# Why do textbooks use the square-law model to design amplifiers?

Status
Not open for further replies.

#### CHL

##### Member level 3 Hello

0.18u CMOS process, or even smaller than that, was developed in 20th century.

However, textbooks have used the square-law model to design amplifiers until now.

for basic microelectronics, it is understandable, but even books for graduate students use the square-law model.

What is the reason?

Are there any books considering short channel effect and narrow width effect when they design amplifiers?

#### ljp2706 The analysis is more complicated when you introduce terms such as velocity saturation and channel length modulation. The reason why they would use the ideal square law is to arrive at a conclusion that make sense...it's a lot easier to deduce something from a simpler equation. For example using the basic equation it's very easy to see that overdrive voltage has an impact on the ICMR of a differential amplifier.

By the way, even with introducing velocity saturation and channel length modulation, the square law equation is fundamentally flawed as it grossly underestimates depletion charge(due to linearizing the depletion charge and assuming a slope of unity), meaning that it overestimates inversion charge and by that it overestimates drain current.

• CHL

### CHL

Points: 2

#### CHL

##### Member level 3 The analysis is more complicated when you introduce terms such as velocity saturation and channel length modulation. The reason why they would use the ideal square law is to arrive at a conclusion that make sense...it's a lot easier to deduce something from a simpler equation. For example using the basic equation it's very easy to see that overdrive voltage has an impact on the ICMR of a differential amplifier.

By the way, even with introducing velocity saturation and channel length modulation, the square law equation is fundamentally flawed as it grossly underestimates depletion charge(due to linearizing the depletion charge and assuming a slope of unity), meaning that it overestimates inversion charge and by that it overestimates drain current.

Mm.. However, if we use a short-channel device, all the calculations with the square law may be wrong.

so I wonder why the authors use the old model even in the advanced courses although it is not practical in new technologies.

#### dick_freebird Textbooks are meant to lead you to an ability to analyze and
understand the complex, by way of tractable simple examples.
Giving you too big a spoon just makes a mess.

But also, textbooks by the nature of the process always lag
the state of the art. Especially if your professor writing it wears
elbow patches on their tweed jacket. In the 21st century.

• CHL

Points: 2