# MOSFET Design: Solving Q4 with R1, R2, k, V_T and I_D

• Engineering
• wirefree
In summary, wirefree attempted to solve a 10-part question, fourth of which was concerning R_D. He found that the value of R_D does not match any of the given answers. He asks for help in correcting his procedure.
wirefree
Homework Statement
Determine the value of R_D for which the amplitude of drain voltage swing will be maximum
Relevant Equations
Saturation condition: v_DS >= v_GS - V_T

Drain current:
i_D = k*(v_GS - V_T)^2 * (1+y*v_DS)
where y: channel length modulation parameter
V_T: Threshold Voltage
V_XY: Voltage between X & Y
[D: Drain S: Source G: Gate]
I greatly appreciate the opportunity afforded by this forum to submit questions.

I am presently tackling a 10-part question, fourth of which this post is concerning. Values provided at the start are: R1, R2, k, V_T and I_D.

In the previous 3 parts, Source Resistor, Transconductance (g_m) and slope of i_D-v_DS curve (r_o) have been calculated.

My attempt at a solution is pretty straight-forward but the answer does not match any of the provided options. The said approach involves:
- ascertaining V_G via Voltage Divider
- invoking the Saturation condition to obtain R_D
- Further still, setting V_D to halfway between VDD and Ground to allow maximum swing and finding R_D again

My working is for your purview in the attachment.

I would be indebted for advice on possible sources of error.

Best regards and Namaste,
wirefree

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As I keenly await Respected Members to respond, I am taking this opportunity to better explain my procedure.

Given quantities & circuit:

* The last quantity on the right is V_S (it's calculated)

The procedure to determine R_D is as follows:
1) Calculate V_S for given I_D and R_S (calculated earlier using the Drain current equation)

2) Determine minimum value of V_DS from Saturation condition and add to it V_S to obtain V_D
3) Center V_D at mid-point between 0V & 5V, i.e. 2.5V, and apply KVL to obtain R_D
This procedure ensures that V_DS meets the Saturation condition, and that maximum swing is available for V_DS, as much as I understand the situation.

However, the value of R_D does not match any of the given answers, which are in the 16-19 kOhm region.

Kindly correct me where I am wrong.
wirefree

Do you see an inconsistency between these two statements?
wirefree said:
2) Determine minimum value of V_DS from Saturation condition and add to it V_S to obtain V_D
wirefree said:
3) Center V_D at mid-point between 0V & 5V, i.e. 2.5V,

wirefree
Tom.G said:
Do you see an inconsistency between these two statements?

I do now.

Thank you, Sir.

Tom.G

## 1. What is a MOSFET and how does it work?

A MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) is a type of transistor used in electronic circuits. It works by controlling the flow of current between the source and drain terminals using an electric field created by the gate terminal.

## 2. What is the purpose of using R1 and R2 in MOSFET design?

R1 and R2, also known as the gate resistors, are used to limit the current flowing into the gate terminal of a MOSFET. This helps protect the transistor from damage and ensures proper operation.

## 3. How do k and VT affect MOSFET design?

k (transconductance) and VT (threshold voltage) are important parameters in MOSFET design. They determine the gain and switching characteristics of the transistor, respectively. A higher k value results in a higher gain, while a lower VT allows for better control of the transistor.

## 4. What is the significance of ID in MOSFET design?

ID (drain current) is the current that flows from the source to the drain terminal of a MOSFET. It is an important parameter to consider in design as it affects the power dissipation and overall performance of the transistor.

## 5. How can Q4 be solved with R1, R2, k, VT, and ID in MOSFET design?

Q4, also known as the operating point or quiescent point, is the point at which the transistor operates in the active region. This can be solved by using the given values of R1, R2, k, VT, and ID in the appropriate equations and calculating the corresponding values for the gate and drain voltages.