Optimization of Parameters
When all the calculations have been made, based upon the first cut of the design, it may be found that some or all functional requirements will not conform to the required specifications. If this is the case, then there will have to be a decision made as to what tradeoff will have to be made, or what changes will have to be considered in the winding techniques. The coil set may have to be redesigned. This may or may not be possible. If this is the case, then tradeoffs will have to be considered and then a determination of the final functional values will be made.
The size of the core used is based upon the package size constraints. This ties the design down to a maximum size that can be used. Therefore, the turns are set and the wire size and winding geometry are the only variables that can be changed to improve the electrical parameters.
The flow chart included below shows the steps that have to be considered to optimize the design. When one parameter is reduced, another may increase. This can be experienced when reducing the leakage inductance. The distributed and interwinding capacitance may increase. The calculations of the bandwidth and rise times must be reviewed when these changes are made.
In an effort to reduce the leakage inductance by twisting the wire, the coupling between the windings is improved, but the capacitance between the windings is increased. Depending on the wire separation from turn to turn due to the twisting randomness, the distributed capacitance may be decreased.
The estimate of parasitic parameters is achieved by multiplying the factors below for the coupling capacitance and substituting the wire cable diameter, dC , for the wire diameter, dW , in the bifilar winding formulas.
Leakage Inductance for Twisted Wires
In an effort to reduce the leakage inductance, it may be necessary to change the wire size to a larger wire diameter, or smaller AWG, to have more copper covering the core. This is only possible if the current winding doesn’t totally cover the core. The danger here is that there could not be enough room on the core for one single layer (optimum) and then crossovers of the wire would occur. This could increase the leakage inductance. It must be made clear that crossovers may occur while winding the coils and the values calculated may change.
Another possible solution would be to twist the primary and secondary winding wire together to improve the coupling coefficient and thus lower the leakage inductance. The formula for cable diameter is:
dC = 1.21 (dW) (TPI)0.49
where: dW = wire diameter dC = cable diameter
TPI = twists per inch
Then, there should be a check made as to whether this twisted wire cable diameter will fit on one layer on the ID of the core. Determine the circumference that appears in the middle of the cable diameter when the cable is wound on the core.
Circ. = ( ID – dC ) π
Where: π = 3.14159
Determine the turns per layer around the core ID circumference.
Turns per layer = Circ. / dC = NP
This calculation refers to the number of turns of the twisted wire cable consisting of the primary and secondary windings. These should be the same number of turns as the primary winding.
Reducing the leakage inductance by twisting the wire causes the coupling capacitance to increase. This may be a problem in reducing the bandwidth and deteriorating the Insertion Loss and Return Loss. The coupling capacitance increase due to twisting can be estimated by the following formula. This factor is multiplied by the calculated coupling capacitance between the windings on the toroid. What we end up with is a juggling act.
Because the circuit requires a centertap on the primary side of the transformer, it will be necessary to wind the transformer quadfilar using half the number of winding turns twisted to improve the coupling of the windings. The secondary would end up with a splice instead of a centertap. This could either be buried in the coil or connected to a pad on the PC board of the module if this is the case. Care should be exercised when burying the splice so that there is not a hipot failure or excessive wire length.
The calculation for leakage inductance is then performed using the twisted wire cable diameter.
LL = 0.003 lW [ 2.3 LOG (( 4 lW / dC) – 0,75)]
Where: dC = cable diameter lW = winding length on the core
Coupling Capacitance for Twisted Wires
By twisting the wires together, there is an assurance that the wires will be closer together and thus, the coupling capacitance will increase. To estimate this effect, the following formula factors can be multiplied by the coupling capacitance calculated for the twisted cable diameter. These formulas can be used for all insulation thicknesses.
The coupling capacitance is then calculated, using the cable diameter, dC , in lieu of the wire diameter, dW .
This value will have to be modified by a factor that determines the effect of twisting two versus four wires together. These factor formulas are:
Two wires:
Four wires:
Depending upon what the number of wires being twisted is, the final coupling capacitance is calculated by multiplying the calculated capacitance by the above factor.
The new coupling capacitance can now be compared to the bifilar wound capacitance to see if there was a significant change. This will have an effect on the cutoff frequency and thus, the bandwidth.
Distributed Capacitance for Twisted Wires
To calculate the effective circumference of the OD and ID of the coil to the center of the cable use the following formulas. The center of the cable will provide the average distance between the twisted wires.
C1 = 0.95 ( ID – dC ) ( cover/360 )
C2 = 0.95 ( OD + dC ) ( cover/360 )
Next, calculate the average distance between the cables when wound on the core.
l1 = [ C1 – ( NP ) ( dC )] / ( NP – 1 )
l2 = [ C2 – ( NP ) ( dC )] / ( NP – 1 )
Average distance = dt = ( l1 + l2 ) / 2 inches
Now calculate the surface area of the wires facing each other on the cable. Use the wire diameter of the chosen insulation on the wire.
AW = [( OD – ID ) + 2H ] dC ( 1.5708 ) ( L/T ) sq. inches
Where: L/T = length per turn of the wire
Calculate the distributed capacitance of the cable.
Cd = [( 0.224 K AW ( N – 1 ) 10-12 ) / dt ] pf.
Waveform Analysis
The remainder of the waveform analysis can be calculated as shown in the flow chart in this chapter.