• Parameters #1 and #2 are the (X,Y) location of the non–linear breakpoint for the FM
curve.
The Time/Frequency behavior of the pulse can be drawn in a coordinate system whose
abscissa ranges from -1 to +1 over the complete time duration of the pulse, and whose
ordinate ranges from -1 to +1 over the complete frequency span of the pulse.
See 6.8.1 Interpreting Ambiguity Plots (page 160).
• The class of non–linear FM curves always pass through the points (- 1,-,1), (0,0), and
(1,1).
They begin at the lowest frequency at the start of the pulse, end at the highest
frequency when the pulse completes, and pass through the origin (to maintain
symmetry across both halves of the pulse). Between the points (0,0) and (1,1) the
curves also pass through the tunable (X,Y) breakpoint
defined by the first two
parameters. The positive time portion of the FM curve consists of two linear segments;
one from (0,0) to (X,Y), and the other from (X,Y) to (1,1).
By tuning the breakpoint we create a diverse class of FM modulations, but all of them
adhere to the physical bandwidth and pulse width limits imposed by the earlier setup
questions. Note that to maintain symmetry, the breakpoint is also mirrored on the
negative–,time side as line segments from (-1,-1) to (–X,–Y), and from (–X,–Y) to (0,0).
• Parameter #3
specifies the X location of the start of the amplitude taper of the non–
linear FM waveform. For example, setting X to 0.95 results in a pulse having full
amplitude over the middle 95% of its duration, but then having raised cosine amplitude
weighting applied to the leading and trailing 5% of its edges.
Table 33 Linear FM Class Examples
Example Description
P1 = 0.0, P2 =
0.0, P3 = 1.0
P1 and P2 place the FM breakpoint at the origin.
Because the FM curve passes through that point, the response reverts to linear FM.
P3 indicates that amplitude modulation should not be applied until the very end of the
pulse, and thus does not occur at all.
The resulting waveform is linear FM having abrupt
On/O transitions.
P1 = 0.9, P2 =
0.7, P3 = 1.0
During the middle 90% of the waveform's duration, the frequency chirp uses 70% of
its available bandwidth.
Within the 10% pulse tails, the remaining 30% of the bandwidth suddenly gets
covered.
No amplitude modulation is applied.
Pulses of this type have been studied theoretically, but do not perform very well for a
given total bandwidth that includes the leading/trailing "ears".
P1 = 0.9, P2 =
1.0, P3 = 0.8
The entire frequency band is chirped within the middle 90% of the pulse duration, so
that the frequency remains constant in the 10% pulse tails.
An amplitude modulation is applied over 20% of the pulse tails, that is, encompassing
both the ends of the chirp and the entire constant frequency intervals.
Pulses of this type have superior sidelobe behavior and fit neatly within their
prescribed bandwidth limits.
We recommend using non–linear FM waveforms that combine chirp limits and
amplitude modulation in this manner.
Chapter 5 – TTY Non-volatile Setups
125
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