RCs Impact Switchmode Power Supply Performance
RC components of an SMPS have many characteristics that aren't shown on a typical schematic diagram. Each component exhibits parasitic behavior that degrades the SMPS conversion efficiency. Other components also contribute to efficiency loss: The SMPS switch (usually a MOSFET) has several characteristics that degrade efficiency, and power consumption in the SMPS controller obviously reduces efficiency. Even p. c. board traces can degrade efficiency to a small degree if poorly designed.
Ideal resistor equations apply to dc and ac circuits of low to moderate frequency. For high-frequency circuits and those that switch voltage or current very quickly, actual resistors are no longer ideal — they exhibit parasitic inductance and capacitance.
The model for an actual resistor is quite different from that of an ideal resistor, and it varies according to the resistor type. Common types include carbon composition, carbon film, metal film, and wire wound. Wire-wound resistors, used almost exclusively in dc or low-frequency power applications, exhibit high parasitic inductance.
As modeled in Fig. 1, the parasitic characteristics of a resistor derive mainly from the resistor's construction and packaging. For example, resistor leads introduce the parasitic inductance shown. Because through-hole resistors have relatively long leads between their bodies and the p.c. board, their parasitic inductance is higher than those of surface-mount resistors, whose leads are very short.
Lead spacing on the resistor package gives rise to the resistor's parasitic capacitance. Here, two adjacent leads serve as the plates of the capacitor, and air between them serves as the dielectric. As two conductors approach each other, the capacitance between them increases. Thus, the behavior of parasitic capacitance is opposite to that of parasitic inductance: Through-hole resistors exhibit less parasitic capacitance than those of surface-mount resistors.
A common technique for current measurement places resistors in the power path of an SMPS. The resistor values are very small (tens of milliohms). Their parasitic inductance and capacitance values are proportionally small as well, so the parasitic characteristics of current-sense resistors in an SMPS are often ignored. However, when the SMPS switching frequency exceeds approximately 1 MHz, the parasitics may have a small degrading affect on overall performance.
Capacitors
An ideal capacitor is a pure capacitance without parasitic characteristics. Actual capacitors have parasitic resistance and inductance, as seen in the typical model of Fig. 2. Its physical construction causes a capacitor's parasitic behavior. To construct a crude capacitor, imagine two long strips of aluminum foil separated by a dielectric insulator. You form the capacitor by rolling that sandwiched combination into a cylinder and connecting a wire to each piece of foil.
Electrons must accumulate evenly across the foil when a capacitor is charging, and must therefore travel a resistive path from one end of the foil to the other. The resistance of that path is known as equivalent series resistance (ESR). Because the foil is a conductor wrapped in a coil, current flow in the conductor encounters parasitic inductance, known as equivalent series inductance (ESL). The resulting impedance is:
XREAL C = (XCC + XLC + ESRC)//RLEAK
Where:
XCC = Impedance due to the capacitance
XLC = Impedance due to the inductance
RLEAK = Parallel resistance known as dielectric leakage resistance
XCC and XLC are frequency dependent (Fig. 3). The impedance at dc and low frequency (equal to the leakage impedance) is very high, as expected. As frequency goes up, impedance goes down — yet it never reaches zero. The lowest impedance occurs where the sum of XC, ESR, and XL is minimum (RLEAK is insignificant).
Inductive parasitic become dominant at higher frequencies, causing the capacitor impedance to actually increase. Because RF engineers understand this behavior, they often connect small RF-bypass capacitors across larger-valued capacitors. The resulting curve of capacitor impedance vs. frequency has a lower and wider valley that helps filter out noise over a much broader range of frequencies.
Switchmode Converters
An inductive switchmode converter contains capacitors, at least one inductor, and (usually) at least one resistor (Fig. 4). The main parasitic losses are associated with components in the converter's main power path: the inductor, resistor, and input and output capacitors. Minimizing such losses optimizes the conversion efficiency.
The current-sense resistor (RCS) in Fig. 4 represents a common method for measuring inductor current in the SMPS. The resistor value is generally small (tens of milliohms). When the MOSFET turns on, current flows through the inductor and the resistor, creating a voltage across RCS that is measured by the SMPS controller to determine inductor current. Obviously, current through the resistor creates a power loss of P = I2 × R. More efficient methods of current sensing eliminate this power loss by eliminating the resistor and measuring a voltage drop across the MOSFET instead.
The operation of most inductive SMPS converters is not fast enough to be affected by a resistor's parasitic components. Generally, therefore, one considers only the pure resistance of a resistor. The resistor only needs to handle a purely resistive power loss.
Capacitor parasitics have an effect on SMPS efficiency. Because regulated SMPS typically employ negative feedback control, the controller's stability may be affected by parasitic characteristics.
To understand how the parasitic characteristics of capacitors affect efficiency, it's important to understand the action of input and output capacitors in a SMPS. Input capacitors bypass the SMPS input to ground, and output capacitors bypass the SMPS output to ground (Fig. 4). Their purpose is to maintain constant input and output voltages. By also reducing input and output noise, the capacitors usually increase the SMPS stability, but at the expense of efficiency.
To maintain constant voltage at an SMPS input, the input capacitor must supply current to the SMPS on demand. An SMPS works in cycles, and its current demand occurs only for part of a cycle. The impedance of most sources is relatively high when compared with that of capacitors, and the voltage drop across the source impedance subtracts from the source voltage applied to the SMPS input. The input capacitor's job is to supply current to the SMPS as necessary to minimize attenuation of the input voltage. When current demand ends (during the next portion of the cycle), the input capacitor charges (via the source) back to the nominal input voltage.
Thus, the input capacitor charges and discharges during an SMPS cycle. Its ESR causes a power loss of I2 × ESR, which creates heat and adds to power loss in the SMPS. In addition, the output capacitor charges and discharges during an SMPS cycle, supplying various amounts of energy to the load. An SMPS supplies more energy than needed during certain parts of its cycle, and not enough during other parts. The job of the output capacitor is to maintain a constant output voltage, and the resulting charge/discharge currents through its ESR create a power loss.
Parasitic inductance in the input/output capacitors can also affect SMPS efficiency. It tends to be a second-order effect; however, losses can be significant because the capacitor inductance can be very large. A capacitor's impedance depends on the applied frequency. The current can be almost discontinuous in an input or output capacitor, and it can change direction (between charging and discharging) at high frequency. Thus, capacitor ESL creates a voltage drop in addition to the ESR drop. The additional I2 × R loss produces heat and adds to the total power loss. Capacitor-ESL effects often go unnoticed, because the inductance value is small at the switching frequencies typical of an SMPS.
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