Radiation pattern

Python Code

"""Antenna Engineering — Radiation pattern (8-element ULA, broadside)."""


import numpy as np
import plotly.graph_objects as go


def generate():
    N = 8          # elements
    d = 0.5        # spacing in wavelengths
    beta = 0.0     # progressive phase shift (broadside)

    theta = np.linspace(0, 2 * np.pi, 3600)

    # Phase difference per element
    psi = 2 * np.pi * d * np.cos(theta) + beta

    # Array factor: use sinc-like formula; handle ψ→0
    # AF = sin(N*ψ/2) / sin(ψ/2)
    half_psi = psi / 2
    with np.errstate(divide="ignore", invalid="ignore"):
        AF = np.where(
            np.abs(np.sin(half_psi)) < 1e-10,
            float(N),
            np.abs(np.sin(N * half_psi) / np.sin(half_psi)),
        )

    AF_norm = AF / N   # normalize main lobe to 1.0

    # Convert to dB and clip at -40 dB
    AF_dB = 20 * np.log10(AF_norm + 1e-10)
    AF_dB = np.maximum(AF_dB, -40.0)

    # Shift to positive for scatterpolar (add 40)
    r_vals = AF_dB + 40  # range [0, 40]

    fig = go.Figure()

    fig.add_trace(go.Scatterpolar(
        r=r_vals,
        theta=np.degrees(theta),
        mode="lines",
        name="Array factor",
        line=dict(color=VIOLET, width=2),
        hovertemplate="θ=%{theta:.1f}°, %{r:.1f}−40 dB<extra></extra>",
    ))

    fig.update_layout(
        polar=dict(
            radialaxis=dict(
                range=[0, 42],
                tickvals=[0, 10, 20, 30, 40],
                ticktext=["−40", "−30", "−20", "−10", "0"],
                title="dB",
            ),
            angularaxis=dict(direction="clockwise", rotation=90),
        ),
        legend=dict(orientation="h", y=1.06),
        margin=dict(t=60, b=60, l=60, r=60),
        height=560,
    )
    return fig


if __name__ == "__main__":
    generate()

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