Four amateur radio operators (Alice, Bob, Carol, and Dave) are setting up 10 GHz microwave links. Each has a different antenna polarization: Horizontal, Vertical, Right-Hand Circular (RHC), and Left-Hand Circular (LHC).
Polarization Loss Rules
Same polarization: 0 dB loss
Cross-polarized linear (H vs V): 20+ dB loss
Circular to linear: 3 dB loss (either direction)
Opposite circular (RHC vs LHC): 20+ dB loss
The Clues
1. Alice can communicate with Bob with perfect signal strength (0 dB loss).
2. Alice gets terrible reception from Carol (20+ dB loss).
3. Alice receives Dave’s signal at reduced power (3 dB loss).
4. Bob can barely hear Carol (20+ dB loss).
5. Bob gets a good but reduced signal from Dave (3 dB loss).
6. Carol receives Dave’s signal at reduced power (3 dB loss).
7. One operator forgot to rotate their new IC-905 dish from its factory vertical polarization setting.
8. Bob notices that a 10 degree rotation resulted in a lot of signal loss.
Who has which antenna polarization?
Solution:
Alice: Horizontal
Bob: Horizontal
Carol: Vertical (IC-905 factory setting – forgot to rotate!)
Dave: Right-Hand Circular (RHCP)
From clue 1, Alice and Bob have 0 dB loss, therefore they have identical polarization.
From clues 2 & 4, both Alice and Bob get 20+ dB loss from Carol, so Carol has the orthogonal polarization to Alice/Bob. This 20+ dB loss could happen in two scenarios:
1. Alice/Bob are one linear polarization (for example, Horizontal), Carol is the orthogonal linear (for example, Vertical).
2. Alice/Bob are one circular polarization (for example, RHCP), Carol is the opposite circular (for example, LHCP).
From Clue 8, Bob has either vertical or horizontal polarization, as rotating the antenna results in noticeable loss. Rotating a circular polarized antenna doesn’t result in much loss.
From clues 3, 5, & 6, Dave gets 3 dB loss from Alice, Bob, and Carol. Since 3 dB loss occurs between circular and linear polarizations, and we suspect Bob is linear, then Dave must be circular.
Dave can get 3 dB from all three is if Alice/Bob/Carol are all linear polarizations, and Dave is circular.
Then clue 7 (IC-905 vertical) helps us determine which linear polarizations they have.
From clue 7, someone has an IC-905 in vertical polarization. This some “one” must be Carol (since she’s orthogonal to Alice/Bob). Only one operator forgot to rotate, so it can’t be both Alice and Bob with vertical.
Therefore: Carol = Vertical,
Alice/Bob = Horizontal.
Since we have Horizontal (Alice/Bob), Vertical (Carol), and one circular (Dave), Dave must be either RHCP or LHCP. We are going to say RHCP, but it is arbitrary. LHCP is correct too.