Finding Width of MOSFET

We are struggling with part iv of the question above where we have to find the width of both MOSFETS. As you can see from our working out, we have found a width of 2 meters for the nMOS, which we know is way too big. Is there something wrong with our working or are we going about working it out completely the wrong way?

$$\First \space find \space I_b:\$$

$$\\beta_f = \frac{I_c}{I_b} \approx \frac{I_e}{I_b}\$$

$$\Rearrange\space to\space find \space I_{b}\$$

$$\I_b = \frac{I_e}{\beta_f} = \frac{3mA}{200} = 1.5 \times 10^{-5}A\$$

$$\I_d \space (of \space MOSFET)= I_b\space (of \space BJT)\$$

$$\Substitute\space I_d\space into:\$$

$$\g_m = \frac{I_d}{V_{Th}} = \frac{1.5\times 10^{-5}}{25mV} = 6 \times 10^{-4} \$$

$$\Now\space using:\$$

$$\g_m = \frac{2I_d}{V_{gs} - V_t}\$$

$$\Rearrange\space to\space find \space V_{gs}\$$

$$\V_{gs} = \frac{2I_d + g_mV_t}{g_m} = \frac{(2 \times 1.5 \times 10^{-5}) + (6 \times 10^{-4} \times 0.8)}{6 \times 10^{-4}} = 0.85 \$$

$$\Now\space using:\$$

$$\I_d = \frac{K'}{2}\frac{W}{L}(V_{gs} - V_t)^2\$$

$$\Rearrange\space to\space find \space W\$$

$$\nMOS \space W = \frac{2I_dL}{K'(V_{gs} - V_T)^2} = \frac{(2 \times 1.5 \times 10^{-5}) \times 5 \times 10^{-6}}{3 \times 10^{-8} \times (0.95 - 0.8)^2} = 2\$$

$$\pMOS \space W = \frac{2I_dL}{K'(V_{gs} - V_T)^2} = \frac{(2 \times 1.5 \times 10^{-5}) \times 5 \times 10^{-6}}{1 \times 10^{-6} \times (0.95 - 0.8)^2} = 0.06\$$

• 2 meters seems a bit large for a mosfet. – brhans Jan 18 at 15:17
• Could you maybe transcribe the work into the question? Not everyone can reliably read even the cleanest handwriting, and the pictures being sideways certainly doesn't help. – Hearth Jan 18 at 15:22
• Added a rough transcription – ECEHELPPELAE Jan 18 at 15:33
• Neat cropping! How come we have had three or four channel width questions within one week? Is it that time of the year in some class? – winny Jan 18 at 15:46
• The site does support latex, please format your question or at least put the pictures right side up. – Voltage Spike Jan 18 at 16:34