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ps3 - EE/BIOE 497e PROBLEM SET 3 DUE 18 April 2008 Problem...

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EE/BIOE 497e PROBLEM SET 3 DUE: 18 April 2008 Problem 1: (60 Points) It is desired to observe and detect a magnetic resonance transition located at ω o rad/sec in an electrically lossy material. At this frequency, a network analyzer reveals that the probe coil has a self-inductance L and a series resistance R due to the self-resistance of the probe and losses within the sample. Looking into the matched probe, the spectrometer must see a real impedance of R 0 at the transition frequency ω 0 in order to power match the power amplifier and noise-match the receiver preamplifier. As the series resistance R of the probe is less than the characteristic impedance R 0 , the matching network uses the parallel-series configuration in Figure 1. Figure 1: The impedance looking into the parallel-series matching network at the transition frequency ω o must be R o . 1. (10 points) Find expressions for C p and C s in terms of the parameters L , R , R 0 and ω 0 . 2. (2 points) Is the parallel-series network useful when R 0 R ? Explain your answer. 3. (8 points) Figure 2 shows a simplified schematic of the spectrometer during measurement of the nuclear reso- nance signal v nr ( t ). Find an expression for the transfer function from the induced signal V nr ( s ) to the input voltage V i ( s ) across the preamplifier input, and place your answer in the standard form V i ( s ) V nr ( s ) = b m s m + b m - 1 s m -
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