Question

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

Answer 1

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).