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Establish an average model for the primary-side regulated flyback converter
AC analysis plays a crucial role in the traditional flyback topology and involves the use of an optocoupler paired with a shunt regulator like the widely-used TL431. In recent years, with the rise of smartphones and tablets, there's a growing demand in the adapter market—specifically the portable adapter segment—to minimize the size and cost of this "black box" component connected to the power supply. How can manufacturers achieve these objectives?
One potential solution is to simplify the feedback loop and adopt a primary-side adjustment structure. While adjusting via the primary winding is a well-established practice, recent advancements have improved overall accuracy and enabled control of the output current without requiring direct measurement. These primary side regulation (PSR) controllers are now commonly found in various applications, competing with traditional optocoupler-based designs. However, compensation strategies for PSR topologies are often overlooked in literature. To stabilize the power supply, an AC analysis must be conducted, typically using an average model.
This article explores the key differences between a conventional flyback converter with an optocoupler and a PSR flyback. Next, we’ll examine how to construct an average model of a PSR flyback (including the necessary sample-and-hold circuit) and simplify it without impacting the transfer function. We’ll evaluate the transfer function, compare the Mathcad-generated graph with the simulation results of the converter, and plot the loop compensation while performing the necessary calculations to adjust the phase margin.
**Classic Flyback vs. PSR**
The term "classic flyback" refers to a feedback loop involving a secondary shunt regulator like the TL431 and an optocoupler used to transmit information to the primary side. A typical schematic of this converter is illustrated in Figure 1.
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In this setup, the output voltage is directly monitored on the secondary side. By modulating the optocoupler’s LED current, regulation information is sent to the primary-side controller, which adjusts the frequency and/or peak primary current to maintain the output voltage at its rated value.
However, optocouplers are relatively costly components that occupy more PCB space (such as 0603 packages) compared to simpler surface-mount resistors or capacitors. Given that millions of travel adapters are shipped annually with mobile phones, eliminating the secondary-side circuitry and optocoupler would yield significant economic benefits for manufacturers. Thus, innovative solutions have emerged to remove these components while preserving the accuracy of regulation comparable to that achieved by traditional flyback designs, as shown in Figure 2.
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**Working Principle of PSR**
From the schematic in Figure 2, it’s clear that the only connection between the high-voltage primary side and the isolated low-voltage secondary side is the transformer. Removing the optocoupler improves safety and reliability, as aging optocouplers can experience drift (e.g., declining current transfer ratio, CTR) and are vulnerable to external disturbances.
How does the primary-side adjustment mechanism work? Let’s examine the signals around the transformer, as depicted in Figure 3.
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During shutdown, the drain voltage (VDS) equals the sum of the input voltage and the output voltage, scaled by the primary-to-secondary turns ratio NPS (Ns/Np).
Next, we focus on the secondary winding voltage (VSEC). During the off-period (when the primary MOSFET is off), this voltage equals the sum of the output voltage and the voltage determined by the output rectifier and capacitor. When the output rectifier diode turns on during toff, it powers the load and charges the output capacitor. If we amplify the secondary winding voltage, as shown in Figure 4, we observe that the voltage drops with the diode current. This slope stems from the diode's dynamic resistance rd.
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In reality, the voltage drop across the diode consists of two components:
1. Turn-on threshold: VT0
2. Voltage drop across the dynamic resistance: rd × Idiode
VT0 is a technology-specific parameter, while rd depends on the diode’s operating point. The voltage on the auxiliary winding follows the same pattern as the secondary winding voltage but is influenced by the auxiliary turns ratio. From Figure 4, we can see that if the controller samples the voltage at the beginning of the demagnetization period (the first vertical dashed line in Figure 4), the output voltage information is impacted by the current. Under full-load conditions, the output voltage will be lower than under light-load conditions. The presence of dynamic resistance causes this discrepancy.
To accurately send information to the controller, our PSR circuit precisely detects the end of core demagnetization—the auxiliary voltage inflection point—before sampling the voltage. This technique naturally produces an accurate output voltage expression. Practically, this functionality is implemented within the controller die, utilizing a sample-and-hold circuit connected to the Vs/ZCD pin (used to detect the zero-crossing point of the auxiliary voltage) and the CV-regulated pin. The sampled signal is then compared to a reference voltage, and a constant voltage regulation is achieved via the operational transconductance amplifier (OTA) shown in Figure 5.
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The waveform in Figure 6 illustrates the refresh voltage for CV adjustment. The signal connected to the red curve (OTA) is compared to the reference voltage and refreshed periodically, unaffected by the output current. Thanks to this method, constant voltage regulation remains accurate under varying output loads or input voltages. The load regulation performance, as shown in Figure 7, achieves excellent results of 0.5% across the output power range, something not achievable with a conventional auxiliary-based converter.
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**Average Model for PSR Flyback**
One approach to analyzing the stability of our converters is to use an averaging model. To construct this model, we leverage the pulse width modulation (PWM) switching model introduced in the 1990s, referenced in [1], and adapted for quasi-resonant (QR) operation. The PWM switch model simplifies the diode and main MOSFET into a three-pin model that creates discontinuities during switching, forming a straightforward large-signal model that can be linearized for frequency response studies. Since this method is well-documented (see references [1] and [2]), we won’t delve further into it here.
Using the PWM switch model for the QR flyback topology, we can plot the schematic in Figure 8.
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This schematic incorporates all the devices surrounding the transformer and isn’t simplified yet. Connected to the secondary winding, we identify the output capacitor (Cout), its equivalent series resistance (Resr1), and the output load (Rload). On the auxiliary winding, we see the Vcc capacitor (CVcc) in series with ESR (Resr2), along with the IC modeled by resistor RIC. Additionally, there’s a resistor connecting the auxiliary winding to the ZCD pin. Simulating this schematic in SPICE, we can extract the control-to-output Bode plot of the power stage (Ctrl node to Vout). Figure 9 shows the results. Note that although the specific values used in Figure 8 aren’t provided here, they represent realistic applications.
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At a crossover frequency fc of 1 kHz—a compromise between fast transient response and robust noise immunity—the power stage attenuation measures at 19.5 dB, with a phase of -88.9 degrees.
Since the feedback signal originates from the auxiliary winding, we need to create a Bode plot identical to what’s observed at the Vaux node (Figure 10). While the phase shape remains unchanged, the amplitude curve is influenced by the transformer turns ratio:
\[ V_{\text{aux}} = \frac{N_{\text{PA}}}{N_{\text{PS}}} \cdot V_{\text{out}} \]
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With this average model configuration, all devices at the output are automatically reflected onto the auxiliary winding. Here, both diodes are assumed to have negligible dynamic resistance and are treated as short circuits.
**Simplifying the Average Model**
The next step involves simplifying the schematic and reducing the number of components without altering the transfer function. In Figure 8, we see three windings: the primary winding, the secondary winding responsible for power transfer, and the auxiliary winding used to monitor the output voltage and power the controller. Our ultimate goal is to derive the open-loop transfer function, so we aim to simplify the transformer as much as possible with a single secondary winding. All Bode plots won’t be displayed in this article. The initial step is removing the IC’s resistance, followed by the Vcc capacitor. The final simplification involves reflecting the devices connecting the secondary side to the auxiliary winding.
Let’s focus on the transformer shown in Figure 11. Compared to Figure 8, the number of components connected to the auxiliary winding is now reduced to the ZCD pin bridge resistance. The turns ratios connecting the primary to the secondary and auxiliary windings are denoted as NPS and NPA, respectively.
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Figure 11 shows the simplified transformer and secondary components. Reducing this schematic allows us to simplify the power-level averaging model.
To clarify and make understanding easier, we’ll proceed in two steps. First, we’ll reflect the output capacitor and resistive load to the primary side, as shown in Figure 12. These elements will then be reflected from the primary to the auxiliary winding.
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Figure 12 demonstrates the output capacitance and load reflected to the primary side.
**Reflection Around the Transformer**
Considering circuit devices as ideal, how do these devices reflect onto the transformer, especially when the diode has zero dynamic resistance? Let’s review the equation of the ideal transformer depicted in Figure 13.
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**Practical Application**
An NCP1365-based PSR converter was assembled as shown in Figure 26. The previously calculated component values were used to compensate for the design and soldered onto the board. The 5V output supports loads ranging from 1A to 2A. As demonstrated in Figure 27, the transient response remains excellent regardless of the input voltage.
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The PSR board from ON Semiconductor’s NCP1365 has been assembled. It provides 5V and up to 2A of output current.
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The transient response measured under low and high voltage conditions confirms the excellent stability of the converter.
**Conclusion**
This article discusses two main topics: the operation mode of the flyback converter under primary-side regulation and the use of a power-level average model to analyze its operation. Progress was made in the modeling process by first simulating a simple QR power stage to which an auxiliary winding was added. Finally, a sample-and-hold circuit was incorporated.
With modern primary-side regulation controllers, the difference between the traditional flyback topology and PSR lies in the implementation of regulation. With a well-designed transformer, regulation and stability closely resemble those of optocoupler-based power supplies.
In the second part of this article, we demonstrated the calculation of the transfer function of a primary-side regulation converter that integrates the sample-and-hold circuit in the controller IC. Using Mathcad software, we constructed a Bode plot from the transfer function and compared it to the simulation model mentioned earlier in this article. The two waveforms matched closely.
Ultimately, the required compensation circuitry was defined and specified as a phase margin requirement. Based on this article, you can design a Type-2 compensation circuit for a converter that uses PSR. Naturally, the same approach can be applied to other topologies, such as those for power factor correction.
In reality, some PSR controllers have built-in compensation, eliminating this design choice for engineers. However, with the ON Semiconductor PSR controllers discussed here (and others in the future), the ability to design external compensation circuits through modeling removes the trial-and-error methods that designers may have previously relied upon.
This article provides a foundation for understanding PSR flyback converters and their control methodologies, enabling engineers to optimize their designs efficiently.