## The Basics of MRI

### Single-Turn Solenoids

A single-turn solenoid (STS) is a tubular inductor with a capacitive gap running along the length of the tube.
The tube can be solid
or perforated,
and circular, oval, square, rectangular,
or asymmetrical
in cross section. Two or more tubes may be joined together to form a resonant device.

The resonance frequency, n, of a STS is given by the equation

where L is the inductance of the tube and C the capacitance created either by the gap in the tube or by capacitors spanning the gap. The inductance of a cylindrical inductor or radius r and length *l* is given by

L = m p r^{2} / *l*
where m is the permeability constant (4p x 10^{-7} N/A^{2}).
The inductance of a rectangular inductor of width *w*, height *h*, and length *l* is given by

L = m *w h* (*l* + d)^{-1}
where d is an empirical constant and *w h* is the cross sectional area of the tube.

An STS is typically constructed by adhering copper foil to an insulating material, such as PVC.
The longitudinal gap in the resultant inductor is spanned by either discrete high-Q chip capacitors, or a parallel plate capacitor formed by low-loss circuit board.
Power is coupled into and out of the resonant circuit by a coupling loop.
The impedance of the resonant circuit can be adjusted by varying the distance between the loop and the inductor. Therefore, a coupling capacitor is not needed in the circuit.

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