We did a quadrature-signal phase rotator in an FPGA, and I did this just to check my rusty high-school trig. The FPGA data is signed 16-bit fractional. We digitize an incoming sine wave (called I) and delay one path through a FIFO to get 90 degree lag, which we flip to be lead (called Q) and apply the I and Q data streams to the rotator block. We get I' and Q' out, the rotated pair.
I used the natural convention that a phase shift of +90 makes a sine wave happen
1/4 cycle earlier in time, which LT Spice agrees with. I was a little surprised that my customer assumed the opposite convention. We included a bit in the FPGA to give him the choice.
Version 4 SHEET 1 920 680 WIRE 96 -336 -64 -336 WIRE 144 -336 96 -336 WIRE 672 -336 496 -336 WIRE 720 -336 672 -336 WIRE -64 -272 -64 -336 WIRE 496 -256 496 -336 WIRE -64 -144 -64 -192 WIRE 496 -128 496 -176 WIRE 64 96 -64 96 WIRE 112 96 64 96 WIRE 144 96 112 96 WIRE 640 96 512 96 WIRE 688 96 640 96 WIRE 720 96 688 96 WIRE -64 160 -64 96 WIRE 64 160 64 96 WIRE 512 160 512 96 WIRE 640 160 640 96 WIRE -64 288 -64 240 WIRE 64 288 64 240 WIRE 512 288 512 240 WIRE 640 288 640 240 FLAG -64 288 0 FLAG 512 288 0 FLAG 64 288 0 FLAG 640 288 0 FLAG 112 96 I FLAG 688 96 Q FLAG -64 -144 0 FLAG 496 -128 0 FLAG 96 -336 I2 FLAG 672 -336 Q2 SYMBOL voltage -64 144 R0 WINDOW 0 -90 60 Left 2 WINDOW 3 -296 121 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName VI SYMATTR Value SINE(0 1 107.142K 0 0 0) SYMBOL voltage 512 144 R0 WINDOW 0 -94 61 Left 2 WINDOW 3 -309 120 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName VQ SYMATTR Value SINE(0 1 107.142K 0 0 90) SYMBOL res 48 144 R0 WINDOW 0 61 44 Left 2 WINDOW 3 66 76 Left 2 SYMATTR InstName R1 SYMATTR Value 1 SYMBOL res 624 144 R0 WINDOW 0 61 41 Left 2 WINDOW 3 68 75 Left 2 SYMATTR InstName R2 SYMATTR Value 1 SYMBOL bv -64 -288 R0 WINDOW 0 48 16 Left 2 WINDOW 3 56 120 Left 2 SYMATTR InstName B1 SYMATTR Value V=V(Q) * sin(T) + V(I) * cos(T) SYMBOL bv 496 -272 R0 WINDOW 0 53 7 Left 2 WINDOW 3 53 116 Left 2 SYMATTR InstName B2 SYMATTR Value V=V(Q) * cos(T) - V(I) * sin(T) TEXT -224 24 Left 2 !.tran 20u TEXT -64 344 Left 2 ;107.142 KHz SINEWAVE TEXT -64 384 Left 2 ;1 VOLT PEAK TEXT 104 384 Left 2 ;ANGLE 0 TEXT 504 384 Left 2 ;1 VOLT PEAK TEXT 680 384 Left 2 ;ANGLE +90 TEXT 504 344 Left 2 ;107.142 KHz SINEWAVE TEXT 584 -208 Left 2 ;x' = x*cos(t) - y*sin(t) TEXT 24 -216 Left 2 ;y' = x*sin(t) + y*cos(t) TEXT -296 -24 Left 2 !.PARAM T = 30/57.296 TEXT 96 128 Left 2 ;sine TEXT 688 120 Left 2 ;cos TEXT 208 -48 Left 2 ;PHASE ROTATOR TEXT 216 -8 Left 2 ;JL JAN 7 2014 TEXT -272 -72 Left 2 ;T = PHASE LEAD TEXT 56 -296 Left 2 ;rotated sine TEXT 600 -304 Left 2 ;rotated cos TEXT 280 128 Left 2 ;INPUT TEXT 280 -296 Left 2 ;OUTPUT