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hwset1solution - ECE 453 Homework Assignment 1 Solution...

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ECE 453: Homework Assignment 1 Solution 1-16 Solution The bandwidth of a raised-cosine pulse is W = 1 2 T (1 + β ) . With T = 1 μs and β = 0 . 5 , W = 750 kHz . The bandwidth occupied by a DSB-SC signal is 2W, hence the bandwidth occupied by the transmitted signal is 1.5 MHz. 3-2 Solution The 8 possible topologies for a 2-terminal RLC circuit are shown below (a) R L C (b) L C R (c) L R C (d) C R L (e) C L R (f) C L R (g) C R L (h) L R C Figure 1: Eight possible two-terminal RLC circuits. Only (c), (e), (f), (g) have impedance with finite real part at 0 Hz. Of these, (e) and (f) can be ruled out, because each of these has impedance with finite real part in the limit ω → ∞ , whereas the data show that the real part goes to zero in the limit. Case (g) can be ruled out because that topology will have impedance that will behave like j ω L in the limit ω → ∞ whereas the data show an impedance that is capacitive at high frequencies. Hence, the circuit must have topology (c). The impedance for (c) is: Z = 1 j ω C || ( R + j ω L ) or Z = ( R + j ω L ) j ω C ( R + j ω L + 1 / ( j ω
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