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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.976 High Speed Communication Circuits and Systems Mid-Term Exam Copyright © 2003 by Michael H. Perrott Name__________________________ Problem 1 ______________ Problem 2 ______________ Problem 3 ______________ Problem 4 ______________ Total ______________ 1. (20 points) Consider the circuit network connected to lossless transmission lines of characteristic impedance Z1 and Z2 as shown in the figure below. Assume in all cases that Z1 and Z2 are purely real. 2-Port for S-parameter calculation Z1 Z2 R1 C1 S11 S22 a. Derive an expression for S11 in terms of Z1, Z2, R1, and C1. b. Derive an expression for S22 in terms of Z1, Z2, R1, and C1. c. Derive an expression for S21 in terms of Z1, Z2, R1, and C1. d. Consider the case where a pulse is launched down the left transmission line (with impedance Z1). Will the initial portion of the voltage reflection back down the left transmission line be positive, negative, or zero given Z1 = 50 Ohms, R1 = 75 Ohms, C1 = 1 pF, and Z2 = 100 Ohms? Explain your answer. e. Consider the case where a pulse is launched down the right transmission line (with impedance Z2). Will the initial portion of the voltage reflection back down the right transmission line be positive, negative, or zero given Z1 = 50 Ohms, R1 = 75 Ohms, C1 = 1pF, and Z2 = 100 Ohms? Explain your answer. 2. (25 points) Now consider the linearized VCO model shown in the figure below. Negative Resistance Amplifier Ideal Transformer 1:10 2 in -1 gm Ain R C L Vout Aout where: 2 in = 4kT2gm Accompanying noise source not shown for R a. Calculate the value of gm for the negative resistance amplifier for which steadystate oscillation is achieved. b. Given the linearized VCO model illustrated on the previous page, derive an expression for the phase noise of the oscillator, L(∆f). Your expression should be a function of Ain, R, Q of the tank, and kT. c. State the difference (in dB) between the minimum phase noise that can be achieved with the oscillator shown in the initial figure of this problem versus the oscillator shown below. Assume that the voltage swing at the active element output, Ain, is constrained in value to 2 V for both VCO structures, whereas the voltage across the tank itself is not constrained in either case. Negative Resistance Amplifier 2 in -1 gm Ain R C where: 2 in = 4kT2gm Accompanying noise source not shown for R L Vout 3) (25 points) Consider the CMOS mixer shown below. Assume for all parts in this problem that the frequency of the RF input, VRF, is 900 MHz, while the frequency of the LO output, VLO, is 1 GHz. Also assume for all parts that the opamp has zero offset voltage, infinite DC gain, and infinite unity gain bandwidth. 1.8 V 10 kΩ 0V 0V VLO VRF V1 M1 VIF 10 pF 0V a. Calculate the conversion gain of the mixer given that the channel resistance of M1 (from source to drain) is infinite when VLO = 0 V, and equals 1 kΩ when VLO = 1.8 V. b. Calculate IIP3 of the mixer (in units of peak voltage squared, Vp2) given that the channel resistance of M1 (from source to drain) is infinite when VLO = 0 V, but equals the following expression when VLO = 1.8 V: Channel resistance = dVds/dId = 1 kΩ/(Vgs-0.8V-Vds2/2) 4) (30 points) Consider the distributed amplifier shown below consisting of N transistors whose input and outputs are connected through lossless transmission lines with characteristic impedance Z0. For all parts to follow, ignore all loading effects of the transistors (i.e., ignore Cgs, Cgd, Cdb, and ro), and assume that all transmission line sections have equal delay. Also, ignore induced gate noise, and assume that the drain noise of each transistor is related to its transconductance as 2 id = 4kT2gm ∆f In addition, assume that a fixed current density is chosen for the transistors such that the transconductance for each transistor is related to its bias current as gm= α Ibias delay RL=Z0 RL=Z0 Zo Zo Ibias delay Rs=Z0 vin Zo Zo Ibias Zo vout Ibias M1 M2 MN Zo Zo Zo RL=Z0 Source a. Compute the overall gain of the amplifier (vout/vin) as a function of the number of stages in the amplifier, N. Your answer should be expressed in terms of Ibias, α, Zo, and N. b. Compute the noise factor of the overall amplifier as function of N. Your answer should be expressed in terms of Ibias, α, kT, Zo, and N. Suppose that loading by the transistors can only be neglected if their individual area, At, is smaller than Ao. Assume that a specific current density is desired for each transistor such that its area is related to its bias current as At= β Ibias Given this constraint, derive expressions for the following parts (c) and (d) c. Determine the minimum number of stages, N, that are required to achieve an overall amplifier gain (vout/vin) of G. For simplicity, assume that N does not need to be expressed as an integer value. d. Suppose you desire to achieve the best noise factor given a fixed overall gain, G. Do you do better, worse, or the same for noise factor if you set N higher than the minimum value calculated in the previous part? Explain your answer. ...
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This note was uploaded on 10/29/2011 for the course EE 6.976 taught by Professor Michaelperrott during the Spring '03 term at MIT.

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