open and close producing square
wave voltage on the primary.
Starting at t = 0, flux increases
according to Φ = (V/N)t, producing
triangle wave flux in the core as
shown in Figure 7 (triangular as long
as μ doesn't change much with
Φ). The current in the coil is also
■ FIGURE 6
Two points about Figure 7: First,
flux goes from - Φm to + Φm, so
Φ=2Φm. Second, Δt is half the period, so Δt = T/2 =1/2f.
increases copper loss.
Putting a load on the secondary
causes primary current to increase,
but not flux in the core. The mmf
caused by current in the secondary
cancels mmf caused by the
additional primary current, so there's
no net change in flux.
Terminology and Units
Turns per Volt
Table 1 shows the two sets of magnetic units.
Table 2 shows how to convert from one to the other.
The unit for mmf is actually just amps. The number of
turns is a dimensionless multiplier.
Rewrite Faraday's Law:
V=N(ΔΦ/Δt) = N(2Φm)/(1/2f) = 4NΦmƒ
Choosing a Core
Rearranging terms yields an important parameter:
the turns-per-volt (N/V). N/V = 1/(4Φmƒ). But Φm =
Bm x Ae, where Ae is the effective cross section area of
the core, so:
N/V = 1 / ( 4 Bm Ae ƒ).
Magnetizing Current (Im)
The flux linking primary to secondary in a transformer
is generated by the primary mmf which is 90O out of phase
with primary voltage as seen in Figure 7. Since Φ ∝ I,
primary current is also 90O out of phase with primary
voltage so, except for losses, no power flows in. The
primary looks like an inductor. The current in that inductor
is the magnetizing current:
Hm = Bm/μ ⇒ NIm/le = Bm/μ ⇒ Im = (Bm le)/μN
where le is the effective length of the flux path. High Im
We want a core that is efficient at 100 kHz with an
internal diameter big enough so winding turns is easy.
To minimize the number of turns, N/V should be between
1 and 2.
The core chosen for this project is a FERROXCUBE
TX16/9.1/4.7 epoxy coated toroid. The part number gives
the dimensions: 16 mm OD, 9 mm ID, 5 mm thickness.
It's made from their 3C90 ferrite material, designed for
power applications up to 200 kHz. From its datasheet,
Ae = 14. 7 mm2 and le = 37.2 mm. Core loss at 100 kHz
and 100 m T is less than 55 m W. Similar cores from
other manufacturers like MAGNETICS and Fair-Rite would
Bmax for 3C90 is about 350 milli-Tesla (m T) at 25OC.
Using Bmax would lead to higher core loss and the
danger of saturation. To be conservative, let Bm = 100 m T.
The turns per volt is:
= 1/( 4 Bm Aeƒ)
= 1/( 4 • 0.1 • 14. 7× 10-6 • 1×1005) = 1.7
■ TABLE 1
Magnetic Field Strength
■ FIGURE 7