Rectifier and Smoothing Capacitor Calculator: Ripple, Diodes and Transformer VA

The secondary is not an ideal voltage source. In the model, the entered voltage is the RMS voltage at no load, or more precisely the EMF of the equivalent sinusoidal source, followed by the equivalent series resistance. This resistance limits recharge current together with impedances not represented by the model, such as leakage inductance and wiring.

The series resistance is the secondary resistance plus the primary resistance referred to the secondary through the square of the turns ratio. If you measured the transformer with the identification tool, this is the “equivalent resistance” from its card 5. If you only know a nominal voltage specified at full load, using it together with R_s introduces some approximation because the internal voltage drop is already partly included in that specified voltage.

R_s can vary greatly with power, voltage and construction. If the measured DC resistance is very small, the model becomes more sensitive to omitted impedances, especially leakage inductance and wiring. In that case it is better to try several plausible values and treat the result as an estimate rather than a measurement of the real peak current.

The three classic topologies differ in forward drops, recharge frequency and required reverse voltage. A bridge has two diode drops, but each diode sees a PIV on the order of the secondary peak. A center-tapped rectifier has only one forward drop, but the reverse-biased diode can see nearly twice the peak of one half-secondary. In a half-wave rectifier with a charged capacitor, worst-case PIV is also on the order of twice the peak.

With a center tap, the voltage entered in card 1 is the voltage between the tap and one end, i.e. one half of the secondary. This is the voltage that actually feeds the rectifier during each half-cycle.

Reverse voltage is checked at maximum mains. For the bridge, the secondary peak is used; for center-tapped and half-wave circuits the calculator conservatively uses approximately \(2V_{pk}\), corresponding to the no-load case where the capacitor remains near the positive peak while the source reaches the opposite peak.

The capacitor must hold up the voltage between one recharge pulse and the next. A larger capacitor reduces voltage droop but narrows the conduction interval: the same charge still has to be transferred, and if there is less time to do so the peak current rises. Increasing capacitance therefore comes at the cost of higher pulsed current.

Ripple current is one of the main factors determining capacitor life. Electrolytic capacitors have a specified allowable RMS ripple current at a given temperature; exceeding it heats them internally and accelerates drying. In a power supply designed for long service life, ripple current is as important a design constraint as working voltage.

Constant-current mode is a good first-order representation of the input of a linear regulator while it remains in regulation, neglecting its own quiescent current. Resistive mode instead represents a true resistive load; with small ripple its current varies only slightly around \(V_{dc}/R\). The calculator nevertheless integrates instantaneous current in both modes.

A diode cannot be selected from a single number. Average current and thermal conditions, RMS current when relevant to package and interconnects, repetitive peak current and repetitive reverse voltage all need to be checked. This card shows the maxima across minimum, nominal and maximum mains so the component is not sized only for the nominal condition.

The displayed dissipation uses the constant-drop model \(V_f\), so it is \(V_f I_{avg}\). This is useful as a first estimate, but a real component has a \(V_f\) that depends on current and temperature; for a tight design, use the datasheet characteristic and the package thermal resistance.

The repetitive peak must not be confused with the non-repetitive turn-on surge, which is a different quantity and is handled in card 5. Datasheets specify both: I_FRM for the first, I_FSM for the second, usually specified for a single 50 Hz half-cycle.

At turn-on, a discharged capacitor requires a large charging pulse. This card calculates only the inrush caused by the capacitor in the equivalent circuit referred to the secondary; it does not calculate transformer magnetizing inrush, which is a separate phenomenon and can be significant, especially with toroidal transformers. Fuses and protection devices must therefore be checked considering both effects.

The displayed energy is an estimate of the energy dissipated in the resistive network during charging. If the physical limiter is on the primary side, its cold resistance must first be referred to the secondary using \(R’_p = R_p(V_s/V_p)^2\). The displayed current is therefore an equivalent secondary-side current, not the current that directly flows through an NTC installed on the primary.

The energy expression applies to charging through a resistor from a constant source. Here the source is AC and charging occurs during only part of a half-cycle, so the displayed value is a close estimate rather than an exact identity.

An NTC that has already operated is hot and its resistance has fallen to a fraction of its cold value, so after a short power-off interval there is almost no protection. If the equipment is frequently switched off and on again, the limiter should be bypassed by a relay after charging, or replaced by a fixed resistor with a bypass relay.

This card closes the loop with the transformer calculators. Secondary copper heating is determined by RMS current, not average current, and in a capacitor-input rectifier those two values can be very different. The form factor shows by how much: it is the ratio between the actual RMS secondary current and the DC current delivered to the load.

From this you obtain the VA required from the transformer: secondary RMS voltage multiplied by the RMS current flowing in it. This is the number to use as the design power in the laminated-core or toroidal transformer calculator—not the load watts.

A commonly quoted rule of thumb for a bridge rectifier with a capacitor-input filter is \(I_{sec,RMS} \approx 1.6\text{–}1.8\,I_{DC}\) under typical conditions. This is a current ratio, not a universal VA/W factor. The actual value changes with R_s, capacitance, voltage and load: this card directly uses the RMS value obtained from the simulation.

The current reflected back to the mains is not sinusoidal. With bridge and full-wave rectification the waveform is ideally symmetric between the two half-cycles, so odd harmonics dominate; with half-wave rectification there is also a DC component and even harmonics appear. The graph shows the lower harmonic orders, while the numerical THD is derived from the total RMS value and is therefore not limited to the displayed bars.

Power factor and the cosine of the fundamental phase angle can differ greatly: a strongly distorted current can have its fundamental nearly in phase with the voltage and still exhibit a low power factor. When cos φ is already close to one, ordinary reactive power-factor correction does not remove the loss caused by harmonic distortion.

Within its scope, IEC/EN 61000-3-2 regulates harmonic currents injected into public low-voltage mains by equipment with rated current up to 16 A per phase. Limits, classes, exceptions and test conditions depend on the equipment type; there is no simple general wattage threshold. This tool displays a normalized spectrum of the secondary current and is not a compliance test; a compliance assessment requires the current version of the standard and measurements under the prescribed conditions.

This is one of the most common mistakes after undersizing the smoothing capacitor: the design is checked using average voltage, apparently with plenty of margin, and yet the output develops unexplained 100 Hz ripple. The reason is that the regulator sees the instantaneous voltage, and at the ripple valley that voltage is below the average by roughly half the peak-to-peak ripple.

Dropout margin must be checked at minimum mains and maximum load. Thermal dissipation is instead estimated at maximum mains, but only if the regulator remains in regulation there as well; otherwise the constant-output-voltage model is no longer self-consistent and the field is left unavailable.

The preset dropout voltages are indicative values: always check the datasheet at the intended current and temperature. This card is active only when card 3 is set to “Constant current”, because that mode represents the load presented by a linear regulator while it is in regulation; with a resistive load the check would be applied to a different circuit.

To obtain two symmetric voltages, a bridge can be used on a center-tapped secondary with the tap connected to the 0 V point between the two capacitors. With balanced loads, each rail is equivalent, from the viewpoint of its own voltage, to full-wave rectification with one diode drop and the voltage of one half-secondary.

With equal loads the two rails use the secondary symmetrically, and a single rail can be calculated to derive the total current and VA. This card has its own R_s: enter the equivalent resistance seen by one half of the secondary, without automatically reusing the value from card 1 if this is a different transformer.

The symmetry holds as long as the two loads are equal. With strongly unbalanced loads this identical-rail model is no longer sufficient: the rail voltages can diverge, and the two branches should be analyzed explicitly or with a complete circuit simulation.

A voltage doubler is useful when a voltage higher than the available secondary voltage is needed and the required current is relatively modest. The no-load limit approaches twice the peak minus the diode drops; under load, regulation worsens because charge is transferred through the capacitors. This card uses its own R_s equivalent secondary resistance, independently of card 1.

The symmetrical circuit consists of two half-wave rectifiers connected in series, one for each half-cycle. Their ripple waveforms are shifted by half a period and partially cancel, so the resulting ripple is at twice the mains frequency and is smaller than the sum of the two individual ripples. The midpoint between the capacitors sits at half the total voltage; this midpoint is exactly why switchable 115/230 V equipment uses this arrangement: a bridge at 230 V and a doubler at 115 V produce approximately the same DC bus voltage.

The capacitor voltages are not the same in the two circuits. In the Delon doubler, each capacitor charges to approximately one secondary peak and the output is their sum. In the Villard/Greinacher circuit, the pump capacitor sees about one peak while the output capacitor can approach the doubled voltage. In both cases the diodes require a reverse-voltage rating on the order of \(2V_{pk}\).