We will now jump to other SMPS topologies, such as boost, inverter, and flyback, after extensively detailing the behaviors for a buck converter in the previous parts of this series. Once again, to establish the transfer function between Vout and Vin, the same power balancing method between the input and output is used.
Boost Converter in CCM Operation
Figure 1: Boost Converter in CCM Operation
In this boost scheme, current is balanced within one period (T) through the inductor (L). When the switch is ON, the inductor is charged through Vin. During Toff, L is discharged with a slope (Vin-Vout)/L. In solving the equation, Vout = Vin/(1-d), which gives Vout > Vin. Vout could go to infinity (theoretically). But it’s impossible for Vout to be smaller.
Boost Converter in DCM Operation
Figure 2: Boost Converter in DCM Operation
The same principle applied in determining the transfer function for a buck converter can be adapted for a boost converter. The power balance method remains a key tool in this process. By using the power balance method, we find that Vout = Vin/2 + (Vin/2)*(1+2d²TR/L)1/2. The details are shown below.
Figure 3: Boost Converter in DCM: Transfer Function Development
As stated in the previous blog, Power injected from input (Pin) is Vin*<IL> = Vin * Ipeak * (Ton +Toff1)/2T Power collected at the output (Pout) is simply the average current in the load R since there is no accumulated current in a capacitor at steady state: Pout = Vout²/R . The illustration shows two triangles in which Ipeak is reached during Ton with a slope of Vin/L and that same Ipeak is discharged to zero with a slope –Vout/L during Toff. By solving the equations, we find that Vout = Vin/2 + Vin/2*(1+2d²TR/L)1/2.
Inverter (Buck-Boost) Converter in CCM Operation
Figure 4: Buck-Boost Converter in CCM Operation
The current through the inductor (L) must be balanced in each period (T). When the switch is ON, the inductor charges using the input voltage (Vin), and when the switch is OFF, the inductor discharges through the output voltage (Vout). We get Vout = -Vin*d/(1-d). Here, we are considering CCM. With d ranges between 0 and 1, Vout can be larger or smaller than Vin. Inverters are characterized by their ability to produce an output voltage of the opposite polarity to the input voltage. This feature, while sometimes inconvenient, is essential for applications requiring a polarity reversal from the input supply.
Inverter (Buck-Boost) Converter in DCM Operation
Figure 5: Buck-Boost Converter in DCM Operation
In a similar development process by balancing the input and output power, and after several steps in solving different equations, we arrive at an expression for Vout as shown. This includes the switching period (T), duty cycle (d), inductance (L), and the load resistance (R). And as for the buck and boost, there is also a critical inductor (Lcrit) that determines the circuit to be in BCM. The larger L is (versus Lcrit), the more likely the circuit will operate in CCM, and vice-versa in DCM.
Flyback Converter in CCM and DCM Operation
Figure 6: Flyback Converter Basic Structure
Figure 7: Flyback Behaviors in CCM and DCM Comparison
We apply the same analysis for flyback converters. The basic operation is based on a coupled inductor, which, in addition to aiding in power conversion, also provides galvanic isolation between Vin and Vout.
It otherwise has the same basic elements as other switching converter topologies:
- Two switches: the MOSFET and diode; the latter can be replaced by another MOSFET controlled in the opposite way (synchronized controller)
- An output capacitor
The switches are on and off alternatively, with a Ton phase charging the primary inductor and a Toff phase discharging the secondary coil through the load. During Ton, the MOSFET is on and current flows from the input through the primary inductor, linearly charging the coupled inductor and creating a magnetic field around it. On the secondary side, the rectifier diode D is reverse-biased, disconnecting the transformer from the output. The charge stored in the output capacitor is responsible for maintaining a stable voltage at the load.
If the MOSFET switches from Toff to Ton before the inductor is completely discharged, then the current in the inductor is never zero: we are in CCM. Alternatively, if Toff lasts long enough for the primary inductor to completely discharge, then there is a period of time during which the current in the inductor is zero. This causes both the diode and the MOSFET to be in an off state, in DCM.
Conclusion
We have completed the analysis of all the basic SMPS circuits (buck, boost, inverter, and flyback) in the various conduction modes: CCM, DCM, and BCM. It’s important to note that any SMPS circuit can operate in all three modes. Switching from one mode to another can occur without the designer or user realizing.
See blogs in the DCM & CCM in SMPS series.
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