Consider the following Voltage Transfer Characteristic (VTC) function of inverters of different widths. Assume all inverters have the same channel length and all Wps are the same. Which VTC has the smallest Wp/Wn ratio?

Question

BlackTom AI · Accepted Answer

This question asks which VTC curve corresponds to the smallest Wp/Wn ratio, given multiple inverter widths and the same channel length and Wps.
Option: The right-most one. Consider what lowering Wp/Wn means: the p-channel is relatively weaker compared to the n-channel. When the p transistor is weaker, the inverter switches on the output (pulls down) earlier as Vin increases, and the VTC shifts toward lower Vin values. In the plot, the right-most curve represents a case where the transition occurs earlier (closer to Vin = 0), which would actually correspond to a larger Wp/Wn, not the smallest. Therefore this option misattributes the shift direction.
Option: The left-most one. This is the curve that transitions at a lower Vin, indicating the n-transistor is stronger relative to the p-transistor, i.e., a smaller Wp/Wn ratio. A reduced p-channel drive (smaller Wp) compared with the n-channel drive causes the inverter to switch earlier as Vin rises, moving the VTC toward the left. Hence this curve matches the smallest Wp/Wn.
Option: The middle one with beta ratio of 1. A beta ratio of 1 means Wp and Wn are balanced, giving a symmetric or mid-point threshold around Vin ≈ Vdd/2. This is not the smallest Wp/Wn; it represents a relatively strong p relative to n (or at least balanced), depending on the exact device parameters, but not the minimal ratio scenario.
Option: More information is required to determine the answer. The figure provides the relative positions of the curves for different beta_p/beta_n values (and thus different Wp/Wn ratios). Since you can infer the ordering from the curves, no additional data is strictly necessary to identify the smallest ratio here.

FA25 ECE 555 001 Final

Consider the following Voltage Transfer Characteristic (VTC) function of inverters of different widths. Assume all inverters have the same channel length and all Wps are the same. Which VTC has the smallest Wp/Wn ratio?

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