Varactor Tuned Loop Antenna.pdf

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A Simple Varactor-Tuned
Loop Antenna Matching Network
by
Chris Trask / N7ZWY
Sonoran Radio Research
P.O. Box 25240
Tempe, AZ 85285-5240
Senior Member IEEE
Email: christrask@earthlink.net
27 August 2008
Revised 28 August 2008
Revised 30 August 2008
Revised 2 September 2008
Revised 16 September 2008
Trask, “Varactor Tuned Loop Antenna”
1
16 September 2008
Introduction
Loop antennas are of interest to a wide
range of users, from shortwave listeners
(SWLs) and radio amateurs to designers of
direction-finding receiver systems. SWLs and
radio amateurs living in confined areas such
as apartments or in communities having an-
tenna restrictions find loop antennas and es-
pecially active loop antennas to be a practical
solution as they can offer directional perform-
ance similar to that of a dipole antenna while
taking up a considerably smaller space, and
their small size makes them readily adaptable
to mechanical rotation.
However, the high inductive reactance of
the loop antenna impedance is detrimental to
wideband performance, and remote tuning is
often employed for achieving good perform-
ance and enjoying the highly desireable mag-
netic field response, which provides some de-
gree of immunity from electric field noise from
sources such as lightning discharges, faulty
mains transformers, and fluorescent lighting.
Loop Antenna Impedance
Before we address the design of remotely
tunable matching networks, we need to gain an
understanding and appreciation of the imped-
ance of loop antennas, the nature of which pre-
cludes the design of wideband matching net-
works. It is well known that the loop antenna
impedance consists of a small real part R
ant
(consisting of the radiation resistance plus bulk
and induced losses) in series with a large in-
ductance L
ant
, which renders the loop antenna
as being a high Q source (1):
Q
ant
=
ω
L
ant
R
ant
(1)
really does not need to be repeated here, and
very thorough treatments are available from King
(2), Kraus (3), Terman (4) and Padhi (5). Most
authors provide little discussion about the im-
pedance of the loop antenna, other than to dem-
onstrate that the impedance is dominated by a
large series inductance and is a cascade of
parallel and series resonances (6). A few go
further and show that the loop antenna imped-
ance can be seen as a shorted transmission
line. Terman (4) makes use of this method,
which is usable for frequencies below the first
parallel resonance.
An IEEE paper published in 1984 (7), pro-
vides a very useful means for estimating the real
and imaginary parts of the loop antenna imped-
ance, the latter of which is a refinement of the
method proposed by Terman, and which the
authors of that paper further refine by providing
scalar coefficients for use with a wide variety
of geometries that are commonly used in the
construction of loop antennas. In their approxi-
mation, the radiation resistance is determined
by:
k
L
R
ant
= a
tan
b
0
(2)
2
where L is the perimeter length of the loop an-
tenna and the wave number k
0
is defined as:
k
0
=
ω μ
0
ε
0
(3)
where
µ
0
is the permeability of free space (4
π
10
-7
H/m), and
ε
0
is the permittivity of free space
(8.8542 10
-12
F/m). The coefficients
a
and
b
in
Eq. 2 are dependent on the geometry and the
perimeter length of the loop antenna, a list of
values being provided in Table 1.
The inductive reactance of the loop an-
tenna impedance is determined by:
k
L
X
ant
=
j
Z
0
tan
0
2
(4)
where
ω
is the frequency in radians per sec-
ond.
There is more than enough literature avail-
able about loop antennas that the basic theory
Trask, “Varactor Tuned Loop Antenna”
2
where Z
0
is the characteristic impedance of the
equivalent parallel wire transmission line, de-
16 September 2008
Configuration
Circular
Square (side driven)
Square (corner driven)
Triangular (side driven)
Triangular (corner driven)
Hexagonal
L/λ
≤
0.2
a
b
1.793
3.928
1.126
3.950
1.140
3.958
0.694
3.998
0.688
3.995
1.588
4.293
0.2
≤
L/λ
≤
0.5
a
b
1.722
3.676
1.073
3.271
1.065
3.452
0.755
2.632
0.667
3.280
1.385
3.525
Table 1 - Coefficients to be Used with Equation 2
fined as:
4A
Z
0
= 276
ln
Lr
(5)
In the process of designing matching net-
works for adverse impedances such as those
of loop antennas, it is very useful to devise
lumped element equivalent models as some
analysis and optimization routines, such as
PSpice, do not have provisions for including
tables of measured data for interpolation. Fig.
2 illustrates two rudimentary lumped element
models, the first being usable up to and slightly
beyond the first parallel resonance and the sec-
ond being usable to the point prior to where the
impedance becomes asymptotic, or about
25% below the first parallel resonance. Far
more detailed models can be devised that in-
clude subsequent resonances and anti-
resonances (10), but they would serve little pur-
tion patterns from those that are fed balanced
(9).
where A is the enclosed area of the loop an-
tenna and r is the radius of the antenna con-
ductor.
A highly detailed report from the Ohio
State University Electroscience Laboratory in
1968 (8) provides a thorough analytical means
for estimating the real and imaginary parts of
the impedance of single and multi-turn loop
antennas, as well as the antenna efficiency.
Computer simulation routines such as
EZNEC also provide a useful means for esti-
mating the loop antenna impedance. Together
with papers and reports such as those men-
tioned herein, they allow the designer to gain
an understanding of the nature of the loop an-
tenna impedance. They are not, however, suit-
able substitutes for actual measurements and
the designer should always rely to measured
data, especialy when designing matching net-
works.
Fig. 1 shows the measured terminal im-
pedance of a 1m diameter loop made with
0.25” copper tubing. In order to ensure that the
loop antenna is properly balanced, a 1:1 BalUn
transformer is used to interface the loop an-
tenna with the impedance bridge. Loop anten-
nas that are fed unbalanced have dramatically
different impedance characteristics and radia-
Trask, “Varactor Tuned Loop Antenna”
3
1M 1T 0.25" Antenna
2000
1800
Measured Reactance (0.25")
1600
1400
Measured Resistance (0.25")
160
140
120
100
80
60
40
20
0
0
5
10
15
20
200
180
1200
1000
800
600
400
200
0
Frequency (MHz)
Fig. 1 - Measured Impedance of 1 meter
Diameter Loop Antenna made with
0.25” Copper Tubing
16 September 2008
Resistance (ohms)
Reactance (ohms)
Fig. 2 - The Loop Antenna (left) Together with Detailed (centre) and
Simplified (right) Lumped Element Impedance Equivalent Models.
pose here as the application here is focused
on frequencies below the first resonance.
In general, I use the more detailed model
for PSpice simulations and the simpler one for
illustrations such as those to be used here later.
For the 1m diameter loop made from 0.25”
copper tubing, the element values are roughly:
Ra
1
= 5k ohms
Ca
1
= 300pF
Ra
2
= 0.6 ohm
Ra
3
= 1.0 ohm
La
1
= 0.4uH
La
2
= 0.05uH
La
3
= 2.2uH
common-môde interference signals such as
lightning discharges, faulty mains transformers,
fluorescent lighting, as well as nearby high-
power broadcasting stations.
Simple Matching Networks
At first glance, the simplified equivalent
model in Fig. 2 readily suggests that adding a
capacitor in series with each antenna terminal
would provide a good match. This approach,
illustrated in Fig. 3 provides for suberb signal-
to-noise performance as the loop antenna can
These values were used in the evaluation
of a wide variety of passive matching networks
suitable for adaptation to remote tuning, the goal
being to devise a varactor-tuned matching net-
work that could be coupled directly to a coaxial
cable having an impedance of 50-ohms or to a
subsequent amplifier stage or stages of com-
parable impedance.
In the overall scheme, balanced networks
a prefered as they allow for the supression of
Trask, “Varactor Tuned Loop Antenna”
4
Fig. 3 - Passive Series Tuning
16 September 2008
be matched properly to the load (1, 11). In ad-
dition, the magnetic field performance of the
loop antenna can be thoroughly enjoyed, reduc-
ing the effects of noise from electric field
sources, though not to the degree as would be
experienced with a shielded loop antenna.
Once the reactance portion of the loop
antenna impedance is adequately tuned, the
impedance of the antenna seen at the output
terminal of Fig. 3 becomes a very small resist-
ance, which can be less than an ohm for anten-
nas made with large radius conductors such as
1/2” copper tubing. The design now becomes
a matter of devising a series of good quality
wideband transformers so as to provide a good
match between this low resistance and the char-
acteristic impedance of the feed line, which is
usually 50-ohm coaxial cable.
Matching Network Design
Many designs for matching loop antennas
make us of a single transformer between the
feed line and the antenna. In such approaches,
the coupling coefficient between the primary
and secondary windings is generally poor due
to the high turns ratio between the two windings
and the low impedance of the tuned loop. In
transmitting applications, the lower coupling
coefficient results in loss of radiated power and
heating of the magnetic materials used in the
transformer core. In receiver applications, the
lower coupling coefficient and subsequent
power loss results in a higher antenna tempera-
ture and receiver system noise figure (NF).
Twisted bifilar and trifilar wires typically
used in wideband transformers provide high
coupling coefficients that approach unity (12,
13, 14). However, the high turns ratio of the
primary and secondary windings of the single
transformer approach shown in Fig. 3 precludes
the use of combining both windings as a single
grouping of twisted wires.
Fig. 4 illustrates a matching network that
can be realized with wideband transformers
made with bifilar and trifilar twisted wires. Here,
transformer T1 is a Guanella 4:1 impedance
balanced-to-balanced (BalBal) transformer (15,
16, 17) made with two bifilar pairs of twisted
Fig. 4 - Varactor-Tuned Loop Antenna Matching Network Schematic
Trask, “Varactor Tuned Loop Antenna”
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16 September 2008

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