A COMPARISON OF RESISTIVE AND REACTIVE CORPORATE
POWER DIVIDER NETWORKS FOR PHASED ARRAY ANTENNAS
Kevin W. Ornmodt
Raytheon TI Systems
McKinney, TX
1
Abstract
Certain communication systems do not require the low sidelobe levels that
are typical of radar systems. Because of this, phased array antennas for these
communication systems do not need the tight control on element amplitude and
phase errors that guarantee low sidelobe levels. In turn, this then calls into
question the need for using resistive power dividers which help maintain low
element errors. The alternative, reactive dividers, can introduce higher element
errors but are smaller and less costly to implement.
paper answers the question of whether reactive dividers can be used
1for largeThisphased
arrays without rigorous sidelobe requirements. The results of a
theoretical analysis of a large phased array antenna with both a resistive and a
reactive corporate power dividing network are presented. The effect of each of
'these divider networks is assessed on the overall array radiation pattern and the
'differences in performance are highlighted. The results indicate that reactive
!dividers may be used under certain conditions.
1. Introduction
There has been significant interest in using phased array antennas for a
variety of communication systems in recent years.
This differs from the
traditional purpose for which they have been used, namely scanning radar
systems. Radar systems typically require low sidelobe levels for proper operation,
while certain communications systems do not require low sidelobe levels. For
these communication systems, high gain is a more critical requirement. For such
a communication system to maximize antenna gain, a uniform amplitude
distribution is needed across the array to eliminate taper loss. This results in high
sidelobes, i.e. -13 dB for a square aperture and -17 dB for a circular aperture. If
an antenna by definition is going to have high sidelobes, the need for maintaining
tight control of amplitude and phase errors in the array is lessened, since the
1 primary reason for doing this is to provide low sidelobe levels.
If higher element amplitude and phase errors can be tolerated, then perhaps
unconventional techniques in the corporate manifold can be considered which
result in simpler fabrication. In this paper we will consider the effect of using
reactive power dividers in the corporate power dividing network of a large phased
array instead of the more conventional approach of using resistive power dividers.
The use of reactive dividers should result in a simpler and cheaper fabrication
process.
2. Corporate Divider Networks
Corporate power dividing networks are commonly used for distributing
microwave power throughout a phased array antenna system. Often Wilkinson
power dividers [1] are used as the individual power splitters throughout the
corporate manifold. They utilize a resistor to dissipate imbalances between the
two output ports which results in good isolation over the design frequency band.
Reactive dividers are an alternative to Wilkinson dividers. They do not
incorporate resistors and hence have degraded isolation between the output ports
as well as degraded output port match. Figures 1 and 2 show the theoretical
performance of equal power split Wilkinson and reactive power dividers,
respectively. From the figures we can see that the reactive divider provides 6 dB
of isolation and output port return loss while the isolation and output match of the
Wilkinson divider at center frequency is perfect.
From a purely performance based point of view, the Wilkinson divider is
superior. However, from a fabrication point of view, the Wilkinson divider is
complicated by the need to include the isolation resistor. For example, consider a
corporate manifold implemented in stripline.
The conventional method for
implementing the resistors in such a circuit would be to use discrete devices
which are soldered in place, often by hand. For a large array of N elements, N-1
resistors must be attached. This can be a painstaking and expensive process. A
newer method of fabricating the resistors which is gaining acceptance is the use of
etched or printed resistors which are fabricated into the stripline board. This can
reduce the amount of labor required to implement the resistors, but it adds several
extra processing steps to the fabrication cycle for the stripline board, which results
in extra cost.
A secondary concern with the use of Wilkinson dividers is the size of the
divider. Reactive dividers are in general more compact than Wilkinson dividers,
and so as circuit densities continue to increase, the reactive divider may become
more attractive from this standpoint as well.
3. Two Way Divider Example
The question then remains, what performance penalty exists for the use of
reactive power dividers. To answer this question, we will first consider a simple
two divider section of a phased array antenna as shown in Figure 3, complete with
phase shifters and amplifiers. We note that for this example the phase shifter has
a loss of 6 dB (we assume that solid state phase shifters which tend to have
significant loss are being used) and the amplifier has a gain of 25 dB. For now
we will ignore mutual coupling between the antenna elements. Lf the components
in each path are identical and are all matched to the system characteristic
impedance, then the performance will be the same regardless of whether
Wilkinson or reactive dividers are used. However, this is not a realistic case. In
reality the components in the two paths will not be identical and they will not have
perfect match to the system impedance.
To better understand what happens in the presence of mismatch, let us
consider a mismatch at the input to the channel 1 amplifier in Figure 3. If we
assume that this amplifier has a large mismatch of say -3 dB return loss, then we
will certainly induce imbalance in the two channels which should show a
performance difference between the Wilkinson and reactive dividers.
To give an indication of what is happening within the circuit, let us
consider the first order reflected components which travel within the circuit. If we
apply a 0 dB signal at the input to the circuit, we can see in Figure 4 what
happens in the Wilkinson divider case. The input signal is split at the divider into
two components of -3 dB each. These signals travel through the phase shifter
where they are attenuated by 6 dB. The signal in channel
1 encounters the
mismatch at the amplifier while the signal in channel 2 encounters no mismatch at
the amplifier and travels out to the antenna where it is radiated. The component
that is reflected at the amplifier in channel 1 is of most interest to us. This
reflected signal travels back through the phase shifter (where it is again attenuated
by 6 dB) and then it encounters the Wilkinson divider where it is split equally
with half the power going back to the input port and half being dissipated in the
isolation resistor.
We can now consider the same situation for the reactive divider case as
shown in Figure 5. The applied signal is the same and so a similar reflected
component is generated which returns to the divider from channel 1. This time,
however, the power is split three ways at the divider, with half returning to the
input port (like the Wilkinson case), one quarter being reflected back into channel
1 and one quarter traveling through the divider over to channel 2. Obviously it is
the last two components which cause the performance degradation in terms of
element amplitude and phase error.
However we note that both of these
components must travel through a phase shifter two more times than the direct
path, which for our example is an attenuation of 12 dB. Altogether, the reflected
components are at least 21 dB down from the direct signal. From this we see that
the phase shifters act in a manner similar to isolation resistors. Normally phase
shifter loss is considered to be a hindrance to the overall system performance, but
for this particular issue it is beneficial in attenuating the reflected signal. Of
course, if a large mismatch occurs on the divider side of the phase shifter, the loss
in the phase shifter will not help in attenuating the reflected signal.
Now we haven't considered mutual coupling effects in the prior
discussion, however, the isolation of the amplifier should prevent any significant
power from traveling back down to the divider junction from the antenna element.
Hence, mutual coupling effects should not present a problem for the reactive
divider.
4. Large Array Model
In order to see if the principles discussed in the previous section hold true
for a large array, we will consider extending the simple two element model of the
previous section to a large array of 1024 elements. The array is 32 x 32 elements
on a triangular grid with the sides of the equilateral triangle being .3 17" in length
as shown in Figure 6. A schematic showing the network is presented in Figure 7.
We will consider a receive antenna for this section as shown in Figure 7. A
corporate power divider network with 1023 dividers is used. For the phase shifter
an S-matrix of the form
-10dBLOdeg
-6dBLo
1
-6dBL$,
-1 0dBLO deg
where
(i,= Appropriate phase for element i.
We note that the phase shifter loss is set at 6 dB. The phase shifter settings were
set based upon theoretical values, i.e. no phase shifter quantization effects are
included to avoid confusing the issue with quantization effects. An S-matrix of
the form
[
-1 5dBLO deg - 100dBLOdeg
s., = 25dBLOdeg -15dBLOdeg
1
is used to model the amplifier.. The antenna elements are assumed to have a
perfect 50 ohm match, mutual coupling effects are again ignored, and a uniform
taper distribution is used across the array.
A proprietary linear network analysis program, MICRONET [2], was used
to calculate the scattering matrix of the resulting 1025 port network.
The
amplitude and phase coefficients through the corporate divider were then summed
to form an array factor which was multiplied by an element pattern of cosn8 ,
where n = 1.25 to yield the overall array radiation pattern. This procedure was
carried out for corporate networks with both Wilkinson and reactive dividers in
place at a frequency of 20.7 GHz. Figure 8 shows the radiation pattern for the
case of broadside scan and scan to 70 degrees in 8 with $ = 0. We see that the
patterns for the Wilkinson and reactive dividers are essentially identical for these
cases. In both of the scan cases, the peak gain of the two patterns differs by less
than .O1 dB.
5. Element Failure Analysis
From the analysis of the previous section we have found little difference in
the overall radiated pattern when Wilkinson or reactive dividers are used. This
comparison, however, assumed that all of the channels of the array were active. In
an actual large operating phased array, some of the elements might be expected to
fail with time and so we now shall consider the effect that element failures might
have on the comparison.
From the example we considered in Section 3 we saw that a large
mismatch on the antenna side of the phase shifter is attenuated by the phase shifter
loss, and so this type of failure should produce minimal differences between the
reactive and Wilkinson cases. A more problematic failure is that of a failure of
the phase shifter itself. If a large mismatch (such as an open or short) were to be
placed on the divider side of the phase shifter in Figure 3, significant imbalance
between the channels will develop unattenuated by phase shifter loss. This is
obviously a more severe failure mechanism than an amplifier failure in terms of
producing channel imbalance. Given this fact, we will use this type of a failure to
determine if the reactive dividers will provide acceptable performance with
element failures in the array.
We will again use the 1024 element model from Section 4, but we now
will place a short circuit on the corporate divider side of the phase shifter for 6%
of the elements randomly distributed throughout the array.
Rerunning the
comparisons between the Wilkinson and reactive dividers, the array radiation
patterns of Figures 9 and 10 result for scan angles of 0, 30, 50 and 70 degrees in
theta with phi = 0 degrees. Again we see that the patterns show little difference
except in the far out sidelobe structure. Only small differences in the peak gain
occurs (maximum of .2 1 dB) for the four cases.
6. Conclusion
From a cost and size standpoint, reactive power dividers are an attractive
alternative to Wilkinson power dividers for use in corporate power dividing
networks for phased array antenna systems. From a performance standpoint the
degraded channel to channel isolation and poor output match of reactive dividers
present potential drawbacks. However, under some circumstances the effect of
these negative qualities on the overall system performance is minimized.
Specifically, for large phased array systems that do not require low sidelobe levels
and therefore can tolerate higher element errors, reactive dividers may be an
alternative. We have seen that a theoretical comparison of the radiation patterns of
a large array with both Wilkinson and reactive dividers shows only minor
differences in sidelobe structure when the phase shifters are relatively lossy (6 dB
of loss). In this case, the phase shifters act as a pseudo isolation resistor for the
corporate divider. Though the possibility of using a less costly corporate divider
network may be attractive, this result should not be interpreted too broadly. The
use of reactive dividers in arrays with high sidelobes is not appropriate if either
low loss phase shifters are used or phase shifters with high inputloutput match are
used.
Acknowledgments
The author would like to acknowledge discussions with Bill Powers and Oren
Kesler of Raytheon TI Systems and Jeffrey Herd of Rome Laboratory.
Portions of this work were supported by Rome Laboratory (Air Force Material
Command and Space and Missile Systems Center) under contract number
F30602-95-C-0055.
References
[I] E. Wilkinson, "An N-Way Hybrid Power Divider," IEEE Trans. Microwave
Theory Tech., vol. 8, pp. 116-1 18, January 1960.
[2] B. Powers, "MICRONET User's Guide," Texas Instruments, Inc., 1988.
70.7 ohms
50 ohms
i
1
50 ohms
Port 1 e
-
~
t
-
100 ohms
4-7
m
70.7 ohms
-
3
port3
50 ohms
-t
Quarter Wavelength
Wilkinson Divider
l
0.6
l
'
'
~
'
l
l
l
~
l
0.8
1 .O
1.2
Normalized Frequency
.
l
'
.
1.4
Figure 1. Theoretical Performance for Wilkinson Divider
'
l
Port 2
50 ohms
35.4 ohms
Port 1 C
Port 3
Reactive Divider
~ ' S 2 1 " " " " ' " " ~
1 .O
1.2
Normalized Frequency
0.8
Figure 2. Theoretical Performance for Reactive Divider.
Channel 2
Channel 1
V '7
Antenna Element
Amplifier
Gain = 2 S dB
Phase Shifter
-=6dB
or Reactive)
Figure 3. Two Channel Phased Array Section.
Channel 2
No Mismatch
Channel 1
- Direct Path
7h
-----. Refleded Path
,
Phase
6 d B h
Wlkinson Divider
-21 dB
Figure 4, First Order Reflection in Two Channel Array with Wilkinson
Divider.
Channel 2
Channel 1
r 7
Direct Path
Figure 5. First Order Reflection in Two Channel Array with Reactive
Divider.
Figure 6. Array Grid Dimensions.
Figure 7. Large Array Model Schematic
Scan = 0
Arrav Radiation Pattern
o : r ' 7 1 ' 1 " / ' 1 ' 1 7 1 ' 1 '
E - Wilkinson Dividers
E - - - Reactive Dividers
- 1 0 ~
-90
-70
-50
-30
-10 10 30
Theta (deg)
Array Radiation P a t t e r n
50
70
90
Scan = 70
o ~ ' " ' " " " ' " " " ~
-10
E
-90
- Wilkinson Dividers
- - - Reactive Dividers
-70
-50
-30
-10 10 30
Theta (deg)
50
70
90
Figure 8. Array Radiation Pattern with No Element Failures and Scan
Angles of 0 and 70 degrees.
- Wilkinson Dividers
- - - R e a c t i v e Dividers
-90
-70
-50
-30
-10
30
10
50
70
90
Theta (deg)
Array Radiation Pattern
n
L
'
t
7
1
'
l
v
Scan = 30
l
'
~
'
~
'
~
T
f
[ - Wilkinson Dividers
-10
- - R e a c t i v e Dividers
T h e t a (deg)
Figure 9. Array Radiation Pattern with 6% Element Failures and Scan
Angles of 0 and 30 degrees.
~
J
Scan = 50
Array Radiation P a t t e r n
~
L
-90
-70
'
I
-50
-30
'
" 1 - Wilkinson Dividers
I
~
-10
10
30
Theta (deg)
Array Radiation Pattern
I
~
I
50
70
90
~
Scan = 70
0 t " " " " " " " " ' ~
- Wilkinson Dividers
- - - Reactive Dividers
- 10
-90
-70
-50
-30
-10
10 30
Theta (deg)
50
70
90
Figure 10. Array Radiation Pattern with 6% Element Failures and Scan
Angles of 50 and 70 degrees.
I
~
~
'