86.5. Current Mirror Constructed by BJTs

Now, in this example, we do have Q1 and Q2, now it is forming the current mirror and in this case, just for a change, instead of giving a reference current, we are giving a resistor here. Supply voltage is given to us as 12 V. This RRESISTOR in resistance it is 22.8 kΩ and then we can assume that VBE voltage for both the transistors is approximately 0.6 V.

In this segment, we are discussing a current mirror circuit created using BJTs (Bipolar Junction Transistors). Here, the current mirror consists of two transistors, Q1 and Q2. Instead of utilizing a direct reference current, a resistor is implemented in the circuit, which indicates a different approach to creating the current mirror. The supply voltage for this circuit is specified as 12V, and there’s a specified resistor value of 22.8 kΩ, which will contribute to the reference current through Ohm's Law. The VBE, or base-emitter voltage for both transistors, is approximated to 0.6V, a typical value for silicon BJTs in active mode.

Think of the current mirror circuit like a team of rowers in a boat where one rower (the reference current through the resistor) sets the pace. The other rowers (the transistors Q1 and Q2) must replicate this effort to keep the boat moving smoothly. While the first rower determines how fast they should go, the resistor acts like an external source, determining speed and making sure the rowers work uniformly using the provided power from the battery.

To get the Ireference current, we need to find what will be the IREF = (VBIAS - VBE) / RBIAS = (12V - 0.6V) / 22.8kΩ = 0.5 mA.

To determine the reference current in a current mirror circuit involving BJTs, you can use the formula IREF = (VBIAS - VBE) / RBIAS. Substituting known values, we first calculate how much voltage is available for current flow after subtracting the base-emitter voltage (0.6V). With a total supply voltage (12V) after subtracting the VBE, we get 11.4V. Dividing this voltage by the resistance (22.8kΩ) gives us a reference current of approximately 0.5mA, which is critical for setting the performance of the current mirror.

Imagine a water pipe system: the supply voltage is like the water pressure available in the tank, while the resistor functions as a valve that controls how much water (current) flows out. By knowing the pressure and how much the valve restricts the flow, you can calculate exactly how much water exits the pipe—just like calculating the reference current in the current mirror circuit.

Now, if I consider a simple situation, considering that both the β’s are very high, early voltages are also very high which means that non-ideality factor we can assume is ≈ 1.

In a basic analysis of the current mirror made from BJTs, we often assume that both the current gain factors (β) of the transistors are significantly high. This represents an ideal scenario where the influence of the base current loss is negligible, thus allowing us to approximate the non-ideality factor as close to 1. This set of assumptions simplifies our calculations and models while providing a baseline understanding of how accurately the current mirror performs under ideal circumstances.

Consider a well-oiled machine: when all parts work flawlessly together—like the high β in BJTs—the machine runs at peak efficiency, with minimal energy loss. Just as a perfectly functioning machine operates without noticeable issues, when we assume ideal conditions for the transistors, we simplify our problem-solving process to focus purely on the main function of the current mirror.

So that gives us the output current = 1.5 mA based on the assumption of high β.

Based on the ideal conditions and computations discussed in the previous sections, we can calculate the output current of the current mirror as 1.5 mA. This current reflects how Q2 replicates the input current defined by Q1 when conditions are optimal. This relationship illustrates how current mirrors are used in analog circuits to create predictable and stable currents that can drive other circuit components or load structures accurately.

Picture a multi-singer choir: if the lead singer sings at a consistent volume, the other singers (Q2, in this analogy) are trained to match that volume for harmony. Here, the output current equates to the collective harmony; similarly, the current mirror permits a precise 'copying' of input current under ideal conditions, ensuring all parts of the circuit work together smoothly.

Now, if we consider the effect of β namely, the current loss due to whatever the currents flowing here. So this means that this is no more = 1, and to get this non-ideality factor you may recall that this part...

When realistic conditions are applied, the ideal performance conditions start to fade. The β factor of each transistor affects how much current is lost in the form of base currents, implying our initial assumption of the non-ideality factor being equal to one is no longer valid. By considering finite β values, we influence how accurately the output current reflects the reference current. Discussions on Early voltage also illustrate that variations in the characteristics of BJTs can lead to discrepancies in current output.

Imagine driving a vehicle up a steep hill. On a flat road, you need minimal effort to maintain speed (ideal conditions). Yet, as the incline increases, you expend more energy to keep pace, analogous to how non-ideal conditions (finite β) affect functionality and output in the current mirror circuit. Scaling up becomes inherently more challenging as conditions deviate from ideal.

To calculate this current we need to multiply by this non-ideality factor of 1.03. In fact, if you calculate what we are getting here it is 1.456 mA.

With the introduction of non-ideality factors, we revise our previous current calculation to reflect losses incurred via base current draw and deviations from ideal behavior. By applying the calculated non-ideality factors, we find the actual output current reduces to 1.456 mA, illustrating how real-world applications need these considerations for accurate function in circuits.

Think of preparing a recipe: while the ingredients may call for exact measurements, using slightly less or more due to human error can affect the final dish. The non-ideality factor serves a similar role in circuit design; it adjusts our calculations to reflect real outputs rather than sticking strictly to theoretical ideals, thereby fostering a practical understanding.

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