twisted magnet wire tx

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148 IEEE TRANSACTIONS ON PARTS, HYBRIDS, AND PACKAGING, VOL. PHP-7, NO. 4, DECEMBER 1971

Twisted Magnet Wire Transmission Line

PETER LEFFERSON

Abstract - Transm ission line principles are applied to twisted

magnet wire lines made of two wires to establish design limits.

Express ions are developed to predict the effects of wire film insulation

and of twisting. A design procedure is developed to realize a desired

characte ristic impedance for the design of radio frequency broad-band

transformers , signal combine rs, and pulse transformers.

INTRODUCTION

B

OAD-BAND transformers and signal combiners for HF

thru UHF and the digital field using twisted magnet wire

transmission line, have been discussed in the literature and are

widely used. [l]-[3]. The terminal impedances of these

passive devices are a function of: the transmission-line charac-

teristic impedance, line length, core material, and source

impedance at other te rminals. If the line impedance can be

controlled, these devices can be built with a wide frequency

range without requiring additional lumped elements. The

terminal reactance can be tailored in the same way to improve

matching into active devices.

This paper will consider only the twisted magnet wire

transmission line and a design procedure will be given as a

function of wire size, wire insulation thickness, insulation

relative dielectric constant, and wire twist.

Twisted magnet wire transmission lines using the wire size

range from 4 to 44 can be realized with characteristic

impedances ranging from 10 to 85 R. More practical examples

would be a 50-a line made with a pair of number 40 wires and

a 25,a line made with a pair of number 15 wires.

Basic Dimension Standard

The United States military specification for magnet wire,

MIL-W-583, will be used for a well-ordered base on which to

build a design procedure. Among other th ings, this specifica-

tion defines round magnet wire having film insulation. It lists

American Wire Gage sizes 4-44 in four insulation thickness

groups with their dimensions and tolerances. The minimum

insulation thickness for each wire s ize in groups 2-4 is

approximately the minimum thickness for the wire size in

group one multiplied by the group number. The maximum

thickness is about equa l to the minimum of the next higher

group. These data from MIL-W-583 is repeated in Table I.

Using the dimensions from this table and the expression for

Manuscript eceived une 9, 1971; evisedSeptember 3, 1971.

The author

s with the Milton Roy Company , St. Petersburg, Fla .

C.L. Ruthroff, Some broad band transformers , Proc. IEEE, vol.

47, pp. 1337 - 1342, Aug. 1959.

0. Pitzalis, Jr., Practica l design information for braod-band

transmission line transformers,

Proc. IEEE, vol. 56, pp. 738 - 739,

Am. 1968.

* 3R.E. Matick, Transmission line pulse transformers - Theory and

application,P roc. IEEE, vol. 56, pp. 47 - 62, Jan. 1968.

characteristic impedance of two parallel wires [4]

Z1 = p cash-4.

-

(1)

Vt req

u

The computer calculated characteristic impedances are plotted

in Fig. 1 for a relative dielectric constant of 1 O.D and d are

the wire diameters with and without the insulation film,

respectively. freq is the equivalent relative dielectric constant.

Fig. 1 shows the calculated impedances for the film-thickness

extremes.

WIRE TWIST AND PITCH ANGLE

The effect of twisting the line can be normalized for all

wire sizes if the twist per inch T is equated to the angle

included between each wire and a line drawn down the center

of the transmission line (pitch angle0). For bifilar w ire, twist

is given by

tan 0

j-z-----

I-iD

(2)

The relation of tw ist and pitch angle is plotted in Fig. 2 for

wire sizes 4-44 and the insulation thicknesses of classes one

and four.

Experimental data suggest that optimum performance is

obtained from lines having pitch angles between 20-45.

When the line twis t is loose, it becomes difficult to maintain

continuous line geometry as the line is wound on a form. This

is seen as a large reflection on a time-domain reflectometer.

The transmission line is subjected to excessive stress as the

twist angle approaches 50.5 and in the vicinity of 50.5 it will

break. Equation 2 and. he maximum pitch angle are developed

in the Appendix.

A line impedance rise of 1 or 2 S2can be anticipated when

the line is wound of a ferrite form.

FILM DIELECTRIC

The equivalent dielectric constant that must be considered

in order to give meaning to the theoretical characteristic

impedance of F ig. 1, is a function of the film insulation and

pitch angle. It is common to express a system having two

dielectrics as

freq = (YE~I+ /3Er* CX /3 = 1

=Erl (1 -P)+PEr*

= 91 + P (Er2 - frl>,

where erI and er2 are the relative dielectric constants of air (or

some other surround ing material) and the film insulation ,

41nternationa1 Telephone and Telegraph Co., Reference Data for

Radio Engineers, 5th ed.

New York: Sames, 1969, ch. 22, p. 22.

Authorized licensed use limited to: Universidad de Antioquia. Downloaded on November 20, 2009 at 11:47 from IEEE Xplore. Restrictions apply.


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LEFFERSON: TWISTED MAGNET WIRE

149

TABLE I

MINIMUM INCREASE IN DIAMETER OF BARE ROUND WIRE AND THE MAXIMUM

OVERALL DIAMETBR DUE TO FILM INSULATION

Wire size

(AWG)

CLASS 1

CLASS 2 CLASS 3

CLASS 4

Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximbm

Diameter increase in overall increase in overall

increase in overall

increase in overall

nominal diameter diameter diameter diameter diameter

diameter diatieter diameter

(W (InI (In)

(InI (In) (InI

(InI (InI

(In)

4---

5---

6-e-

7---

8--m

9---

lO---

ll---

12---

13---

14---

15---

16---

17---

18---

19---

20---

21---

22---

23---

24---

25---

26---

27---

28---

29---

30---

31---

32---

33---

34---

35---

36---

37---

38---

39---

40---

41---

42---

43---

44---

0.2043

. 1819

.

1620

.

1443

. 1285

. 144

. 1019

. 0907

.0808

.0720

.0641

0571

: 0508

.0453

.0403

.

0359

.0320

. 0285

.0253

. 0226

. 0201

.

0179

. 6159

.

0142

.

0126

. 0113

.

0100

. 0089

.0080

. 0071

.0063

. 0056

.

0050

.0045

.0040

.0035

.

0031

. 0028

.0025

.0022

.0020

0.0019

. 0019

.0018

.0017

.0016

.bo16

.0015

.0015

.0014

.0014

.

0014

.0013

.0012

.0012

.OOll

.OOll

. 0010

.OOlO

.OOlO

. 0009

.

boo9

. 0009

.0008

.0008

.0007

.0007

.0006

.0006

.0006

.0005

.0005

.0004

.0004

.0003

.0003

.0002

.0002

.0002

.0002

.0002

. 0001

0.2093 0.0037 0.2111 0.0049

. 1867 .0036 . 1884 .0048

. 1665 .0035 . 1682 .0047

. 1485 .0034 . 1502 .0046

. 1324 .0033 . 1342 .0045

. 1181 .0032 . 1198 .0044

. 1054 .0031 . 1071 .0043

. 0941 .0030 . 0957 . 0042

.0840 .0029

.0855 .004b

.0750 .0028 . 0765 .0039

.0&70 .0027 .0684 .0038

. 0599 .0026

.0613 .0037

.0534 .0026

.0548 .0036

.0478 .0025 . 0492 .0035

.0426 .0024 .0440 .0034

-0382 t 0023

. 0395 .0033

.0341 .0022 .0353 .0031

.0306 .OOZl . 0317 .0030

.Q273 .0020

. 0284 .0029

.0244 .0019 .0255 .0028

.0218 .0019 . 0229 .0027

. 0195 .0018

.0206 .0026

. 0174 .0017

.0185 .0025

. 0156 .0016

. 0165 .0023

0139 .0015

. 0148 .0022

. 0126 .0014 . 0134 .0021

. 0112 .0013

. 0120 .0020

. 0100 .0013 . 0108 .0019

. 0091 .0012 . 0098 no018

.0081 .OOll . 0088 .0017

.0072 .OOlO

. 0078 .0015

.oo64 .0009 .0070 . ooi4

.0058 .0008 .0063 .0013

.0052 .0008

.0057 .0012

.0047 .0007 . 0051 .OOll

.0041 .0006 .0045 . 0010

.0037 .0006 .0040 .0009

.0033 .0005 . 0036 .0008

.0030 .0004 .0032 .0008

.oO26 ,0004 . 0029 .0007

.0024 .0004

.0027 .0006

0.2125 0.0064

. 1897 .0062

. 1695

. 1515

: 0059

0059

.1355 .0058

. 1211 .0057

: 0969084 .00540056

.0867 .0052

. 0776 .0050

. 0695 .0049

.0624 .0048

.0558 .0046

.0502 .0045

. 0450 .0044

.0404 :0042

.0362 .0040

.0326 .0039

. 0292 .0037

.0263 .0036

. 0237 .0035

. 0214 .0034

. 0192 .0032

. 0172 .0030

. 0155 .0029

. 0141 .0028

. 0127 ,0027

. 0115 .0026

. 0105 .0025

. 0095 .0024

. 0084 .0021

.0076 .0020

. 0069 .0019

; 0062 .0017

.0056 .0016

. 0050 .0015

.0044 .0013

.0040 .OOlO

.0037 .OOlO

.0033 .OOlO

.0030 .0009

0.2148

.

1920

.1717

, 1537

.

1377

. 1233

.1106

.

0991

.0888

. 0796

.0715

.0644

.0577

.

0520

.0468

.0422

.

0379

.0342

.0308

. 0279

.0252

.0228

.0206

.

0185

.

0166

.

0152

.

0137

.

0124

.0113

.0102

.

0091

.0082

.0074

.0067

.0060

.0053

.0047

.0043

.0038

.0035

.0032



3/7

150

IEEE TRANSACTIONS ON PARTS, HYBRIDS, AND PACKAGING, DECEMBER 1971

130-

120-

llO-

LO-

O

Z_W-

c

z 8Q-

2

E 70-

I

ua-

E

B so-

ti

24D-

1

Jo-

M-

10 -

I

I I I II I I I I I I I I, I I I I1 I I I II I I I I I I II II 1 I I1 I I I

5

10 15

20

25

30

35

40 44

WIRE SIZE (AWG)

Fig. 1. Characteristic impedance for bifilar magnet wire transmission line based on MIL-W-583 dimensions and with relative

1DODt

loo-

5

E -

w

P lo-

t -

F -

c -

1.0 -

dielectric constant of one.

I CLASS 1

- - CLASS 4

0.1 6 1

0 10

20 30 40 50

60

PITCH ANGLE IN DEGREES

Fig. 2. Bifilar transmission line twist per inch versus pitch angle for wire sizes 4-44 having class-l and 4 insulation thickness.



4/7


151

E

.q FROM C- MEASUREMENTS

E

4 ; 10 1; 2b 25 ;D 3; 4b i-0


Fig. 3.

Measured equivalent dielectric constant versus pitch angle for a sample of no. 29 magnet wire having class-2

insulation thickness.

respectively . erl and er2 are published constants, but 0 is a domain re flectometer. The film relative dielectric constants

function of pitch angle.

were calculated from capacitance measurements of wire

The behavior of fi can be seen by observing ereq as the

samples in a mercury bath.

pitch angle is increased, If one assumes that the internal,

It was observed that the measured relative dielectric

external, and mutual inductance of the line are not changed by

constant can be greater than the published value for the film

twist, ereq can be calculated from measurem ents of the actual material. This might be expected because as the twist is made

characteristics impedance by

very tight, the wire dimension and the film thickness change

SO

calculated Zo for flat parallel wires

that they no longer fit the model for which the theoretical

Greq =

with E req = 1

parameters were calculated.

measuredZO

(4)

When the /3 is calculated from the equivalent dielectric

constant measurements, it is found to fit the expression .

It can also be calculated from capacitance measurements of

the line by

p = 0.25 + 4 x 1o-4 8 2.

(7)

measured capacitance

In Fig. 4 this expression is used to predict the characteristic

(5) .

ereq =

calculated capacitance for the same ength of

impedances for three magnet wire sizes, as samples. It is seen

to consistently predict the correct impedance sufficiently

flat parallel wires with ereq =l

closely to yield a voltage standing-wave ratio (VSWR) within

It can be calculated from the electrical line length by

l.l:l.

Greq = measure

measured electrical length

d h srcal length of the twisted liney . (6)

Laboratory data show agreement among all three of these

within the measurement accuracy of wire dimension, charac-

teristic impedance, and relative dielectric constant of the film.

Five percent random impedance fluctuation along a twisted

line is common. Fig. 3 illustrates an example using number 29

wire having a class-2 thickness of polyester film insulation. The

example shows Ereq

calculated from capacitance, electrical

length, and impedance measurements of four line samples

twisted to different pitch angles.

The slope of fi versus 8 in (7) is a function of the softness

of the wire insulation. Equation (7) holds for most modern

magnet wire insulating films but it w ill change if the insulation

is very soft. Polytetrafluoroethy lene (Teflon) covered hook-up

wire is a good example that shows how far it can change. The

relative dielectric constant versus pitch angle is given in Fig. 5

for a sample of no. 24 19-strand wire. A fit is found by using

The characteristic impedance and electrical length data

were taken with the Hewlett-Packard model 1415A time

The following steps form a useful outline for designing a

twisted magnet bifilar wire transmission line for a required

characteristic impedance.

p=o.zs+ 1 x1o-3 02 .

03)

DESIGN PROCEDURE



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152


Fig. 4.

Comparison of measured to estimated characteristic impedance for 3 wire sizes versus pitch angle.

~~ MEASUREhiENTS

t

,1

1

1

I

I I

I

0

I,,

5 10

15

20 25

,

t

0 35

40 45

50


Fig. 5.

Measured equivalent dielectric constant versus pitch angle for a sample of Teflon-covered no. 24 19-strand wire.



6/7


153

Fig. 6.

Bifilar wire transmission line twisted to its maximum pitch angle of 50.5.

1) Choose a film insulation thickness group and film

relative dielectric constant. (These are usually limited by their

availability and other physical and electrical considerations.)

2) Calculate the relative dielectric constant assuming pitch

angle of 30 from (3) and (7):

ereq = err + 0.61 (LIZ - err)

where err = 1 for air.

3) Calculate the required characteristic impedance for

relative dielectric constant of 1 from

Zl = N&q;

where

Zl

impedance when Ereq = 1;

Z desired impedance.

4) Use Fig. 1 to choose the correct wire size.

5) Use Fig. 2 to determine the required twis t per in.

CONCLUSION

The characteristic impedance of any twisted magnet wire

transmission line can be found if the dimensions and the

dielectric constant are known. Figs. 1 and 6 give the impedance

at the expected tolerance limits for standard wire sizes having

an insulation dielectric constant of 1. This is modified by the

equivalent d ielectric constant, which is a function of the

relative dielectric constant of the film insulation

and

increases as the line is twisted. The twist for various pitch

angles [determined by (2)] is shown in Fig. 2 for wire sizes

4-44. The equivalent relative dielectric constant is related to

the pitch angle by (3) and (7).

The electrical length of a twisted line is related to the

square root of the equivalent dielectric constant in (6).

Using these basic expressions the following statement can

be made.

1) The impedance increases as the wire dimensions de-

crease.

2) The impedance decreases as the wire twist is increased.

(The pitch angle increases.)

3) The relative dielectric constant for the line is controlled

more by the film dielectric constant as the pitch angle

increases.

4) For small pitch angles the line impedance can be

reduced by immersing the line in a material other than air.

5) For large pitch angles the line impedance can be

reduced by using a wire insulating film having a high dielectric

constant. The useful pitch angle range is bounded by the

limitation on line uniformity at about 20 and the strength of

copper at about 4.5.

For a film dielectric constant of 3.5 and with air as the

surrounding medium, the useful impedance range for twisted

magnet wire transmission lines is lCM50a.

Over 60 magnet wire transmission lines of many different

forms have verified the conclusions of this paper.

APPENDIX

The cen ter lines of two twisted wires form a helix as shown

in Fig. 6. The helix diameter is one wire diameter. It forms a

sine wave in the longitudinal plane.

A = (D/2) sin (2 71Td)

(9)



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154


where

lines is D and twist can be expressed as

D wire diameter;

T twist per inch;

Tmax = (sin 0 )/(2D).

00

d distance along the transmission line.

The pitch angle comes out of this as

The maximum pitch angle of 50.5 is found by equating 9 and

tan 0 = 71TD

(lo) 11. It is not a function of wire diameter.

The actual wire length can also be seen n Fig. 6 where one

where 43 is the pitch angle defined in Fig. 6.

twist is unwrapped. The wire length for one twist is

The maximum pitch angle occurs when the line has been

wound to the point where the distance between wire center

nDJ1 + l@n 01.

(12)

Peter Lefferson received the B.E.E. and M.E. degrees from the University of Florida, Gainesville, in 1962

and 1965, respectively.

He worked for NASA as an Instrumentation Engineer for one year. He spent five and one half,years with

Electronic Communication Inc., in design of UHF transceivers. Presently, he is with Milton Roy Company,

St. Petersburg, Fla.

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