2) The other parameter that is

important with transmission line

transformers is the permeability.

High permeability of core materials

results in shorter transmission lines.

This directly benefits Ruthroff ’s boot-

strap approach, which adds a delayed

voltage to a direct voltage. Further,

with shorter transmission lines, their

characteristic impedance is some-

what less critical. If a toroid is used

for the core, the magnetizing induc-

tance L M (in henrys) is:

Material

Supplier

Permeability

Bulk Resistivity

(µ i )

(W-cm)

10 8

Q1 (NiZn)

Allen-Bradley

125

(formerly Indiana General)

10 9

Q2 (NiZn)

Allen-Bradley

10 4 –10 5

H (NiZn)

Allen-Bradley

850

10 -2

E (Powdered Iron) Arnold Engineering

3×10 7

C2050 (NiZn)

Ceramic Magnetics

100

5×10 6

C2025 (NiZn)

Ceramic Magnetics

175

10 6

CN20 (NiZn)

Ceramic Magnetics

800

7×10 9

CMD5005 (NiZn)

Ceramic Magnetics

1400

10 8

61 (NiZn)

Fair-Rite

125

10 5

43 (NiZn)

Fair-Rite

850

10 2

77 (MnZn)

Fair-Rite

2000

10 2 –10 3

3C8 (MnZn)

Ferroxcube

2700

2×10 6

K5 (NiZn)

MH&W Intl. (TDK)

290

10 5 –10 6

KR6 (NiZn)

MH&W Intl. (TDK)

2000

Table 1 · Cores, suppliers and specifications for the experiments

described in this paper. [The list is not comprehensive and includes some

materials not examined by the author. Readers should note that other

materials are also available for TLT applications—editor.)

Figure 5 shows the results of 4

transformers using nickel zinc cores,

but with different permeabilities. It

is interesting to note that the core

CMD5005 has the same efficiency

but with a much higher permeability.

Table 1 shows that this ferrite also

has a very high bulk resistivity,

which contributes to its performance

at the 200:50 ohm level.

Figure 6 shows three other ferrite

cores, which can be seen performing

quite poorly at the 200:50 ohm level.

Of particular note is the 3C8 curve.

This is a manganese zinc core, which

has a high permeability and a low

bulk resistivity, as shown in Table 1.

where N is the number of turns, µ 0 is

the permeability of the core, A e is the

effective cross-sectional area of the

core, and L e is the average magnetic

path length in the core.

We can see from the above equa-

tion that by increasing the perme-

ability ten-fold, the number of turns

Concluding Remarks

After consideration of the infor-

mation displayed in Table 1 and in

Figures 3 through 6, we can reach the

Figure 5 · Loss vs frequency for four core materials from

Ceramic Magnetics with optimized windings for the

50:12.5 ohm level.

Figure 6 · Measurements of 3C8, KR6 and H materials

at the 200:50 ohm level.

High Frequency Electronics

is reduced by about one-third. Thus,

for a Ruthroff transformer, which

adds a delayed voltage to a direct

voltage, the high frequency response

is about three times greater.

3) When looking at the table and

the figures, two properties of the core

material stand out: permeability and

bulk resistivity. In fact, a figure of

merit can be defined in this case,

which is permeability times bulk

resistivity.

Also, as seen from the figures,

powdered iron and manganese zinc

(MnZn) ferrite are not recommended

for the broadest bandwidth. Again,

from the experimental results it is

seen that the nickel zinc (NiZn) fer-

rite CMD5005 has the highest figure

of merit. In recent discussions with

the supplier it was learned that the

typical value for the permeability is

1,500 and the bulk resistivity is 10 10

ohm-centimeters.

ity vs. frequency. Ferrites generally

have a flat µ i curve up to a cutoff fre-

quency. Just below this cutoff fre-

quency, the permeability often

increases, then begins a roll-off with

increasing frequency. This behavior

reduces the effective inductance with

increasing frequency, which can, in

some cases, affect high frequency

response.

Also, ferrites typically have a dis-

tinct frequency where maximum Q is

obtained. This characteristic results

in a “sweet spot” of lowest loss in

many transformers, even when loss is

generally low over a wider band-

width. For maximum performance, a

designer will choose the material

that is a best fit with the frequency

range of the application.

We recommend that readers con-

tact ferrite manufacturers for addi-

tional information. These companies

represent the best available source of

technical information on magnetic

materials.

References

1. G. Guanella, “Novel Matching

Systems for High Frequencies,”

Brown-Boveri Review , Vol. 31, Sep.

1944, pp. 327-329.

2. W. K. Ruthroff, “Some Broad-

Band Transformers,” Proc. IRE , vol.

47, Aug 1959, pp. 1337-1342.

3. J. Sevick, Transmission Line

Transformers , Noble Publishing,

Fourth Edition, 2001.

Author Information

Jerry Sevick is retired from Bell

Laboratories and remains active as

an occasional consultant and lectur-

er. He can be reached by e-mail at:

w2fmi@worldnet.att.net

Editor’s Notes

In addition to the dominant per-

formance factors of permeability and

bulk resistivity, there are other char-

acteristics of ferrite materials that

affect loss and optimum frequency of

operation. Among these parameters

are hysteresis and other dynamic

responses to magnetizing forces,

temperature stability, and permeabil-

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