SUMMARY
The discussion focuses on determining the angle \(\theta\) from the antenna field pattern equation \(\frac{1}{N} \left[\frac{\sin(N\theta)}{\sin\theta}\right] = 0.7071\), where \(N\) is an integer greater than 1. The identity \(\sin N\theta = \sum_{k=0}^N \binom{N}{k} \cos^k \theta\,\sin^{N-k} \theta\,\sin\left(\frac{1}{2}(N-k)\pi\right)\) is suggested to derive a polynomial in \(\sin \theta\). For values of \(N\) greater than 3, numerical methods are necessary to solve for \(\theta\).
PREREQUISITES
- Understanding of antenna field pattern calculations
- Familiarity with trigonometric identities
- Knowledge of polynomial equations
- Experience with numerical methods for solving equations
NEXT STEPS
- Research numerical methods for solving polynomial equations
- Explore advanced trigonometric identities and their applications
- Learn about antenna theory and field pattern analysis
- Investigate software tools for numerical computation, such as MATLAB or Python's NumPy
USEFUL FOR
Electrical engineers, antenna designers, and researchers involved in antenna theory and field pattern analysis will benefit from this discussion.