Explain all of your steps and follow a logical train of thought. Clearly describe all design rationale.

1)  Design a device to deliver a sinusoidal 500kHz pulse through a piezoelectric device, given a signal source that can deliver 10 mV (peak-to-peak) voltage at that frequency. Use realistic circuit components and fully characterize the circuit input and output impedance, and gain.

2)  You have designed an instrumentation amplifier using a standard op-amp with an open-loop gain of 100 dB at DC. You notice that the gain of your circuit starts to fall at about 1kHz, even though you have not used any inductors or capacitors in your circuit. Explain what may have caused this. Sketch any supporting figures.

3)  You are trying to measure the ECG of a baby in utero. Describe why and how this could be done, and whether it could be done noninvasively. Explain limitations to detecting and differentiating the signal from maternal "noise", and how these limitations might be overcome.

4)  Describe how a wheatstone bridge works, and design one to detect a 10 ohm change in resistance. What determines the precision of your measurement? Give an example with realistic components.

5)  Explain why electrical current can flow through an insulator sandwiched between two conductors. What happens (physically) when superconductors are used instead, and what can this effect be used to measure? Estimate the size of a typical characteristic current of a junction (J_0), where J=J_0sin(p_1-p_2), where p_1 and p_2 are the phases on each side of the insulator. Estimate the size of the maximum current generated by a typical SQUID detector.

6)  A colleague tells you she has made some nanometer-sized particles that act as tiny injectable SQUID detectors. She tells you the particles operate by sensing a field in the SQUID, and transmitting a current to a conductor surrounding the particles, which in turn changes the local magnetic field. This is in turn detected with MRI. What, if anything, makes you skeptical of her nanoparticles? Could SQUID detectors be implanted? Can they be made on a nm scale?