87.1.5. Numerical Examples on Current Mirror and its Applications (Part-B)

So, dear students welcome back after the break. Before the break we were talking about the numerical examples of the current mirror.

In this section, we reintroduce the topic of current mirrors, which are fundamental components in analog electronics. A current mirror is used to copy (or 'mirror') a current from one branch of a circuit to another, maintaining the same current value. This ability is crucial for biasing transistors in various configurations, ensuring stability and accuracy in circuit operation.

Think of a current mirror like a series of identical twin siblings, where one twin ('the reference') is set to a specific height (current), and the other twin ('the output') tries to match that height exactly, regardless of changes in their environment.

We have used Beta-helper to improve the non-ideality factor coming due to the base current loss namely, this base current loss.

In current mirrors, base current loss can lead to inaccuracies due to the finite base currents in bipolar junction transistors (BJT). Beta-helper is a technique involving additional components that help offset these losses, ensuring that the current mirror operates more ideally and closely matches the desired reference current.

Imagine trying to fill a water tank (the current) while some water leaks through a small crack (the base current loss). Adding a drainage system (Beta-helper) helps to prevent the loss and keeps the tank full, ensuring we achieve the desired water level.

We like to place one cascode transistor here and that improves the output resistance of the current mirror.

The introduction of a cascode transistor in a current mirror configuration is a common technique to enhance the output resistance. By stacking transistors, the effective output impedance increases significantly, which leads to better performance of the current mirror under varying load conditions. This ensures that the mirrored current remains stable even as output voltage changes.

Think of the cascode transistor as an additional layer of insulation in a thermos. The first layer keeps your drink hot, while the second layer keeps it even hotter for longer, improving overall heat retention regardless of the temperature outside.

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 section discusses the importance of transistor sizing and parameters in the current mirror. Different transistors in a current mirror can have different transconductance values (1 mA/V² for transistor-1 and 4 mA/V² for transistors-2 and -3). This difference influences the current that flows through each transistor, which is critical for ensuring that the current mirror functions correctly.

This is like having different sizes of water pipes. A small pipe (transistor-1) can only carry a limited amount of water, while a larger pipe (transistors-2 and -3) can carry much more. The size of each pipe impacts the overall flow of water in the system.

To calculate that, we use V = V ‒ I × R.

To determine the gate-source voltage for the transistors, we refer to the relationship defined as V = Vₒ - I × R, where Vₒ is the voltage supply, I is the current through the bias resistor, and R is the resistor value. This equation helps to compute the necessary voltage to ensure that transistors operate in the saturation region.

Imagine you’re measuring how much rainwater is collected in a barrel after a storm (Vₒ). If some of that rainwater flows out through a hose (current I), the remaining water level in the barrel (V) depends on how strongly water is flowing out (R, the resistance).

From this we can obtain V with value calculations leading to I = 0.5 mA.

After substituting the known values into the equations, we can derive the gate-source voltage (VGS) and determine the current flowing through each transistor. For example, a computed current of 0.5 mA indicates how much current is accurately mirrored by the circuit, which is a critical aspect for maintaining performance in practical applications.

It's akin to determining how much electricity flows through a power line based on the voltage and resistance. Once you know these factors, you can calculate exactly how much energy reaches your home (mirrored current).

Next thing is that for V, if it is say 5 V then what do you expect? Here we do have 2.5 So, V...

In this part, we calculate the small-signal output resistance of the current mirror circuit. By analyzing the circuit parameters and operational conditions, we can determine that the output resistance is essential for improving the current mirror’s performance. A higher output resistance implies that the circuit can better maintain a constant current across varying load conditions.

This is similar to a shopkeeper adjusting prices based on sales demand. By keeping prices steady, even if more customers start buying (changing voltage), the shopkeeper ensures that profits remain consistent (constant current).

We can use the information of the current at 5 V...

This section illustrates how current flow through the branches of a current mirror changes when the voltage supply is altered. Specifically, the analysis shows how small changes in output voltage can result in tiny variations in current flow, reinforcing the importance of a high output resistance to minimize such fluctuations.

Just like how a heavy-duty tire performs better and maintains balance over rough terrains, a current mirror with enhanced output resistance ensures that minor variations don’t create significant disruptions in current flow, leading to a more reliable circuit operation.

So, this is again it is called the cascode current mirror...

The current mirror is wrapped up by summarizing the advantages of the cascode design. This configuration not only improves the output resistance but also prevents variations in output current, ensuring that the circuit performs accurately even under different load conditions.

Imagine a tightrope walker (the current) balancing with a long staff (the cascode configuration) that helps them navigate more smoothly and stay upright despite the swaying wind (output voltage variations).

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