Where S is a Sinusoidal function and S<90 is the same as S signal whose phase is 90 degree lag. And C is another Sinusoidal function with a different frequency. I want to know what is the output of this system. I have not seen a balanced modulator with this schematic. As I know it can be used for create upper and lower side-band.
You can calculate the output signal by using geometric equations.
It's classical Differentially driven Balanced IQ Modulator ( LO Signals are differential only, Input Signals are single ended.).Don't let be you to confuse its balanced structure, principal is always same.
More information, search internet.