
496 Microwave Engineering
a. The gain parameter from Equation 12.94 is
C ≡ (I
0
Z
0
/4 V
0
)
1/3
= {(40 × 10
−3
× 10)/(4 × 5 × 10
3
)}
1/3
= 2.7144 × 10
−2
b. The output power gain from Equation 12.96 is
A
p
= −9.54 + 47.3 NC = −9.54 + 47.3 × 40 × 2.7144 × 10
−2
= 41.816448
c. Phase constant of velocity modulated electron beam is
β
e
=
ω
/
υ
0
= (2
π
f)/(0.5932 × 10
6
√V
a
)
= (2 ×
π
× 10
10
)/(0.5932 × 10
6
√5000)
= 1497.94 rad/m
d. The four propagation constants are given by Equation 12.93:
γ β β
1
3 2 1 2= − + +
e e
C j C( ) ( )/ /
γ β β
2
3 2 1 2= + +
e e
C j C( ) ( )/ /
γ
3
= j
β
e
(1 − C)
γ
4
= −j
β
e
(1 − C
3
/4)
β
e
C √3/2 = 1.49794 × 10
3
× 2.7144 × 10
−2
× 0.866