HFE0204_Sevick(2).pdf

From February 2004 High Frequency Electronics

High Frequency Design

TRANSFORMERS

A Simplified Analysis of the

Broadband Transmission

Line Transformer

By Jerry Sevick

Bell Laboratories (Retired) and Consultant

T his paper presents

The TLT first appeared upon the scene in

1944 in a classic paper by George Guanella in

the Brown Boverie Review . The title of his

paper was “Novel Matching Systems for High

Frequencies” [1]. The second classic paper was

written by Clyde Ruthroff at Bell Labs and

was published fifteen years later in the

Proceedings of the IRE. His paper was named

“Some Broadband Transformers” [2] and

introduced the 1:4 unbalanced-to-unbalanced

transformer (unun).

Guanella’s basic designs were balanced-to-

unbalanced (balun) transformers. They con-

sisted of transmission lines connected in a

parallel/series arrangement. They are the

basis for the later “equal-delay” TLTs.

Ruthroff on the other hand, applied the input

voltage to part of the output, which has been

known as a “Bootstrap Effect.” His transform-

ers usually added a delayed voltage to a direct

voltage therefore a cancellation effect took

place limiting the high frequency response.

Guanella’s goal was to develop a balun to

match the balanced internal impedance of a

push-pull vacuum-tube amplifier of 960 ohms

to the unbalanced impedance of a coaxial

cable of 60 ohms, a 16:1 ratio. Since Guanella

did not have access to the modern nickel-zinc

ferrites of today, his goal was never realized.

Even today it would be a formidable task.

Ruthroff on the other hand, designed ununs to

match the low impedance of transistors up to

50 ohm coaxial cable.

Since the TLT can also operate as a very

efficient isolation transformer it is now possi-

ble to convert a balun to an unun or vice versa.

Therefore, the classification on these devices

can be simplified, resulting in only four basic

classifications: 1) TLTs with 1:1 ratios, 2) TLTs

This article presents the

fundamental concepts and

describes the impedance-

matching capabilities of

broadband transmission

line transformers

an easily under-

stood analysis of

the transmission line

transformer (TLT). It also

includes some history and

the author’s suggestion

for the future of these

devices. It is hoped that future device develop-

ment and application will be encouraged.

The Transmission Line Transformer

The TLT transmits the energy from input

to output by a transmission line mode and not

by flux-linkages as in the conventional trans-

former. As a result the TLT has much wider

bandwidth and higher efficiencies than its

conventional counterpart. With proper core

materials and impedance levels of 100 ohms

or less, bandwidths of about 100 MHz and effi-

ciencies approaching 99% are possible today

when matching 50 ohms up to 100 ohms and

50 ohms down to about 3 ohms. Future

research and development, especially with

impedance ratios less than 4:1, should make

TLTs operate at much wider bandwidths.

The TLT and conventional transformer

have two models used in their analysis. The low

frequency models are similar, usually contain-

ing an inductive impedance in parallel with the

input impedance. The high frequency model of

the conventional transformer consists of a dis-

tributed capacitance in parallel with the leak-

age inductance. The TLT in turn contains a con-

figuration of transmission lines in the high fre-

quency model. Therefore, the conventional

transformer model only requires a background

in circuit theory, while the TLT requires both

circuit and transmission line theory.

High Frequency Electronics

High Frequency Design

TRANSFORMERS

Figure 1 · Guanella’s basic building block, a transmis-

sion line segment with input and output isolated by the

inductive reactance of the windings.

Figure 2 · Ruthroff’s 1:1 balun design, which includes

an isolated transmission line section, along with a third

winding acting as a voltage divider.

with 1:4 ratios, 3) TLTs with less than 1:4 ratios and final-

ly TLTs with ratios greater than 1:4. These will be covered

in the next sections.

TLTs with a Ratio of 1:4

Figure 3 shows Guanella’s version of a 1:4 balun. The

two transmission lines are connected in parallel at the

low impedance side and in series at the high end. For an

ideal match, the characteristic impedance of the two

transmission lines should be R L /2. Thus, if the transmis-

sion lines are terminated in their characteristic

impedance, Z 0 , the high-frequency limit is that of a regu-

lar transmission line. Further, by grounding terminal 8,

the device can act as a phase-inverter and by grounding

terminal 2 it performs as a 1:4 unun.

Figure 4 shows the low frequency model of Guanella’s

1:4 transformer. As a 1:1 balun the reactance of winding

3-4 in series of winding 5-6, wound on two separate cores,

should be greater than 10 times the input impedance.

When terminal 2 is grounded, the reactance winding 1-2

is eliminated and therefore should be considered when

using Guanella’s 1:4 transformer acting as an unun.

Figure 5 shows the schematics of Ruthroff ’s 1:4 TLTs.

(A) is his 1:4 unun, with terminal 2 connected to the input

TLTs with 1:1 Ratios

Figure 1 shows Guanella’s basic building block. With

terminal 5 grounded, the device operates as a balun,

matching the unbalanced source to the balance load R L .

In this case, the low-frequency performance is determined

by the reactance of winding 3-4. In practice, this reac-

tance should be 10 times greater than R L /2 (or 5 times

greater than R L ). If terminal 4 is grounded, the building

block performs as a phase-inverter. Thus, terminal 2

becomes negative. In this case the reactance of inductor 3-

4 should be 10 times greater than R L . If terminal 2 is

grounded, the result is a simple delay line. In this case no

reactance is necessary. Instead of coil windings, ferrite-

loaded straight transmission lines can also be used,

although the required inductance may be impractical to

obtain at lower frequencies.

Figure 2 shows Ruthroff ’s version of the 1:1 balun.

Windings 3-4 and 5-6 act as a voltage divider. Windings 3-

4 and 1-2 act as Guanella’s basic building block. In this

case the reactance of 5-6 should be 10 times greater than

R L . When the reactance of 5-6 is much greater than R L , its

high impedance is swamped by the lower impedance of R L

and the device acts exactly the same as a Guanella build-

ing block.

Figure 3 · Schematic of Guanella’s 1:4 balun, showing

the inputs in parallel and outputs in series.

Figure 4 · Low-frequency model of Guanella’s 1:4

balun.

High Frequency Electronics

High Frequency Design

TRANSFORMERS

Figure 6 · Low frequency models for the Ruthroff 1:4

unun (A) and balun (B).

three inductors in series on the same core, the low fre-

quency end is greatly aided. Also, as this device adds two

direct voltages in series with one delayed voltage the high

frequency performance is much better than Ruthroff ’s 1:4

unun. This device has produced exceptional bandwidth

and efficiencies. This TLT can be tapped on the “top”

winding to obtain other impedance ratios. For example, if

the tap is set for V 0 = 1.414(V 1 ) the ratio is exactly 1:2.

Figure 8 shows two high frequency models using

ratios of 1:1.56. (A) is designed to match 50 ohms to 78

ohms while (B) is optimized to match 32 ohms to 50 ohms.

This device has 5 transmission lines in series to help the

low frequency performance, and because it adds a delayed

voltage of only V 1 /5 it can have a better high frequency

response than its trifilar counterpart.

Figure 5 · Ruthroff’s 1:4 transformer, (A) as an unun and

(B) as a balun.

terminal 3, thus raising this transmission line by the

input voltage V 1 . This is called the “Bootstrap Effect.” The

output voltage V 2 is delayed as it travels the transmission

line. Because of this, Ruthroff ’s 1:4 design does not have

the high frequency response of Guanella’s, but if the

transmission lines are short compared to the wave length,

Ruthroff ’s design is practical. Figure 5(B) shows

Ruthroff ’s 1:4 balun, first acting as a phase inverter, fol-

lowed by R L between terminals 3 and 2 to become a 1:4

balun. This configuration also adds a direct voltage to a

delayed voltage, limiting its high frequency performance.

Figure 6 shows the low frequency models of Ruthroff ’s

1:4 TLTs. (A) is the unun model and (B) the balun model.

TLTs with Ratios Greater than 1:4

Figure 9 shows Guanella’s models of his 1:9 TLT. (A)

shows the high frequency model and (B) its low frequen-

cy counterpart. Since each line has an equal delay, this

TLT has high frequency performance the same as a sim-

ple transmission line. As seen in the diagram each trans-

mission sees 1/3 of the load R L . In matching 50 ohms to

TLTs with Ratios Less than 1:4

Figure 7 shows the high frequency model of a trifilar

“Bootstrap” model of an unun yielding a ratio of 1:2.25.

Since the low frequency model for this device would show

Figure 7 · Trifilar 1:2.25 Bootstrap TLT, showing how a

tap can be used to obtain variable matching.

Figure 8 · 5-winding 1:1.56 Bootstrap TLT connections:

(A) higher impedance; (B) lower impedance.

High Frequency Electronics

Figure 10 · A four-winding transformer with multiple

connections that provide eight impedance ratios.

efficient, they can be connected in series, yielding ratios

between 1:9 and 1:4. This compound TLT obviously favors

matching 50 ohms to lower impedances.

Closing Remarks

This paper attempts to summarize the simple basics of

these broadband TLTs. There are many details regarding

the use of magnetic materials, examples of transmission

lines, and additional TLT models that have not been

included. This would take an entire book or more [3,4]. It

is hoped that these notes stimulate an interest in these

devices and provide a feeling for their capabilities.

Although the TLT was first intended to be used for

matching vacuum tubes its real strength lies in matching

to low impedance solid state devices. Further work in the

design and application of these lower impedance TLTs

needs to be done. Also, continued research on magnetic

materials is encouraged. Equal-delayed TLTs acting as

ununs appears to be a key technique for the future.

Finally it should be pointed out that the TLT is designed

to match broadband loads, that is impedances that have

no (or small) reactive components.

Figure 9 · The Guanella 1:9 TLT, using three two-con-

ductor transmission line windings, each of which may

be a coaxial cable.

450 ohms the optimum characteristics impedance Z 0 is

150 ohms. In matching 50 ohms to 5.5 ohms the optimum

characteristics impedance is 17 ohms. Since the low

impedance version requires much smaller inductances in

order to have enough reactance for input-output isolation,

its performance at this low impedance level should be

vastly greater than the high impedance version. This fac-

tor is especially beneficial at lower frequencies.

Figure 10 shows a schematic of a quadrifilar-wound

transformer providing ratios as high as 1:9 when con-

necting terminal A to terminal D and as low as a 1:1.36

ratio when connecting terminal B to terminal F. In the 1:9

ratio three transmission lines are in series which aids the

low frequency response, but a single direct voltage is

added to a twice delayed voltage yielding a poorer high

frequency response than its 1:4 counterpart. When

matching 50 ohms on the right to lower impedances on

the left this unun is a practical multimatch transformer.

Since these broadband TLTs can also be made very

References

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

Frequencies,” Brown-Boveri Review , Vol 31, Sep 1944, pp.

327-329.

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

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

3. Sevick, J., Transmission Line Transformers , Noble

Publishing Corp., 4th Edition 2001.

4. Sevick, J., Building and using Baluns and Ununs ,

CQ Communications, Inc., 1st Edition 1994.

Author Information

Jerry Sevick is retired from AT&T Bell Laboratories,

and remains an occasional consultant and lecturer.

February 2004

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