Question E9D06:
What happens to SWR bandwidth when one or more loading coils are used to resonate an electrically short antenna?  

Choices:  
A: It is increased  
B: It is decreased  
C: It is unchanged if the loading coil is located at the feed point  
D: It is unchanged if the loading coil is located at a voltage maximum point    

Correct Answer is  B: It is decreased  

Correct answer: B — It is decreased.

1) Why B is correct
- An electrically short antenna has low radiation resistance and large capacitive reactance. To resonate it, we add inductance (a loading coil), creating a high-Q series resonant circuit.
- Higher Q means narrower bandwidth. The basic relationship is:
  $$Q = \frac{\omega_0 L}{R} = \frac{1}{\omega_0 C R} \quad\Rightarrow\quad BW \approx \frac{f_0}{Q}$$
  where:
  - $R$ is the small series resistance (radiation resistance plus losses),
  - $L$ (or $C$) is the reactance used to resonate the antenna,
  - $BW$ is the approximate 2:1 SWR bandwidth near resonance.
- Because $R$ is small in a short antenna and significant $L$ is needed to resonate it, $Q$ becomes large and the SWR bandwidth decreases.

2) Why the other choices are incorrect
- A: Increased — Incorrect. Adding a loading coil raises $Q$, and higher $Q$ narrows bandwidth.
- C: Unchanged if the coil is at the feed point — Incorrect. Base-loading typically yields the narrowest bandwidth because the coil carries maximum current, increasing stored energy (and often losses), thus higher $Q$ and narrower bandwidth.
- D: Unchanged if the coil is at a voltage maximum — Incorrect. Moving the coil toward a voltage maximum (near the end) reduces coil current and can improve bandwidth relative to base-loading, but it still remains narrower than a full-size, non-loaded antenna; it is not unchanged. (Top-loading with a capacitance hat helps more than an inductor, but still does not make the bandwidth unchanged.)

3) Useful formulas and rules of thumb
- Series-resonant Q:
  $$Q = \frac{\omega_0 L}{R} = \frac{1}{\omega_0 C R}$$
- Approximate SWR bandwidth near resonance:
  $$BW_{2:1} \approx \frac{f_0}{Q}$$
- Radiation resistance of a short dipole (helps explain small R and high Q):
  $$R_r \approx 80\pi^2\left(\frac{\ell}{\lambda}\right)^2$$
  Small $R_r$ leads to large $Q$ when resonance is achieved with loading, hence decreased SWR bandwidth.