46.3.1. Input Resistance Calculation

So, we do have let us move to the next slide to do that.

So, let us concentrate on the input resistance and here, we do have the same small signal equivalent circuit and for input resistance, what we have it is if we are applying v here in whatever the i it is flowing. If I get the expression of i in terms of v that gives us the corresponding input resistance. So, R it is ; whereas, i , it is the base terminal current and base terminal current is . So, the expression of i it is .

Input resistance is a crucial aspect of amplifier circuits. It represents how much resistance the circuit offers at the input terminal. In this case, to find the input resistance (R), we consider the input voltage (v) applied at the base of the transistor and the corresponding base current (i). By determining the relationship between the voltage and current, we create an equation that allows us to compute the input resistance of the amplifier.

Think of a funnel representing the input resistance of a circuit. When you pour liquid (input voltage) into the funnel, the amount of liquid flowing out (base current) is determined by how wide or narrow the funnel is. A wider funnel allows for more flow, similar to a lower input resistance, whereas a narrower funnel restricts flow, analogous to a higher input resistance.

So, now if I apply KCL at the emitter node, what we are getting? Here, it is current flowing through this this r which is . So, that is equal to the summation of the two currents; one is the base current and other is the through the active device. So, the base current is and the current flowing through this voltage dependent current source, it is g v rather ‒ v going from going from yeah v .

Applying Kirchhoff's Current Law (KCL) at the emitter node helps us analyze the behavior of currents in the circuit. KCL states that the sum of currents entering a node must equal the sum of currents leaving the node. In this case, the current flowing through one resistor (r) at the emitter is equal to the sum of the base current and the current flowing through a voltage-dependent current source. This relationship allows us to express the total current in terms of base and other device-related currents.

Imagine a water junction where several pipes converge. According to the principle of conservation of mass, the amount of water flowing into the junction must equal the amount flowing out. In the same way, KCL ensures that the total current flowing into the emitter node matches the sum of different currents flowing out, helping us understand how the amplifier operates and how to calculate the input resistance.

So, from this relationship, between v and v that gives us the voltage gain. In fact, we can say that v = v ( ). In fact, if you see here this part it is common here and here. So, effectively you may say that the relationship between v and v if I say, it is the impedance here which is r and the impedance of rest of the circuit there.

The relationship between the input voltage (vin) and output voltage (vout) is crucial for determining the voltage gain of the amplifier circuit. This relationship can typically be expressed in terms of the impedances involved in the circuit. When analyzing the gain, we also consider how various resistances interact to contribute to the overall voltage gain. Essentially, the circuit's parameters create a feedback loop affecting both the input and output, which influences performance.

Consider a stereo system where the volume knob manages how loud the music plays (voltage gain). The higher the setting, the greater the output volume. However, the characteristics of the speakers (impedance) can influence how effectively music is amplified. A good speaker can increase the experience without distortion, just as effective resistance values in the circuit can enhance the amplifier's performance.

So, the effect of non-zero value of this R , it is increasing this resistance even higher. So, anyway that is in our favour considering the required input port characteristic. So, we have seen the voltage gain, we have seen the input resistance.

Introducing a non-zero collector resistance (Rc) adds additional resistance to the overall input resistance of the circuit. This increased resistance can improve the input characteristics of the amplifier, ensuring it better matches the desired specifications for low input current and high voltage gain. The functionality benefits from the increased resistance as it can provide better stability and performance in signal amplification.

Think of a network of roads where certain routes (the collector resistance) are intended to guide traffic more smoothly. By directing more cars through optimal paths, you reduce congestion and improve overall flow. In electronics, by carefully managing resistance, you help signals pass through circuits more efficiently, resulting in better performance.

--