By I.D. Poole
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Additional info for Antennas for VHF and UHF (BP)
Responses of directional coupler Moreover, if we want an equal energy on the two ports 2 and 4: P2 = P4 which means: 1 – k2 = k2 27 28 Passive and Active RF-Microwave Circuits We must have a coupling coefficient of k = 1 and this is a 3 dB 2 coupler. 13. 14). 14. 7. Enlargement of the bandwidth We consider a coupler with n stages with characteristic impedances Zo1 , Zo 2 ,…, Zo n . This remains to study a line consisted of a cascade of n lines of characteristic impedances Zoe1 , Zoe 2 ,…, Zoe n .
Transmission and reflection on the iris The scattering matrix ( S ) of the iris is symmetrical and lossless, so: ⎛ρ (S ) = ⎜ ⎝t t⎞ t * ⎟ with ( S ) ( S ) = ( I ) ρ⎠ This gives: ⎧⎪ ρ 2 + t 2 = 1 ⎨ * * ⎪⎩ ρ t + ρ t = 0 Analysis of a Guide Resonator with Direct Couplings 63 With general solutions: ⎧⎪t = sin φ e − jΨ ⎨ − jψ ⎪⎩ ρ = j cos φ e Using the property t − ρ = 1 we have: t − ρ = ( sin φ − j cos φ ) e− jψ = − j e− j (φ −ψ ) = e− j (φ −ψ −π 2) ≡ 1 This is satisfied when: ψ =φ − π 2 Then: ⎧⎪ ρ = − cos φ e − jφ ⎨ − jφ ⎪⎩t = j sin φ e φ is the opening angle of the diagram.
Antennas for VHF and UHF (BP) by I.D. Poole