87.1.4. Lecture - 87

So dear students welcome back after the break. So, before the break we are talking about the numerical examples of the current mirror. As you can see here, and there we have used Beta-helper to improve the non-ideality factor coming due to the base current loss namely, this base current loss. So in the next example, what we will see that improvisation of the numeric current mirror circuit to take care of the non-ideality factor due to early voltage.

In this section, the instructor welcomes the students back and summarizes the previous discussion about current mirrors and the challenges associated with them, specifically focusing on the non-ideality factors. One such factor is the 'base current loss' in transistors. The upcoming example will illustrate how to improve current mirror circuits by addressing another non-ideality factor known as 'early voltage' by adding a cascode transistor.

Think of a current mirror as a lamp that imitates another lamp's brightness. The base current loss is like a dimming effect due to an obstruction that makes one lamp appear less bright. By optimizing the circuit, we can ensure both lamps shine with even brightness, similar to fixing the obstruction.

To be more precise, we like to place one cascode transistor here and that improves the output resistance of the current mirror.

The instructor explains that adding a cascode transistor to the current mirror configuration enhances its performance by increasing the output resistance. This is essential in maintaining a stable current output despite fluctuations in voltage, ensuring consistent performance in various conditions.

Imagine using a multi-tiered stand to display different sizes of fruits. Each tier is like a transistor: the stand gives better visibility and stability to the fruits, akin to how the cascode transistor boosts output resistance, providing a more stable current in the circuit.

Now coming to the different sizes of different transistors given here, we do have for transistor-1, we do have the it is 1 mA/V2. On the other hand for transistor-2 and transistor-3, we do have = 4 mA/V2.

The instructor introduces the specifications of three transistors used in the current mirror example. The transconductance (K) values for these transistors indicate their ability to control current flow: transistor-1 has a standard K value, while the other two are designed to have higher values, enhancing their current handling capabilities. Keeping other operational parameters the same allows for easier calculations.

Think of K value as the horsepower of an engine. Different engines (transistors) have different horsepower ratings, which affect how powerfully they can propel a car (current). By adjusting the horsepower, we can improve stability and efficiency in driving.

So to calculate that, in some of our previous examples we have done that this current which is I , it is also creating a drop here and after subtracting this drop, say from 12 V supply, it is giving us the V .

This section details the calculation process for determining the gate voltage. The instructor highlights that the current through the circuit creates a voltage drop affecting the available voltage at the gate of the transistor. Hence, to find the gate voltage (VGS), one must subtract the drop due to the current from the total supply voltage.

Consider a water tank. The water level at the tap (gate voltage) depends on how much water is flowing out (current) and the initial height of the tank (supply voltage). If too much water flows out, the tap will be low, similar to how the voltage drop affects the gate voltage.

So we need to find what will be the small signal output resistance. And R is g m3 r + r .

Here, the small-signal output resistance of the current mirror is expressed using the transconductance (g) and output resistances (r) of the transistors. This form of resistance is crucial in understanding the output behavior of the circuit under small signal conditions. The combination of these resistances helps ensure the current mirror provides stable operation across a range of output voltages.

Think of a flexible bridge (output resistance) that can support various weights. The sturdiness of each supporting column (g and r values) determines how much weight the bridge can safely hold when cars drive over it (small signals) without collapsing.

So, the corresponding current here at this point it is 2 mA + 3 × 10‒7 A. So, we can say that this current = 2.0003 mA.

The instructor calculates how the current flowing through the circuit changes due to the output resistance when the voltage is altered from 5 V to 8 V. The main current is 2 mA, but because of the high output resistance, only a tiny additional current influences the total current flowing through the branch, showing the circuit's stability despite changes in voltage.

Picture a large river (2 mA) flowing steadily, and then a small stream (3 × 10‒7 A) entering it. The overall flow increases, but the river's strong current means that the small stream's effect is barely noticeable, demonstrating stability even when slightly altered.

But then it is little inconvenient to get this voltage and to overcome this problem, what we can do we can put a transistor here which is also diode connected and that produces a voltage and that is normally that is what it is getting applied.

The instructor offers a solution to the inconvenient voltage measurement by suggesting adding a diode-connected transistor to the circuit. This transistor will assist in generating a necessary voltage internally, reducing reliance on external measurements and simplifying the design.

Imagine adding a water pump (diode-connected transistor) to a natural spring (circuit), which automatically keeps the water level consistent no matter the changes in the environment (output voltage) instead of needing constant manual checks.

So that is how we can make the output current very less sensitive to the voltage for improved current mirror or which is referred as cascode commonly known as cascode current mirror.

The instructor concludes this section by summarizing the improvements made to the current mirror design through the addition of the cascode configuration. This design effectively stabilizes the output current against voltage variations, thereby enhancing performance and reliability.

Think of the cascode current mirror as a highway overpass. While the surface street may be affected by traffic lights (voltage changes), the overpass allows for a continuous flow of cars (current) without interruption, maintaining smooth operation regardless of obstructions below.

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