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					University of Michigan
Physics REU Program
Summer 2003
Jeffrey D. Germond
During the summer of 2003, I participated in the REU program sponsored by the University of Michigan Physics
Department and the NSF. My advisor during the program was Professor Timothy Chupp. The following page outlin
my project during the REU program.

My project began with the need for a stable current supply for a solenoid magnet in the operation of a dual specie
Maser. First it is important to understand what a Maser is, and why does it need a stable magnetic field.

MASER stands for Microwave Amplification by Stimulation Emission of Radiation, which essentially means it is like a
laser with a wavelength in the microwave region. In the system I was dealing with there is a cell that contains He
and Xe and Rb. The Maser optically pumps the Rb. Through spin exchange, the Rb polarizes the He and Xe. The
system uses a pulsed RF frequency to tip the spins. Normally the spins would undergo free induction decay (FID),
which the spin re-align with the magnetic field , but in this case there is a feedback loop that keeps the spins
precessing at their individual atomic frequencies. Because a the frequency is related to the magnetic field by a
constant, a constant magnetic field will provide a constant frequency.

The best way to provide a constant magnetic field is with a solenoid. In a solenoid, the current is directly
proportional to the magnetic field strength. The basic idea behind the circuit is simple. There will be a sense
resistor (Rs ) in series with a magnet (Rload). Feedback will be used to control the amount of current that flows
through Rs. Usually, resistors have some temperature dependence. To help improve the performance of the circu
Rs will be chosen such that it will have a low temperature coefficient; it will also be temperature controlled.

These are some of the components used in the circuit.

Operational Amplifiers (Figure 1.): Op Amps are some of the most important components in electrical design. An
amp has four inputs and one output. The top and bottom inputs are for the power supply (usually +15V and -15V).
Some times the power supply inputs are ignored because they are not as important to determining t        he output
behavior. The remaining two inputs on the left hand side are called the inverting input (-) and the non-inverting
input(+). The behavior of an op amp is governed by two rules: 1) the input voltages are equal, the output of the o
amp attempts to do what ever necessary to make the input voltages equal; and 2) the inputs draw no current, whi
gives op amps high input impedance.

Ideally op amps have infinite gain (Gain = Output Voltage/Input voltage); any difference in the inputs will cause a
large output voltage. A way to limit the gain and to the two rules from above is to introduce a feedback network.
By coupling the output to one of the inputs, negative feedback can be used to control the gain of an op amp. If lo
of negative feedback is used, the gain of the o   p amp can depend more on component values of the feedback
network and less on its open-loop (no feedback) properties. An example of negative feedback is illustrated in figu
2. The gain of this op amp is -R12/R14, it is called an inverting amplifier. The gain depends only on the values of t
resistances, in this particular case the gain of the op amp is -1.

Field Effect Transistors (FET): More specifically, in this circuit, MOSFET (Figure3.) (metal oxide semiconductor
FET). This component is essentially used as an electronic switch. To turn the switch on, it is necessary to apply a
positive voltage to the gate. A positive voltage applied to the gate allows current to flow from the drain to the
source.       If the gate is at zero or negative voltage, no current can flow. The gate is insulated from the drain an
the source by design. This keeps current from flowing from the drain to gate or gate to source. Excess current flo
is called leakage current. The current that flows matches the amount of voltage supplied to the gate.

This is the circuit design :
The blue areas are temperature controlled by the Lakeshore Model 340 Temperature controller with a Proportiona
Integral loop (PI loop). The Temperature controller controls the specified areas to within ±5 mK.

The main power supply is in the top right corner (a), and provides a voltage for the load and the Rs (the sense
resistor, which is temperature controlled). The voltage across the Rs is then looked at through the followers at po
b, which draw no current because of the high input impedance. Point c is a difference amplifier with gain of 1. A
point d, an open loop op amp compares the voltage from the difference amp (this voltage should be equal to the
voltage over Rs) and a voltage reference. By controlling the voltage reference at point e, the voltage across the
sense resistor can be controlled. If I can control the voltage across Rs, I can control the current. Because the loa
and Rs are connected in series, the same current also flows through the load. Point e is a designed 5 V reference
that uses a voltage divider to select the correct magnitude of voltage for comparison at point d. The rest of the
network is designed to make sure the voltage signal at the MOSFET (f), remains constant.

When the first model of the circuit was installed it was over two times better than the previous magnet controller
But by using this more refined circuit we were able to     produce a voltage stability of a part in 105 and a
frequency of drift in the Xe of ±25 mHz. This is over 100x better than even the circuit preliminary runs (figure 5).
As a note, the top two plots are of Voltage in mV, not current.

 There is, however, still room for improvement. By finding an even more stable voltage reference, it should be
possible to improve the precision even further. Other issues that could be improved more are the isolation of the
circuit compared to the surroundings and the freedom of the leads going into the circuit box.

It has been a good summer during the REU program. I really enjoyed the experience, and I feel I learned a great

Thanks to Professor Tim Chupp and his research group, Professor Meiners, Matt Blank, The National Science
Foundation, and the University of Michigan Physics Department.

References for further reading.

Horowitz, Paul . Hill, Winfield. The Art of Electron ics. Cambridge Univer sity Pr ess. Cambridge. 1989. Chapters 1-5
Tietze, U. S che nk Ch. Electronic Circuits: Design and Applications S pringer-Verlag Berlin, Heidel berg. 1991 p. 286