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Cascode Ampli combination of CE and CB.
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In CE Ampli we get moderate i/p impedance and large value of voltage gain but due to miller effect the overall BW of CE Ampli is less.

In CB Ampli there is no miller effect and also it provides large value of voltage gain, but i/p impedance of CB Ampli is very low hence we can not use CB configuration alone as a Ampli.

Hence to overcome this problem we use cascode Ampli which is a combination of CE and CB.

In cacode Ampli CE stage is mainly used to provide high i/p impedance and in order to avoid miller effect it is designed for unity voltage gain. the purpose of CB Ampli is to, provide high voltage gain and large B.W. the fig. below shows ckt diagram of cascode Ampli

In order to perform AC analysis making the DC supply zero and short citing all the capacitors and replacing BJT with it's hybrid II model, then ckt reduces as shown below,

Let Zi is over all i/p impedance of cascode Ampli

Zi = $R_1 || R_2 || R_\pi$

Let Zo is overall o/p impedance of Ampli by looking ther' collector of TX $Q_2$

Zo = $Rc_2 || R_L$

Let A2 is gain of 2nd stage

A2 = $\frac{vo}{vi2}$

vo = -$\beta$ib2 (Rca || RL)

Vi2 = -$\beta$b2r$\pi$

$\therefore$ A2 = $\frac{\beta(Rc || Rl)}{r\pi}$

Let A1 is gain of 1st stage

A = $\frac{vo1}{vi}$

Vo1 = Vi2 = -ib2r$\pi$

Vi = ib1 r$\pi$

A1 = $\frac{ib2r\pi}{ib1r\pi}$

$\because$ ic1 = ic, $\beta_1 = \beta_2$

$\because$ ib1 = ib2

A1 = -1

$\therefore$ overall voltage gain

A = A x $A_2$

A = $\frac{-\beta(Rc || Rc )}{r\pi}$