17.6.2. Transconductance and Gain

Now, this slope of this line namely that gives us the gain; that means, if I vary this input by some amount how much the corresponding effect will be observing at the output that gives us the gain.

In electronic circuits, gain refers to the ratio of output to input. In simpler terms, if you change the input by a small amount, the gain tells you how much the output will change as a result. The slope of the input-output characteristic curve represents this idea: if you have a greater slope, even a small change in input will produce a larger change in output, indicating higher gain.

Think of gain like the volume control on a speaker. If you turn the dial a little bit, the volume increases significantly if the gain is high. Conversely, if the gain is low, it takes a larger turn of the dial to notice a change in sound. This illustrates how small changes in input can lead to large changes in output, depending on the gain of the system.

And, as we have discussed for BJT circuit here this gain it is it primarily depends on the slope of this line. So, you can think of it as a mirror.

Transconductance is a key parameter in amplifiers, particularly those involving MOSFETs and BJTs. It measures how effectively a voltage change at the input results in a current change at the output. Think of transconductance (denoted as gm) as a ‘mirror’ that reflects the changes in input to the output: a higher transconductance means a more responsive amplification with smaller input changes leading to larger output changes.

Consider a dimmer switch for your home lighting. When you slowly turn the knob (input change), the lights get brighter much more intensely if the switch is very responsive (high transconductance). This reflects how effective the circuit is in converting input voltage changes into output current changes.

So, if I consider slope of this line and then inverse slope of this line that gives us the voltage gain here. So, the gain here it becomes actually g × R with of course a ‒ sign.

In practical circuits, the voltage gain can be calculated by multiplying the transconductance (gm) by the load resistance (R). The negative sign indicates that an increase in input voltage typically results in a decrease in output voltage, characteristic of inverting amplifiers. Thus, when designing circuits, it’s essential to pay attention to both gm and R to achieve the desired amplification.

Picture a seesaw at a park. The transconductance is like the effort you put in at one end to lift the other end (which represents the load resistance). The better your input force is distributed (higher gm), the more the other side lifts (output voltage), but often in the opposite direction (the negative gain).

So, for different values of V if I observe the corresponding V what we can get it is input versus rather input to output transfer characteristic.

The input-output transfer characteristics describe how outputs respond to various inputs in a circuit. By plotting this relationship, we can visualize how output changes when different inputs are applied, which is fundamental in analyzing amplifier performance. It shows that for certain ranges of input voltage, outputs will change linearly, while outside those ranges, the response may become non-linear.

Imagine you are in a car. If you gently press the accelerator (input), the car speeds up smoothly (output). However, if you floor it suddenly, the car may react unpredictably (non-linear response). The transfer characteristics help us understand and predict the behavior of our circuit just like how car performance can be analyzed based on how you apply the accelerator.

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