21.6.5. Output Conductance

Now, if we consider that, what we will be getting is that of course, this I is dependent through this ( ) part, we may get a drain to source one conducting element. And, that conducting element is nothing, but the output conductance or drain conductance.

Output conductance, denoted as g_d, describes how the output current (I_ds) of a device like a MOSFET changes in relation to the output voltage (V_ds). In simpler terms, it quantifies how much current flows from drain to source when the voltage changes. This is crucial for analyzing how well a MOSFET performs in a circuit, as a higher output conductance means that the current can change more with small changes in voltage.

Think of output conductance like the responsiveness of a water tap. If you twist the tap slightly and a lot of water flows out, it has high responsiveness (akin to high output conductance). If only a little water flows out with the same twist, it is less responsive (akin to low output conductance).

So, it is definition is; so, again here it is partial derivative of I , but with respect to V .

The output conductance (g_d) is mathematically defined as the partial derivative of the drain-source current (I_ds) with respect to the drain-source voltage (V_ds). This means we look at how much I_ds changes for a small change in V_ds, giving us an indication of the output's behavior. Essentially, g_d = ∂I_ds / ∂V_ds. This precise definition allows engineers to predict circuit performance accurately and makes it easier to design circuits using MOSFETs.

Imagine you are measuring how your car's speed changes when you press the accelerator pedal. If pressing it a little makes the car speed up a lot, the car is very responsive (akin to high output conductance) versus if the car hardly speeds up even with a full press, it shows low responsiveness (akin to low output conductance).

So, we are going to discuss the expression of g_d. And, that we are getting from this definition and this I it is having an expression, it is ( ).

The expression for output conductance (g_d) is derived from the characteristic equations of the MOSFET. By taking the derivative of I_ds (the drain current) with respect to V_ds (the drain-source voltage), we can derive an expression for g_d that reflects how the device operates under varying conditions. This typically involves parameters like the current flowing through the device and the output voltage. Keep in mind, g_d can vary based on the specific conditions of the circuit, such as the operating point.

Think of this process like calibrating a scale. When you adjust the weight slightly, the scale shows a new number. The way that number changes with each added weight helps you understand how precise the scale is; similarly, the output conductance helps us understand how the MOSFET behaves as voltage changes.

So, that is the expression of the output conductance drain conductance λ × I , again here also you can see that it directly depends on the operating point.

The output conductance (g_d) can be expressed as λ multiplied by I_ds. Here, λ represents the channel length modulation parameter, showing how output current can be affected by voltage at the drain terminal. This means the g_d becomes a crucial aspect for designers, particularly as it relates to the operating point of the device, which refers to the specific conditions (like voltage and current) under which the MOSFET is functioning. The operating point will significantly influence the performance and the overall gain of the circuit.

Consider a staircase: the more steps you go up (higher voltage), the more effort (current) is required to keep climbing. If you try to sprint (representing more current), how steep or flat (operating point) the stairs are will affect how quickly you can move upward (output conductance).

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