Stabilizing Operation in a DCM Flyback with a Positive Feedback Network
Flyback converters are a popular choice for lowpower Switched Mode Power Supply (SMPS) systems because they’re lightweight and relatively inexpensive. When used as part of adapters and chargers, many flyback controllers employ a negative feedback network that makes operation more stable in Discontinuous Conduction Mode (DCM).
In some of these applications, the output load current needs to be sensed as part of the control mechanism for the output voltage. One way to sense the load current is to use a sensing resistor and measure the voltage on the resistor directly, but this often results in higher conduction losses. A different way, which doesn’t produce such high conduction losses, is to sense load current indirectly.
A common method for indirect sensing is to use the duty cycle and the input voltage to emulate the load current. This approach requires adding a positive feedback network.
Figure 1 shows a basic flyback controller, built using a FPS™ power switch, with a secondary circuit for sensing load current indirectly. The basic circuit is a negative feedback network, while the added secondary circuit is a positive feedback network. The voltage on C_{f} is proportional to V_{in} and the duty cycle of the FPS power switch. The output voltage (V_{O}) is regulated by changes in the load current.
Figure 1. Using a positive feedback network to sense load current indirectly
When taken on its own, without the added circuitry for emulating the output current, the negative feedback network of the basic flyback converter is quite stable. A rise in v_{O} is eventually offset by a decrease in v_{O}. As can be traced in Figure 1, when v_{O} increases, i_{1} increases, i_{comp} increases, v_{OP} decreases, v_{FB} decreases, i_{D} decreases, and v_{O} decreases.
With the addition of the positive feedback network, however, an increase in the duty cycle leads to an increase in v_{O}, but without an offset mechanism to bring v_{O} back down. Going back to Figure 1 to trace the operation, when the duty cycle increases, i_{D} increases, v_{O} increases, v_{Cf} increases, i_{C} increases, i_{comp} decreases, v_{OP} increases, v_{FB} increases, and then the duty cycle increases again, as do i_{D} and v_{O}.
What this means is that adding a positive feedback network to the flyback controller may provide an effective way to measure the output load current, but it poses the risk of making the overall system unstable.
Fortunately, there are ways to make the new circuit stable again. Through the use of smallsignal modeling and analysis of the loop gain, we can configure the positive feedback network so it doesn’t interfere with the basic operation of the flyback controller.
CurrentSec Balance
First, it’s important to note that the currentsec balance of C_{f} makes it possible to describe V_{cf} and V_{in}, as shown in Equation 1:
V_{ref} is the reference voltage of the shunt regulator.
DCM Flyback Converter (Negative Feedback Network)
Assuming the load resistor R_{O} is much greater than the Effective Series Resistor (ESR) of the output capacitor, R_{esr}, we can obtain the transfer function of the feedback voltage to output voltage, as shown in Equation 2:
Added Circuit
Using the state space averaging method, the voltage on C_{f} can be described as a function of the output voltage and the feedback voltage. This is shown in Equation 3:
Feedback Loop
In the feedback loop, the transfer function of the output voltage and V_{cf} to the feedback voltage can be determined using Equation 4:
Loop Gain
Figure 2 shows us that, by solving the simultaneous equations given in Equations 2, 3, and 4, we can arrive at the transfer function for the loop, Equation 5.
Figure 2. Block diagram for the loop gain T(s)
Design Example
The values provided in Table 1, which are from an actual design, can serve as examples for using the equations shown above.
Table 1. System Parameters for a Sample Circuit
Parameter 
Value 
Parameter 
Value 
V_{in,min} 
120 V 
R_{O} 
2.12 Ω 
V_{O,max} 
5.33 V 
C_{B} 
10 nF 
I_{O,max} 
2.5 A 
L_{m} 
500 uH 
n 
13.33 
f_{s} 
66 kHz 
D_{max} 
0.247 
V_{ref} 
2.5 V 
D_{2} 
0.417 
R_{B} 
2.5 kΩ 
K 
0.4202 
R_{1} 
75 kΩ 
CTR 
1 
R_{2} 
91 kΩ 
R_{bias} 
1.2 kΩ 
Added circuit parameter 

R_{sense} 
0.68 Ω 
R_{C} 
150 kΩ 
C_{O} 
720 uF 
R_{f} 
270 kΩ 
esr of C_{O} 
25 mΩ 
C_{f} 
1 uF 
To guarantee total system stability, we can obtain the feedback component values (C_{H }and R_{H}) by using Equations 6 and 7:
Figure 3 shows the Bode plot of the loop gain T(s) with a C_{H} of 410 nF and an R_{H} of 270 kΩ.
Figure 3. Bode plot of the loop gain T(s)
With a cutoff frequency of 5.2 kHz and more than 80° of phase margin, the modified flyback controller, equipped with its added positive feedback network for measuring the output load current, delivers highly stable operation.
Conclusion
Adding a positive feedback network to a flyback controller, so as to measure output load current and control the output voltage, can be problematic because the circuit may become unstable. Overall stability depends on the size of the positive feedback portion. As shown in our example circuit, based on a FPS power switch, making good use of a few key equations can yield a design that is both stable and efficient.
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