8.6.2. Base Current and Collector Current Expressions

BJT particularly say n-p-n transistor it is having three regions namely n, then p-region and n-region. In between it is having junction, junction-1 and also junction-2. They may be having different cross sectional area A and A. For active region of operation, J1 particularly one of these junctions to be forward biased by this voltage; base to emitter voltage and this junction on the other hand; it will be reverse biased.

In a BJT, or Bipolar Junction Transistor, the device consists of three regions: two n-type regions (the emitter and collector) and one p-type region (the base). The junctions between these regions (Junction-1 and Junction-2) play a critical role in how the BJT functions. In standard operation, Junction-1 is forward biased, meaning it's set up to allow current to flow easily from the base to the emitter (due to a positive voltage applied from base to emitter), while Junction-2 is reverse biased, which prevents current from flowing easily the other way. This configuration allows the BJT to amplify current because a small current at the base can control a larger current flowing from collector to emitter.

Think of a BJT like a valve in a pipe system. The base acts like a control lever that adjusts the flow between the emitter and collector. When you push the lever (apply voltage to the base), a small twist allows a large flow of water (current) to pass through the collector side.

The junction current I1 is having two current components namely the current carried by electrons I_n1 and then current carried by holes I_p1. Likewise, I2 also having two current components namely I_n2 and I_p2.

When analyzing the currents in a BJT during operation, we see that each junction (Junction-1 and Junction-2) contributes to two components of current. In Junction-1, which is forward biased, there are two currents: one due to electron movement (I_n1) and one due to hole movement (I_p1). In Junction-2, which is reverse biased, the current also has two components: I_n2 and I_p2. The key point here is that while the forward bias allows for easy movement of both types of charge carriers (electrons and holes), the reverse bias condition at Junction-2 restricts movement, primarily allowing for the so-called reverse saturation current.

Imagine a busy intersection where cars (electrons) and bicycles (holes) can freely flow in one direction due to a green light (forward bias). However, when the light turns red (reverse bias), only a few bicycles are allowed to slowly pass while cars are entirely halted, symbolizing how Junction-2 operates during reverse bias.

By considering different junction current components; we may be able to easily get the terminal current namely this current I_E; it is a summation of these two currents. Likewise, I_C will be summation of these two minus whatever these two currents are there.

The total currents at the terminals of the BJT are derived from summing up the contributions of the junction currents. The emitter current (I_E) is the sum of the current components associated with Junction-1 (I_n1 and I_p1), while the collector current (I_C) is obtained by summing the contributions of Junction-2 (I_n2 and I_p2) and subtracting from it the reverse component due to the base current. This systematic summation allows us to understand how the total current at each terminal relates directly to the junction characteristics.

Think of the BJT as a workplace where different employees (electrons and holes) contribute to the overall output (current) of the company (transistor). The employees at one department (emitter) add their productivity together to get the total output, while the employees at another department (collector) sometimes offset each other's contributions, showcasing how each part of the device works together to achieve overall productivity.

The collector current is having as I say that the injected current namely whatever the movements of these electrons coming here; they are contributing in this terminal current. So, this part under certain condition; this is also dominating and this current it is again exponential function of the V_BE.

The collector current (I_C) is heavily influenced by the voltage applied at the base-emitter junction (V_BE). Specifically, as the forward bias increases (higher V_BE), it exponentially increases the number of electrons that can move across Junction-1 into the base and subsequently into the collector. This exponential relationship is fundamental to the operation of BJTs, as it enables even small changes in the base voltage to lead to large changes in collector current, allowing for effective amplification.

If we think of the base-emitter junction as a water pump, increasing the voltage (turning up the pump) causes a surge in the flow of water (current) out of the collector, demonstrating how fine adjustments can significantly affect the output.

All of the current components are having exponential dependency and so what we can say that this base current, collector current, and injected current are function of the V_BE.

Every significant current within the BJT—be it base current (I_B), collector current (I_C), or the injected current due to the electrons—exhibits an exponential relationship with the base-emitter voltage (V_BE). This characteristic is critical as it dictates how the transistor amplifies signals. The more you increase V_BE, the more pronounced the currents become, enabling the BJT's amplification properties by providing a larger resultant collector current relative to the base current.

Imagine how a car accelerator works: pressing harder on the pedal (increasing V_BE) prompts the car to accelerate faster (increasing collector current). Even a slight push can lead to a large change in speed, showcasing the exponential impact of the small input signal.

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