Consider the circuit of Fig. 6.2 and assume that (W/L)1,2 = 50/0.5, (W/L)3,4 = 100/0.5, and ISS = 1 mA. What is the C2/C1 ratio when the closed-loop voltage gain is 5% lower than that in the ideal case where the loop gain βA0 >> 1.
Parallel Connection of MOSFETs For an NMOS in saturation, IDS = 1/2Kn(Vgs - VTN)2. Imagine connecting two same NMOS in parallel (connect the gates, drains, and sources together), as shown in Figure 1. How would the IDS change compare to the IDS of a single NMOS given the same VD, VG, and VS [RP1]? Which parameter in the IDS equation (other than IDS ) is effectively changed by the parallel NMOS connection [RP1]? How would that parameter and IDS change if n NMOS are connected in parallel [RP1]? Figure 1: Parallel-connected NMOS Inverter
An NMOS transistor is operating at the edge of saturation with an overdrive voltage Vov and a drain current of ID. If Vov is doubled, how does the drain current change? ID increases by a factor of 4 ID increases by a factor of 2 ID decreases by a factor of 4 ID does not change
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].
Series/parallel MOSFETS: Consider the arrangement of MOSFETs shown at the right, with two transistors of size WT/LT connected in parallel, in series with one transistor of size WB/LB. Assume that the MOSFETs are biased above threshold, and neglect body effect and output resistance in the following questions. Use symbolic equations (not simulation results). a) Show that transistor MB can never operate in the saturation region, i.e. it is always in either triode or cut-off. b) What is the size (width and length) of a single transistor Ml that is equivalent to MT1/MT2/MB? Remember to use the I-V characteristic for the appropriate region of operation for each transistor. c) What is the transconductance of MT1/MT2/MB?
a) Find values for the current ratios Ib1/Ib2 and Ib2/Io? : (Note: 2xMb3 indicates that 2 identical devices are connected in parallel). Hint: All equal type MOS devices are perfectly matched. b) Determine the bias resistor Rb such that Ib1 = 100 µA. Hint: Write down KVL for the loop marked by the curved arrow. c) What is the minimum value of V0 that still keeps the current source working as intended? A symbolic expression suffices. P-MOS N-MOS kp = 200 µA/V2 kn = 200 µA/V2 Vtp = -0.8 V Vtn = +0.8 V λp = 0.02 V-1 λn = 0.02 V-1 k = µCoxW/L All n-channel and all p-channel devices are perfectly matched.
In this amplifier circuit, it is known that the MOSFET transistor has a constant kn = 0.1 mA/V2 and that the BJT has a beta (β) equal to 100 . It is given that the NMOS transistor operates in saturation having a current: IDS = 2.52 μA. a) What is the small signal gain at midband conditions? Av = vo/vi b) What is the value of this amplifier's input resistance? c) What is the value of this amplifier output resistance d) Draw a circuit model for this voltage amplifier consisting of an input resistor, a dependent voltage source and an output resistor.
The MOSFET in the common source amplifier is shown below. All the MOSFETs are identical. Assume negligible channel length modulation. VTn = +1 V, μ = 600 cm2/V⋅s, Cox’ = 0.23 μF/cm2, Cgs = 1 pF, and Cgd = 0.2 pF. (50pts) RS = 1 MΩ RG = 1 MΩ RD = 10 kΩ RL = 10 kΩ (i) Calculate the MOSFET W/L such that the bias current of M1 and transconductance of M1 are 1 mA and 5 mS, respectively. (ii) Find the mid frequency voltage gain in dB. (iii) Find the upper 3-dB frequency, fH. (iv) Find the value of CG, CS, and CD such that the corresponding poles are at 1 Hz, 100 Hz, and 10 Hz, respectively. (v) Write down all the zeros and poles of the overall amplifier (3 zeros and 3 poles for the lower frequency response and 1 pole for the higher frequency response). Sketch and carefully label the Bode plot for the gain magnitude (indicate the corner frequency and the slope). Specify the lower 3-dB frequency fL.
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.