Two micro aspects of the rectenna design are addressed: evaluation of the degradation in net rectenna RF to DC conversion efficiency due to power density variations across the rectenna (power combining analysis) and design of Yagi-Uda receiving elements to reduce rectenna cost by decreasing the number of conversion circuits (directional receiving elements). The first of these micro aspects involves resolving a fundamental question of efficiency potential with a rectenna, while the second involves a design modification with a large potential cost saving

Gutmann, R. J.

English

NASA Technical Reports Server

Rectenna Session : Micro Aspects 
Dr. Ronald J .  Gutmann 
Renssel aer Polytechnic Institute 
There are two micro aspects of the rectenna design which will be 
addressed in this presentation: evaluation of the degradation in net rec- 
tenna RF to DC conversion efficiency due to power density variations 
across the rectenna (power combining analysis) and design of Yagi-Uda 
receiving elements to  reduce rectenna cost by decreasing the number of 
conversion circuits (directional receiving elements). The f i r s t  of these 
micro aspects involves resolving a fundamental question of efficiency 
potential with a rectenna, while the second involves a design modifica- 
tion with a large potential cost saving. These tasks were investigated 
under contract with JSC during 1978. 
Power Combining Analysis 
In the rectenna, numerous rec t i f ie r  circuits share a common DC load 
to achieve useful power levels. The rec t i f ie r  outputs can be combined in 
series and/or parallel t o  enhance the voltage and/or current level res- 
pectively, with previous rectennas designed with f i r s t  stage parallel 
combining followed by series combining. 
A fundamental question in this receiving, rectification and power 
combining process i s  caused by the power taper of the incident microwave 
beam. The incident power density can vary by 10 dB over the rectenna 
area since a high percentage of the transmitted microwave power needs to 
be collected and the power beam sidelobe level must be kept reasonably 
low. Since the output (DC terminal) characteristics of the rec t i f ie r  are 
power dependent, rect if iers  a t  different power levels that share a common 
DC load cannot be operated a t  optimum conditions. With individual recti - 
f i e r s  near 90% maximum efficiency, the resultant efficiency degradation 
could be significant. In this  work the efficiency degradation that results 
when an array of microwave power rect if iers  shares a comon DC load was 
evaluated for  the f i r s t  time. 
In analyzing the degradation, we assume that the output load line or 
volt-ampere (V-I) characteristics of each of the rectifying circuits to be 
combined are known. This V-I characteristic can be determined by either 
https://ntrs.nasa.gov/search.jsp?R=19810008043 2020-03-21T15:12:38+00:00Z
a circuit  analysis of the rectenna element, by a computer simulation or  
by direct measurement s f  the output voltage and current for several load 
resistances. I t  i s  assumed that the V-I characteristics are a function 
of some parameter 8 of the rectenna element (-in our case incident RF 
power). Given the V-I characteristics, i t  i s  possible to determine the 
operating point for maximum power output. 
In Fig, 1 we show the V - I  characteristics of two dissimilar rectenna 
elements as well as the points a t  which each of them deliver maximum power 
i f  operating independently. The same figure shows that i f  the elements 
are operated i n  parallel (common output voltage) or in series (common 
output current), they will not operate a t  their  optimum power output and 
their combined power output w i  11 be 1 ess than i f  operated independently . 
We have developed expressions for the power combining inefficiency [re- 
duction in output power compared to collected power assuming each recti- 
f i e r  operated in i t s  own optimum DC load) for both series and parallel 
combining. (1 >2) 
In order to evaluate the power combining inefficiency an accurate 
output equivalent circuit  model of the conversion circuitry i s  needed. 
This was obtained using two independent approaches. First ,  an approxi- 
mate closed form circuit  model of the rec t i f ie r  was developed assuming an 
ideal diode and lossless circuit  elements. The output load line was then 
obtained an~ ly t i ca l  ly . Seccnd, a more precise computer sinul ation model 
was used, and the output equivalent circuit  was obtained by varying the DC 
load resistance and plotting the resultant output load 1 ine. 
We have shown that assuming an ideal diode, the circuit  indicated in 
Figure 2A has yielded 100% conversion efficiency i f  L3 - C3, L5 - C5 etc. 
form odd harmonic para1 lel  resonant circuits , C1 series resonates the 
resultant inductive impedance a t  the fundamental frequency and RL = 
(n2/8) R ~ .  (' Figure 28 indicates the more exact computer simulati on 
model, a reasonable representation of the actual circuitry used i n  experi- 
mental rectennas. The models and the resul L ing  load lines w i  11 be dis- 
cussed further in the presentation. 
When using these models and various assumed power density variations, 
we find that parallel combining i s  marginally better than series combining 
and that the closed form analytical model slightly underestimates the power 
combining inefficiency compared t o  the  computer simulation resu l t s .  4ssuming 
a uniform power density dis t r ibut ion,  the power combining inefficiency is 
1.0% when the ra t io  of maximum to  m i n i m u m  power density i s  2.0 to  1.0, re- 
ducing t o  0.3% i f  the r a t i o  i s  1 .4  t o  1 .O. This has an important e f f ec t  on 
the design of the rectenna DC power combining network, favoring ring com- 
bining ra ther  than row combining par t icular ly  near the rectenna edge. 
Directional Receiving Elements 
A principal advantage of the rectenna concept f o r  the receiver i n  f ree-  
space microwave power transmission systems i s  tha t  the  effect ive  receiver 
pattern i s  su f f ic ien t ly  non-directional ( i  .e. beamwidth suf f ic ien t ly  large) 
t ha t  receiver steering i s  not required. However i n  evaluating the require- 
ments fo r  a so la r  power sate1 l i t e  (SPS) with a small o rb i t  eccentr ic i ty  
i n  a  near zero inclination geostationary o rb i t ,  i t  became apparent tha t  the 
half wave dipole separated by % 0.2 X from a conducting ground plane has a 
more non-directional pattern than needed. That i s  the beamwidth of the 
receiver pattern a t  which 1% of the incident power i s  not received (0.04 dB 
* 
beamwidth) i s  much larger than the off  normal incidence due t o  o rb i t  con- 
s iderat ions .  Since the rectenna cost  i s  projected t o  be .L 25% of the to ta l  
system cost ,  consideration of more directiona1,receiving elements i s  c lear ly  
desirable.  
In most applications fewer RF t o  DC conversion c i r cu i t s  (favoring 
directional elements) and pokier beam pointing requirements (favoring non- 
directional el ements) are expected t o  domi nate the d i rec t i  onali ty issue.  
An additional factor  with the present GaAs Schottky diode r ec t i f i e r s  and 
present SPS design values i s  tha t  higher RF to DC conversion efficiency i s  
possible a t  higher power levels (power density limited by nonlinear in te r -  
actions i n  ionosphere and possibly biological fac to rs ) ,  thus favoring some- 
what more directional elements. An additional disadvantage to  directional 
receiving elements are more s t r ingent  requirements f o r  a . s t ab le  rectenna 
s t ructure  and precise element tolerances. 
In considering a l t e rna te  receiving elements a t  the  modest gain enhance- 
ment considered desirable,  we focused on the Yagi-Uda element because of 
* 
Since e f f i c i en t  power transmission is paramount i n  the SPS application,  
a 1% beamwidth i s  more applicable than e i t he r  the 3 dB or  1 dB beamwidth 
used i n  many microwave applications. 
i t s  simplicity. Including proximity effects i n  an actual array configura- 
tion was beyond the scope of our program. Instead we utilized antenna 
performance of isolated Yagi -Uda arrays in arriving a t  the expected elec- 
rical performance depicted in Table 1. (1,3) 
Based upon this  electrical performance we designed three and six 
element Yagi-Uda arrays, w i t h  and without ground plane reflector,  in 
both conventional baseline construction and in printed circuit  form. De- 
sign of three element Yagi-Uda elements without ground planes are depicted 
i n  Fig. 3.  These designs will be discussed further in the presentation. 
The resultant costs obtained are in our investigation presented in 
Table 2 ,  the trend toward lower cost with increased rectenna element 
gain being apparent. As expected, the cost reduction per unit rectenna 
area varies between the rat io of element densities (dependent upon effec- 
t ive  area of each receiving element) and the square root of th is  ratio 
(dependent upon linear density of element rows). The net result i s  
clear: THERE IS A LARGE RECTENNA COST SAVIF!G POSSIBLE BY UTILIZATION OF 
H I R E  DIRECTIONAL RECEIVING ELEMENTS LIKE YAGI-UDA ELEMENTS. In a typical 
2 SPS rectenna there would be % 75 km area, so that  a cost reduction of 
2 $l/m i s  equivalent to a 75 million dollar reduction in capital costs. 
Thus savings of 300 to 450 million dollars per rectenna may be possible 
with the more directional Yagi-Uda element (capital costs in 1978 dollars).  
The comparison between conventional construction and printed circuit  
implementation i s  less apparent. The printed circuit  estimates are 
based upon less detailed design, but these results do not indicate a sub- 
stantial reduction with printed circuit  implementation. Only i f  socket 
and DC buss bar cost can be reduced will a large cost advantage result. 
These may be possible with careful structural designs requireing less 
material usage and low cost manufacturing, 5 mm diameter aluminum buss 
bars being assumed in our work. However, the conversion efficiency of 
printed c i rcui t  implementations will be somewhat lower, so baseline con- 
struction definitely seems preferred. 
We have shown that more directional receiving elements are expected 
t o  lower rectenna costs in free-space microwave power transmission sys- 
tems such as the SPS where the microwave power beam i s  relatively stationary 
with respect to  the rectenna. Yagi-Uda receiving elements are considered 
most desirable when moderate gains of perhaps 8 t o  14 dB (yi  th .  respect 
t o  an isot ropic  radia tor)  are  optimum. Yagi-Uda antennas become un- 
desirably awkward a t  higher gain, and a l t e rna t ives  such as shor t  back- 
f i r e  antennas should be considered. However i t  i s  believed t h a t  higher 
gain may r e s u l t  i n  unreal i s t i  cal l y  s t r ingen t  power beamrectenna a1 ign- 
ment requirements i n  the SPS. 
References 
1.  R .  J .  Gutmann and J .  M. Borrego, "Solar Power S a t e l l i t e s  Rectenna 
Design Study: Directional Receiving Elements and Para1 lel-Series 
Combining Analysis", Rensselaer Polytechnic I n s t i t u t e  Report under 
Contract NAS9-15453 w i t h  NASA Johnson Space Center, December 1978. 
2. R.  J .  Gutmann and J .  M. Borrego, "Power Combining i n  an Array of 
Microwave Power Rect i f iers" ,  IEEE Trans. Microwave Theory and 
Techniques, MTT-27, December 1979. 
3. R .  J .  Gutmann and R.  Gworek, "Yagi-Uda Receiving Elements in  Micro- 
wave Power Transmission System Rectennas", Journal of Microwave 
v Power, 2, September 1979. 
PARALLEL 
CONNECTION 
Figure 1 Output Load Line fo r  Two Different Rectif iers 
2 9 5 
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Table I 
Expected Optimal Performance of Yagi-Uda Receiving Elements 
Gain (wrt   so tropic) dB P/B Ratio dB 
3 Element-Low FIB r a t i o  11 5 
3 Element-Moderate FIB r a t i o  10  15 
3 Element-High F/B r a t i o  8.5 25 
h) 
\O 
w 6 Element-Low FIB r a t i o  111 5 
6 Element-Moderate FIB r a t i o  1 3  15 
6 Element-High FIB r a t i o  11.5 25 
Receiving Element *. 
Reduction Pactor* 
.x. Relative t o  6.5 dB Half'-Wave Dipole Separated by .20h from a Conducting Ground Plsne 
A, Printed Circuit  Board Implementation 
2 (costs a r e  given i n  $/n ) 
Half-wave 3 e lmen t  k'egi 6 element Yagi 
Dipole with with %zithost without grow6 pllene 
ground plane ground plane ground plane (average siz;) 
Socket 
32 buss ber 
Printed Ci rcu i t  Board .24 .24 .k .a 
Diodes a t  S.01 each $1.92 $ .81 $1.23 
~ o t d  cost/m2 $7.77 $5.16 $5.00 
B. Conventional m e  Construction 
2 (costs a re  given i n  $/m ) 
Ha-wave 3 element Yegi 6 element Yagi 
Dipole ~d tfi w i  A& kri t haut withoilf grsm? 2lans 
ground plane ground plane ground plane 
elem flemsr?t i3ensity (-) 192 2 81 
m 
123 57 
- 
: .crepl~ne Core $3 0 13 $1.47 $2.09 
L l ~ d n m  shield/  
Structur-al Member 2.14 1.40 
0 92 
Yagi-Ucia Additions . 00 30 en 
Ground U n e  1. 91 
- - 1.91 .00 
2 
cost/= $7.18 $5 -08 $3.72 
Ziodes a= $.OX each 1 0 %  
-
-81 
- - 1.23 
2 mtel  ~ o s t / m  $9.10 $5 89 $4 95 
Table '2 Rectenna Cost Estimates (excluding recterrna frame) 
29 9 


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