# hw7 - EE 101 Handout 21 Prof A El Gamal Homework...

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Unformatted text preview: EE 101 Handout # 21 Prof. A. El Gamal February 27, 2003 Homework Assignment #7 Due: Thursday 3/6 The fourth and last quiz will be on Thursday 3/6. It will cover SSS circuit analysis (the last three problems of HW6 and this homework). Your total quiz score for the class will be the sum of your highest three quiz scores (will drop your lowest score). 1. In some applications we operate in sinusoidal steady state and need an impedance with positive reactance ( i.e. , inductive), but cannot, due to technology limitations, build an inductor. A good example of this cccurs in the design of CMOS Radio Frequency (RF) integrated circuits. In this case it is often difficult to build an on-chip inductor. So instead of using an off-chip inductor we can use the circuit in the figure below (it is easy to build R s, C s and dependent sources in CMOS). For a given ω we choose R and C so that the circuit has the desired impedance. (a) Find the equivalent impedance between the two input terminals. (b) Let g = 10- 5 . For what values of R and C is the reactive part positive? v ( t ) R C gv ( t ) + +-- 2. The circuit in the figure below is in sinusoidal steady state. (a) Write the node voltage equations for the circuit expressed as Y E = ˜ I , where E is the node voltage phasor vector, ˜ I is a (complex valued) constant vector, and Y is a (complex valued) constant matrix. Use the node labels indicated on the figure. Express all entries of Y and ˜ I in the form a + jb . (b) Use the equations of part (a) to find v out ( t ) expressed as a cos( ωt + φ ). 1 2 cos (2 t ) 1Ω 1Ω 1F 1F + +-- v ( t ) 2 v ( t ) 2Ω . 5H v out ( t ) n 1 n 2 n 3 n 4 3. An electrical element that is described by an impedance at 100rad/sec is subjected to four experiments. In the first experiment, the element is connected to a voltageto four experiments....
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hw7 - EE 101 Handout 21 Prof A El Gamal Homework...

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