Coil design
<Requirements>
- High voltage to force gain;
- Low power consumption (heat is low);
- Producing smooth (weak position dependence) magnetic field in the vicinity of the magnets fixed on the floating plate;
<Estimate>
- voltage to force gain:
Here we make a rough estimate before making a numerical calculation. The force of the coil is proportional to number of turn n and the current I. Since the current is equal to I=V/R and the resistance R=\rho l/S with l the length of wire and S the cross-sectional area, we have
While on the other hand 
with 
the mean radius of the coil, we finally arrive at
Interestingly, this is independent of the wire length. It only depends on the cross-sectional area of the wire and the mean radius of the coil. This basically indicates that different coils with the same mean radius could have the same transfer function even though the number of turns are different. This is indeed confirmed by the second stage experiment where the number of turns for four coils are different while the gain are almost the same.
Therefore, in order to have a large voltage to force gain, we should use thick wire and make the coil small.
- Maximal power:
The current buffer we are going to use is BUF643. From its datasheet, we can learn that the maximal current we can draw is 250mA. The output voltage swing is around 
. Therefore, the maximal power that it can deliver is around 4W. In order not to saturate the current output, the load resistance needs to be larger than 40 Om. If the coil has a small resistance, we need to add a resistor in series to the coil.
- Smooth control magnetic field:
It is very important that the control magnetic field by the coil need to be smooth, or the control force should have a small position dependence (a position dependent force will couple the ground motion to the floating plate.) Here we make an estimate by using the formula of the attraction force between two current loops given in the basic principle page. The mathematica notebook for calculating the force is attached (notebook). When the coil diameter is much larger than the diameter of the magnet on the floating plate, the force can be approximately as
where R is the radius of the coil and d is the distance from the coil center in the vertical direction. The maximum (where the force is locally position independent) is achieved when
In the experiment, we would like to have the control force to be smooth around the working point of the experiment.
<Numerical calculation>
Electronics for QPD
Laser driver
Ask experts