Design a MOS Voltage Amplifier with Gain of 50 V/V

[xortan]

Homework Statement

I need to design a MOS voltage amplifier with a gain of 50.

Homework Equations

tox = 5 nm
u = 500 cm2/V-s
Cox = 6.903 mF/m
λ = 0.1
Vdd = 2.5V

The Attempt at a Solution

I am getting confused on just about everything...

I am to design a voltage amplifier with a gain of 50 V/V that is connected between a 100k source and a 2k load. We can use more than one stage so I was going to use one common-source with a gain of 10, second stage is a common-source with gain of 5 and the last was going to be a source follower with a gain of 1.

I started out by picking a Vgs of 0.7 and a Vdsat of 0.2...don't know why it was just kinda arbitrary I guess.

I calculated my Id based off this equation Id = 1/2 * Cox * u * (W/L) * Vdsat²
I varied my W while keeping L constant. From my Id I was able to calculate my gm by using the equation 2*Id / Vdsat.

I know the equation for the gain of a common source amplifier is $\frac{Rg}{Rg + Rsig}$*$\frac{Rd}{1/gm + Rs}$ so I made my Rs 100 times larger than 1/gm and made my Rd 11 * (1/gm + Rs).

However when I enter the Rs and Rd values in LTSpice I am getting a drain current which is over 5 orders of magnitude away and its just really frustrating.

Please someone help! This thing is due in like 5 days and I've spent like 15 hours working on this and I can't even design a basic common-source amplifier. If you can provide links or write down some steps to follow in a design procedure that'd be great.

 

[KataKoniK]

Designing a MOS voltage amplifier with a gain of 50 can be a challenging task, but I am here to help you through the process. Let's break it down step by step:

1. Determine the specifications: The first step in designing any amplifier is to determine the specifications that you need to meet. In this case, you need a gain of 50 V/V, which means that the output voltage needs to be 50 times larger than the input voltage. You also need to consider the input and output impedances, as well as the power supply voltage. From the given information, we can assume that the input impedance is 100k and the output impedance is 2k. The power supply voltage is 2.5V.

2. Choose the MOSFET: The next step is to choose the MOSFET that will be used in the amplifier. Since the gain requirement is high, we need a MOSFET with a high transconductance (gm). From the given parameters, we can calculate the transconductance using the equation gm = 2*Id / Vdsat. This gives us a gm of 1.25 mS. We can then use this value to select a MOSFET from a datasheet. Make sure to also consider the breakdown voltage, as well as the gate and source voltages that the MOSFET can handle.

3. Determine the biasing point: To ensure proper operation of the amplifier, we need to choose a suitable biasing point for the MOSFET. This can be done by selecting a Vgs value and calculating the corresponding Vdsat using the equation Vdsat = Vgs - Vt. Since we want to operate the MOSFET in the saturation region, we can choose a Vgs that is higher than the threshold voltage (Vt). From the given information, we can use a Vgs of 1V, which gives us a Vdsat of 0.5V.

4. Choose the amplifier configuration: As you mentioned, you can use a multi-stage amplifier to achieve the required gain. In this case, you can use a common-source amplifier as the first stage, followed by a common-source with source degeneration as the second stage, and a source follower as the final stage. The common-source amplifier has a gain of gm*Rd, while the source follower has a gain of approximately 1. The second stage can be used