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Consider the circuit shown in Figure 2 below, with gm1 = 100 mA/V, gm2 = 20 mA/V, gm3 = 3 mA/V, R1 = 2 kΩ, R2 = 1 kΩ, VDD = 5 V, and all NMOS devices are in saturation. Channel length modulation and the body effect should be ignored for this problem. (And, hopefully, it is obvious that gm1, gm2, and gm3 correspond to the device transconductances of NMOS devices M1, M2, and M3, respectively: if this wasn't obvious, note that the next time you see something like this, I probably won't spell it out for you so explicitly. if at all, so please make a mental note of these kinds of things.) a) Determine the numerical small-signal voltage gain: i) Av = Vout/Vin in units of V/V and ii) |Av| in units of dB. Be sure to indicate whether your numerical answers are positive-valued or negative-valued (numerical answers with ambiguous signs will receive little, if any: credit, partial or otherwise). List your numerical answers in proper engineering notation format with appropriate units, and show your work. b) Determine the numerical small-signal resistance "seen" looking into node Vin. List your numerical answer in proper engineering notation format with appropriate units, and show your work. c) Determine the numerical small-signal resistance "seen" looking into node Vx. List your numerical answer in proper engineering notation format with appropriate units, and show your work. d) Determine the numerical small-signal resistance "seen" looking into node Vy. List your numerical answer in proper engineering notation format with appropriate units, and show your work. e) Determine the numerical small-signal resistance "seen" looking into node Vout. List your numerical answer in proper engineering notation format with appropriate units. and show your work.

Consider the circuit shown in Figure 2 below, with gm1 = 100 mA/V, gm2 = 20 mA/V, gm3 = 3 mA/V, R1 = 2 kΩ, R2 = 1 kΩ, VDD = 5 V, and all NMOS devices are in saturation. Channel length modulation and the body effect should be ignored for this problem. (And, hopefully, it is obvious that gm1, gm2, and gm3 correspond to the device transconductances of NMOS devices M1, M2, and M3, respectively: if this wasn't obvious, note that the next time you see something like this, I probably won't spell it out for you so explicitly. if at all, so please make a mental note of these kinds of things.) a) Determine the numerical small-signal voltage gain: i) Av = Vout/Vin in units of V/V and ii) |Av| in units of dB. Be sure to indicate whether your numerical answers are positive-valued or negative-valued (numerical answers with ambiguous signs will receive little, if any: credit, partial or otherwise). List your numerical answers in proper engineering notation format with appropriate units, and show your work. b) Determine the numerical small-signal resistance "seen" looking into node Vin. List your numerical answer in proper engineering notation format with appropriate units, and show your work. c) Determine the numerical small-signal resistance "seen" looking into node Vx. List your numerical answer in proper engineering notation format with appropriate units, and show your work. d) Determine the numerical small-signal resistance "seen" looking into node Vy. List your numerical answer in proper engineering notation format with appropriate units, and show your work. e) Determine the numerical small-signal resistance "seen" looking into node Vout. List your numerical answer in proper engineering notation format with appropriate units. and show your work.

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Consider the circuit shown in Figure 2 below, with gm1 = 100 mA/V, gm2 = 20 mA/V, gm3 = 3 mA/V, R1 = 2 kΩ, R2 = 1 kΩ, VDD = 5 V, and all NMOS devices are in saturation. Channel length modulation and the body effect should be ignored for this problem. (And, hopefully, it is obvious that gm1, gm2, and gm3 correspond to the device transconductances of NMOS devices M1, M2, and M3, respectively: if this wasn't obvious, note that the next time you see something like this, I probably won't spell it out for you so explicitly. if at all, so please make a mental note of these kinds of things.) a) Determine the numerical small-signal voltage gain: i) Av = Vout/Vin in units of V/V and ii) |Av| in units of dB. Be sure to indicate whether your numerical answers are positive-valued or negative-valued (numerical answers with ambiguous signs will receive little, if any: credit, partial or otherwise). List your numerical answers in proper engineering notation format with appropriate units, and show your work. b) Determine the numerical small-signal resistance "seen" looking into node Vin. List your numerical answer in proper engineering notation format with appropriate units, and show your work. c) Determine the numerical small-signal resistance "seen" looking into node Vx. List your numerical answer in proper engineering notation format with appropriate units, and show your work. d) Determine the numerical small-signal resistance "seen" looking into node Vy. List your numerical answer in proper engineering notation format with appropriate units, and show your work. e) Determine the numerical small-signal resistance "seen" looking into node Vout. List your numerical answer in proper engineering notation format with appropriate units. and show your work.

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For the circuit shown in Figure 1, NMOS device M1 has the following properties: kn’(W/L) = 180 μA/V2, VT0 = 2 V, λ = 0.02 V-1, γ = 0.4 V1/2, 2ϕF = 0.7 V, and ID = 10 mA. Note that capacitor Cbig is a DC blocking cap, i.e., Cbig is an open at DC and a short at all other frequencies. Figure 1. Circuit for Problem 1. a) Determine the numerical value of bias voltage Vbias which is needed to achieve a drain current of ID = 10 mA. b) Draw the small-signal equivalent circuit. c) Analyze the small-signal circuit to find Rin, Rout, and Av = Vout/Vin. Find the analytic expression for each quantity first, before determining the numerical answers. d) Recall that gmb/gm = χ. Determine the numerical value of χ for this problem. [Note that this part has nothing to do with parts (b) and (c).] e) What is the threshold voltage of device M1? [Note that this part has nothing to do with parts (b) and (c).] Show your work, list all numerical values in proper engineering notation format with appropriate units and with at least two decimal places of precision.
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