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In the following CMOS inverter, the threshold voltages of the n- and p-channel transistors are VTn and −|VTp|, respectively: a) Draw the input to output voltage transfer characteristic (VTC) for this inverter. Express and label clearly all voltage levels on the VTC plot. (20 points) b) Indicate the noise margins NML and NMH on the VTC. c) Indicate the logic high and low output voltage levels VOH, VOL on the VTC. d) Indicate the logic high and low input voltage levels VIH, VIL on the VTC. e) Indicate clearly the mode of operation in each region of the VTC.

In the following CMOS inverter, the threshold voltages of the n- and p-channel transistors are VTn and −|VTp|, respectively: a) Draw the input to output voltage transfer characteristic (VTC) for this inverter. Express and label clearly all voltage levels on the VTC plot. (20 points) b) Indicate the noise margins NML and NMH on the VTC. c) Indicate the logic high and low output voltage levels VOH, VOL on the VTC. d) Indicate the logic high and low input voltage levels VIH, VIL on the VTC. e) Indicate clearly the mode of operation in each region of the VTC.

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In the following CMOS inverter, the threshold voltages of the n - and p -channel transistors are V T n and − | V T p | , respectively: a) Draw the input to output voltage transfer characteristic (VTC) for this inverter. Express and label clearly all voltage levels on the VTC plot. (20 points) b) Indicate the noise margins N M L and N M H on the VTC. c) Indicate the logic high and low output voltage levels V O H , V O L on the VTC. d) Indicate the logic high and low input voltage levels V I H , V I L on the VTC. e) Indicate clearly the mode of operation in each region of the VTC.

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Transient Point (Threshold Voltage) In practice, in an inverter circuit, there is an unstable transient point at which both transistors are on and in saturation mode. The input voltage (connected to the gate) for this point is called the threshold voltage (Vin = VTH). At this point, VGS/VSG of the NMOS / PMOS is equal to Vin/VDD-Vin. Note that this threshold voltage is different from the intrinsic threshold voltage of transistors (VTN or VTP). Derive an expression for this threshold voltage [RP2]. Verify your work with the expression below: What happens to VTH when Kp > Kn, Kp = Kn, and Kp < Kn? What haapens when Kp approaches 0 or when Kn approaches 0? Use words to generalize how various Kn and Kp values change VTH and describe how the values of Kn and Kp can be tuned by parallel MOSFET connection [RP2]. Noise Margin Please read section 6.9.4 of the textbook or search on the internet about noise margin. Sketch a typical transfer function of an inverter (non-ideal one) with 1 PMOS and 1 NMOS and label VIL, VOH, VOL,VIH, NMH, and NML on your sketch [RP3]. Why is the metric of noise margin useful [RP3]? Make a reasoned guess about how the change in the threshold voltage VTH (or the change in Kn/Kp ) affects each of the noise margin parameters [RP4].

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