Two channels system analysis¶

The following figure show a two channels stacked ADC:

We first consider an ideal system with a static amplifier $G_1=32$ and $H_0=1$ , $H_1=1/G_1$ .

The resolution of the two ADCs is 10 bit with a reference voltage of $V_r=1~V$ .

The input range (without saturation) of each ADC is $V_{in} \in [-V_r,V_r]$ .

The signal $x_0$ is a sinewave with amplitude $a_0$ .

Give the signal to quantization noise ratio $SQNR_0$ at the output $y_0$ in function of $a_0$
Give the signal to quantization noise ratio $SQNR_1$ at the output $y_1$ in function of $a_0$
Knowing that the output chosen ( $y_0$ or $y_1$ ) is that which leads to the best signal-to-noise ratio, give the final maximum $SQNR$ of this architecture in function of $a_0$ .
Give the number of bits necessary to represent the output word $y$