ELEC4410 Chap.5 Single-Phase Controlled Rectifiers
Single-Phase Controlled Rectifiers
A controlled rectifier changes average DC output by delaying conduction from the natural forward-biased point. The firing angle names that delay, but the equation comes from the actual conduction window.
Mark alpha on the source waveform, identify which device or bridge pair conducts, write the output voltage during that interval, and integrate only across the interval supported by the load and topology.
For a resistive load, current follows voltage and ends when the applied voltage no longer supports it.
Inductance stores energy and resists an instantaneous current change, so conduction can persist after the source changes sign when a valid current path remains. The load assumption therefore changes both waveform and average value; it cannot be appended after using a memorised formula.
Convert RMS source voltage to peak before substituting into an expression written with Vm.
Boundary checks are decisive: zero firing delay should give the maximum controlled average for the stated circuit, while moving alpha toward pi collapses the resistive conduction interval and drives its average toward zero.
What this chapter covers
- 01
Firing angle
- 02
Conduction windows and device paths
- 03
Resistive versus inductive load current
- 04
Average output from waveform integration
- 05
RMS-to-peak and firing-angle checks
Worked example · free
Find firing angle from an average-current target
- +1Convert target current to 72 V average output and convert 120 V RMS source voltage to peak 169.71 V.
- +2Substitute 72 = (169.71/pi)(1 + cos alpha), giving cos alpha = 0.333 and alpha = 70.5 degrees.
- +1Confirm that a positive delay produces less average output than the alpha-equals-zero boundary.
Key terms
- Single-Phase Controlled Rectifiers
- A core ELEC4410 topic used to organise firing angle, conduction intervals, resistive and inductive loads, and average output.
Single-Phase Controlled Rectifiers FAQ
What does firing angle control in a rectifier?
It delays the start of controlled-device conduction relative to the natural forward-biased point. That shift changes the source-voltage segment applied to the load and therefore changes average output.
Why must the load type be stated before integrating?
A resistive current follows the applied voltage, whereas inductance can keep current flowing after source polarity changes if a path exists. The conduction interval and output waveform therefore depend on the load.
Which boundary checks catch a wrong firing-angle result?
At zero delay the stated resistive circuit should produce its maximum controlled average. As alpha approaches pi, its conduction interval collapses and average output should approach zero, not increase.
Exam move
Draw the source sine wave and shade the actual output segment before touching an integral. Mark alpha, pi and any extinction point, then draw the load-current path under the circuit. Work resistive and inductive cases side by side so the reason for continuing current remains visible. On every numerical problem, label the source value as RMS or peak and perform the conversion on its own line.
Recalculate the example at a smaller and larger firing angle, predicting the direction of average output first. Finish by testing alpha equal to zero and alpha approaching pi. If the formula fails either boundary, revisit the conduction interval rather than repairing the arithmetic. Use the oscilloscope trace you would expect as a final verification sketch.
Add device-voltage traces below the load waveform and label each conducting or blocking interval. This makes a mistaken bridge pair visible before integration. Practise solving for average output from alpha and solving backward for alpha from a current target, writing the inverse-cosine branch explicitly.
Finish each backward solution by drawing the calculated window and checking that the physical interval matches the algebraic angle Compare half-wave, resistive bridge and continuous-current bridge waveforms without sharing one coefficient between them.
Under each sketch, write the exact integral bounds and the device pair, then confirm that the calculated average changes in the same direction as the shaded conduction area Finish by checking angle range, load assumption and output direction against the waveform rather than the calculator alone Label every shaded interval before integration.
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