Highschool trigonometry mixed with four-quadrant multipliers could be exploited to yield sinusoidal frequency doublers. Nothing non-linear is concerned, which implies no probably strident filtering necessities.
Beginning with some sinusoidal sign and needing to derive new sinusoidal alerts at multiples of the unique sinusoidal frequency, a bit trigonometry and four-quadrant multipliers could be helpful. Think about the next SPICE simulation in Determine 1.
Determine 1 Two analog frequency doublers, A1 + U1 and A2 + U2, in cascade to kind a frequency quadruple.
The above sketch exhibits the pair A1 and U1 configured as a frequency doubler from V1 to V2, and the pair A2 and U2 configured as one other frequency doubler from V2 to V3. Collectively, the 2 of them kind a frequency quadrupler from V1 to V3. With extra circuits, you can also make an octupler and so forth throughout the bandwidth limits of the energetic semiconductors, in fact.
Frequency doubler operation is predicated on these trigonometric identities:
sin² (x) = 0.5 * ( 1 – cos (2x) ) and cos² (x) = 0.5 * ( 1 + cos (2x) )
sin² (x) = 0.5 – 0.5 * cos (2x) and cos² (x) = 0.5 + 0.5* cos (2x)
Take your choose, each equations yield a DC offset plus a sinusoid at twice the frequency you began with. Do a DC block as with C1 and R1 above, and you’re left with a doubled-frequency sinusoid at half the unique amplitude. Comply with that up with a occasions two acquire stage, and you’ve got made a sinusoid at twice the unique frequency and on the similar amplitude with which you began.
This fashion of doing issues takes much less stuff than having to do some non-linear course of on the enter sinusoid to generate a harmonic comb after which having to filter out every little thing besides the one frequency you need.
Though there may really be another harmonics at every op-amp output, relying on how non-ideal the multiplier and op-amp may be, this course of doesn’t nominally generate different undesirable harmonics. Such harmonics as may by the way come up gained’t require a high-performance filter for his or her elimination.
John Dunn is an electronics advisor, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York College (MSEE).
Associated Content material
- Frequency doubler with 50 p.c responsibility cycle
- A 50 MHz 50:50-square wave output frequency doubler/quadrupler
- Frequency doubler operates on triangle wave
- Quick(er) frequency doubler with sq. wave output
- Triangle waves drive easy frequency doubler
The put up Analog frequency doublers appeared first on EDN.
