86.3. Simple Current Mirror Constructed by MOSFET

So, let me start with the calculation of V or for I = 0.5 mA so, that is the I = its corresponding K which is 1 mA/V2 by 2 × ( ).

This part introduces the concept of a simple current mirror constructed using MOSFETs. The current mirror is a basic circuit that allows a current to be copied from one branch to another while maintaining the same characteristics. Here, we are focusing on the calculation of the output voltage (V) and how it relates to the reference current (I) of 0.5 mA, which is an essential starting point for understanding how current mirrors operate.

Think of a current mirror like a water fountain where water flows from one container to another. No matter how wide the container at the output is, as long as the inlet (reference current) stays the same, the flow (output current) will replicate what’s needed to maintain balance.

So note that for this calculation, we are ignoring ( ). Even if the λ is given, we normally ignore that.

In this segment, we discuss the calculation of output current (I_DS2) based on the reference current (I_REF) and the transconductance parameters (K values) of the transistors involved. By applying the principle of proportional scaling, we can find that the output current flows based on the ratio of their K values. Ignoring any effects due to channel length modulation (λ) simplifies the calculations and highlights how current mirrors function under ideal conditions.

Imagine two cooks in a kitchen, one is preparing a meal (I_REF) while the other is copying their technique (I_DS2). As long as the first cook uses the same amount of ingredients (representing the K values), the second cook will yield the same meal size. The minute details (like λ) can be ignored for this high-level overview.

So, to keep this transistor in saturation, we know that the drain voltage it should be higher than the gate voltage minus V_th.

Here we discuss the necessity of setting the drain-source voltage for transistor-2 sufficiently high to ensure that it remains in saturation. A transistor operates effectively in this region for linear amplification and current mirroring purposes. The equation V_D > V_GS - V_th outlines the conditions needed for the output transistor to function correctly within the circuit.

Think of the transistor as a light switch for your room. If there’s not enough voltage at the switch (V_GS), the light (output current) won’t turn on. It’s essential to have a certain minimum voltage to ensure that everything operates as expected.

In fact, it is a continuation of this example, but we are considering λ = 0.01 V‒1.

This chunk deals with the effects of transitioning from an ideal scenario (ignoring λ) to a more realistic one where channel length modulation (λ) comes into play. Now, with a finite value of λ, we can perform calculations to assess how this factor influences the output current. At this point, we derive expressions that show how I_DS2 changes with varying drain-source voltages, demonstrating the importance of considering non-ideal behaviors in practical circuit design.

Imagine baking a cake and adjusting the oven temperature. If you follow the recipe exactly (ideal), your cake turns out perfectly every time. However, if your oven has inconsistencies (like finite λ), you must account for those variations to achieve the same delicious result, showing just how critical those adjustments can be for achieving reliable outcomes.

So, to calculate the small signal output resistance what we can see here it is we can get the calculate the slope of this line and reciprocal of that is the small signal output resistance.

We conclude with a discussion on calculating the small signal output resistance of the current mirror. By observing the relationship between changes in output voltage and current, we can determine the slope of this line, which, when taken reciprocally, gives us the small signal output resistance (R_out). This parameter is key in determining the performance and stability of the current mirror under varying load conditions.

Consider a water hose where you can control the flow at different points. By adjusting the nozzle (output voltage) and measuring how much water comes out (output current), you can understand the resistance in the system. The smoother the flow with adjustments (high R_out), the better your current mirror performs.

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