88.2.2. Assumptions of Identical Transistors

So, we are assuming that Q and Q are identical and also we are assuming that whatever this Q and Q are also identical.

In electronic circuits, particularly in amplifiers and current mirrors, it is often assumed that transistors used in a circuit are identical. This means they have the same characteristics such as current gain (β), collector-emitter saturation voltage, and thermal performance. By assuming that transistors Q1 and Q2 in the circuit are identical, we can simplify the analysis of current flowing through the transistors, allowing us to calculate important parameters with less complexity.

Think of identical transistors like two people using the same smartphone model. If both phones have the same battery capacity, features, and capabilities, then any calculation regarding battery life or performance becomes straightforward because you can expect them to behave the same way under similar conditions.

To get the I_c current of transistor-1 and collector current of transistor-4 equal, we want the current flow through transistor-2 should be equal to current flow through transistor-1.

In current mirrors, the goal is to replicate a specific current from one transistor (like Q1) to another (like Q4). The assumption that the transistors are identical means that the current flowing through Q1 (denoted as I_c for collector current) can be mirrored exactly by Q4. This is because if both transistors behave identically, the output current should match the desired current flowing through the active load. This allows for efficient and accurate current control in various circuit applications.

Imagine you have two identical water pumps connected in a way that one pump feeds the other. If both pumps have the same capacity and efficiency, the water flow from the first pump can be exactly matched by the second pump. Similarly, in circuits, if the transistors are identical, the current can be effortlessly mirrored from one to the other.

Since Q and Q are identical having the same β value of 100, the value of this resistance should be identical to this transistor's bias resistance R1.

The β value, or current gain, of the transistors is a critical characteristic in ensuring that they function as intended in a circuit. If both transistors have the same β, it implies that they will respond to input signals in the same manner. Hence, the bias resistances used in the circuit must also be identical to ensure that base currents match and the transistors operate correctly. This uniformity helps in achieving balanced performance in the circuit design.

This scenario is similar to tuning two identical cars to perform equally. If both cars have the same engine capacity (β), tire pressure (resistances), and fuel type (current input), they will accelerate and handle the road similarly. Thus, understanding and matching these parameters is crucial for optimal performance.

We do have other information namely all the devices are having early voltage 100 V.

Early voltage is an important parameter that characterizes the output resistance of a transistor. In this context, the assumption that all devices have an Early voltage (V_EA) of 100V greatly simplifies the calculations involving the output current and voltage levels in the circuit. This uniformity aids in predicting the voltage gain and allows for more precise design of amplifiers and other circuits that depend on current mirrors.

You can think of Early voltage like the capacity limit of a water reservoir. If all reservoirs in a town have the same capacity (100 m), it makes planning the town's water supply much easier compared to if each reservoir had different capacities. This standardization helps in managing expectations and improving efficiency in water distribution, just as it does when dealing with transistors.

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