43.5.2. Upper Cutoff Frequency Considerations

In the frequency response what we have seen in the CE cascaded amplifier. First of all, its voltage gain; voltage gain overall voltage gain $A_{overall} = A_1 \times A_2 \times \text{attenuation}$

When amplifiers are cascaded, meaning one is connected to the output of another, we expect the overall gain of the system to be the product of the gains of the individual stages and an attenuation factor that results from how these stages interact. If we denote the first amplifier's gain as $A_1$ and the second's as $A_2$, the overall gain will be the multiplication of these two gains adjusted by an additional factor to account for any reduction in voltage that occurs as the signal passes from one stage to the next.

Imagine a relay race where each runner needs to pass the baton to the next. The first runner’s speed represents the first amplifier’s gain, while the second runner’s speed represents the second amplifier’s gain. However, due to a delay in passing the baton (representing the attenuation), the combined speed of both runners isn’t just the sum of their speeds, but slightly less due to time lost in the handoff.

The upper cutoff frequency it is having two candidates one is the cutoff frequency coming due to this R and C, and second one it is of course, this resistance loaded with R and then whatever the input capacitance.

The upper cutoff frequency in a cascaded amplifier scenario is defined by two key factors: the first is determined by the resistances and capacitances of the individual stages, while the second arises from the combined effect of the load resistance and the capacitive effects introduced at the cascading node. When amplifiers are connected, the input and output capacitances interact with the resistive elements causing shifts in the frequency response. The overall upper cutoff frequency is thus given by the minimum of these two candidates, meaning the one that limits the frequency response the most.

Think of a water pipe (where the water flow is akin to the signal). The upper cutoff frequency can be compared to the maximum flow rate that can be achieved through the pipe. If two pipes with different diameters are joined, the narrower pipe (or any restriction) will ultimately limit the overall flow rate even if the wider pipe can handle more. Similarly, the overall circuit’s ability to handle high frequencies is limited by the lowest cutoff condition determined by these resistive and capacitative interactions.

If we put a buffer; so if we put a buffer say or say some intermediate circuit having some important feature we will be discussing that such that, the input resistance of this stage; call R_{in ext{_buffer}}. If it is quite high then whatever the attenuation it will be getting introduced by R and R.

Introducing a buffer circuit between amplifiers can have a significant positive effect on the overall system performance. A buffer is designed to have a high input resistance and low output capacitance, which minimizes the loading effect on the preceding stage and helps maintain original signal integrity while allowing for the subsequent amplification. By effectively isolating the stages, the buffer enables the system to operate closer to the theoretically expected gains without significant degradation from interacting stages.

Imagine using a strong battery to power multiple devices. If the devices were directly connected to the battery, some might draw too much power causing a drain and inefficiency. By placing a voltage regulator (like a buffer) between the battery and the devices, the devices can receive stable power without drawing too much and affecting each other, leading to better performance across the system.

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