43.4.2. Cutoff Frequency Modifications

When two identical common emitter amplifiers are cascaded, we expect the overall gain and bandwidth to be the product of the two individual gains. However, this assumption does not hold true in practice.

In a typical scenario, when we cascade two common emitter amplifiers, we might expect their gain (A) to be multiplied (i.e., A_total = A1 × A2). But due to loading effects and other interactions, the actual gain often becomes less than this theoretical value. This is primarily because the output of the first amplifier influences the input of the second amplifier, leading to changes in gain and bandwidth.

Imagine you are trying to fill two buckets with water using a hose. If the first bucket (first amplifier) fills normally, it should, in theory, fill the second bucket (second amplifier) faster. But if the hose (the connection between the two) has a kink or is too narrow, the flow to the second bucket slows down, and it doesn’t fill as quickly as expected. This is similar to what happens in cascading amplifiers where loading effects reduce the overall gain.

The interaction between the output resistance of the first amplifier and the input resistance of the second can introduce an attenuation effect, resulting in lower-than-expected overall gain.

Loading occurs when the output impedance of one stage affects the input impedance of the next stage. When the output resistance (R_o) of the first amplifier feeds into the input resistance (R_in) of the second, they form a voltage divider. This divider can reduce the voltage seen by the second stage, causing a drop in gain. Thus, despite calculating the gain based on multiplying the individual gains, we're often faced with a value that’s lower due to this effect.

Consider a road with traffic lights. If one light is red (output is low), cars cannot move to the next intersection (the next stage) effectively. The cars waiting at the first light are like the signal being sent to the second amplifier; if the first light stays red too long, the flow to the second light is reduced. This results in decreased efficiency, similar to how loading reduces effective gain.

Cascading amplifiers changes their cutoff frequencies, particularly affecting the upper cutoff frequency. The effective cutoff frequency becomes defined by the lowest cutoff frequency of the individual circuits.

In a cascaded system, the cutoff frequency is determined by the bandwidth of the individual amplifiers. When combined, the upper cutoff frequency can be altered depending on the circuit components. Specifically, any increase in loading effect can lower the cutoff frequency, meaning that the cascaded system might not perform effectively at high frequencies compared to individual amplifiers. Therefore, the overall bandwidth is effectively determined by the weakest link in the chain, often leading to a bandwidth reduction.

Think of a team of runners in a relay race. The speed of the entire team is limited by the slowest runner; if one runner cannot keep up, the entire team’s performance suffers. In the context of amplifiers, if one amplifier has a low cutoff frequency, it drags down the performance of the cascaded amplifiers, making the entire system less effective at high speeds (or frequencies).

To retain efficiencies in gain and frequency response when cascading amplifiers, buffer circuits can be introduced between stages.

Buffers serve as isolation stages that prevent the loading effect from one amplifier affecting the other. By ensuring that the buffer has high input impedance and low output impedance, it efficiently transfers the signal without significant losses. This helps in preserving gain and bandwidth, making the overall system more efficient. Additionally, choosing buffers with minimal capacitance reduces the effect on the upper cutoff frequency, enabling the system to operate closer to its ideal performance.

Imagine a relay in a sports team where one player is tasked only with passing the baton without running. By doing so, they don't impact the overall speed of the runners. It helps maintain the pace and performance of the team, just like how a buffer helps maintain the performance of amplifiers in a cascade arrangement, ensuring that none of the stages compromise the overall signal quality.

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