# How to Determine Correct Node Voltages in NMOS Circuit Analysis?

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In summary, the conversation is discussing the determination of labelled node voltages, using given values for kn and Vtn, and neglecting channel length modulation. The condition for saturation is mentioned and a quadratic equation is used to solve for the drain current and source current, resulting in two possible solutions for each. The correct solution must meet the condition for saturation, with Vgs being greater than Vth.
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## Homework Statement

Find the labelled node voltages. Assume ##k_n = 0.5 \frac{mA}{V^2}## and ##V_{tn} = 0.8V##. Neglect channel length modulation ##(\lambda = 0)##.

## The Attempt at a Solution

f) For this problem, I see ##V_D = V_G \Rightarrow V_G - V_D = 0V \Rightarrow V_{GD} = 0 V##.

Now ##V_{GD} = 0V < 0.8V = V_{tn}## which implies saturation mode.

The drain current is then given by:

$$I_D = \frac{1}{2} k_n V_{ov}^2$$

By using KVL, ##I_D = \frac{5V - V_D}{100k \Omega}##.

Now, ##V_{ov} = V_{GS} - V_{tn}##, but we know ##V_{GS} = V_G - V_S = V_G - 0V = V_G##. We also know that ##V_G = V_D##, so ##V_{GS} = V_G = V_D##. Hence we can write ##V_{ov} = V_D - V_{tn}##.

Subbing these into the drain current equation we obtain:

$$\frac{5V - V_D}{100k \Omega} = \frac{1}{2} k_n (V_D - V_{tn})^2$$

This yields a quadratic in ##V_D##, which has two solutions:

##V_D = 0.37V## and ##V_D = 1.2V##.

I am unsure how to exactly reason which of these is the proper solution.
h) For this problem, ##V_D = 5V## and ##V_G = 0V##. So ##V_{GD} = V_G - V_D = - 5V##.

Now ##V_{GD} < V_{tn}## which implies saturation operation.

The drain current is equal to the source current since ##I_G = 0##, so ##I_D = I_S = \frac{1}{2} k_n V_{ov}^2##.

Writing KVL we see: ##I_S = \frac{V_S + 5V}{100k}##.

Now, ##V_{ov} = V_{GS} - V_{tn}##, but we know ##V_{GS} = V_G - V_S = 0V - V_S = - V_S##. Hence we can write ##V_{ov} = - V_S - V_{tn}##.

Subbing these into the source current equation we obtain:

$$\frac{V_S + 5V}{100k} = \frac{1}{2} k_n (- V_S - V_{tn})^2$$
$$\frac{V_S + 5V}{100k} = \frac{1}{2} k_n (V_S + V_{tn})^2$$

This is another quadratic in ##V_S## that yields two solutions:

##V_S = -1.2V## or ##V_S = - 0.37V##.

Once again I would like to ensure my understanding of which solution is correct.

If someone could help me understand how to choose the right solution it would be very appreciated.

Thank you.

Zondrina said:
.
The condition for saturation includes Vgs > Vth. Both your answers of Vgs = 0.37V do not meet that requirement so are obviously invalid.

## 1. What is NMOS node voltage analysis?

NMOS node voltage analysis is a method used to analyze the voltage values at different nodes or points in a circuit that contains NMOS (n-type metal-oxide-semiconductor) transistors. It is a critical tool in circuit analysis and is used to determine the behavior and performance of circuits that use NMOS transistors.

## 2. How is NMOS node voltage analysis performed?

NMOS node voltage analysis is performed by applying Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) to the circuit. The circuit is then simplified using Ohm's Law and the equations governing the behavior of NMOS transistors. The resulting equations are then solved to determine the voltage values at the desired nodes.

## 3. What are the benefits of using NMOS node voltage analysis?

NMOS node voltage analysis provides a way to analyze the performance of circuits that use NMOS transistors without having to physically build the circuit. This saves time and resources and allows for quick and accurate evaluation of different circuit designs. It also helps in identifying potential problems or bottlenecks in the circuit design.

## 4. What are the limitations of NMOS node voltage analysis?

NMOS node voltage analysis assumes ideal conditions and may not accurately reflect the behavior of the circuit in real-world scenarios. It also requires a good understanding of circuit theory and the behavior of NMOS transistors. Additionally, it may not be suitable for circuits that use other types of transistors.

## 5. How is NMOS node voltage analysis used in practical applications?

NMOS node voltage analysis is used in the design and optimization of electronic circuits that use NMOS transistors, such as digital logic circuits, amplifiers, and memory devices. It is also used in the evaluation of different circuit designs and in troubleshooting issues in existing circuits.

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