62.2.5. Small Signal Equivalent Circuit Analysis

So, here we do have the circuit we do have the original common source followed by common gate. And as I said that if we remove this capacitor, and then what we are looking for M1. It required some DC current need to be supplied to its drain. And at the same time M2 needs its source current need to be consumed by some bias circuit.

In a cascode amplifier, we first start with a common source circuit which is followed by a common gate circuit. The goal is to optimize the amplifier's performance. When we eliminate the coupling capacitor between the two stages, we observe that the current output from the first stage (M1) is necessary to supply the DC current into the drain of the second stage (M2). This creates a direct link that allows the two circuits to operate effectively together without the additional influence of an external bias circuit.

Think of a cascading relay system where the first relay must activate another relay directly without any delay or external power supply affecting it. Just like the current from the first stage needs to make sure the second stage has enough power, ensuring each part works harmoniously results in an efficient system.

So, here the connection it is direct connection and similar to BJT cascode, here we are we will be discussing that how the signal it is propagating from this stage; the common source stage to the common gate stage.

The direct connection between the transistors allows for efficient current sharing. The current produced by M1 (the common source stage) flows directly into M2 (the common gate stage). This interaction is crucial for maintaining the operating point of both devices. If we provide the right signals and biases, M2 can effectively boost the performance of M1 by appropriately managing its output without additional components.

Imagine two workers passing a baton in a relay race. The first runner (M1) has to ensure they hand over the baton (current) to the next runner (M2) seamlessly for the team to win. If they miscalculate the timing or force, the whole race might fall apart, similar to how the transistors need to work together effectively.

Now, while this M1 it is getting its gate voltage and source node it is connected to ground. So, that gives us VGS for this transistor. And then this VGS and its dimension it provides an expression of this current.

For a transistor to operate correctly, it needs to be biased properly. M1 receives a gate voltage (VGS) that sets it into the required operational region. This gate voltage is crucial because it helps establish the correct bias current that flows through M1 and subsequently to M2. By ensuring that VGS is within limits, we can avoid pushing the transistors into undesired regions of operation, such as the triode region, which can impact performance.

Think of setting the thermostat in your home. If you set it too low (or too high), the heating (or cooling) system can fail to operate efficiently or even break down. Similarly, by ensuring the gate voltage is set properly, we help the transistors function smoothly, which is important for maintaining the amplifier's overall performance.

So, if we look into this circuit that is the output resistance. And, we also have discussed about the Rout resistance for such kind of circuit.

The output impedance of a cascode amplifier is a critical factor that contributes to its ability to deliver voltage gain effectively. In a cascode configuration, the output impedance is significantly higher than in a single-stage amplifier. This is beneficial because it allows the amplifier to deliver more voltage gain while sacrificing minimal current. Thus, the increased output resistance is a trade-off that must be managed with respect to bandwidth and signal integrity.

Imagine a water tower supplying a neighborhood with water. The taller the tower (representing high impedance), the more pressure (voltage gain) it can generate to push water through the pipes (the amplifier’s output). However, if too much water demand happens at once, like a sudden surge in usage, the pressure might drop, causing issues. Similarly, while high output resistance boosts performance, managing signal demand is crucial to prevent potential problems in circuits.

On the other hand, the input capacitance here it is Cgs1 + 2Cgd1. On the other hand, if I consider simple common source amplifier, as we know that for common source amplifier, the corresponding Cin it is Cgs + Cgd(1 + its voltage gain).

The input capacitance impacts the frequency response of the amplifier. In a cascode configuration, the effective input capacitance is reduced as compared to a simple common source amplifier. This reduction can lead to an increase in bandwidth. If the bandwidth of the amplifier is largely defined by the RC time constant determined by the input resistance and capacitance, lowering the input capacitance directly allows for a broader frequency response.

Think of a highway that can expand from two lanes to four lanes. As more lanes are added, more cars can travel smoothly without traffic jams (analogous to increased bandwidth). The less congested the road (lower capacitance), the faster the cars can move through—just like signals through the amplifier.

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