50.1.3. Relationship between Input and Output Currents

So, here we do have the common base configuration. We do have the corresponding circuit here and to get the current gain what we have to do? At the output node we have to make their corresponding terminal unloaded. What do you mean by unloaded? We have to basically short this node to ac ground and then we have to find how much the current it is coming from the circuit signal current.

The common base configuration is a type of transistor amplifier setup where the base terminal is held at a constant voltage (common). To measure how well the circuit amplifies current (current gain), we start by 'unloading' the output node. This means connecting it to AC ground, which allows us to isolate the current flowing through the output without any influence from load resistance. By doing so, we can accurately measure the current supplied by the input signal.

Imagine a water pipe where some pressure is being used to push water through. The common base configuration is like ensuring that the end of the pipe is open (unloaded) so you can measure how much water (current) is being pushed through without any resistance from a faucet or valve at the end.

And we know that if the signal it is in current form unloaded condition should be the corresponding impedance or the terminating impedance should be 0. So, small signal model if you see the corresponding situation here it is this node the corresponding collector node it is ground and we are observing the corresponding signal current i , for their input signal it is i .

In the unloaded condition for the common base configuration, the impedance at the output terminal is considered zero. This simplification allows us to develop and use a small signal model that focuses on the small variations in current caused by the input signal. In this case, we label the output signal current as i_o, and the input signal current as i_in, allowing us to analyze the relationship between these two currents effectively.

Think of a straw you are using to drink from a cup. If the other end of the straw is underwater with no obstruction, it's easy to measure how much liquid is being drawn through. This is similar to our 'unloaded' condition, allowing us to observe the flow (current) without added resistance.

Now if you see this circuit again the base node it is grounded, voltage at the emitter we do have v. So, the v it is v it is ‒ v right and part of the current is also flowing here. So, we can say that i , it is having different component; one is this part another is this part right and then we also have this current and this current.

In the circuit, the input signal current (i_in) consists of various components contributing to its overall value. The voltage at the emitter (v_e), which is driven by the input signal, results in separate currents flowing, which include the transconductance current (g_m * v) associated with the input signal and additional current components flowing through other circuit elements. Understanding these components helps in determining how the input signal translates into output behavior.

Consider a traffic intersection where multiple roads converge at a single point. Some cars (current components) are turning left, others are going straight, contributing to the total flow of traffic (input current). Each route represents a different current component that together defines the overall traffic at that point.

So, in summary we can say that i it is it can be directly written in terms of v. On the other hand if you see the current at the output terminal here. So, if this is the current. In fact, this current of course, this node it is grounded. So, the current here it is actually 0 because this is also ground this is also ground. So, the current here it is 0. So, the i on the other hand, it is summation of only these two currents we do have this current and we do have this current.

To compute the relationship between the input current (i_in) and the output current (i_o), we express i in terms of the input voltage (v_e). Notably, when considering the output current, if the output terminal is grounded, the observed current will be zero. Thus, the actual output current at the collector consists solely of the sum of specific current components coming from the base and emitter.

If you think of a scale measuring how much weight you push down with your hand (input current), but the other side (output) is fixed (grounded), you can only feel the pressure you apply without any response from that side. The total effect is measured by how your hand's pushing translates to movement on the scale.

So, if I take ratio of this two what we are getting here it is the v this is getting cancelled. So, the current gain = . In fact, if you see because this gm it is dominating we may consider rest of the things it is very small. In fact, you may call this is practically it is .

By taking the ratio of input to output currents, we can derive the expression for current gain. The voltage terms cancel, allowing us to focus on the transconductance (g_m) and its effect on the current gain, where other minor current components can often be ignored. This highlights that the current gain primarily depends on the transconductance of the transistor, often leading to very close values to 1.

Imagine a sponge soaking up water: for every drop of water you pour onto the sponge (input current), a significant amount drains out the other side (output current). The current gain represents how effectively the sponge transfers the water from one side to the other, and in this case, most of the water is effectively transferred, resembling a gain close to 1.

So, we can say that this current gain it is less than 1, but it is very close to 1. So, that gives us good you know conclusion that this circuit namely the common base, since its input resistance is low output resistance is high and the current gain it is it is close to 1. So, it is a good circuit for current mode buffer.

The characteristics of the common base configuration indicate that its current gain is slightly less than 1, meaning it provides a nearly one-to-one transfer of input to output current. Furthermore, this configuration has low input resistance and high output resistance, making it efficient for applications where the primary goal is to buffer currents rather than voltages.

Think of a translator converting spoken language into another language. While it's not a perfect one-to-one translation (current gain slightly less than 1), the translator conveys most of the meaning effectively (high efficiency), making communication smoother without losing much of the original intent (buffering currents well).

--