43.6.2. Expression for Overall Gain with Buffer

When we cascade two amplifiers like common emitter (CE) or common source (CS) amplifiers, we expect an overall gain that multiplies the gains of the individual stages. For example, if the gain of the first stage is A1 and the second is A2, we expect the overall gain A to be A = A1 × A2.

In electrical circuits, cascading refers to connecting multiple amplifying stages together to increase the total amplification factor. Each amplifier has its own gain, and when connected correctly, the total gain is simply the product of the individual gains. However, this assumes ideal conditions without losses.

Think of cascading amplification like stacking several amplifiers together to make a louder sound. For instance, if you have 2 speakers, one amplifying the sound at 2 times the original volume and another at 3 times, you’d typically expect the total volume to be 2 × 3 = 6 times louder. But due to losses, the total output might be less than expected.

However, when the output of the first amplifier connects to the input of the second, it can cause loading effects which reduce the gain. The output resistance of the first amplifier may load down the input of the second amplifier, leading to an attenuation factor, which affects the overall gain.

When two stages of amplification are connected, the output of one can affect the input of the next. The output voltage level may drop because of a loading effect, which is where the resistor effect of the second amplifier pulls down the voltage of the first. This results in a reduction of the overall gain, referred to as attenuation.

Imagine you’re filling a water tank (first stage amplifier), but then you attach a pipe that’s too narrow (second stage amplifier). The narrow pipe can restrict the flow of water from the tank, reducing the amount that comes out at the other end. This is similar to how loading can restrict the voltage.

The cutoff frequencies of the cascaded amplifiers also interplay when connected. The lower cutoff frequency is generally determined by whichever stage has the lower cutoff frequency, and the upper cutoff frequency is defined by the stage with the lowest cutoff frequency.

Cutoff frequencies indicate the limits of frequency from which an amplifier can operate effectively. When cascading two amplifiers, the overall frequency response can be altered. The lower cutoff frequency will be dictated by the stage that has the lowest response (lower frequency limit), while the upper cutoff is decided by the stage that limits the highest frequency response.

Consider a double-layer filter—a fine mesh and a coarse mesh combined. The overall ability to filter will depend on the openings of the more restrictive layer. In audio terms, if one speaker can only replicate low frequencies, the final sound output will still only reproduce sounds within that limited range, even if the other speaker can handle highs.

To mitigate the negative effects of cascading amplifiers, a buffer is often employed between stages. The buffer serves to isolate the stages, maintaining high input impedance and low output impedance, ensuring maximum signal transfer and minimal loading.

Buffers are used in amplifier circuits to separate stages and maintain the integrity of the signal being amplified. A good buffer will have a high input impedance, which means it will not load down the previous stage's output significantly, and a low output impedance, allowing it to drive the next stage effectively without losing signal strength.

Consider a buffer as a funnel helping to direct an incoming water flow (signal) into a smaller channel. The funnel prevents backflow and keeps the water flow strong into the channel, ensuring that the process continues smoothly without interruptions.

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