Phase II Final Report - NASA's Institute for Advanced Concepts

Chapter 4.0 Entomopter Flight Operations
4.3 Entomopter-borne Active Emitters for Navigation and Communication
The pulse width was determined from the required range resolution ∆Rmin as [174]
2 ∆R
min
T w
=
Equation 4-16
c
The MGW time constant Tmgw was determined, as suggested in [291], as
T
Tmgw = w
4
Equation 4-17
to include 99.5% coverage of a Gaussian pulse. The pulse-interpulse period T was determined
by the application, but must be greater than the value associated with unambiguous range detection.
We designate R u as the required unambiguous range, thus the minimum interpulse period
T min is [174]
T
2R
c
u
Equation 4-18
= min
The unambiguous range is the maximum range for each application. The corresponding duty
cycle and average transmitter power can be expressed as in Equations 4-11 and 4-12, respectively.
The gain of the transmitting antenna can be expressed in terms of its effective area, A eff , as
4πA
eff
Equation 4-19
G
T
=
2
λ
Equation 4-19 implies that we can take two approaches for frequency variations in our link analyses.
The effective area of the antenna can be held constant, which implies the gain will increase
with increased frequency, or the gain can be held constant and the antenna physically scaled to
operate at the desired frequency. We will take the latter approach and assume the gain will
remain fixed with frequency. In this manner, we can take advantage of the reduction in antenna
size with increased frequency.
Rewriting Equation 4-14 in terms of the above assumptions to better see how the required peak
power varies with system parameters, as follows:
3 4 4 2 ⎛ 2 ∆R
min
SNR k
BTo
Lo
4 π r c ⎜
=
⎝ 4c
PT
2
2 2 ⎛ c ⎞ ⎛ 2 ∆R
min ⎞
σ GT
⎜ ⎟ ⎜ ⎟ 3
⎝ f ⎠ ⎝ c ⎠
2
⎞
⎟
⎠
⎡ ⎛
⎜ 2
⎢ −
⎝
3⎢1
+ e
⎢
⎢⎣
⎡
⎢ ⎛ 2 ∆R
min
⎢1
+ ⎜2π
f
⎢ ⎝ 4c
⎢⎣
2 ∆R
min
π f
4c
2
2
⎞
⎟
⎠
+ e
2
⎞
⎟
⎠
⎤
⎥
⎥
⎥
⎥⎦
⎛ 2 ∆
⎜ 2π
f
−
⎝
2
2
R min ⎞
⎟ ⎤
4c
⎠ ⎥
⎥
⎥
⎥⎦
Equation 4-20
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