High Order Harmonic Oscillators in Microwave and Millimeter-wave ...

2 Oscillators
from the two sub-circuits.
V osc1 = a 1 e jω 0t + a 2 e j2ω 0t + a 3 e j3ω 0t + · · · (2.41)
V osc2 = a 1 e jω 0(t−∆t) + a 2 e j2ω 0(t−∆t) + a 3 e j3ω 0(t−∆t) + · · · (2.42)
The fundamental signals of the two signals are out-of-phase, which is expressed by (2.43)
ω 0 ∆t = 2πf 0 ∆t = π. (2.43)
The combined output signal (V out ) can then be expressed by (2.44) as follows:
V out = A 2 e j2ω 0t + A 4 e j4ω 0t + A 6 e j6ω 0t + A 8 e j8ω 0t + · · · + A 2n e j2nω 0t
(2.44)
The fundamental signal and odd harmonics (f 0 , 3f 0 , 5f 0 , 7f 0 , · · ·) are, canceled out and
the even harmonics (2f 0 , 4f 0 , 6f 0 , 8f 0 , · · ·) are combined in-phase and enhanced.
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