Question E9B09:
What type of analysis is commonly used for modeling antennas?  

Choices:  
A: Graphical analysis  
B: Method of Moments  
C: Mutual impedance analysis  
D: Calculus differentiation with respect to physical properties    

Correct Answer is  B: Method of Moments  

Correct answer: B — Method of Moments

Why B is correct:
- The Method of Moments (MoM) is the standard numerical technique used in popular antenna modeling programs like NEC. It solves field integral equations for currents on conductors, then derives input impedance, patterns, and gain.
- The continuous integral equation is discretized into a matrix form:
  $$\mathbf{Z}\mathbf{I} = \mathbf{V}$$
  where:
  - $\mathbf{Z}$ = impedance matrix (self and mutual terms)
  - $\mathbf{I}$ = unknown segment currents
  - $\mathbf{V}$ = excitation vector (source)

Why the other choices are incorrect:
- A: Graphical analysis  
  - Useful for visualization (e.g., Smith charts, plots) but not a rigorous computational method for antenna modeling.
- C: Mutual impedance analysis  
  - Mutual impedance is a concept within antenna arrays and is part of the MoM matrix ($Z_{mn}$ terms), but it’s not the overarching modeling methodology.
- D: Calculus differentiation with respect to physical properties  
  - Calculus underpins EM theory, but “differentiation with respect to physical properties” is not a recognized antenna modeling method like MoM, FEM, or FDTD.

Useful formulas and tips:
- MoM starts from an integral equation (e.g., EFIE for thin wires):
  $$\int Z(\mathbf{r},\mathbf{r}')\, I(\mathbf{r}')\, d\mathbf{r}' = V(\mathbf{r})$$
  Discretize to get $\mathbf{Z}\mathbf{I}=\mathbf{V}$ and solve for currents.
- Once $I$ is known:
  - Input impedance: $$Z_{in} = \frac{V_{source}}{I_{source}}$$
  - Far-field pattern is computed from the current distribution (superposition of segment contributions).
- Modeling rule of thumb (NEC/MoM):
  - Segment length ≤ 0.1λ (better: 0.05λ) for accuracy.
  - Use several segments per half-wave; keep wire radius small compared to segment length.
  - Place the voltage source at a segment center.