rad-lab/apps/exercises/7_1-3_linear_arrays_figs24_28.py at main · JohnNehls/rad-lab · GitHub

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#!/usr/bin/env python
"""Recreate textbook figures 24-28 for uniform linear arrays.

Figure 24: Effect of number of elements on the array factor (lambda/2 spacing).
Figure 25: Effect of element spacing on the array factor (10 elements).
           Note: spacing > lambda/2 introduces grating lobes.
Figure 27: Weighted array factors (Chebyshev and Taylor) vs unweighted.
           Weighting suppresses sidelobes at the cost of mainlobe width.
Figure 28: Beam steering to 15, 45, and -60 degrees.
           Steering broadens the beam and reduces peak gain at large angles.

Discrepancies with reference document:
  - Figures 24 and 25 appear to use 10*log10 instead of 20*log10 in the
    original document, causing a 2x scaling error.
  - Our figures 27 and 28 match the document correctly.
"""

from scipy import signal
import matplotlib.pyplot as plt
import rad_lab.uniform_linear_arrays as ula


plt.rcParams["text.usetex"] = True

## Figure 24: Unweighted, lambda/2 spacing, 10 vs 40 elements ##############
fig, axs = plt.subplots(1, 2)
fig.suptitle(r"Unweighted Array Factor for $\lambda/2$ spacing")

theta, gain = ula.linear_antenna_gain_N_db(10, 1 / 2, plot=False)
axs[0].plot(theta, gain)
axs[0].set_title("10 elements")

theta, gain = ula.linear_antenna_gain_N_db(40, 1 / 2, plot=False)
axs[1].plot(theta, gain)
axs[1].set_title("40 elements")

for ax in axs:
    ax.grid()
    ax.set_ylim((-60, 40))
    ax.set_xlabel(r"Angle $\theta$ [deg]")
    ax.set_ylabel("Gain [dBi]")

plt.tight_layout()

## Figure 25: 10 elements, varying spacing ##################################
# lambda/4: oversampled, no grating lobes
# lambda/2: critical spacing, no grating lobes
# lambda:   undersampled, grating lobes appear at ±90 deg
fig, axs = plt.subplots(1, 3)
fig.suptitle("Unweighted Array Factor for 10 Elements")

theta, gain = ula.linear_antenna_gain_N_db(10, 1 / 4, plot=False)
axs[0].plot(theta, gain - gain.max())
axs[0].set_title(r"$\lambda/4$ spacing")

theta, gain = ula.linear_antenna_gain_N_db(10, 1 / 2, plot=False)
axs[1].plot(theta, gain - gain.max())
axs[1].set_title(r"$\lambda/2$ spacing")

theta, gain = ula.linear_antenna_gain_N_db(10, 1, plot=False)
axs[2].plot(theta, gain - gain.max())
axs[2].set_title(r"$\lambda$ spacing")

for ax in axs:
    ax.grid()
    ax.set_ylim((-80, 10))
    ax.set_xlabel(r"Angle $\theta$ [deg]")
    ax.set_ylabel("Normalized Gain [dBi]")

plt.tight_layout()

## Figure 27: Weighted vs unweighted, 40 elements ##########################
Nel = 40
chebWindow = signal.windows.chebwin(Nel, 30)  # 30 dB Chebyshev sidelobe level
tayWindow = signal.windows.taylor(Nel, sll=35)  # 35 dB Taylor sidelobe level

fig, axs = plt.subplots(1, 2)
fig.suptitle(r"Array Factor with Different Weights: 40 elements, $\lambda/2$ spacing")

theta, gain = ula.linear_antenna_gain_N_db(Nel, 1 / 2, plot=False)
theta, gain_cheb = ula.linear_antenna_gain_N_db(Nel, 1 / 2, weight_vec=chebWindow, plot=False)
theta, gain_tay = ula.linear_antenna_gain_N_db(Nel, 1 / 2, weight_vec=tayWindow, plot=False)

# Left: full angular range; Right: zoomed into mainlobe
axs[0].set_xlim((-90, 90))
axs[1].set_xlim((-8, 8))

for ax in axs:
    ax.plot(theta, gain - gain.max(), label="unweighted")
    ax.plot(theta, gain_cheb - gain_cheb.max(), "-.r", label="30 dB Cheb.")
    ax.plot(theta, gain_tay - gain_tay.max(), "--k", label="35 dB Taylor")
    ax.set_xlabel(r"Angle $\theta$ [deg]")
    ax.set_ylabel("Normalized Gain [dBi]")
    ax.set_ylim((-60, 5))
    ax.grid()

axs[1].legend()
plt.tight_layout()

## Figure 28: Beam steering, 20 elements ###################################
# Applying a linear phase taper across elements steers the beam.
fig, axs = plt.subplots(1, 3)
fig.suptitle(r"Weighted Array Factor: $\lambda/2$ spacing, 20 elements")

Nel = 20
dx = 1 / 2
for ax, angle in zip(axs, [15, 45, -60]):
    theta, gain = ula.linear_antenna_gain_N_db(Nel, dx, steer_angle=angle, plot=False)
    ax.plot(theta, gain - gain.max())
    ax.set_title(rf"Steered to {angle} deg")
    ax.grid()
    ax.set_ylim((-60, 5))
    ax.set_xlabel(r"Angle $\theta$ [deg]")
    ax.set_ylabel("Normalized Gain [dBi]")

plt.tight_layout()

plt.show()