83.4. Small Signal Model Analysis

We need to understand the small signal model of current mirror and to go into the small signal model we do have two possible situations: one is the current mirror may not be carrying any signal namely under DC condition what is the small signal equivalent circuit and then we do have the second possible situation where the current mirror may carry signal in the form of current.

In electronic circuits, particularly when analyzing amplifiers, we often use small signal models to simplify calculations. The small signal model represents the behavior of the circuit under small variations around a DC operating point. There are two situations to consider: 1) When the circuit is in a DC state without any AC signals (i.e., it isn't amplifying any signal). In this case, we determine how the circuit behaves just based on the DC values. 2) When the circuit does have an input signal, which could be an AC current or voltage applied to the circuit. This results in a different analysis because we need to account for the variations due to the signal.

Think of a small signal model like analyzing the effect of a bump in a flat road. When the road is flat (DC condition), we can predict how a car moves smoothly on it. However, when there is a bump (AC signal), we have to analyze how the car reacts — the vibration, speed change, etc. just like the circuit reacts to the input signal.

We do have the current mirror circuit, we do have transistor-1; it is diode connected and the reference current DC current that is getting mirrored into this branch through this transistor-2 and here we do have the application circuit.

In a current mirror circuit using MOSFETs, one transistor is connected in such a way that it sets a reference current through it, which is then mirrored by another transistor that is used in the application circuit. This configuration allows us to produce a consistent current output, matching the input reference current under DC conditions. We need to analyze how small signals affect this configuration by replacing the heavy components in the circuit with simplified representations.

Imagine a perfectly balanced scale at a market. The first weight that sets the balance is like the reference current. The scale measures other weights (the mirrored current) against the reference weight. If you add a tiny weight (small signal) to one side, the balance shifts slightly, and we study how that affects the balance — that's similar to how we analyze small variations in electrical signals.

For small signal model this is DC current so; obviously, we have to make the current here it is since it is 0. So, we can say it is this circuit is open.

When analyzing a small signal model, if the DC current is at zero (or in a situation that has no input signal), we treat the input as an open circuit. This simplification means we disregard any AC signal effects and only focus on the DC components. Due to this simplification, we can conclude that some voltages in the circuit will also be zero, making it easier to derive the small signal equivalent circuit without the complexity of active components.

Think of it like a water line with no water flowing (representing the open circuit condition). If no water is flowing, you can ignore the connections and only visualize the pipes intact, making it easier to determine how it would behave if water were to flow at a later time.

Now, if we want to analyze a situation where the current mirror has an input current (AC signal), we need to consider how the signal interacts with this DC current.

In this case, when we introduce an AC signal current into the current mirror, we have to carefully analyze how this input affects the output through its interactions with the existing DC conditions. We represent these interactions with voltage-dependent current sources and resistance, creating an accurate representation of how signals affect the circuit's operation.

Imagine a conveyor belt in a factory where boxes (the signal) are added occasionally on top of a fixed weight of boxes already on it (the DC component). As the input changes, the force on the conveyor changes too, altering the overall behavior of how quickly the boxes move down the line. This is similar to how small signals influence the output in electrical circuits.

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