# Compute the output of frequency doubler. If the inputs Vx = Vsinωt and Vy = Vsin(ωt+θ) are applied to a four quadrant multiplier?

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Compute the output of frequency doubler. If the inputs Vx = Vsinωt and Vy = Vsin(ωt+θ) are applied to a four quadrant multiplier?

(a) Vo= { Vx×Vy× [cosθ-(cosθ×cos2ωt)+(sinθ×sin2ωt)]}/ Vref

(b) Vo= { Vx×Vy× [cosθ-(cosθ×cos2ωt)+(sinθ×sin2ωt)]}/ 2

(c) Vo= { Vx×Vy× [cosθ-(cosθ×cos2ωt)+(sinθ×sin2ωt)]}/(2×Vref)

(d) Vo= – { Vx×Vy× [cosθ-(cosθ×cos2ωt)+(sinθ×sin2ωt)]}/(2×Vref)

I got this question in an online quiz.

My doubt stems from Multiplier and Divider topic in section Operational Amplifier Applications of Linear Integrated Circuits

by (39.8k points)
Accurate choice is (c) Vo= { Vx×Vy× [cosθ-(cosθ×cos2ωt)+(sinθ×sin2ωt)]}/(2×Vref)

Simplify with an easy explanation: The output of frequency doubler, Vo= (Vx×Vy)/Vref = [(Vsinωt +Vsin(ωt+θ)]/ Vref

= {Vx×Vy×[(sin^2ωt×cosθ)+(sinθ×sinωt×cosωt)]}/ Vref

=> Vo= { Vx×Vy× [cosθ-(cosθ×cos2ωt)+(sinθ×sin2ωt)]}/(2×Vref).

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