Amplitude-Only Synthesis
Understanding Amplitude-Only Synthesis
When designing a phased array or a fixed antenna array, the engineer must decide how much RF power (amplitude) and what phase delay to feed into each individual radiating element. If every element is fed the exact same amount of power (a "Uniform" distribution), the antenna achieves the absolute maximum possible main beam gain, but suffers from terrible sidelobes (the first sidelobe is always a massive -13.2 dB below the main beam). Amplitude-Only Synthesis is the mathematical process of deliberately varying the power fed to each element to fix this problem.
By keeping the phase of every element identical (uniform phase) but tapering the amplitude—feeding the most power to the elements in the center of the array, and feeding very little power to the elements on the outer edges—an engineer can drastically suppress or even eliminate sidelobes. The trade-off for this suppression is a widening of the main beam (lower resolution) and a slight drop in overall antenna gain. This technique is universally used in air-traffic control radars and satellite uplinks where sidelobe interference is unacceptable.
The Dolph-Chebyshev Method
The most famous algorithm for amplitude-only synthesis is the Dolph-Chebyshev method. By applying Chebyshev polynomials to the amplitude weights, the engineer can force all the sidelobes to be exactly the same height (e.g., all sidelobes perfectly suppressed to -30 dB). This is the mathematical optimum: it provides the narrowest possible main beam for a mathematically guaranteed maximum sidelobe level.
Max Directivity, Narrowest Beamwidth, Terrible Sidelobes (-13.2 dB)
Heavy Taper (e.g., Binomial):
Lower Directivity, Widest Beamwidth, Zero Sidelobes (-∞ dB)
Dolph-Chebyshev Taper:
Optimal compromise. You explicitly choose the desired sidelobe level (e.g., -25 dB), and the math provides the amplitude weights to achieve the narrowest possible beam for that specific restriction.
Comparison
| Amplitude Distribution | Edge Element Power | First Sidelobe Level | Main Beam Width |
|---|---|---|---|
| Uniform (No Taper) | 100% of Center | -13.2 dB | Extremely Narrow (Sharp) |
| Taylor Taper | ~ 10% to 30% | -20 to -40 dB (Decaying) | Moderate |
| Dolph-Chebyshev | Specific Math Value | -25 dB (Equal Ripple) | Optimal for given SLL |
| Binomial Taper | Near 0% | None (No sidelobes) | Extremely Wide (Blurry) |
Frequently Asked Questions
Why does putting less power on the edge elements reduce sidelobes?
Sidelobes are caused by hard 'discontinuities' in the physical size of the antenna array. In a uniform array, the power goes from 100% at the edge element to 0% in the empty space immediately next to it. That massive cliff causes electromagnetic 'ringing' in the far-field (sidelobes). Tapering the amplitude smoothly rolls the power off to zero, removing the discontinuity and preventing the ringing.
How are amplitude weights actually applied in a physical antenna?
In an Active Phased Array (AESA), the digital controller simply turns down the variable gain amplifier in the T/R modules on the edges of the array. In a passive corporate-fed array, engineers use unequal Wilkinson power dividers (e.g., a 70/30 split instead of a 50/50 split) to physically route more RF power to the center elements than the edge elements.
Can you steer a beam using only amplitude synthesis?
No. Amplitude-only synthesis can only change the shape of the beam (width and sidelobes), not its direction. To physically steer the beam off-center (away from boresight), you must introduce a progressive phase delay across the array. Steering requires phase control.