14.1.9. Finding Collector Current

Then its collector current, it is having exponential dependency on base to emitter voltage incidentally that is base voltage V_B. And, also it is having this the parameter of the device; you may say that this is a reverse saturation current equivalent to a diode reverse saturation current.

The collector current (C) in a BJT transistor is greatly influenced by the voltage difference between the base and emitter terminals (V_BE). This relationship is exponential, meaning that even a small increase in the base-emitter voltage results in a significantly increased collector current. Additionally, there is a component called reverse saturation current, which is the current that flows through the transistor when the base-emitter junction is reverse-biased, similar to a diode's reverse saturation current.

Think of the base-emitter voltage as the key to a locked door. Just as a little pressure on the key (voltage) can unlock a door and allow a rush of people (current) to enter, a small increase in V_BE can dramatically increase the collector current in the transistor.

So, probably we can say that first we can find the value of this I_B or the expression of the I_C, then we can get the I_C, and then we can go to the V_CE.

To find the collector current (I_C), we first calculate the base current (I_B). If we know the base-emitter voltage and the parameters of the BJT, we can apply certain equations like the exponential relation of I_B. After determining I_B, we can obtain the value of I_C by multiplying I_B with the transistor's current gain (β), which provides the relationship between the base and collector currents. Lastly, we can use these currents to calculate the collector-emitter voltage (V_CE) based on the circuit conditions.

Imagine baking a cake where I_B is the amount of flour you start with. Once you have the flour (I_B), you know how much sugar (I_C) you can add by a specific ratio (current gain β). Finally, using the amount of cake (current) baked, you determine how much icing (V_CE) you can spread on top.

Now, how do you find the collector to emitter voltage V_CE? We do have this circuit where we do have the V_CC connected here. You might have observed that whenever we are writing this node as V indicating that with respect to ground one DC source is connected here as you can see here.

To find the collector-emitter voltage (V_CE), we look at the circuit configuration, particularly where the collector is connected to a voltage supply (V_CC) through a resistor. By applying Kirchhoff's voltage law (KVL), we can establish a relationship between the voltage drop across the collector resistor and the voltage at the collector terminal. This allows us to derive V_CE based on the known currents from our earlier steps and the voltage supply.

Consider V_CC as a water tank filled to a certain level. V_CE is like the height of the outlet water pipe (the collector) from the tank. To find out how much water we can utilize (V_CE), we need to account for the height of the tank (V_CC) and consider any blockage (voltage drop across resistors) that might restrict water flow.

So, we can call this part is the pull-up and this part it is pull-down part. So, let us see the generalized procedure to find the V_CE since this kind of circuit will be frequently experiencing.

In circuits containing BJTs, we analyze the collector-emitter voltage (V_CE) graphically by considering pull-up and pull-down characteristics. The pull-up characteristic relates to the resistor connected to the collector, while the pull-down relates to the BJT behavior at its junctions. By plotting both characteristics, we can find the intersection point, which indicates the operating point of the circuit where both currents are balanced.

Think of this method like finding the meeting point of two friends on a busy street. Each friend has a different route (the pull-up and pull-down characteristics), and where they finally meet on the street signifies the perfect balance point (operating point) where both can continue their journey together.

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