Question E9A01:
What is an isotropic radiator?  

Choices:  
A: A calibrated, unidirectional antenna used to make precise antenna gain measurements  
B: An omnidirectional, horizontally polarized, precisely calibrated antenna used to make field measurements of antenna gain  
C: A hypothetical, lossless antenna having equal radiation intensity in all directions used as a reference for antenna gain  
D: A spacecraft antenna used to direct signals toward Earth    

Correct Answer is  C: A hypothetical, lossless antenna having equal radiation intensity in all directions used as a reference for antenna gain  

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Correct answer: C — A hypothetical, lossless antenna having equal radiation intensity in all directions used as a reference for antenna gain

1) Why C is correct
- An isotropic radiator is an idealized point source that radiates equally in all directions (spherically), with no preferred direction and no loss.
- It is used as the 0 dBi reference for antenna gain.
- Its radiation intensity is constant:  
  $$U(\theta,\phi) = \frac{P_{\text{rad}}}{4\pi}$$
- Directivity and gain (lossless) are 1 (linear), i.e.,  
  $$D = 1,\quad G_{\text{lin}} = 1,\quad G_{\text{dBi}} = 0\ \text{dB}$$

2) Why the other choices are incorrect
- A: “Calibrated, unidirectional antenna…”  
  That describes a real gain standard (e.g., a standard gain horn), not an isotropic radiator.
- B: “Omnidirectional, horizontally polarized, precisely calibrated…”  
  Isotropic is hypothetical (not a real calibrated antenna), and it has no specific polarization; “omnidirectional” in practice often means uniform only in azimuth, not truly spherical.
- D: “A spacecraft antenna…”  
  Not a definition; some spacecraft antennas are directional. This has nothing to do with the isotropic reference.

3) Useful formulas and rules of thumb
- Gain relative to isotropic:  
  $$G_{\text{dBi}} = 10\log_{10}(G_{\text{lin}})$$
  For isotropic: $G_{\text{lin}}=1 \Rightarrow G_{\text{dBi}}=0$.
- dBd to dBi conversion (half-wave dipole has 2.15 dB over isotropic):  
  $$G_{\text{dBi}} = G_{\text{dBd}} + 2.15$$
- EIRP (relative to isotropic):  
  $$\text{EIRP} = P_T \times G_{\text{iso}} \quad (\text{linear gain})$$
  With feedline loss $L$ (linear):  
  $$\text{EIRP} = \frac{P_T \times G}{L}$$
- ERP (relative to a dipole):  
  $$\text{ERP} = \frac{\text{EIRP}}{1.64}$$
  since a half-wave dipole gain is $1.64$ (2.15 dB) over isotropic.
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