Feb. 17,1942;
'
P.‘ s. CARTER ‘
'
- I
2,273,455
TRANSMISSION LINE MATCHING .
'
Filed March 14, ‘1959
'.
h “INVEA'ITOR.
BY
‘pH/up s. CARTER‘
‘
ATTORNEY.
2,273,465
Patented Feb. 17,1942
_ UNITED STATES PATENT OFFICE‘
TRANSMISSION LINE MATCHING _
Philip 8. Carter, Port ‘Jeiierson, N; Y., assignor to
Radio Corporation of America, a corporation
of Delaware
‘ Application March 14, 1939, Serial No. 261,745
8 Claims. (Cl..178—44)
The present invention relates to a means for
present invention wherein 2 quarter wave line
vmatching a transmission line having a predeter
mined value of surge impedance with an anten
na or a load circuit having a widely different
value of impedance.
.
~ More particularly, the present invention re
lates to means for matching a transmission line
to an antenna whereby the frequency band width
of the antenna is not curtailed. Both experi
ence and theory show that when an antenna
having a_ broad frequency characteristic is
matched to‘the transmission line by means of
sections connected in series are interposed be
tween the transmission line and the load.
Figure 1 shows a transmission line having a
surge impedance indicated by Z00, connected to
a load having an impedance Z1. equal to sixteen
times the impedance Zoo. Connected between the
transmission line and load is shown a matching
section M having a length equal to a quarter of
the length of the operating wave and having a
surge impedance ZM equal to four times the surge
impedance Zoo of the transmission line.
one of the usual type matching‘ circuits, the fre
In Figure 2 the same transmission line and
quency band. width is considerably narrowed.
same load are shown as in Figure 1. Interposed
The extent of the detrimentaleifect of such a 15 between the transmission line and the load .are
circuit isdirectly proportioned to the ratiov of
two impedance matching sections M1 and M2 con
the impedance change.
'
The present invention relates to methods of,
nected in series and each having a length equal
.to a quarter of the length of the operating wave 7
and means for matching a transmission line to
at the midband frequency. a load circuit by means of which the above men 20 According to my invention ‘the surge im
tioned di?iculty is, for most practical purposes, i pedance Z01 of the ?rst matching section M1 is
eliminated.
-
An object of the present invention is to match
the impedance of an antenna having a broad fre- ~ -
quency characteristic to the surge impedance of
a transmission line ‘without destroying the ire- -
made equal to the one-quarterpower of the im-.
pedance ratio between, the transmission line and
the load or, in the speci?c example shown in
Figure 2, twice the surge impedance of the trans
mission line. The surge impedance Z02 of the
second matching section M2 is made equal to
the three-quarter power of ‘the impedance ratio
quency characteristic of the antenna.
Another object of the present invention is to
provide matching means for the impedance of‘
the transmission line and the load or,
an antenna to the surge impedance of a-trans 30‘ between
in the ‘speci?c example shown in Figure 2, equal
mission line having a value of surgeimpedance
to‘ eight times the impedance of the transmissiop
widely different from the impedance of the an-‘
line.
=
'
tenna without restricting the frequency band
While I have shown the use of two matching '‘
width of the antenna.
Still another object of the present invention is 35 ‘sections in Figure 2 it is to be clearly understood
that a number of matching sections may be any
to provide means. for matching the impedance of
one radio frequency translating means to the ' even number in accordance with the invention.
In the following-detailed mathematical theory
impedance of another translating means having
of. broad band impedance matching according to
a'value of impedance ‘widely different from the
impedance of the ?rst translating means without 40 my invention, n sections will be considered each
restricting the frequency band width over which
section being equal to a quarter of the length of
said means are operative.
I;
the operating wave at the midband frequency.
Brie?y, my invention involves the use of an
even number of quarter wave line sections in
series between the antenna or other load and
the transmission line or other translating means,
the ratio of impedances of said sections bearing
such a relationship to the ratio of the impedances
of .the‘ transmission line and antenna that the
transmission line is matched to the load over .a
v
comparatively wide band 0_ frequencies.
Referring, now, for 'a more complete under
standing of the inventio , to the following de
tailed description which is accompanied by draw
ing in which Figure 1 illustrates ‘a method of
matching a transmission line to a load circuit
having a value of impedance di?erent from the
impedance of the transmission line and is shown
only for the purposes of explanation; Figure 2
illustrates diagrammatically an example of the
The number n w?l be considered even in ac
cordance with the invention. Usually two sec
tions (n=2) are su?icient.
.
If R is the impedance ratio to be changed and
if Z01, Z0: . . .,Z0n are the surge impedances of
the quarter wave lines and Zoo the surge im-'
pedance of the main line, we make:
11-1 ‘
In the discussion to follow it will be assumed
that n=2 for simplicity.
At the mid band frequency, where the length]
2
2,273,465
. _
The input impedance Z11 of section M1 looking‘
of each section is exactly M4, the section Z02
changes the impedance from RZoo to
and the section Z01, from
. 4R2.»
t0 Zoo.
Let p=the ratio of increase in frequency to the
mid-band frequency
i. e.
'’
Rx+1
.7" .71’
10 =Zoo exp (7'0) which indicates a perfect match
with the approximations made. In any case the
_A_f
phase angle introduced into the input impedance
f0
of one line section is almost perfectly cancelled
by an opposite phase shift due to the action of
the other section when working off the mid-band
where Af=change in frequency and fo=mid-band
frequency.
1
i
Let 0=line angle=
frequency. There is, however, a small decrease
in the ?nal input resistance.
email
A _
c
A speci?c case will now be dealt with using the
values given in the drawing. Assume a load of
where l=line length, A=wave length, ,f=frequency
20 16 times the surge impedance of a main line to
and c=velocity of light.
be matched thereto. If the matching is done in
one step a quarter wave line is used as shown in
Figure 1 with a surge impedance equal to 4Zoo
where Zoois the surge impedance of the main
25 line. If the frequency is 5 percent highthe in
Then '
radians.
'
~
put impedance becomes
on a line section where (K) is the magnitude,
¢ the phase angle and exp (M) =4‘
I_{ is de?ned by the relation
‘
Thus it will be seen that there is introduced a
30 reactive component equal to about 30% of the
resistive component.
This causes a re?ection on
the main line of about 15 percent, which is three
times the allowable limit of 5% in television
impedance of the transmission line.
practice.
From fundamental relations the input imped
Now suppose the transformation is done in two
steps in accordance with the invention and as
shown in Figure 2. In this case Zo1=(16) .1/4Zoo=
ance Z1 of any line section is
2Zoo and Zo2=(16) 3/4Zno=8Zoo. Calculation, with
out the approximations previously made, shows
For matching section Mix with Zo2=R3/4Zoo and
load RZoo
the ?nal input impedance at a frequency 5 per
cent high to be Zoo x 0.978/0.08°. The reactive
-
component is negligible. The slight miss-match
in the resistive component produces a re?ection
of 1.1% on the main line, and its effect is prac
and the input impedance Zn of section M2 be
comes
tically negligible.
_
vWhile I have shown and particularly described
several embodiments of my invention, it is to be
distinctly understood that my invention is not
When p1r is not great so that cos p77‘ w 1 and sin
50 limited thereto but that modi?cations within'the
p'ir “Pr and p1r<<1 the above becomes
scope of my invention may be made.
I claim:
.
i
1. In combination, a wide band antenna system
and a transmission line connected thereto, the
impedance of said antenna being R times the
55 surge impedance Zoo of said line, an even number
Mast-earn]
n of matching line sections connected in series
and interposed between said antenna and trans
mission line, each of said sections having a
length equal to one-quarter of the length of the
00 operating wave at midband frequency and‘ hav
This impedance constitutes the load for the
section M1 having a surge-impedance Zo1-K1 for
ratio of the surge impedance of the ?rst of said
sections to that of said line being
this section is given by:
‘
ing surge impedances of Zoi,'Zo2, . . ., Zon, the.
1
65
z_01
Z _R
00
that of the second section to the line being
K
i
70
3
e
in
_
Z00 _ 13(5) 1 . . .
and that of the nth section to the line being
2,273,405
3
2. In combination, a radio frequency load and v‘ quencies removed from midband the reactance
a transmission line connected therein, the im
pedance of said load being R times the surge im
pedance Zoo of said line, ,an even number, n of
matching line sections connected in series and
‘ introduced by each section is counterbalanced by
an opposite reactance introduced by another of
said sections, the surge impedance of each of said
sections having values between the ‘limits de
termined by the impedances of said load and
said transmission line, the surge impedance of
interposed between said radio frequency load and
transmission line, each of said sections having a
length equal to one-quarter of the length of the '
each section beingless than one adjacent inn-=-v
operating wave at midbandifrequency and hav
pedance and greater than the other adjacent ime
ing surge impedances of Z01, Z02, . . .-, Zon, the 10
> ratio of the surge impedance of the ?rst of said
sections to that of said line being
‘that of the second section to said line being
a
L2 _ R (a
andthat of the nth section to said line being
.
.
.
n—1
Zl__R(TF
Zoo_
pedance.
.
6. In combination with a wide band antenna
' and a transmission line, of means for matching
, said transmission line to said antenna over said
wide band comprising a pair of series connected
matching sections interposed between said trans
mission line and antenna, each having a length
equal to one-quarter of the length of the operat- ‘
Ying wave at midband frequency, the surge im
pedance of each of said sections being so pro
20 portioned with respect to the ratio of said an
tenna impedance to line impedance that at fre
quencies removed frommidband the reactance
introduced by one section is counterbalanced by
an equal and an opposite reactance introduced
by the other of said sections, the surge impedance
3. In ‘combination, a radio frequency load and 25> of each of said sections having values between
a transmission line connected thereto, the im
the values of impedance of said antenna and the
pedance of said load being R times the surge
impedance of said transmission line, the surge
impedance of the transmission line, a pair of
impedance of each section being less than one
matching line sections connected in series and ,
adjacent impedance and greater than the other
interposed between said load and transmission so adjacent impedance.
line, each of said sections having a length equal
7.
In
combination,
a
pair
of
radio
frequency
to one-quarter of the length of the operating
translating elements connected together, the im
wave at midband frequency, the section adjacent . pedance of one of said elements being R times
said transmission line having an impedance R1“ 35 the surge impedance Zoo of the other of said
times the surge impedance of said transmission
elements, an even number n of matching line
line and the second_ section having an impedance
sections connected in series and interposed be
R3" times the surge impedance of said transmis
sion line.
,
.
> tween said elements, each of said sections having
a length equal to one quarter of the length of the
4. In combination with a wide band antenna
operating wave and having surge impedances
40
system and a transmission line connected there
of Z01, Z02, . . ., Zo», the ratio of the surge im
to, the impedance of said antenna being It times
pedahce
of each of said sections to the next ad
the surge impedance of the transmission line, of
jacent impedance progressing from one of said
means for matching said transmission line to
elements to the other of said elements in the
said antenna over said wide band comprising a
relationship
'
‘ pair of matching line sections connected in series 45
and interposed between said antenna and trans
01
mission line, each of said sections having a length
Zoo“
.
,
equal to one-quarter of the length of the operat
ing wave at midband frequency, the section ad
'8. In combination, a ?rst radio frequency
iacent said transmission line having an im 50' translating means and a second translating
pedance R1/4 times the surge’ impedance of said
means connected thereto, the impedance of. said
?rst translating means being R times the surge
transmission line and the second section having
impedance of the second translating means, a
an impedance R3" times the surge impedance of
pair of matching line ‘sections connected in series
said transmission line.
0 ,
and interposed between said translating means,
5. In combination, a radio frequency load
each of said sections having a length equal to
operable over a wide band of frequenciesand a
transmission line, an even number of series con- ‘
v nected matching sections interposed between
- one-quarter of the length of the operating fre
quency at midband frequency, the section ad
jacent said second translating means having an
‘said transmission line and load, each havinga
length equal to one-quarter of the length of the 60 impedance Rl/i times the surge impedance of
said second translating means and the second
operating wave at midband frequency, the surge
impedance of each of said sections being so pro
section having an impedance R3" times the surge
portioned with respect to the ratio of said load
impedance to the line impedance that at fre-'
impedance of said second translating means.
PHILIP S. CARTER.
,