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

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Discussion Overview

The discussion revolves around solving a specific part of a multi-part question related to MOSFET design, focusing on the calculation of resistor values (R_D) using parameters such as R1, R2, k, V_T, and I_D. The context includes technical reasoning and potential sources of error in the calculations.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • Participant wirefree outlines their approach to calculating R_D, which involves using a voltage divider to ascertain V_G, applying the saturation condition, and centering V_D for maximum swing.
  • Wirefree notes that their calculated value of R_D does not match the expected range of 16-19 kOhm, suggesting a potential error in their method.
  • Wirefree describes a procedure that includes calculating V_S, determining V_D based on the saturation condition, and ensuring V_D is centered at 2.5V.
  • Another participant questions the consistency between two statements made by wirefree regarding the determination of V_D, indicating a possible misunderstanding in the calculations.
  • Wirefree acknowledges the inconsistency pointed out and expresses gratitude for the clarification.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of wirefree's approach, as there are indications of confusion and potential errors in the calculations. The discussion remains unresolved regarding the accurate calculation of R_D.

Contextual Notes

Participants have not fully explored the implications of the saturation condition or the assumptions made in calculating V_S and V_D. There may be dependencies on specific definitions or interpretations of the circuit parameters that are not fully articulated.

wirefree
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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:
1566404760609.png

1566404776150.png

* 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
1566404956499.png
3) Center V_D at mid-point between 0V & 5V, i.e. 2.5V, and apply KVL to obtain R_D
1566404978163.png
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,
 
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Tom.G said:
Do you see an inconsistency between these two statements?

I do now.

Thank you, Sir.
 
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