Voltage spectrum design formulas of modified fully differential amplitude, frequency or phase transmitter from the transistor level

This paper presents the realistic modulation analysis at the transistor level from schematic such as Modified Gilbert Multiplier and fully differential microwave power amplifier based on common-emitter connection. Output signal from the output node of the Gilbert Multiplier can be plotted in time domain from more realistic equation compared with ideal modulation theory from textbook. The spectrum of the output signal of the modulator is derived for the first time by using simplified Gummel-Poon collector current model and discrete inverse Laplace's transform or discrete inverse Fourier's transform.