83.4.2.2. Small Signal Model Analysis for Transistor-2

To understand or to appreciate the effect of common current mirror in amplifier standard amplifier where, we normally talk about the linearize circuit whether it is common emitter or common source or common collector or common drain or for that matter even for differential amplifier.

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.

The small signal model helps us analyze how circuits respond to small fluctuations in input signals around their operating point. In this specific case, we are looking at the small signal model of a common current mirror used in amplifiers. There are two scenarios to consider: one where the current mirror is only dealing with a DC reference current, and another where it is dealing with a signal current. This distinction is crucial because it influences how we represent the circuit for analysis.

Think of a current mirror circuit as a fountain that usually flows a constant stream of water (DC current). If we want to see how it reacts to waves of water pushed by a pump (signal current), we need to analyze both the situation when there's just the fountain flow and when there are waves. This analysis helps us understand both the steady-state and dynamic responses of the fountain.

So, let me talk about the small signal model of current mirror implemented by MOSFET. Here we do have the current mirror circuit, we do have transistor-1 it is diode connected and the we do have reference current DC current that is getting mirrored into this branch through this transistor-2.

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.

In small signal analysis, we treat DC conditions as constant sources, effectively turning them into 'open circuits' for the purposes of small signal analysis. In a MOSFET current mirror, transistor-1 is often diode-connected, which means it is configured to always conduct. Now, while analyzing the small signal model, we essentially ignore the DC components to focus only on variations introduced by AC signals. This simplification allows us to predict how the circuit behaves when small fluctuations occur.

Imagine you are trying to measure the ripples on the surface of a calm lake (the small signals) while ignoring the sunlight reflecting off the water (the DC current). By covering your eyes from the sunlight, you can better see the ripples, which is analogous to ignoring the DC components in a circuit analysis.

So, we can say the small signal equivalent circuit whenever we do have a current mirror, then it will be very simple we do have the small signal equivalent circuit of the; small signal equivalent circuit equivalent of application and then we do have simply this resistance r and then of course, in this node it is connected to AC ground.

When we analyze the small signal equivalent circuit of a current mirror, we notice that the output primarily consists of a resistance r, representing how the circuit reacts to small changes in voltage. By grounding the AC components, it allows us to focus on how any small signal coming through is processed by the current mirror without interference from DC levels.

Think of it as tuning into a radio station where the background noise (DC) has been minimized so that you can clearly hear the music (AC signal). You only see how the circuit behaves to those variations, which is how we focus on the small signal aspects.

So, here we do have; here we do have the current mirror and again we do have a reference current is only DC, here we do have the application circuit or application module and we like to draw the small signal equivalent circuit here.

The small signal model for a BJT current mirror is similar to that of a MOSFET, albeit with different parameters due to the inherent characteristics of BJTs. We again treat the DC current as a reference point for analyzing the dynamics of AC signals. In this model, we take into account the internal resistances and configuration of the BJT, allowing us to derive how changes in input current affect output conditions.

Just like listening to how loud the music at a concert gets when the drummer plays harder, we observe the effect of input changes (AC signals) on our output, ignoring the steady hum of the crowd (DC reference current) going on in the background.

Situation when may arise when this reference current may have a signal part namely say i . In that case; obviously, this will; this will not be 0 and this may carry some signal to this voltage dependent current source.

When analyzing the small signal model in the presence of an input signal current i, the situation becomes more complex. Here, we must account for both the DC reference and the varying AC signal input. This means we cannot simply ignore the DC level, as it interacts with the fluctuating signal current. The relationship between the signal current and our small signal parameters becomes crucial for understanding how the circuit operates in real time.

Imagine a busy train station where a train is the steady flow of passengers (DC current), and loud announcements about train schedules are the signal currents. When the announcements are made, they impact the overall atmosphere, making it crucial to take them into account, just like the varying input current affects the circuit's behavior.

Now, we have covered this small signal equivalent circuit of current mirror for different cases namely if it if the current mirror is not having any signal current, then it is the equivalent circuit is very straightforward. Whereas, if the current mirror it is having input current then of course, that current it is coming to the application circuit.

After analyzing the small signal equivalent circuits for both scenarios—no signal current versus with signal current—we can see how current mirrors can be used effectively in amplifiers. If the mirror is under steady DC operation, its function is simpler. However, when signal currents are introduced, the analysis reveals how those currents affect overall amplifier performance. This understanding aids in designing circuits that can handle dynamic inputs.

Think of your silverware drawer. When everything is tidy (DC operation), you know where everything is. When you start preparing a meal (introducing signal currents) and take things in and out, you need to rely on your understanding of the drawer's layout to keep things organized and functional, similar to how a current mirror manages different input types.

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