Guide to Principles and Parameter Calculations for Quasi-Resonant Flyback Switch-Mode Power Supplies, QR Flyback Transformer Parameter Calculation Formulas

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Working Principle of Flyback Switching Power Supply

1. Switch On-State Phase: Due to the polarity relationship of the transformer’s same-name terminals, the secondary diode remains reverse-biased and cut off. During this phase, the primary winding’s inductance stores energy.
2. Switch Off-State Phase: The secondary diode becomes forward-biased and conducts. Energy stored in the primary winding is released, partially charging the capacitor and partially supplying the load.

DCM Operation Mode of Flyback Switching Power Supply

Mode Definition

DCM (Discontinuous Conduction Mode), also known as complete energy transfer mode (discontinuous mode), is characterized by:

• Complete release of energy stored in the magnetic core (corresponding to the i_{\text{p}} waveform in Figure 3).
• The primary switching transistor turns on only after the secondary rectifier diode current reaches zero (corresponding to the i_{\text{s}} waveform in Figure 3).

Associated Waveform Explanations

• Figure 2: V_{\text{DS}} voltage waveform of the switching transistor in DCM mode, illustrating voltage fluctuation characteristics.
• Figure 3: Current waveform in DCM mode, showing primary winding current (i_{\text{p}}) and secondary winding current (i_{\text{s}}), visually demonstrating the complete energy release process.

Advantages and Disadvantages

Advantages

1. No reverse recovery issues in the secondary rectifier diode.
2. Easier stability control for the power supply loop.

Disadvantages

1. Higher peak current and RMS current in the primary winding increase copper losses and MOSFET conduction losses.
2. After complete energy release, the drain terminal exhibits sinusoidal oscillations caused by the MOS junction capacitance and primary leakage inductance.
3. In traditional fixed-frequency flyback converters, the switching transistor may turn on at any point (including peak) of the oscillating voltage, increasing turn-on losses.

CCM Operation Mode of Flyback Switching Power Supply

Mode Definition

CCM (Continuous Conduction Mode), also known as incomplete energy transfer mode (continuous mode), is characterized by:

• Incomplete energy release in the magnetic core (corresponding to the I_{\text{p}} waveform in Figure 5).
• The primary switching transistor turns on before the secondary rectifier diode current fully reaches zero (corresponding to the I_{\text{s}} waveform in Figure 5).

Associated Waveform Explanations

• Figure 4: V_{\text{DS}} voltage waveform in CCM mode, illustrating voltage variation characteristics.
• Figure 5: Current waveform in CCM mode, showing primary winding current (I_{\text{p}}) and secondary winding current (I_{\text{s}}), visually demonstrating the incomplete energy release process.

Advantages and Disadvantages

Advantages

Under the same power conditions, since energy is not fully released and the primary inductance current does not drop to zero, peak current and RMS current are lower than in DCM mode, resulting in reduced copper losses and MOSFET conduction losses.

Disadvantages

1. Secondary rectifier current does not reach zero, causing losses from reverse recovery time.
2. When transitioning from no-load to full-load, the system experiences three stages: DCM→CRM→CCM. The transfer function changes during DCM-to-CCM transition, potentially causing oscillations.
3. Large duty cycles may cause subharmonic oscillations, requiring slope compensation and increasing feedback design complexity.
4. Severe switching losses (MOSFET often turns on at peak voltage).

QR Operation Mode of Flyback Switching Power Supply

Mode Definition

QR (Quasi-Resonant) mode is a variant of DCM (complete energy transfer mode). Its core feature is:

• After full energy release in the magnetic core, the primary inductance and MOS junction capacitance resonate. The primary switching transistor turns on when the junction capacitance discharges to the minimum voltage.

Associated Waveform Explanations

• Figure 6: V_{\text{DS}} voltage waveform under heavy load in QR mode.
• Figure 7: V_{\text{DS}} voltage waveform under light load in QR mode. Both waveforms illustrate the switching transistor conducting at the oscillation voltage valley.

Key Features and Optimization

QR mode inherits most DCM advantages/disadvantages. Its key optimization is the valley detection function: By turning on the switching transistor at the oscillation voltage valley, it achieves zero-voltage/low-voltage turn-on, reducing switching losses and EMI noise.

Implementation Method

Using flux reset detection (typically via an auxiliary winding) combined with control IC logic ensures the switching transistor conducts when oscillation voltage reaches its minimum.

Limitations

QR mode operates with dynamic frequency variations, which may affect the determination of other circuit parameters.

Parameter Determination Process for QR Flyback Power Supply

1. Determine Key QR Parameters

Parameter Item	Description and Values
Input Voltage Range	Minimum V_{\text{acmin}}, Maximum V_{\text{acmax}}. Common ranges: low input (85~135VAC), high input (176~265VAC), universal (85~265VAC)
Input Frequency f_{\text{ac}}	AC frequency, typically 50Hz or 60Hz
Output Voltage V_{\text{out}}	Target power supply output voltage
Output Current I_{\text{out}}	Target power supply output current
System Efficiency \eta	Typically 80%
Minimum Switching Frequency f_{\text{sw}}	Dynamic frequency range. Design for minimum frequency at lowest input voltage and maximum input power, typically 25kHz~100kHz
Maximum Input Power P_{\text{in}}	Formula: P_{\text{in}} = \frac{V_{\text{out}} \times I_{\text{out}}}{\eta}

2. Determine DC Input Voltage

The AC voltage is rectified and filtered to produce high-voltage DC. Key formulas and parameters:

1. Capacitor charging duty cycle: D_{\text{ch}} \approx 0.33
2. Minimum DC input voltage:
   V_{\text{busmin}} = \sqrt{2V_{\text{acmin}}^2 - \frac{P_{\text{in}} \times (1-D_{\text{ch}})}{C_{\text{BUS}} \times f_{\text{ac}}}}
3. Maximum DC input voltage:
   V_{\text{busmax}} = \sqrt{2} \times V_{\text{acmax}}
4. Input Capacitance C_{\text{BUS}} Selection (\mu\text{F/W}):

AC Input Voltage Range	C_{\text{BUS}} Value
85~135VAC	2
176~265VAC	1
85~265VAC	2~3

3. Determine Reflected Voltage V_{\text{RO}}

Reflected voltage is critical for QR mode zero-voltage turn-on. Key considerations:

1. MOSFET rating V_{\text{DS}} components:
   V_{\text{DS}} = V_{\text{busmax}} + V_{\text{clamp}} + \text{Stray inductance voltage} + \text{Switching transistor voltage margin}
   • V_{\text{clamp}} (Clamping voltage): 1.4V_{\text{RO}} minimizes snubber losses
   • Stray inductance voltage: typically 10~20V
   • Switching voltage margin: 10%~20% of V_{\text{DS}}
2. V_{\text{RO}} calculation formula:
   V_{\text{RO}} = \frac{[(80\% \sim 90\%)V_{\text{DS}} - V_{\text{busmax}} - (10 \sim 20)]}{1.4}

4. Determine Maximum On-Time T_{\text{ON}}

Switching period T = T_{\text{ON}} + T_{\text{OFF}} + T_{\text{W}} (T_{\text{OFF}} = demagnetization time, T_{\text{W}} = oscillation time). Key formulas:

1. Oscillation time T_{\text{W}}:
   T_{\text{W}} = \pi \sqrt{L_{\text{P}} \times C_{\text{P}}}
   (L_{\text{P}} = primary inductance, C_{\text{P}} = MOSFET drain capacitance; typically T_{\text{W}} \approx 5\%T)
2. Maximum on-time:
   T_{\text{ON}} = \frac{V_{\text{RO}} \times (0.95 \times T)}{V_{\text{busmin}} + V_{\text{RO}}}

5. Determine Primary Inductance L_{\text{P}}

1. Maximum duty cycle: D_{\text{max}} = \frac{T_{\text{ON}}}{T}
2. Primary peak current:
   I_{\text{ppk}} = \frac{P_{\text{in}} \times 2}{D_{\text{max}} \times V_{\text{busmin}}}
3. Primary inductance:
   L_{\text{P}} = \frac{V_{\text{busmin}} \times T_{\text{ON}}}{I_{\text{ppk}}}

6. Select Transformer (AP Method)

Choose core via AP value:

AP = A_{\text{e}} \times \left( \frac{L_{\text{P}} \times I_{\text{ppk}}^2 \times 10^4}{\Delta B \times 450 \times K_{\text{O}}} \right)^{1.143}

• Parameters:
  • A_{\text{e}}: Core cross-sectional area (determined after AP calculation)
  • \Delta B: Magnetic flux density variation, typically <0.3T
  • 450: Current density (unit: A/cm²)
  • K_{\text{O}}: Window utilization factor, typically 0.2~0.4

7. Determine Transformer Turns Ratio

1. Primary turns:
   N_{\text{P}} = \frac{L_{\text{P}} \times I_{\text{ppk}}}{\Delta B \times A_{\text{e}}}
   (L_{\text{P}} unit: \mu\text{H}, A_{\text{e}} unit: \text{mm}^2)
2. Secondary turns:
   N_{\text{S}} = \frac{(V_{\text{out}} + V_{\text{f}}) \times N_{\text{P}}}{V_{\text{RO}}}
   (V_{\text{f}}: Rectifier voltage drop, typically 0.5~1V)

8. Determine Transformer Air Gap L_{\text{g}}

Formula:

L_{\text{g}} = \frac{\mu_{0} \times N_{\text{P}}^2 \times A_{\text{e}}}{L_{\text{P}}}

• Parameters:
  • \mu_{0}: Vacuum permeability, 4\pi \times 10^{-7}\ \text{H/m}
  • A_{\text{e}}: Core cross-sectional area (\text{m}^2)
  • L_{\text{P}}: Primary inductance (H)

9. Determine Primary/Secondary Coil Wire Gauge

1. Primary parameters:
   • Primary RMS current: I_{\text{Prms}} = I_{\text{ppk}} \times \sqrt{\frac{D_{\text{max}}}{3}}
   • Primary wire diameter: D_{\text{P}} = 1.13 \times \sqrt{\frac{I_{\text{Prms}}}{J}}
2. Secondary parameters:
   • Demagnetization duty cycle: D_{\text{off}} = \frac{T_{\text{OFF}}}{T} (T_{\text{OFF}} = T - T_{\text{ON}} - T_{\text{W}})
   • Secondary peak current: I_{\text{Spk}} = \frac{2 \times I_{\text{out}}}{D_{\text{off}}}
   • Secondary RMS current: I_{\text{Srms}} = I_{\text{Spk}} \times \sqrt{\frac{D_{\text{off}}}{3}}
   • Secondary wire diameter: D_{\text{S}} = 1.13 \times \sqrt{\frac{I_{\text{Srms}}}{J}}

• Current density J: Typically 4~6A/mm², up to 10A/mm² for fewer secondary turns

10. Determine Secondary Rectifier Diode

1. Reverse voltage rating:
   V_{\text{rrrm}} = 1.25 \times (V_{\text{busmax}} \times N + V_{\text{out}})
   (N = \frac{N_{\text{S}}}{N_{\text{P}}}: turns ratio, 1.25: voltage spike margin factor)
2. Forward current:
   I_{\text{F}} = (2 \sim 3) \times I_{\text{Srms}}
   (2~3: derating factor)

11. Determine Output Capacitance

The output capacitor must match voltage rating, capacitance, and ESR (equivalent series resistance). Key parameters:

1. Voltage Rating: Typically 1.25× output voltage: V_{\text{Cout}} = 1.25 \times V_{\text{out}}
2. Capacitance: Output voltage ripple controlled to 1% of output (\Delta V = 1\%V_{\text{out}}):
   C_{\text{out}} = \frac{(I_{\text{Spk}} - I_{\text{out}})^2 \times D_{\text{off}}}{2 \times \Delta V \times I_{\text{Spk}} \times f_{\text{sw}}}
   • I_{\text{Spk}}: Secondary peak current
   • I_{\text{out}}: Output current
   • D_{\text{off}}: Transformer demagnetization duty cycle
   • f_{\text{sw}}: Switching frequency
3. ESR: Critical for ripple control: \text{ESR} = \frac{\Delta V}{I_{\text{Spk}} - I_{\text{out}}}

12. Determine RCD Snubber Parameters

The RCD snubber circuit suppresses MOSFET drain-source voltage spikes. Parameter determination logic:

1. Leakage Inductance L_{\text{ik}}: Typically 1%~5% of primary inductance (estimate within this range if not tested).

2. Clamping Resistor R:
   Formula: R = \frac{2 \times (V_{\text{clamp}} - V_{\text{RO}}) \times V_{\text{clamp}}}{L_{\text{ik}} \times I_{\text{ppk}}^2 \times f_{\text{sw}}}
   Resistor power: P_{\text{R}} = \frac{V_{\text{clamp}}^2}{R}

3. Clamping Capacitor C:
   Capacitor voltage ripple \Delta V = 5%~10% of V_{\text{clamp}}:
   C = \frac{V_{\text{clamp}}}{\Delta V \times R \times f_{\text{sw}}}

   • V_{\text{clamp}}: Clamping voltage (previously defined as 1.4V_{\text{RO}})
   • V_{\text{RO}}: Reflected voltage
   • I_{\text{ppk}}: Primary peak current
   • f_{\text{sw}}: Minimum switching frequency

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