Transmitters
3.3 SPECTRUM AND SIDEBANDS
Crowded radar bands require that the radar transmits only in its allocated band. As more radars are used, these bands become more restricted, and greater control over the spectrum is required. In addition to the radar carrier frequency, the (pulse) modulation of the radar transmitter creates sidebands around the carrier frequency in addition to any modulation sidebands caused by modulation within the pulse.
The sidebands from pulse radars are based on two structures. The dominant coarse structure is determined by the pulse width, Jt seconds, and gives the frequency spectrum
Equation (3.1) is the envelope for the individual spectral lines spaced at the pulse repetition frequency. If the time between the pulses is T seconds, then each line is a spectrum of the formt
The envelopes of the peaks are given by and . The factor always appears together so the spectra may be plotted in terms of frequency times pulse width. This is shown in decibels for a transmitter with a pulse width of 1 µs and pulse repetition frequency of 10 000 Hz, T = 100 µs in Figure 3.2.
Radar transmitters produce peak powers often in the order of megawatts and the decibel scale with respect to 1 MW corresponds to Table 3.1.
Table 3.1
Attenuation required for screening against a 1 MW transmitter
Decibels Power Decibels Power
0 1 MW 90 1 mW
30 1 kW 120 1 µW
60 1 W
These large powers easily overload the amplifiers in nearby electronic equipment, so very good screening is required.
Where the interference is caused by the signal from the antenna, the antenna gain, up to maybe 30 dB, must be taken into account. The great dynamic range between the peak transmitter power and receivers causes spectral components to be detectable at frequencies well away from the transmitter frequency. In contrast to antennas and filters, which normally have rounded peaks, the most efficient transmitter pulse is rectangular because the transmitter often runs in a saturated mode. The leading and trailing edges are the only area of freedom for control of the spectrum to reduce interference at neighboring frequencies.
-35 -30 -25 -20 -15 -10 -5 0
-20 MHz -10 MHz 0 10 MHz 20 MHz
-25 -20 -15 -10 -5 0
-600 -400 -200 200 400 600kHz
1 Envelope BfJt
Structure of each lobe
Structure of each line
.
Complete spectrum ' Spectrum of leading edge
% spectrum of constant center section
% spectrum of trailing edge
fJt
Jt av Jt edge
Figure 3.2 The levels of the structure of a pulse spectrum.
(3.3) Commonly with amplifying output stages, a high-voltage pulse is applied for a time slightly longer than the transmitter pulse so the electron beam remains stable during the radio frequency drive pulse. This drive pulse is often large enough to saturate the output stage, but the leading and trailing edges may be shaped to control the output spectrum.
The spectra of the pulse waveforms may be constructed from the sum of the spectra of the components. Namely,
It is assumed that the center section is symmetric about zero time to give a symmetrical, real spectrum. The waveforms of the edges are offset in time to fit the leading and trailing edges of the center section. Each of these edge spectra is complex, and the imaginary parts of these two spectra add to zero. Thus, the spectrum of the symmetrical composite pulse has real components only. In the following discussions, all the diagrams are normalized for a pulse width of unity. The spectra are plotted in terms of the frequency-time product, .
3.3.1 Trapezoidal edges
The first attempts to control the transmitter spectra used trapezoidal pulse waveforms which are shown in a normalized form in Figure 3.3. The width of the pulse, , at the 50% voltage point is unity and the widths of the edges, , are expressed as a percentage.
Trapezoidal spectrum ' sin(BfJt av) BfJt av
sin(BfJt edge) BfJt edge
-100 -80 -60 -40 -20 0
-40 -30 -20 -10 10 20 30 40
1%
3%
5%
5%
10%
20%
1%
3% 5% 3%
5%
5%
5%
5%
10% 10%
10%
10%
10%
10%
10%
3%
fJJJJ
. Edge
width
Figure 3.3 Normalized trapezoidal waveforms with edges from 1% to 20%.
(3.4)
Figure 3.4 Normalized spectra of trapezoidal pulses with edges from 1% to 20%.
The spectra from these shaped pulses are given by [1]
Spectra for 1%, 3%, 5%, 10%, and 20% edges are shown in Figure 3.4.
Cosine edges Cosine squared edges
.
-80 -70 -60 -50 -40 -30 -20 -10 0
-40 -30 -20 -10 10 20 30 40
-80 -70 -60 -50 -40 -30 -20 -10 0
-40 -30 -20 -10 10 20 30 40
-80 -70 -60 -50 -40 -30 -20 -10 0
-40 -30 -20 -10 10 20 30 40
-80 -70 -60 -50 -40 -30 -20 -10 0
-40 -30 -20 -10 10 20 30 40
-80 -70 -60 -50 -40 -30 -20 -10 0
-40 -30 -20 -10 10 20 30 40
-80 -70 -60 -50 -40 -30 -20 -10 0
-40 -30 -20 -10 10 20 30 40
Sin(B fJ)/B fJ envelope 1 B fJ
1%
3%
5%
10%
20%
Edge width
fJJJJ
Figure 3.5 Pulses with normalized cosine (left) and cosine squared (right) edges of 1%, 3%, 5%, 10%, and 20%.
Figure 3.6 Normalized spectra for pulses with cosine edges, widths 1%, 3%, 5%, 10%, and 20%.
3.3.2 Cosine and cosine squared edges
Corners in any waveform produce sidebands. Cosine edges remove the corners at the top of the waveform and cosine squared edges also remove the corners at the bottom, as shown in Figure 3.5. These spectra have been obtained by performing the Fourier transform numerically. Higher cosine powers do not improve matters. The spectra with cosine edges for edge widths of 1%, 3%, 5%, 10%, and 20% are shown in Figure 3.6. The line above the 1% edge line is the spectrum without shaping. Figure 3.7 shows the spectra for cosine squared edges.
-100 -80 -60 -40 -20 0
-40 -30 -20 -10 10 20 30 40
-100 -80 -60 -40 -20 0
-40 -30 -20 -10 10 20 30 40
-100 -80 -60 -40 -20 0
-40 -30 -20 -10 10 20 30 40
-100 -80 -60 -40 -20 0
-40 -30 -20 -10 10 20 30 40
-100 -80 -60 -40 -20 0
-40 -30 -20 -10 10 20 30 40
1%
3%
5%
10%
20%
-100 -80 -60 -40 -20 0
-40 -30 -20 -10 10 20 30 40
sin BfJ BfJ
fJJJJ
5%
3%
3% 10% 5%
10%
10%
10%
.
Efficiency ' 1
Jav%Jflank
I
Jav%Jflank 2
&Jav&Jflank 2
(drive modulation voltage)² dt
Figure 3.7 Normalized spectra for pulses with cosine squared edges, widths 1%, 3%, 5%, 10%, and 20%.
(3.5) 3.3.3 Extra modulator power needed for shaping
The beam in the output tube must be fully switched on and stabilized before the shaped radio frequency drive starts.
Figure 3.3 and Figure 3.5 also show the extra time during which the modulator must deliver full power. During the pulse edges the modulator is delivering full power but the transmitter delivers only the edge power at its output.
The power output of the tube is proportional to the square of the drive voltage, and the power input is proportional to the time that the modulator is switched on.
Efficiency is defined in (3.5) and is plotted in Figure 3.8.
Control of the spectrum by shaping the driving signal comes at an extra cost. The modulator consumes a large proportion of the power used by the larger radars. A modulator provisionally sized for 5 kW must be increased to 5.556 kW to compensate for a 10% loss. There is extra manufacturing cost, the extra 556 W is consumed throughout the life of the radar, and extra cooling is required.
0.6 0.7 0.8 0.9
0 0.1 0.2 0.3 0.4 0.5
1.0
Fractional edge width Edge width % 100%
90%
80%
70%
60%
10% 20% 30% 40% 50%
Cosine edges
Cosine squared edges Trapezoidal
edges
Figure 3.8 Output stage efficiency with shaping of pulse edges.