smps 2

SMPS Topologies and Conversion Theory

As mentioned in the previous section, SMPSs can convert a DC input voltage into a different DC output voltage, depending on the circuit topology. While there are numerous SMPS topologies used in the engineering world, three are fundamental and seen most often. These topologies (seen in Figure 2) are classified according to their conversion function: step-down (buck), step-up (boost), and step-up/down (buck-boost or inverter). The inductor charge/discharge paths included in the Figure 2 diagrams are discussed in the following paragraphs.


Figure 2. Buck, boost, and buck-boost compose the fundamental SMPS topologies.

All three fundamental topologies include a MOSFET switch, a diode, an output capacitor, and an inductor. The MOSFET, which is the actively controlled component in the circuit, is interfaced to a controller (not shown). This controller applies a pulse-width-modulated (PWM) square-wave signal to the MOSFET's gate, thereby switching the device on and off. To maintain a constant output voltage, the controller senses the SMPS output voltage and varies the duty cycle (D) of the square-wave signal, dictating how long the MOSFET is on during each switching period (T_S). The value of D, which is the ratio of the square wave's on time to its switching period (T_ON/T_S), directly affects the voltage observed at the SMPS output. This relationship is illustrated in equations 4 and 5.

The on and off states of the MOSFET divide the SMPS circuit into two phases: a charge phase and a discharge phase, both of which describe the energy transfer of the inductor (see the path loops in Figure 2). Energy stored in the inductor during the charging phase is transferred to the output load and capacitor during the discharge phase. The capacitor supports the load while the inductor is charging and sustains the output voltage. This cyclical transfer of energy between the circuit elements maintains the output voltage at the proper value, in accordance with its topology.

The inductor is central to the energy transfer from source to load during each switching cycle. Without it, the SMPS would not function when the MOSFET is switched. The energy (E) stored in an inductor (L) is dependent upon its current (I):



Therefore, energy change in the inductor is gauged by the change in its current (ΔI_L), which is due to the voltage applied across it (V_L) over a specific time period (ΔT):



The (ΔI_L) is a linear ramp, as a constant voltage is applied across the inductor during each switching phase (Figure 3). The inductor voltage during the switching phase can be determined by performing a Kirchoff's voltage loop, paying careful attention to polarities and V_IN/V_OUT relationships. For example, inductor voltage for the step-up converter during the discharge phase is -(V_OUT - V_IN). Because V_OUT > V_IN, the inductor voltage is negative.


Figure 3. Voltage and current characteristics are detailed for a steady-state inductor.

During the charge phase, the MOSFET is on, the diode is reverse biased, and energy is transferred from the voltage source to the inductor (Figure 2). Inductor current ramps up because V_L is positive. Also, the output capacitance transfers the energy it stored from the previous cycle to the load in order to maintain a constant output voltage. During the discharge phase, the MOSFET turns off, and the diode becomes forward biased and, therefore, conducts. Because the source is no longer charging the inductor, the inductor's terminals swap polarity as it discharges energy to the load and replenishes the output capacitor (Figure 2). The inductor current ramps down as it imparts energy, according to the same transfer relationship given previously.

The charge/discharge cycles repeat and maintain a steady-state switching condition. During the circuit's progression to a steady state, inductor current builds up to its final level, which is a superposition of DC current and the ramped AC current (or inductor ripple current) developed during the two circuit phases (Figure 3). The DC current level is related to output current, but depends on the position of the inductor in the SMPS circuit.

The ripple current must be filtered out by the SMPS in order to deliver true DC current to the output. This filtering action is accomplished by the output capacitor, which offers little opposition to the high-frequency AC current. The unwanted output-ripple current passes through the output capacitor, and maintains the capacitor's charge as the current passes to ground. Thus, the output capacitor also stabilizes the output voltage. In nonideal applications, however, equivalent series resistance (ESR) of the output capacitor causes output-voltage ripple proportional to the ripple current that flows through it.

So, in summary, energy is shuttled between the source, the inductor, and the output capacitor to maintain a constant output voltage and to supply the load. But, how does the SMPS's energy transfer determine its output voltage-conversion ratio? This ratio is easily calculated when steady state is understood as it applies to periodic waveforms.

To be in a steady state, a variable that repeats with period T_S must be equal at the beginning and end of each period. Because inductor current is periodic due to the charge and discharge phases described previously, the inductor current at the beginning of the PWM period must equal inductor current at the end. This means that the change in inductor current during the charge phase (ΔI_CHARGE) must equal the change in inductor current during the discharge phase (ΔI_DISCHARGE). Equating the change in inductor current for the charge and discharge phases, an interesting result is achieved, which is also referred to as the volt-second rule:



Simply put, the inductor voltage-time product during each circuit phase is equal. This means that, by observing the SMPS circuits of Figure 2, the ideal steady-state voltage-/current-conversion ratios can be found with little effort. For the step-down circuit, a Kirchhoff's voltage loop around the charge phase circuit reveals that inductor voltage is the difference between V_IN and V_OUT. Likewise, inductor voltage during the discharge phase circuit is -V_OUT. Using the volt-second rule from equation 3, the following voltage-conversion ratio is determined:



Further, input power (P_IN) equals output power (P_OUT) in an ideal circuit. Thus, the current-conversion ratio is found:



From these results, it is seen that the step-down converter reduces V_IN by a factor of D, while input current is a D-multiple of load current. Table 1 lists the conversion ratios for the topologies depicted in Figure 2. Generally, all SMPS conversion ratios can be found with the method used to solve equations 3 and 5, though complex topologies can be more difficult to analyze.