87.1. Analog Electronic Circuits

So dear students welcome back after the break. So, before the break we are talking about the numerical examples of the current mirror. As you can see here, and there we have used Beta-helper to improve the non-ideality factor coming due to the base current loss namely, this base current loss.

In this section, we are reestablishing the conversation about current mirrors, which are essential components in analog circuits. The term 'Beta-helper' implies a method or technique used to enhance the current mirror's performance by addressing base current losses that can affect accuracy. Base current loss refers to the small amount of current that is diverted away from the main current path, which can lead to inaccuracies in the current being mirrored.

Think of a current mirror like a team of workers each tasked with carrying a certain load (current). If some workers divert to other tasks (current losses), the overall load carried can drop. Using 'Beta-helper' is like assigning a supervisor to ensure every worker stays focused on just their load.

So in the next example, we will see that improvisation of the numeric current mirror circuit to take care of the non-ideality factor due to early voltage. To be more precise, we like to place one cascode transistor here and that improves the output resistance of the current mirror.

Here, we discuss enhancing the current mirror circuit by adding cascode transistors. A cascode transistor helps to increase the output resistance of the current mirror significantly. The term 'Early voltage' refers to a phenomenon in transistors where the effective output resistance decreases when output voltage is increased. By using a cascode configuration, the impact of Early voltage can be reduced, resulting in more stable current mirroring.

Imagine a multi-story building where each floor represents a stage of support for our load (current). If the lower floors are weak, the whole structure may sway with wind (voltage changes). Adding support beams (cascode transistors) reinforces the whole building, making it more stable against those wind fluctuations.

Now coming to the different sizes of different transistors given here, we do have for transistor-1, we do have the it is 1 mA/V2. On the other hand for transistor-2 and transistor-3, we do have = 4 mA/V2. This is just for a change, we are using different values of the aspect ratio.

In this part, we describe different transistors in the current mirror and their parameters such as transconductance, which is a measure of how effectively each transistor can control the current based on the applied voltage. The values 1 mA/V² and 4 mA/V² relate to how much current the transistors can handle per volt of gate voltage, and we are varying these to explore different circuit behaviors.

Consider these transistors like different athletes. One athlete (transistor-1) is trained for endurance (1 mA/V²), while the other two (transistor-2 and transistor-3) are sprinters (4 mA/V²). Depending on the race (circuit design), you would choose which athlete to rely on for optimal performance.

Now we need to find the value of this V and the current flowing here from whatever the voltage 12 V it is given to us and then R, it is given there. To calculate that, in some of our previous examples we have done that this current which is I, it is also creating a drop here...

In this step, students will learn how to apply Ohm's law and circuit analysis principles to calculate voltage drops across components. The voltage drops result from the current flowing through resistors in the current mirror circuit, and understanding these calculations is crucial for predicting circuit performance.

Think of water flowing through pipes. The pressure (voltage) at different parts of the system can drop when it passes through different sections (resistors). By measuring where those drops occur, we can predict how much pressure remains at the output.

So, we need to find what will be the small signal output resistance. And R is g m3 r o3 r o2 + r o3. Note that r o2 and r o3 we are considering they are synonymous.

This chunk discusses calculating the small signal output resistance of the current mirror circuit. The relationship between transconductance (g) and output resistance (r) is critical for characterizing the circuit’s response to small input signals. The formula provided combines the effects of multiple transistors to yield a total resistance that affects the circuit's performance in small-signal conditions.

Imagine tuning a guitar. The tension on the strings (resistance) needs to be just right to produce the correct sound (small signals). By adjusting the tension and combining the effects of the different strings, you can create harmonious music (optimized circuit performance).

So, using this output resistance, we can calculate the variation of this current. If we vary this V from 1.2 V to 5.2 V; that means a voltage variation of 4 V.

Here, the relationship between output voltage and current flow is discussed. The higher the output resistance (from the cascode configuration), the less the current variations due to voltage changes in the circuit. Thus, the small-signal characteristics maintain stable performance across voltage fluctuations.

Think of a good manager in a company. When company resources (voltage) fluctuate, a good manager can ensure that employee productivity (current) remains stable despite those changes. Thus, the organization's performance stays consistent regardless of the ups and downs.

Now so now we obtain, we have solved this part. Next thing is that for V, if it is say 5 V then what do you expect? Here we do have 2.5...

In this final section, we pull together the calculations to illustrate the effectiveness of cascode current mirrors, emphasizing their high output resistance and robustness against voltage changes. We also hint at real-world applications where such circuits improve performance, for example, in amplifiers where maintaining accuracy at various operating conditions is critical.

A well-engineered car suspension system absorbs bumps (voltage variations) while keeping the passengers comfortable (stable current output). In analog circuits, a solid current mirror design ensures that subtle changes won't derail overall performance.

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