One complete source period; RMS includes DC.
Circuit and current path
D₁/D₂/D₃ connect the highest U/V/W phase to +. D₄/D₅/D₆ return current from − to the lowest phase. The source neutral is not connected to the load. Crossings without a dot do not join phase conductors.
Each sine-wave circle is an AC phase source. The sources share the internal star point N; vU, vV, vW are phase-to-neutral voltages. Only U, V and W connect to the bridge: there is no neutral wire.
Fixed arrows define positive references. Teal paths carry rectifier current; the purple resistor and brown capacitor branches have their own currents. Scroll the diagram at readable size or use Fit diagram.
Steady-state waveforms
Source and output voltages
Load and source currents
io enters the complete load. For R‖C, the dashed purple iR is the resistor current and solid brown iC is the capacitor-branch current: io = iR + iC. Coincident traces are drawn at their true values.
Filtering and branch currents
Actual conduction intervals
Angles describe actual device conduction, rather than phase-selection windows. Capacitor charging or an opposing DC voltage can shorten these intervals.
Ripple = AC RMS / absolute mean, calculated about the actual mean. A zero mean makes the ratio undefined. Nominal pulse frequency describes the balanced periodic topology; a blocked output has no physical ripple.
Model and equations
During source conduction: L dio/dt + Rio + E = vo = upath − ndVF. Set L or E to zero when that series element is absent. During blocked intervals, io = 0 and vo = E.
For R‖C with RC > 0: iR = vo/R, iC = (vo − vC)/RC = C dvC/dt. When blocked, io = 0, iC = −iR, and vC decays with time constant (R + RC)C. Capacitor voltage stays continuous; output voltage can jump at firing.
With the ideal diode capacitor branch, vo = vC. A diode pair recharges only when the selected line voltage meets capacitor voltage plus its two drops. Turn-off occurs at zero complete output current, not necessarily at the source-voltage peak.
Predict, test, explain
Predict which source phases supply and return current at 90°. Check the circuit and all three source-current traces; explain why no neutral is required.
Reveal the explanation
The upper bank connects the highest phase to +; the lower bank connects − to the lowest phase. One phase carries +io, another −io, and their sum is zero. At 90° the lowest V/W phases are tied, so the drawn state is the right-hand limit.
Prepare R‖C. Compare output-current RMS with resistor-current RMS and locate the largest charging pulse. Predict the effect of reducing RC; confirm that capacitor voltage remains continuous.
Reveal the explanation
The resistor sees iR = vo/R. The rectifier must also charge C, so its RMS current can be much larger. RC limits the charging pulse and dissipates RC iC²; it also slightly changes the voltage seen by R. A very small RC is not zero.
Power, stored energy and device currents
Positive input power flows from AC to the load; negative input power flows back to AC. In periodic steady state, mean inductor and capacitor powers are zero. The signed E-source power is E times mean series current.
Instantaneous power and stored energy
Stored energy
Diode-current waveforms
Anode-to-cathode current in amperes, using the device numbers in the circuit. Choose one device to inspect overlapping traces. The cursor is linked to the circuit; mean/RMS values below use the complete source period.
| Device | Full-period mean current | Full-period RMS current |
|---|
Source-current spectrum and power factor
Bars show RMS components of phase-U source current. Frequency labels use the complete repeating pattern. Distortion ratios use the complete waveform and the supply-frequency fundamental RMS, independently of the displayed bars.
Source-current spectrum and power factor
For the sinusoidal source, PF = P/S = DPF × DF. DPF = cos(φ₁); DF = fundamental-current RMS / complete source-current RMS. Ratios are undefined if their denominator is zero. A negative PF indicates net regeneration.
Diode comparison and analytical limits
This mean-voltage formula assumes ideal devices, a continuously conducting series load and no capacitor. The pure R case satisfies those conditions. A blocked or discontinuous load and capacitor filtering need their actual waveform; two constant device drops subtract 2V_F only while a pair conducts.
The ideal diode filter has RC = 0 and vo = vC. Select the small-resistance branch to make a matched comparison with the controlled bridge.
Conventions, limitations and data
U, V and W name phase terminals; italic R names resistance. Current subscript R means the load resistor. The main R‖C current cards refer to that branch. All means, RMS values and spectra use one complete source period, not just the conduction interval.
Periodic steady state with ideal sinusoidal voltage sources. No startup, source impedance, finite commutation overlap, recovery, leakage, temperature or transformer model is included. The small charging resistor is the only extra element in the capacitor branch; it is not source resistance. Current peaks are model results, not safe device ratings.
When every bridge device is blocked, individual AC-to-DC device voltages require a common-mode or leakage model that is absent here. The displayed state describes complete current paths and actual device currents; it does not invent those floating terminal voltages.
Piecewise periodic solutions use bracketed switching events, stable linear-ODE convolution and quadrature split at those events and time constants. The laboratory checks current signs, Kirchhoff and branch laws, state continuity, and instantaneous and periodic power balances before accepting results. No arbitrary minimum L or C is used.
CSV uses SI units and a decimal point. Its event-enhanced grid is not uniform. At a jump, equal angles with limit_side = left/right give exact one-sided states. Source/phase current, complete output current, resistor current and capacitor-branch current have distinct columns. THD fields are dimensionless ratios; displayed THD is a percentage.
Optional technical references
Monolithic Power Systems · Uncontrolled Rectifiers · Three-Phase Full-Wave Rectifiers