88.3.1. Considering Finite Beta Values

As I said that the current flow current flow here and here should be equal and if you see it carefully the DC voltage here it is defined by this V – V drop. So, I should say the voltage here it is 12 V. So, the voltage here it is 12 – 0.6 so, that is 11.4 V.

This chunk introduces the concept of current flow in a circuit with transistors, specifically emphasizing the importance of equal currents in the context of bipolar junction transistors (BJTs). The voltage levels are derived from the supply voltage (12 V) minus the base-emitter voltage (V_BE), which is specified as 0.6 V. The resultant voltage is calculated to be 11.4 V.

Think of a water system where two pipes are supposed to have the same flow rate. If one pipe is delivering more water than the other, it can create pressure differences at various points in the system, affecting overall performance. Similarly, in a circuit, if currents do not match as expected, it can lead to inconsistent voltage levels.

Now, with this 11.4 V here we can say that whatever the current we do have. So, that may be 2 m which is of course, 1 approximation that we are assuming ( ) = 1 please stop here.

In this portion, the assumption is made that the current is approximately 2 mA. This value is critical because it's linked to the output characteristics of the transistors. Assuming a base current of 20 µA and a current gain (β) of 100, the collector current (I_C) can be derived through simple multiplication. Understanding these relationships is fundamental in analyzing electronic circuits.

Imagine a pump in a water park that distributes water (current) to several water slides. The pump's efficiency and pressure (voltage) are determined by how well the pump is calibrated (the BJT's β). If the pump is set for a specific flow rate that doesn't change, it maintains a consistent pressure across the park.

So, with that we do have this current is also 2 mA and if we assume that the base current loss is ignorable, then you can say that collector current of transistor-3 it is also 2 mA which is getting mirrored to transistor-4, so that is making this current also 2 mA.

By assuming 'no base current loss', it reinforces that the collector current in an idealized scenario is 2 mA. This simplified model helps in deducing that current in multiple transistors in the configuration should match, allowing for noise-free operation. The mirroring effect across transistors is a significant point, as it shows that one transistor's performance directly affects another's, maintaining an equal current flow.

Consider a relay system controlling multiple lights; if one relay (transistor) energizes without losing energy, all connected lights receive the same current that they need to stay lit. If any relay has power loss or a mismatch, some lights may dim or flicker, just like different collector currents could change operational efficiency in the circuit.

But of course, if the values of early voltage or in case we cannot ignore say this base current and then of course, the corresponding the current here and here there will be a mismatch and the DC voltage here it will deviate from here.

This portion highlights the reality that in practical applications, certain ideal assumptions may fail. Variations such as early voltage effects and base current losses can lead to discrepancies in expected currents and output voltages. The concept underscores the importance of considering real-world variables that could affect performance, leading to a mismatch in current, and ultimately impacting circuit functionality.

In a factory assembly line, if one station operates at a slower speed due to wear or a malfunction, the entire process can be affected, causing delays or defects. Similarly, in an electrical circuit, if one transistor performs differently than expected, it affects the entire system's output voltages and currents, requiring adjustments to maintain efficiency.

In the next numerical example, it is continuation of this, the same example, but considering finite value of this β of transistor-3 and 4 will be giving us a situation where we need to consider mismatch of the 2 current.

This part introduces a scenario where the actual β values of transistors are taken into account. It prepares the reader for a more nuanced understanding and analysis of current mirrors and transistor behavior, accounting for variations that affect overall performance. Such consideration of finite β will often lead to misalignments of current measurements, emphasizing the need for precise calculations.

Imagine if two conveyor belts are supposed to deliver the same weight of boxes per minute, but one has a slight slowdown due to mechanical issues. Despite starting in sync, if their performance isn't identical over time, they’ll end up delivering unequal amounts. In circuits, finite β leads to unanticipated current variations that can disrupt expected outputs.

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