43.2.2. Frequency Response of Common Emitter and Common Source Amplifier

Now, the frequency response of say common emitter amplifier in this case we have discussed more detail of frequency response of individual common emitter amplifier. Let we talk about today it is we do have two maybe identical common emitter amplifiers or architecturally they are identical. And to achieve say maybe higher gain or maybe for some other reason we like to cascade this CE stage, it is first stage and then you may call it is the second CE stage together.

In this chunk, we start by understanding that we are looking at two identical common emitter amplifiers. When we cascade these amplifiers, it means we are connecting the output of the first amplifier to the input of the second. The purpose of cascading is often to achieve a higher gain than what a single amplifier could provide. However, while cascading can offer advantages, it also introduces certain considerations related to the overall frequency response of the combined circuits.

Think of cascading amplifiers like stacking two stories in a building to make it taller. Each story (amplifier) would contribute to the overall height (gain), but the way in which they connect could also affect aspects like stability and access (frequency response).

So, in nutshell C it is helping us to separate the DC operating point of the first stage and the second stage DC operating point.

Capacitors play a crucial role in cascading amplifiers. Here, capacitor C helps to block the DC voltage from the first stage while allowing the AC signal (our input signal) to pass through to the second stage. This separation is vital since it ensures that the DC operating points of the two amplifiers do not interfere with each other, maintaining the stability and performance of each amplifier.

You can think of this capacitor as a water filter in a piping system. The filter allows clean water (AC signal) to flow through while blocking contaminants (DC components), ensuring that each section of the piping system functions properly without interference.

Now, while we will be connecting this circuit we may be expecting that suppose we do have a gain of this stage; it is say A and then gain of this stage it is say A we may be expecting that the overall gain say A = A × A .

When connecting the two amplifiers, we expect the overall gain, denoted as A, to be the product of the gain of each individual amplifier. If the first stage has a gain of A1 and the second stage has a gain of A2, then theoretically, the overall gain would be A = A1 × A2. However, this ideal expectation does not always hold in practice due to loading effects and other interactions between the stages.

Imagine trying to increase your height by standing on the shoulders of two friends. If both friends are strong (high gain), you would expect to be significantly taller (higher gain). However, if one friend is wearing a low chair (loading effect), they might not give you the expected height boost.

So, in our surprise once we connect the circuit and if we if we make the observation from the primary input to primary output we will see a significant amount of change of this gain namely this gain may drop off here to some other value and also may be the upper cutoff frequency may come down.

Once the amplifiers are cascaded, we can observe that the expected gain does not materialize as predicted. Instead of maintaining a high combined gain, the actual gain may drop, and the upper cutoff frequency can also be reduced. This change occurs because of the loading effects—where the output of the first amplifier affects the input of the second, altering their performance significantly from what was expected theoretically.

This effect can be likened to a relay race where the first runner (the first amplifier) affects the speed (gain) of the second runner (the second amplifier) through the baton pass (the connection). If the baton is heavy (loading effect), the second runner may not reach their full speed as anticipated.

The loading effect introduces one attenuation factor which is defined by R and this R may be having different value, but typically these two resistances may be having the same order of magnitude.

When cascading amplifiers, the output resistance of the first amplifier interacts with the input resistance of the second amplifier. This interaction can cause a drop in the overall gain—a phenomenon known as the loading effect. Essentially, if the output of the first amplifier 'loads down' the input of the second, the voltage transferred is less than expected, affecting the overall gain.

Think of this loading effect as a long chain of interconnected balloons. If one balloon (the first amplifier) is too heavy and pulls down on the next balloon (the second amplifier), the overall height of the chain is reduced, similar to how the loading effect reduces the expected gain.

So, what we can say let me clear here yeah, the cutoff frequency particularly the upper cutoff frequency it is having two candidates one is the cutoff frequency coming due to this R and then C and second one it is of course, this resistance loaded with R and then whatever the input capacitance.

In this chunk, we learn that the upper cutoff frequency of the cascaded amplifiers is influenced by two factors: the resistance and capacitance associated with each stage. When these two amplifiers are cascaded, new poles can form at frequencies that may lower the overall cutoff frequency, meaning that the range of frequencies that can be amplified effectively is reduced.

This is similar to adjusting the settings on a speaker. If you turn the bass up too high, you may lose some of the high frequencies, affecting the range of sounds you can hear (upper cutoff frequency).

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. If it is quite high then whatever the attenuation it will be getting introduced by R and R.

To improve the performance of cascaded amplifiers and prevent the drop in gain and cutoff frequency, we can introduce a buffer circuit. A buffer typically has a very high input resistance and low output resistance, which helps in isolating the two stages. By minimizing the loading effect caused by cascading, the buffer allows each stage to operate closer to its ideal performance without compromising on gain or bandwidth.

Think of a buffer like a strong intermediary negotiator who can help two parties interact without the complications caused by their different strengths (resistances). This negotiator ensures that both parties can achieve their best outcomes without either party being affected too much by the other's weaknesses.

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