Lecture 5 - Uncontrolled rectifier circuits I

Transcription

1 Lecture 5 - Uncontrolled rectifier circuits I ectifier circuits convert A source into source which supplies to a load. The qualities of input current and output voltage waveforms, efficiency input transformer utilization are the important issues. Line frequency rectifiers: normally use slow diodes with large turn-off and recovery times. Load Figure 5.1 High frequency rectifiers: uses fast recovery diodes. EMI (electromagnetic interference) due to the sharp turn-off (current snapping) can be a problem. EMI suppressors are often required. Load Load Figure 5. Lecture 5 Uncontrolled rectifier I 1 F. ahman

2 Analysis of rectifier circuits iode rectifier with resistive load i s v s + V d i L Figure 5.3 i v o V d v s Figure Vd average value of vo V 0 max sintd( t) Vmax (5.1) Lecture 5 Uncontrolled rectifier I F. ahman

3 iode rectifier with -L load i s i + v o il v s V d - L Figure 5.5 Figure 5.6 Lecture 5 Uncontrolled rectifier I 3 F. ahman

4 v V sint s max 1 Vd V sin td( t) 0 max (5.) When the diode conducts, i.e., for 0 t <, di (5.3) vo Vmax sint i L dt V t max L i( t ) sin t Ae Z (5.4) where Z L (5.5) and At 1 L tan Vmax t 0,i 0 sin( ) A L A V max L sin (5.6) V t max i sin t sin e L L (5.7) Lecture 5 Uncontrolled rectifier I 4 F. ahman

5 Also, at t, i 0, so that L sin sin e (5.8) The angle can be found by solving this transcendental equation. V d is then found from (5.). Most diode rectifier circuits are terminated by a capacitor, which acts as a reservoir. In Figure 5.7 the inductor L may be may be used after the diode to reduce the size of the capacitor filter, and is its resistance. More often, L is the net A source inductance. epending on when the A supply is turned on, the capacitor voltage, V d, may have some overshoot. Lecture 5 Uncontrolled rectifier I 5 F. ahman

6 i s S i L i L + I d v s V o V d L Figure 5.7 V d V max i i v v s t Figure 5.8 Assuming that is large, so that V d can be assumed to be constant during each half cycle, conduction through the diode begins when v exceeds V d. This happens at an angle given by Lecture 5 Uncontrolled rectifier I 6 F. ahman

7 V sin V so that max d 1 Vd sin Vmax (5.9) onduction through the diode ceases at angle, as shown below. When the diode conducts, di v Vmax sint i L Vd dt (5.10) Solving (5.10), t max V d L V i (t) sint Ae Z (5.11) The constant A can be found from the condition that at t,i 0, so that V A sin e L max Vd L (5.1) By substituting 5.1 into 5.11, Lecture 5 Uncontrolled rectifier I 7 F. ahman

8 Vmax Vd i sint L V L t max Vd sin e L (5.13) The angle can be found from (5.13), by using the condition that at t, i 0. The output of the diode rectifier is given by, 1 V V sin td t ( a) V o max d (5.14) 1 V Id i d t d (5.15) L Note that in the steady-state, the current in the inductor must equal the current in the load. 1 Irm s idt (5.16) input rms d d P I V I (5.17) Input PF = V P V I Vmax Irms I max o d d rms (5.18) Lecture 5 Uncontrolled rectifier I 8 F. ahman

9 The role of free-wheeling diodes in rectifier circuits ectifiers are sometimes terminated with diodes in order to remove the negative voltage across an inductive load. More often, the terminating diode provides for an alternative path for current to flow when the input voltage to the rectifier tends to go negative. This is necessary for proper operation of the rectifier. This diode conduction is often referred to as freewheeling, which also prevents overvoltage in an inductive circuit when the supply current i s is abruptly switched off. Lecture 5 Uncontrolled rectifier I 9 F. ahman

10 S i i L v s f L v o Figure 5.9 i o i s i f t, sec Figure 5.10 Lecture 5 Uncontrolled rectifier I 10 F. ahman

11 iode models The above analyses use the static or idealized model of the diode: s is the bulk resistance which largely depends on the doping level of the n -1 layer. When dynamic behavior of diode circuits are of interest, for instance, when the behavior of dynamic current sharing in series and parallel connected diodes at turn-on and -off, or when the reverse recovery current of a diode flows through a transistor, a dynamic model of the diode should be used. Lecture 5 Uncontrolled rectifier I 11 F. ahman

12 S i i f v v dq dv d Q = PSpice model of a diode Manufactures often give dynamic PSpice models of each power diode type they supply. Parameters of the model can also be found from manufacturer s data on switching transients using certain curve fitting and approximation techniques. Incorporation of dynamic model parameters in the analyses of forgoing figures will hardly show any deviations because the operation frequency was 50Hz. However when the operating frequency is several 10s or 100s of khz, the dynamic model would indicate significant changes from the behaviour from idealized models. This course will not include the dynamic models of any switching device in any of the converter circuits treated. Lecture 5 Uncontrolled rectifier I 1 F. ahman

13 Note in figure 5.6 that the reverse voltage across the power diode rises abruptly at the extinction angle. Although makes the reverse voltage rise somewhat slower than abrupt, nevertheless, the sharp rise of reverse voltage across the diode at turn-off means large but short-duration reverse current through it. To prevent this, a snubber () circuit in parallel with a power diode is often used. Lecture 5 Uncontrolled rectifier I 13 F. ahman