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

[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

 

[wirefree]

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

 

[Tom.G]

Do you see an inconsistency between these two statements?

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,

 

[wirefree]

Do you see an inconsistency between these two statements?

I do now.

Thank you, Sir.