The enhancement mode n-channel MOSFET M1 is biased at a de drain current ID of 50.0 μA in the saturation region with gate-source and drain-source voltages shown in Figure 3. Small-signal parameters and components for this device at the dc operating point are given below. β = 250 μA/V2 λ = 0 Cgs = 250 fF Cgd = 175fF Cgb = 40fF Cbd = Cbs = 800 fF Apply this data to calculate the gain-bandwidth product ωT in radians/second. Show your work and explain in detail all assumptions you make.
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The enhancement mode n-channel MOSFET M1 is biased at a de drain current ID of 50.0 μA in the saturation region with gate-source and drain-source voltages shown in Figure 3. Small-signal parameters and components for this device at the dc operating point are given below. β = 250 μA/V2 λ = 0 Cgs = 250 fF Cgd = 175fF Cgb = 40fF Cbd = Cbs = 800 fF Apply this data to calculate the gain-bandwidth product ωT in radians/second. Show your work and explain in detail all assumptions you make.
![An NMOS amplifier is shown in Figure 1. Transistor M1 is biased in the saturation region for an amplifier application. The circuit is biased with a resistive voltage divider consisting of R1 and R2, a source degeneration resistor RS, and a load resistor RD. The drain bias current for the design is ID = 500 μA and VDS is 1.625 V. The device parameters are: L = 0.5 μm, W = 10 μm, kn′ = 200 μA/V2, Vtn = 0.5 V, and λn = 0. CMOS 0.5 u Process . op . model NMOS1 nmos (KP = 200 u, VTO = 0.5, LAMBDA = 0) ;tran20 m Figure 1: A NMOS amplifier circuit including a source degeneration resistor RS. a) Determine R1 and R2 for the specified bias point. b) Determine the value for RD for the specified bias point. c) Use the LTSPICE circuit template and verify your bias circuit design. Include a copy of the schematic and the dc operating point results (text log with node voltages and currents). [8] d) Use LTSPICE to evaluate the change in ID for a variation in the technology process parameter kn′. Evaluate the change in ID for a change of ±10% in kn′. Compare the relative change in ID with the relative change in kn′. What do you observe? Explain how the source degeneration resistor RS implements negative feedback which reduces the sensitivity of the bias point to changes in kn′. [8]](https://www.doubtrix.com/uploads/editor/9212363628QZkAUhRzqb.jpg)
![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.](https://www.doubtrix.com/js/ckeditor/filemanager/connectors/php/editor/1701531864-Rjgbdog0ehds.png)