2016年6月28日火曜日

The principle to generate SSB modulated signal by using IQ modulator (PSN method)

The principle to generate SSB modulated signal by using IQ modulator (PSN method)





Assume V1 is “baseband signal” to be input as audio signal.
(eg. we can use microphone to input V1.)
V1 = Vs*sin(ωs*t) …(1)
 here ωs = 2πfs  …(2)
         fs [Hz] is 0 to 20KHz Frequency of baseband signal on Audio frequency


Shift V1 signal to be -90 deg. by “-90 deg. Shifter”.
V2 = Vs*sin(ωs*t-π/2) = -Vs*cos(ωs*t) …(3)


OSC generates ωc[rad*Hz] sin wave voltage.
Vosc = Vr*sin(ωc*t) …(4)
here ωc = 2πfc …(5)
         fc [Hz] is set to RF frequency such as 9MHz so called “Carrier frequency”.


Shift Vosc signal (4) to be -90 deg. by “-90 deg. Shifter” and get V3.
V3 = Vr*sin(ωc*t-π/2) = -Vr*cos(ωc*t) …(6)


Get V4 by multiplying V1 and V3.
V4= V1*V3 = Vs*sin(ωs*t) * (-Vr*cos(ωc*t)) = -Vs*Vr*sin(ωs*t) * cos(ωc*t) …(7)


Get V5 by multiplying V2 and Vosc.
V5 = V2*Vosc = -Vs*cos(ωs*t) * Vr*sin(ωc*t) = -Vs*Vr*cos(ωs*t) *sin(ωc*t) …(8)


When “Adder” used before Vout,
Vout = V4+V5 = -Vs*Vr*sin(ωs*t) * cos(ωc*t) -Vs*Vr*cos(ωs*t) *sin(ωc*t)
       = -Vs*Vr* (sin(ωs*t) * cos(ωc*t)+cos(ωs*t) *sin(ωc*t))
       = -Vs*Vr* (sin(ωs*t+ωc*t) ) = -Vs*Vr*sin((ωs+ωc)*t)  …(9)
       … This (9) means USB generated as output signal Vout.
           (9) is USB signal and Carrier ωc signal voltage is removed here.


When “Subtracter” used before Vout,
Vout = V5-V4 = -Vs*Vr*sin(ωs*t) * cos(ωc*t) + Vs*Vr*cos(ωs*t) *sin(ωc*t)
       = -Vs*Vr* (sin(ωs*t) * cos(ωc*t) - cos(ωs*t) *sin(ωc*t))
       = -Vs*Vr* (sin(ωc*t-ωs*t ) = -Vs*Vr* sin((ωc-ωs)*t)  …(10)
       … This (10) means LSB generated as output signal Vout.
         (10) is LSB signal and Carrier ωc signal voltage is removed here.


“PSN method” by using “IQ modulator” is proved to generate SSB modulated signal
( USB or LSB).

(C) Noboru, Ji1NZL, Jun.21, 2016