Diode Models and Bipolar Models

Introduction

Diode models and bipolar models play a crucial role in CMOS design. These models help in understanding the behavior and characteristics of diodes and bipolar transistors, which are essential components in integrated circuits. In this topic, we will explore the fundamentals of diode models and bipolar models and their significance in CMOS design.

Diode Models

Diode models are mathematical representations of the behavior of diodes. They help in analyzing and designing circuits that include diodes. There are several diode models, each with its own level of complexity and accuracy.

Ideal Diode Model

The ideal diode model is the simplest diode model. It assumes that the diode behaves like a perfect switch, allowing current to flow in one direction and blocking it in the other direction. The ideal diode model has the following characteristics and assumptions:

• The diode has zero resistance when forward biased and infinite resistance when reverse biased.
• The diode has zero voltage drop when forward biased and infinite voltage drop when reverse biased.

The equation and graphical representation of the ideal diode model are as follows:

I = Is * (e^(V/Vt) - 1)

Piecewise Linear Diode Model

The piecewise linear diode model is a more accurate representation of the diode behavior compared to the ideal diode model. It takes into account the voltage drop across the diode when it is forward biased. The piecewise linear diode model has the following characteristics and assumptions:

• The diode has a constant voltage drop (Vd) when forward biased.
• The diode has zero resistance when forward biased and infinite resistance when reverse biased.

The equation and graphical representation of the piecewise linear diode model are as follows:

I = Is * (e^(V/Vt) - 1) - (V/Vd)

Level 1 Diode Model

The level 1 diode model is a more accurate representation of the diode behavior compared to the piecewise linear diode model. It takes into account the reverse saturation current (Is) and the junction capacitance (Cj) of the diode. The level 1 diode model has the following characteristics and assumptions:

• The diode has a constant voltage drop (Vd) when forward biased.
• The diode has a reverse saturation current (Is) that is independent of the voltage across the diode.
• The diode has a junction capacitance (Cj) that is independent of the voltage across the diode.

The equation and graphical representation of the level 1 diode model are as follows:

I = Is * (e^(V/Vt) - 1) - (V/Vd) + (Cj * dV/dt)

Level 2 Diode Model

The level 2 diode model is an enhanced version of the level 1 diode model. It takes into account the junction capacitance modulation (Cjsw) and the junction sidewall capacitance (Cjsw) of the diode. The level 2 diode model has the following characteristics and assumptions:

• The diode has a constant voltage drop (Vd) when forward biased.
• The diode has a reverse saturation current (Is) that is dependent on the voltage across the diode.
• The diode has a junction capacitance (Cj) that is dependent on the voltage across the diode.
• The diode has a junction capacitance modulation (Cjsw) and a junction sidewall capacitance (Cjsw) that are dependent on the voltage across the diode.

The equation and graphical representation of the level 2 diode model are as follows:

I = Is * (e^(V/Vt) - 1) - (V/Vd) + (Cj * dV/dt) + (Cjsw * dVsw/dt) + (Cjsw * dVsw/dt)

Level 3 Diode Model

The level 3 diode model is the most accurate diode model. It takes into account additional parameters such as the series resistance (Rs) and the junction temperature (Tj) of the diode. The level 3 diode model has the following characteristics and assumptions:

• The diode has a constant voltage drop (Vd) when forward biased.
• The diode has a reverse saturation current (Is) that is dependent on the voltage across the diode and the junction temperature (Tj).
• The diode has a junction capacitance (Cj) that is dependent on the voltage across the diode and the junction temperature (Tj).
• The diode has a junction capacitance modulation (Cjsw) and a junction sidewall capacitance (Cjsw) that are dependent on the voltage across the diode and the junction temperature (Tj).
• The diode has a series resistance (Rs) that is independent of the voltage across the diode and the junction temperature (Tj).

The equation and graphical representation of the level 3 diode model are as follows:

I = Is * (e^(V/Vt) - 1) - (V/Vd) + (Cj * dV/dt) + (Cjsw * dVsw/dt) + (Cjsw * dVsw/dt) - (Rs * I)

Step-by-step Walkthrough of Diode Model Problems and Solutions

To understand the application of diode models, let's walk through a step-by-step example problem and its solution.

1. Problem:

Given a diode with a forward voltage drop of 0.7V and a reverse saturation current of 10^-12 A, calculate the current flowing through the diode when it is forward biased with a voltage of 0.8V.

Solution:

Using the ideal diode model equation:

I = Is * (e^(V/Vt) - 1)

Substituting the given values:

I = 10^-12 * (e^(0.8/0.025) - 1)

Calculating the current:

I = 10^-12 * (e^32 - 1)

I ≈ 1.27 mA

Bipolar Models

Bipolar models are mathematical representations of the behavior of bipolar transistors. They help in analyzing and designing circuits that include bipolar transistors. There are several bipolar models, each with its own level of complexity and accuracy.

Ebers-Moll Model

The Ebers-Moll model is the most commonly used bipolar model. It is a two-port network model that describes the behavior of both NPN and PNP bipolar transistors. The Ebers-Moll model has the following characteristics and assumptions:

• The transistor has two junctions: the base-emitter junction and the base-collector junction.
• The base-emitter junction behaves like a forward-biased diode, and the base-collector junction behaves like a reverse-biased diode.
• The transistor has four parameters: the forward current gain (β), the reverse current gain (α), the base-emitter voltage (Vbe), and the base-collector voltage (Vbc).

The equations and graphical representations of the Ebers-Moll model are complex and beyond the scope of this topic. However, it is important to understand the significance of the Ebers-Moll model in bipolar transistor analysis and design.

Summary

Diode models and bipolar models are mathematical representations of the behavior of diodes and bipolar transistors, respectively. Diode models include the ideal diode model, piecewise linear diode model, level 1 diode model, level 2 diode model, and level 3 diode model. Bipolar models include the Ebers-Moll model. The ideal diode model is the simplest diode model, assuming the diode behaves like a perfect switch. The piecewise linear diode model takes into account the voltage drop across the diode when it is forward biased. The level 1 diode model considers the reverse saturation current and the junction capacitance of the diode. The level 2 diode model includes additional parameters such as junction capacitance modulation and junction sidewall capacitance. The level 3 diode model is the most accurate, considering parameters like series resistance and junction temperature. The Ebers-Moll model is a two-port network model that describes the behavior of bipolar transistors. It considers the base-emitter junction, base-collector junction, forward current gain, reverse current gain, base-emitter voltage, and base-collector voltage. Diode models and bipolar models are essential in analyzing and designing circuits that include diodes and bipolar transistors, respectively.

Analogy

Imagine a diode as a one-way valve that allows water to flow in one direction but blocks it in the other direction. The different diode models can be compared to different types of valves with varying levels of accuracy and complexity.