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 power spectral density of a real stationary random process X(t) is given by $$${S_x}\left( f \right) = \left\{ {\matrix{ {{1 \over W},\left| f \right| \le W} \cr {0,\left| f \right| > W} \cr } } \right.$$$

The value of the expectation $$$E\left[ {\pi X\left( t \right)X\left( {t - {1 \over {4W}}} \right)} \right]$$$
is ---------------.