83.3.2. Small Signal Model of Current Mirror

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

The purpose of studying the small signal model of a current mirror is to determine how it affects amplifier circuits. Depending on the specific type of amplifier (common emitter, common source, etc.), the small signal model can help us understand how the current mirror will respond to small variations in the input signal. This models the behavior under small perturbations around a DC operating point, allowing us to predict amplifier performance.

Imagine tuning a musical instrument: your adjustments based on how the instrument sounds represent the small signals. Similarly, the small signal model fine-tunes how we understand the current mirror’s behavior in amplifiers, ensuring that we achieve the smoothest and most expected performance.

We need to understand the small signal model of current mirror under DC condition. 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 the first case, when there is no AC signal (only DC), the small signal model becomes simpler. All signals are treated as zero, and the small signal equivalent circuit behaves like an open circuit because the DC current is constant and does not vary. This means that any change in input signal does not influence the behavior of the current mirror under these DC conditions.

Think about a water faucet that has been turned off. No matter how much you adjust the faucet knobs (signal changes), no water flows (current). This is similar to the way the current mirror behaves under DC conditions—it doesn’t change until you open the faucet again (introducing an AC signal).

When discussing the small signal model of current mirror implemented by MOSFET, we do have the small signal model for transistor-1, it is having g m v gs1 voltage dependent current flow.

For a MOSFET-based current mirror, we analyze small signals by focusing on the transconductance parameter (g_m), which shows how changes in gate voltage (v_gs) affect drain current. This relationship allows us to define a more dynamic model that includes changes in both current and voltage. The small signal equivalent model takes into account how the signal influences the current mirror's output.

Consider a volume knob on a stereo. Adjusting the knob changes the sound output dynamically. The g_m in our equation is like this knob—small changes in the input voltage (volume adjustment) result in proportionally larger changes in the output (sound volume).

Situation when the current mirror may have a signal part namely say i_in, it is also having signal current i_in. So this signal current it is again it is coming from either DC you are whatever it is, but finally, at the collect the drain node of the MOSFET it is arriving and it may be producing a voltage here.

In situations where the current mirror carries a signal current, we need to modify our analysis. The presence of AC signals alters the behavior of the circuit, introducing variables dependent on this signal current. It allows us to utilize the relationship between the input signal current and the output voltage generated by the current mirror, yielding a much richer model that reflects real-world usage.

Think of a busy restaurant where the waiter takes orders (the AC signal) that change frequently. The kitchen (current mirror) needs to adapt and respond to each order quickly, just like the current mirror adapts to changes in signal current. Just as the waiter keeps track of orders, we must track how signal currents affect our circuit performance.

Here we do have the small signal equivalent circuit of the application module. So, this is small signal equivalent circuit of the application module and then only r is there.

Just like the MOSFET analysis, we can also model current mirrors using BJTs. The BJT small signal model incorporates additional elements such as base-emitter resistance and transconductance similar to what we discussed for MOSFETs. Despite the differences in device behavior, the analytical approach follows the same logic of evaluating small signal changes.

Consider a performance by an orchestra where two different conductors are leading different sections (BJT and MOSFET). While each conductor has a distinct style (device behavior), the overall music produced depends on their ability to adapt to the orchestra's performance (small signal response). Both lead their sections in a responsive manner similar to how BJTs and MOSFETs adjust to small signals.

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