Design Scheme of Flyback Transformer Operating in DCM (Krp=1) and CCM (Krp=0.65) Modes

The detailed calculation process and core parameters of the high-frequency transformer are sorted out as follows:

1. Basic Parameter Setting

Before specific calculations, the following basic design parameters are uniformly defined:

2. Minimum and Maximum DC Bus Voltage after Rectification (Vdcmin / Vdcmax)

• Vdcmin: 85Vac×√2 -20V(drop) ≈ 100Vdc

• Vdcmax: 265Vac × √2 ≈ 374Vdc

The above results are obtained via calculation and adopted as the basis for subsequent derivation to simplify the computation.

3. Parameter Calculation for DCM Mode (Krp = 1)

In DCM (Krp=1) mode, the primary current rises linearly from zero with the maximum current ripple ratio.

3.1 Turn Ratio (n)

• Formula: n = Vor / (Vo + Vf)

• Calculation result: n=100V / (20V + 1V) ≈ 4.76

3.2 Peak Current in DCM Mode (Ipk_DCM)

• Formula: Ipk = (2 ∗ Pin) / (Vdcmin ∗ Dmax)

• Calculation result: Ipk_DCM = (2 ∗ 70.59W) / (100V ∗ 0.45) ≈ 3.14A

3.3 Primary Inductance in DCM Mode (Lp_DCM)

• Formula: Lp = (Vdcmin ∗ Dmax) / (Ipk ∗ f)

• Calculation result: Lp_DCM = (100V ∗ 0.45) / (3.14A ∗ 130kHz) ≈ 110.3μH

4. Parameter Calculation for CCM Mode (Krp = 0.65)

Krp=0.65 indicates a relatively large current ripple in CCM mode, while the current does not reach the critical point and still contains partial DC component.

4.1 Turn Ratio (n)

• Formula: n = Vor / (Vo + Vf)

• Calculation result: n = 100V / (20V + 1V) ≈ 4.76

4.2 Average Current in CCM Mode (Iavg_CCM)

• Formula: Iavg = Pin / Vdcmin

• Calculation result: Iavg_CCM = 70.59W / 100V ≈ 0.706A

4.3 Peak Current in CCM Mode (Ipk_CCM)

• Formula: Ipk = Iavg / [ (1-Krp/2) * Dmax ]

• Calculation result: Ipk_CCM=0.706A/[ (1- 0.65/2) * 0.45 ] ≈ 2.29A

4.4 Primary Inductance in CCM Mode (Lp_CCM)

• Formula: Lp = (Vdcmin ∗ Dmax) / (Ipk ∗  Krp ∗ f)

• Calculation result: Lp_CCM=(100V*0.45) / (2.29A ∗ 0.65 ∗ 130kHz) ≈ 232.8μH

5. Transformer Core and Winding Parameters

5.1 Primary Winding Turns (Np) & Selection of Core and Bobbin Parameters (EE25 as example)

Core Model: EE25 (PC95), a commonly used power magnetic core

• Effective Cross-sectional Area (Ae): 52 mm²

• Window Area (Aw): 84.9 mm² (typical value including bobbin)

• Magnetic Path Length (le): 57.5 mm

• Saturation Flux Density (Bsat): 0.39 T @ 100℃

• Maximum Operating Flux Swing (ΔB) for DCM: 0.25 T

• Maximum Operating Flux Swing (ΔB) for CCM: 0.16 T

Note: Due to DC magnetic bias in CCM mode, the allowable AC flux swing ΔB is generally set to a smaller value (0.12～0.18 T) to avoid core saturation. The calculation adopts 0.16 T for rigorous design.

5.2 High-frequency Skin Effect and Wire Gauge Selection

Switching frequency f = 130 kHz, skin depth of copper:

δ=66.1/√f​=66.1/√130000​=0.183mm

To prevent obvious increase of AC resistance, the diameter of single-strand wire shall be less than 2δ≈ 0.366 mm. Multi-strand parallel winding, Litz wire or copper foil is required for windings with large current.

Current density: J = 6A/mm^2 (applicable for natural cooling or forced air cooling).

5.3 Calculation of Winding RMS Current and Wire Gauge / Strand Number

Basic Conditions

V_{dcmin}=100V , D_{max}= 0.45 , f = 130kHz

Reflected voltage V_{or}= 100V , turn ratio n ={V_{or}}/{V_o+V_f} =100/{20+1} = 4.76

1. DCM Mode (ΔB= 0.25T)

Primary turns:

N_p=V_{dcmin}×D_{max}} / {ΔB×A_e×f} =100×0.45 / {0.25×52×10^{-6}×130×10^3} =26.8 →27Turns

Secondary turns:

N_s = N_p/n= 27/4.76= 5.67 → 6Turns

Actual turn ratio n_{real} = 27/6 = 4.5 , reflected voltage V_{or} = 4.5×21=94.5 V. It has negligible impact on primary voltage stress and is acceptable.

2. CCM Mode (ΔB= 0.16T)

Primary turns:

N_p=\frac{100×0.45}{0.16×52×10^{-6}×130×10^3} = 41.7 → 42Turns

Secondary turns:

N_s = 42/4.76 =8.82 → 9Turns

Actual turn ratio n = 42/9=4.67, reflected voltage 4.67×21= 98V.

Note: CCM mode requires more turns to reduce flux swing, which results in larger inductance (232.8 μH) and smaller air gap.

• Cross-sectional area of 0.25 mm enameled wire (bare copper):π×(0.25/2)^2 ≈ 0.0491mm^2

• Total area of 4-strand parallel winding: 0.196mm^2, which meets the current-carrying requirement and reduces loss.

• The diameter of single 0.25 mm wire is less than 2δ=0.366mm, so the skin effect can be ignored.

5.4 Secondary Winding

Output: 20V/3A, RMS current of secondary winding (full-wave rectification):

I_{rms_sec}=I_o√{1-D_{max}/{D_{max}}=3×√{1-0.45}/{0.45}}=3×1.105=3.32A

Note: For the secondary diode rectifier of flyback topology, the RMS current calculation formula is I_o √{(1-D)/D}.

Required bare copper area: 3.32/6=0.553mm^2

Adopt 0.25 mm multi-strand wire: single strand area 0.0491mm^2.

Required strand number: 0.553 / 0.0491 ≈ 11.3 → select 12 strands × 0.25 mm, total copper area 0.589 mm^2.

5.5 Auxiliary Winding (Vcc, 15V/0.1A assumed)

Turns are calculated according to turn ratio. The current is very small, so single-strand 0.15 mm wire is adopted with cross-sectional area 0.0177mm^2. It occupies negligible window area.

5.6 Magnetic Core Air Gap Length (lg)

• Formula: lg = (4π{e}^{-7} × N_p^2 × Ae) / Lp

• Calculation results:

  • DCM: lg ≈ 0.43mm

  • CCM: lg ≈ 0.49mm

5.7 Wire Gauge Selection for Windings

• Primary RMS current (Irms):

  • DCM: {Irms_DCM} = Ipk × √{Dmax/3} ≈ 1.22A

  • CCM: {Irms\_CCM} = Ipk × {√{Krp^2/3} - Krp + 1}} × √{Dmax} ≈ 1.08A

• Secondary RMS current (I_{sec_rms}: 60W output, secondary RMS current ≈ 8.3A.

• Current density (J): 6A/mm^2

• Bare wire cross-sectional area (S): S = Irms / J

• Wire diameter (ϕ): ϕ = 1.13 ×√{S}

Calculated wire gauges for primary and secondary windings:

• DCM Primary: ϕ 0.51 mm (or multi-strand fine wire)

• CCM Primary: ϕ 0.48 mm (or multi-strand fine wire)

• Secondary: ϕ 1.32 mm (multi-strand parallel winding or copper foil is recommended)

5.8 Window Utilization Factor Calculation

Bobbin window area A_w = 84.9mm^2.

Key factors for actual winding:

• Insulation of enameled wire (occupancy factor ≈ 0.85~0.9)

• Interlayer insulating tape (0.05 mm per layer)

• Margin for bobbin and winding process: the actual usable window area is generally 70%~80% of A_w.

Simplified calculation: Copper window factor = Total bare copper area / A_w. The target value for engineering application is 0.2~0.4.

1. Winding Configuration Summary

2. Copper Window Factor (Bare Copper Area / Window Area)

• DCM: 9.02 / 84.9 = 0.106 (10.6%)

• CCM: 13.73 / 84.9 = 0.162 (16.2%)

3. Actual Window Fill Factor Considering Insulation and Winding Process

The outer diameter of 0.25 mm enameled wire is about 0.28 mm (0.02~0.03 mm larger than bare copper due to insulation coating), increasing the occupied area by about 25%. Interlayer tape and bobbin barriers will further reduce utilization rate. In engineering practice, the actual fill factor (including insulation) is approximately 1.3~1.5 times the bare copper window factor.

If the usable window area is set to 75% of A_w (deducting bobbin and process margin):

Maximum allowable bare copper area ≈ 0.75 × 84.9 ≈ 63.7mm^2, which is far larger than the actual value. The window margin is sufficient for both schemes.

6. Difference between Two Modes & Design Summary

Performance Comparison

The above two schemes cover all key theoretical calculations. In practical engineering, transformer parameters usually need fine tuning combined with EMC test and temperature rise test, such as adjusting inductance or turn ratio for optimal performance.