It is known that one can synthesize a signal into a train of boxcar pulses (pwm modulation), each with the same amplitude, if proper low pass filtration is applied to this pulse train before it reaches the load.
Now consider the synthesis of the product of two signals. I have found with some rudimentary matlab simulation (see below) that the average* of the multiplication of two pwm modulated constant** values is equal to the value of the multiplication of two constant signals
*I use the average because it is equivalent to passing only signal at frequency equals zero which is a low pass operation.
**Non constant values are constant across small time intervals so turn up both carrier frequencies and you're golden.
%pwm test %domain n = 5e6; t = linspace(0,1/2,n); %time %sawtooth carriers %Frequencies f1 and f2 should be much different in %magnitude relative to eachother i.e. f1 >> f2 or f2 >> f1. Here I use %the case of f2 >> f1. f1 = 1e3; f2 = 1e5; st1 = sawtooth(2*pi*f1*t)'; st2 = sawtooth(2*pi*f2*t)'; %constant values constant_11 = -1/2*ones(n,1); constant_12 = 1/2*ones(n,1); %pwm modulation pwm1 = sign(st1 - constant_11); pwm2 = sign(st2 - constant_12); %multiply pwm12 = pwm1.*pwm2; av_pwm12 = mean(pwm12)*ones(size(pwm12)); actual12 = constant_11.*constant_12; %visualize plot(actual12),hold on,plot(av_pwm12),hold off
Multiplying the two pwm modulated signals in code like I have shown is like independently toggling two series switches mutually in series with the load i.e. the load only receives current when the state of both switches are closed.
If no one finds an issue with what I have said in the preface, I'd like to ask if there has been any studies done on this type of signal multiplication. If so, could you direct me to information about such study or studies?
I have tried to locate information on this topic but can't seem to dig anything up. Perhaps I am lacking the correct keyword that has been assigned to what I am looking for...Anyway, any help on this would be much appreciated. Thanks in advance.