Page 178 - Maxwell House

158 Chapter 3

19
3.3.12a or more details in Figure 3.4.5b. The same reciprocity principle applies to the antenna
radiation properties such as efficiency, gain, directivity and radiation patterns. We will define
all these parameters in the following chapters.

3.4.5 Ultra-WideBand (UWB) antenna impulse response (time-domain)

It is worth to note that the Lorentz’s reciprocity was established for time-harmonic fields, and
it tells us that there is no need to distinguish antenna as a transmitting or receiving one at each
single frequency. However, what is about an antenna transmitting or receiving broadband signal
like short pulse? Can we be sure that the envelope of such signal is identical when the same
antenna in transmit or receive mode? In general, the correct answer is negative and depends on
the antenna bandpass. Let us look back at Figure 3.4.4 and 3.4.5a assuming that antenna
transmit-receive pair consists of two indistinguishable antennas. Undoubtedly, the network in
Figure 3.4.5a can be broken into two parts as shown in Figure 3.4.5b. The transmitting antenna
in the domain can be considered as a network that transforms a signal ( , t) formed by
1
1
1
the current source ( , t) into the fields ( , t) around this antenna. The structure of such
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near fields depends on antenna design and expected to be quite complicated. Evidently, we have
to generate in order of complex magnitude exactly the same field structure around the receiving
antenna if our wish is to get ( , t) = ( , t) ~ ( , t). But it is impossible when the
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2
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2
receiving antenna is far-away and “sees” the transmitting one as a point-size radiation source.
If you are not completely convinced look at street light bulb standing nearby, then run far-away
from it down the street and compare the light source images. Therefore, the field structures
( , t) and ( , t) in Figure 3.4.5b are not alike by definition, and it would be erroneous to
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suggest that the two transforms ( , t) → ( , t) and ( , t) → ( , t) are identical in
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2
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2
time domain. Consequently, we can expect that the antenna impulse response to the same pulse
boost in transmit and receive mode can be different. It has been shown [4, 5] that these two
responses are really different but not independent. Lorentz’s reciprocity theorem implies the
constraint: “… for a given antenna the (temporal) impulse responses in transmission and
reception are related by a time derivative” [4, 5]. It means that
⁄
( , t) ∼ ( , t) (3.109)
2
1
1
1
( , ω) ∼j ω ( , ω) �
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1
It follows from (3.109) that the described effect must be taken into consideration as soon as our
goal to model, develop or measure UWB antennas. “UWB systems transmit extremely narrow
pulses on the order of 1ns or less resulting the bandwidths in excess of 1 GHz. From a system
design perspective, the impulse response of the antenna is of particular interest because it has
the ability to alter or shape the transmitted or received pulses” [9].
19 This fact may seem surprising at first because antenna usually receive far-field radiation of very simple
structure, but in general, it radiates near-fields of much more complex structure; there’s no a priori reason
to expect any symmetry between these processes. We will explain how to solve this contradiction in the
next paragraph about ultra-wideband antennas.