A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The open-loop gain A_v0, input resistance R_in, and output resistance R₀ for A1 and A2 are as follows:
A1: A_v0 = 10,R_in = 10 kΩ ,R₀ =1 kΩ
A2 : A_v0 = 5,R_in = 5 kΩ , R₀ = 200 Ω
The approximate overall voltage gain $$\frac{{\mathrm V}_\mathrm{out}}{{\mathrm V}_\mathrm{in}}$$ is ______.

In the differential amplifier shown in the figure, the magnitudes of the common-mode and differential-mode gains are 𝐴_cm and 𝐴_d, respectively. If the resistance R_E is increased, then

The feedback topology in the amplifier circuit (the base bias circuit is not shown for simplicity) in the figure is

The input to a 1-bit quantizer is a random variable X with pdf $${f_x}(x) = 2{e^{ - 2x}}\,\,for\,\,x \ge 0$$ and $${f_x}(x) = 0\,\,for\,\,x\, < \,0$$. For outputs to be of equal probability, the quantizer threshold should be _______________.