An antenna array is a collection of individual radiating elements arranged in a specific geometry and fed in such a way that their radiated fields combine to produce a desired radiation pattern. The question describes a specific type of antenna array: a uniformly spaced linear array of identical radiators.

Array Configuration: Uniformly Spaced Linear Array

A uniformly spaced linear array consists of identical antenna elements placed along a straight line with equal spacing between them. This basic configuration is fundamental in antenna design.

• Identical radiators: This implies that all individual antenna elements in the array have the same radiation characteristics when considered in isolation.
• Uniformly spaced: The distance between any two adjacent elements is constant. This spacing, often denoted as 'd', is crucial for determining the array's performance.

Excitation: Uniform Amplitude and Phase Variation

The way each element in the array is fed (excited) significantly influences the overall radiation pattern. The question specifies two key aspects of excitation:

• Uniform amplitude of excitation: This means that all elements in the array are fed with signals of the same power or strength. When combined with identical radiators, uniform amplitude excitation typically contributes to forming a well-defined main lobe, often resembling a pencil beam.
• Linear phase variation with non-zero gradient: This is a critical characteristic.
  • Linear phase variation: This refers to a progressive phase shift from one element to the next across the array. For instance, if the first element has a phase of $\phi_0$, the second might have $\phi_0 + \alpha$, the third $\phi_0 + 2\alpha$, and so on, where $\alpha$ is the constant phase difference between adjacent elements.
  • Non-zero gradient: This means that the phase difference $\alpha$ is not zero. If $\alpha$ were zero, all elements would be in phase, and the main beam would be directed at broadside (perpendicular to the array axis). A non-zero phase gradient causes the main beam to steer away from broadside.

Beam Steering with Linear Phase

The concept of beam steering is achieved by introducing a progressive phase shift (linear phase variation) across the array elements. The direction of the main beam, often denoted as $\theta_0$, is related to the phase shift $\alpha$ by the formula:

$$\alpha = -kd \sin(\theta_0)$$

where:

• $k = \frac{2\pi}{\lambda}$ is the wave number ($\lambda$ is the wavelength).
• $d$ is the spacing between array elements.
• $\theta_0$ is the angle of the main beam from the array normal (broadside).

Since the question states there is a "non-zero gradient" (meaning $\alpha \neq 0$), the angle $\theta_0$ will also be non-zero (unless $d=0$ or $k=0$, which are not practical antenna scenarios). This non-zero $\theta_0$ indicates that the main beam is steered or "scanned" away from the broadside direction.

Pencil Beam Characteristics

A pencil beam is a highly directional antenna pattern characterized by a very narrow main lobe, similar to the tip of a sharpened pencil. Arrays with uniform amplitude excitation, especially when they have a large number of elements, are effective in producing such narrow, well-defined beams. The uniform amplitude helps in maximizing the gain in a particular direction and suppressing side lobes.

Conclusion: Scanned Pencil Beam

Considering all the conditions:

• A uniformly spaced linear array with identical radiators and uniform amplitude of excitation inherently tends to produce a pattern with a well-defined main lobe, often a pencil beam.
• The presence of a linear phase variation with non-zero gradient is the exact mechanism used to physically steer or "scan" the direction of this main beam away from the broadside.

Therefore, the combination of these characteristics results in a scanned pencil beam. This type of antenna array is commonly used in radar systems and other applications where the direction of the transmitted or received signal needs to be precisely controlled and varied.