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Gain of ce-cb cascode is nearly equal to the gain of ce amplifier, because in a ce-cb cascode, the gain of the ce stage is equal to 1, and the gain of the cb stage is nearly equal to an isolated ce amplifier. Hence, gain of both are nearly equal.

On the other hand, Bandwidth of ce-cb cascode is much higher than the bandwidth of ce amplifier because the cb stage in the cascode configration is not subjected to any Miller effect, thereby improving the high frequency response. The absence of Miller effect is due to the fact that the base of the cb stage is grounded thus, shielding the collector signal from being fed back into the emitter input.

To be more clear, the gain of CE stage in cascode is nearly 1, which reduces the miller effect on the cb stage greatly.

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Q: Why is the gain and bandwidth of a ce-cb cascode amplifier greater than a ce amplifier?
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