TUTORIAL
FULL-WAVE RECTIFIERS
2
UNCONTROLLED SINGLE PHASE RECTIFIERS:
1. A single phase bridge rectifier has an RL load with R = 15 Ω and L = 60 mH. The ac
source is 𝑉𝑠 = 100 sin 377𝑡 𝑉. Determine the average and rms currents in the load
and in each diode.
2. A single phase bridge rectifier has an RL load with R = 12 Ω and L = 20 mH. The ac
source is 120 Vrms and 60 Hz. Determine:
a) Average load current
b) The power absorbed by the load
c) The power factor
3. The full wave rectifier of Figure 1 below has 𝑉𝑠(𝜔𝑡) = 340 sin 𝜔𝑡 𝑉. R = 5 Ω, L = 40
mH, Vdc= 96 V and 𝜔 = 2𝜋 60 𝑟𝑎𝑑/𝑠. Determine:
a) The power absorbed by the dc source.
b) The power absorbed by the resistor.
c) The power factor
d) Estimate the peak-peak variation in the load current by considering only the first
ac term in the Fourier series for current.
Figure 1: Bridge rectifier with an RL load
4. The single phase full wave bridge rectifier of Figure 2 has an RL source load with R =
4 Ω, L = 40 mH and Vdc= 24 V. the ac source is 120 Vrms at 60 Hz. Determine:
a) The power absorbed by the dc source.
b) The power absorbed by the resistor.
c) The power factor
Figure 2: Bridge rectifier with an RL-source load
Figure 3: Bridge rectifier with capacitor
5. The Figure 3 shows a single-phase full bridge diode rectifier connected to a smoothing
capacitor𝐶𝑑 . Assume that the capacitance of the smoothing capacitor is so large that 𝑢𝑑 may
be considered to be constant (no ripple). The diode rectifier is connected to a grid with a
sinusoidal voltage 𝑢𝑠 , equal to 230 V (rms) with frequency equal to 50 Hz. The inductance of
the grid 𝐿𝑠 is equal to 1.22 mH.
(a) Calculate the short circuit current of the grid.
(b) The load current, 𝐼𝑑 (average value) is 10 A. Calculate the power the line is supplying.
(c) Calculate the apparent power, S supplied by the grid.
(d) The diode rectifier with a large smoothing capacitor is considered to be a load with a
bad power factor. Explain why the diode rectifier needs so much apparent power.
CONTROLLED SINGLE PHASE RECTIFIERS:
6. The fully controlled full wave converter has a source of 240 Vrms, 50 Hz and 10 Ω, 50
mH series load. If the delay angle is 45⁰. Determine:
a) The average output voltage and current
b) The rms load current
c) The power absorbed by the load
d) The power factor
7. The controlled single phase bridge rectifier of Figure 4 has a 20 Ω resistive load and
has 120 Vrms, 60 Hz ac source. The delay angle is 45⁰. Determine:
a) The average load current
b) The rms load current
c) The rms source current
d) The power factor
Figure 4: Controlled full wave bridge rectifier
8. The controlled single phase bridge rectifier of Figure 5 has an RL load R = 25 Ω and
L = 50 mH. The source is 240 Vrms at 60 Hz. Determine the average load current for α
= 15⁰ and α = 75⁰.
Figure 5: Controlled rectifier with RL load
9. An electromagnet is modeled as a 100 mH inductance in series with a 5 Ω resistance.
The average current in the inductance must be 10 A to establish the required
magnetic field. Determine the delay angle required for a controlled single phase
rectifier to produce the required average current from single phase 120 V, 60 Hz
source. Determine the current in continuous or discontinuous. Estimate peak-peak
variation in current based on the first ac term in Fourier series.
10. The Figure 6 below shows a single-phase thyristor rectifier connected to a 230 V grid. The
load is equivalent to a constant dc current of 𝐼𝐿𝑜𝑎𝑑 = 10A. In the first part of problem 6 A,
assume L = 0, that is assume instantaneous commutation.
Figure 6: Controlled full wave bridge rectifier connected to grid
(a) List the conditions that must be fulfilled for making a thyristor conduct? And what are
the conditions to make it stop conducting?
(b) For a load voltage of 100 V, find the firing angle a.
(c) Sketch Vda(t), is(t), and is,1(t), and indicate which thyristors are conducting, and when
they are conducting.
(d) Calculate the rms value, Is, of the ac current is(t), and its first harmonic, is,1(t).
(e) Calculate apparent power, S, and active power, P. Now, consider the ac inductance, L
=5 mH. The load voltage is still 100V.
(f) Why is the current commutation no longer instantaneous, for example from thyristor T3
to thyristor T1?
(g) For the grid inductance L equal to 5 mH, calculate the firing angle, a, and the
commutation angle, 𝑢.
(h) Sketch Vda(t), is(t), and is,1(t). Indicate the firing angle, 𝛼 and the commutation angle, 𝑢
in the sketch.