Transformer Design
As mentioned in chapter 3, the coil size is determined by the size constraints of the module package inside dimensions.
A worst case analysis is best performed on the design to arrive at the desired inductance to design to so that the minimum inductance of 350uh is met after the core tolerance, DC bias effects and temperature variation are considered.
After reviewing all core vendors’ manganese zinc materials and choosing the ones that had the best characteristics for temperature and coercive force, then the design inductance can be established.
To estimate the number of turns that will be used on the core, start with calculating the core constant needed to fit in the package.
K= AC / lm
N = [ Lmin /uK]^0.5
Example:
Assume K=0.10725 N=[ 350 * 10-6 / 4500 * .10725 ]0.5
N = 26 turns
With an initial estimate of the number of turns, it is now time to calculate the coercive force that 8 ma of DC bias will produce with these turns on that size core.
H= 0.4 * 3.14159 * 26 * 0.008 / 0.894 = 0.2924 oersteds
From the chosen vendor’s catalog, find the flux density that is available with the DC bias applied and the new permeability that the temperature variation causes.
Worst Case Analysis:
Minimum OCL = 350uh.
Allowing for 15% DC bias drop over 0C to +70C,
350/0.85 = 411.7uh
.
Allowing for 20% core tolerance,
411.7/0.8 = 514.7uh nominal
Example:
N = [350 * 10-9 / (4500*.80*.85) * .10725] = 34 turns
These turns are a bit high to meet all the parasitics so we will have to adjust the size of the core. Possibly by raising the core height.
N = [350 * 10-9 / (4500*.80*.85) * .17 = 26 turns
If this is not acceptable, then the OD or ID of the toroid as well as the height will have to be adjusted to the next available size, or request the core vendor make a special tooling.
| | |