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I have tried various methods for calculating N max here, and some have resulted in negative answers while others have resulted in an answer of around 1.

Is my method correct? Or am I missing something in regard to what it means for Vo = Vol max?

The Question: enter image description here

Equations that I used in my given attempt: enter image description here

Attempt at part a: enter image description here

I'm not sure if I should be including the forward current gain or the overdrive factor in my answer for part a. Are they acceptable as transistor parameters?

Attempt at parts b & c : enter image description here

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    \$\begingroup\$ Hi, Peter. Why did you introduce the saturated collector-emitter voltage when developing an equation for (a)? I'm unclear about why. I do think you need to know the minimum "input-high" voltage required at the input: \$V_{\text{IH}_\text{MIN}}\$. \$\endgroup\$
    – jonk
    Commented Aug 24, 2019 at 17:44
  • \$\begingroup\$ In your analysis, does \$V_{\text{CE}_\text{SAT}}=V_{\text{OL}_\text{MAX}}\$? (Because, in my reading of your question and part (a), I believe that the intent is \$V_{\text{CE}_\text{SAT}}\ne V_{\text{OL}_\text{MAX}}\$.) \$\endgroup\$
    – jonk
    Commented Aug 25, 2019 at 1:57

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