## Introduction

Amplifiers, one of the indispensable parts of analog electronics, are circuits that enable low power/amplitude analog input signal to come out of the output in an amplified state. In these circuits, the gain is shown as Av and defined as Av = Vout/Vin.

Common Source (CS) Amplifier circuits can be designed relatively easier and smaller than other amplifier circuits, both in terms of size and design. What we need for this design is 1 MOSFET transistor and 1 load element (resistor, current source etc.). CS Amp. The main feature of the circuits is that the input signal comes out of the gate leg and the output signal comes out of the drain leg, and also that the MOSFET works precisely in the saturation region. Below you can see various CS Amplifier examples.

CS Amp. circuits have a phase shift of 180 degrees as shown below.

The most important method used when analyzing such amplifier designs is the method called “small signal analysis”. In this model, all DC current sources on the circuit are open circuit, and all DC voltage sources are short circuited, and the analysis is made with the remaining AC sources and passive components. So how is this conversion done?

## Small Signal Model

This model is one of the primary methods used to analyze the behavior of the circuit. If we want to draw this model step by step, the steps we will follow are as follows.

- Making all DC current sources open circuit (Not available in this example).
- Short circuiting all DC voltage sources (VDD and Vin,DC).
- Turning the Gate-Source into an open circuit (V1) due to the fact that the MOSFET does not pass current due to its nature.
- Adding the resistor ro formed by the channel (channel) of the MOSFET.
- Addition of current source gmV1, which is the current generated by Vin,AC.
- Adding other passive components (resistor, capacitance, etc.)

If an extra gate (gate) resistor or source (source) resistor or a load capacity is added to the output in our normal circuit, these components should be added to the small signal model in the same way and the analysis should be done from the beginning.

## Example Design

### Analysis

Let’s set some specifications and parameters for our sample design as follows (These constant values can be found in any analog design book).

When current-voltage analysis is performed on the small signal model, the relationship between Vout and Vin is found as follows:

In order to reach the gain value, we first need to find the gm (transconductance) value, and to find it, we need to find the DC current value. Then, there should be a value called small signal resistance (ro), which provides parallelism.

The values we get when the above operations are performed are as follows:

Due to the assumptions we made before the analysis, the gain value (22.2 V/V) we found turned out to be quite larger than the gain value we wanted to find (7 V/V). However, since we use ideal formulas by eliminating many external effects in our processes, these values will not be fully reflected in the simulation results. The Cadence environment calculates all the real parameters for us, giving the following results.