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ELE5PRA Engineering Practice 2007 DC Power Supplies and Zener Regulation 2.1.1 Single phase rectifier vs v s Vm sin t Vm v D - 2 t vo Vm Vm Vo dc vo RL vD 2 2 vr Vm vr Vm Vo dc 2 Figure 3.1.0 (a) Single Phase Diode Rectifier The diode converts ac to dc and the average output voltage Vo dc is found in the following equation. 1 1 Vm Vodc 2 0 vo dt Vm sin t 0.318Vm 2 0 The rms output voltage is 1 1 1 2 2 1 2 2 V Vo dc v o dt Vm sin 2 td t m 0.5Vm 2 0 2 0 2 The pulsating output contains ripple the ripple is expressed as v s Vo dc Vm sin t Vo dc for 0 t vr -Vo dc for t 2 The rms ripple voltage can be calculated to give 1 1 2 2 2 2 Vr rms V 2 o dc V 2 o dc Vo dc 1 1.21Vo dc 4 4 The ripple factor is therefore Vr rms 1.21Vodc RF % 100 121% Vodc Vodc The effectiveness of the rectifier is measured by the rectification efficiency Po dc Vo dc I o dc Vm 2 R 4 40.5% Po ac Vo rms I o rms Vm 22 R 2 Rectifiers are generally supplied through a transformer from a fixed ac input voltage of 120Vrms, figure 3.1.1 below. 1 Electronic Engineering, La Trobe University ELE5PRA Engineering Practice 2007 D1 io RL vp vo vs Figure 3.1.1a : Rectifier with input transfomer 2.1.2 Single Phase rectifier as a battery charger v s Vm sin t 1 2 2 R D1 io vo vs E Vm E t v s Vm sin vp E 1 2 2 Vm Vm E io Vm E R t 1 2 2 Figure 3.1.2 (a) Single Phase Transfomer Diode Rectifier as a battery charger There are many uses for the half wave rectifier of figure 3.1.1. Besides ac to dc conversion a half wave rectifier can be used for peak detection if used with a capacitor filter or as a battery charger. The figure in 3.1.2 shows an example of the single phase rectifier used as a battery charger. 2.1.3 Single Phase Full Wave Center Tapped Rectifier The average dc voltage in a half wave rectifier is low as shown earlier. The full wave rectifier is designed to give a higher dc content, double the one in a half wave rectifier. Referring to figure 3.1.3 below, the output voltage is Vm sin ωt 0 ωt π vo - Vm sin ωt π ωt 2π The average voltage is therefore 2 Electronic Engineering, La Trobe University ELE5PRA Engineering Practice 2007 2 2 2Vm Vo dc 2 0 vo dt Vm sin t 0.636Vm 2 0 v s Vm sin t 2 D1 io vo Vm vs R Vo dc vp t E 2 vs vD 2 t vD PIV PIV 2Vm vr Vm Vdc t Vo dc 2 Figure 3.1.3 (a) Single Phase transfomer center tapped Diode Rectifier The rms output voltage is 1 1 2 2 2 2 2 V Vo dc v 2 o dt Vm sin 2 td t m 0.707Vm 2 0 2 0 2 The ripple content in this waveform is v s Vo dc Vm sin ωt Vo dc for 0 ωt π vr -Vm sin ωt -Vo dc or π ωt 2π f The ripple voltage can be expressed from 1 1 2 2 2 2 Vr rms V 2 o dc V 2 o dc Vo dc 1 0.483Vo dc 8 8 The rectification efficiency 2Vm R 2 Podc Vo dc I o dc 8 2 81% Poac Vo rms I o rms Vm 2 R 2 Twice that of a half wave rectifier. The PIV is 2Vm. The second type of rectifier is a bridge rectifier shown in the figure below. The analysis is the same as the center tapped rectifier yielding exactly the same results. 3 Electronic Engineering, La Trobe University ELE5PRA Engineering Practice 2007 v s Vm sin t 2 io vo D3 D1 Vm Vo dc t E 2 vp Vm sin t vD D2 vr Vm Vdc D4 R t Vo dc 2 Figure 3.1.4 (a) Single Phase Full Wave Bridge Rectifier 2.1.4 Output Filters for Rectifiers The rectifier output contains a dc component as well as cosine components at various frequencies. The magnitudes of these are called harmonics. The desired output is pure dc. Filters are used to smooth out the output. DC filters are C-Filters, L-filters and LC filters. The C filters are used in integrated circuits and the last two filters are more suitable for use in high power applications such as dc power supplies. 2.1.5 L-Filters An inductor is a storage device that mains constant current through the load so that the variations in output voltage are minimized. io D3 D1 vp Vm sin t D2 D4 L R Figure 3.1.5 : Bridge Rectifier with an L - Filter At ripple frequency the inductance has a high impedance and this causes the load current ripple to be reduced. Z RL jnL RL nL n 2 2 Where 4 Electronic Engineering, La Trobe University ELE5PRA Engineering Practice 2007 n tan 1 nL R L The instantaneous load current is 4Vm cos nt n io t I o dc 1 n 1n 1 RL nL 2 2 2, 4, 6 Where 2Vm Vodc I o dc RL RL Taking the first two harmonics and ignoring the higher order harmonics I r2rms I o 2rms I o 4rms 2 2 2 2 1 4Vm 1 1 4Vm 1 .I r2rms .......... ... 2 3 2 15 1 1 RL 2L RL 4L 2 2 2 2 2 2 2.1.6 C-filters A capacitor is a storage device that maintains a constant voltage. The capacitor is connected across the load to minimize the output ripple. io D3 D1 vp Vm sin t D2 D4 C R vo Vc max Vc min a t 2 3 4 t2 vT t1 T 2 VT peak b t 4 2 3 is c t Figure 3.1.6 : Bridge Rectifier with an C - Filter 5 Electronic Engineering, La Trobe University ELE5PRA Engineering Practice 2007 t1 charging time of C, t2 discharge time of C, figure above. Period is the sum of t1 and t2 such that T for a full waverectifier t1 t 2 2 T for a half waverectifier But t2>>t1 so that T for a full waverectifier t2 2 T for a half waverectifier Time interval is redefined such that from t = 0 to the beginning of interval 1. Vm io e t t1 RLC for t 1 t 1 t 2 RL The instantaneous output voltage during the discharge period is vo R L io Vm e t t1 RLC The peak to peak ripple voltage is then Vr pp vo t t1 vo t t1 t 2 Vm Vm e t2 RLC Vm 1 e t2 RLC x Since e 1 x t 2 Vm t 2 Vm Vm 1 1 R C 2 fR C for a full waverectifier RL C Vr pp L L Vm fR C for half waverectifier L The average output then becomes V Vm V 4 fRLC 1 Vm r pp Vm m for a full wave rectifier 2 4 fRLC 4 fRLC Vo dc V Vm Vm 2 fRLC 1 m 2 fRLC for half wave rectifier 2 fRLC Assuming a sine wave peak ripple then the rms is 6 Electronic Engineering, La Trobe University ELE5PRA Engineering Practice 2007 Vr pp Vm for a full waverectifier 2 2 4 2 fRL C Vr rms Vm 2 2 fR C for half waverectifier L The ripple factor RF is therefore Vr rms Vm 4 fRL C 1 RF Vo dc 4 2 fRL C Vm 4 fRL C 1 2 4 fRL C 1 1 2 4 fR C 1 for a full waverectifier L 1 for half waverectifier 2 2 fRL C 1 2.1.7 Zener Diodes and Voltage Regulation Zener diodes operate in the reverse break down region. In this region the diode current increases rapidly with small increases in voltage. The I-V characteristic of the zener is shown in figure 3.1.7. The voltage at the knee is V ZK this is the voltage where the zener enters the breakdown region. The zener voltage is the breakdown voltage at a specific test current I Z I ZT . I Z m ax is current that the zener can withstand and still remain within permissible limits for power dissipation. I Z m in is slightly below the knee on the characteristic curve. The equivalent circuit for a zener diode is shown in figure 3.1.7 (c) and (d). In figure (b) the reverse characteristic can be approximated by a piecewise linear model with a fixed voltage V ZO and an ideal resistor (see equivalent circuit). The equivalent circuit is for v D VZ . RZ depends on the inverse slope of the zener characteristic and is defined as VZ v D RZ I Z atVZ i D for v D 0 and iD 0 7 Electronic Engineering, La Trobe University ELE5PRA Engineering Practice 2007 iD Large voltage Large voltage Small voltage large current small current large current iD I Z min VZ VD max VZ V ZK V D min I ZK vD vD IZ I Z iZ I Z max iZ Figure 3.1.7 a Symbol b Zener characteristics D1 D1 vD vD RD RZ VTD VZO VBR Figure 3.1.7 : c Forward d Reverse Where RZ is the zener resistance. Away from the knee the zener resistance remains fairly constant. Typically the value RZ is a few tens of ohms. At the knee RZ is around 3kΩ. The zener current iZ i D and can be related to V ZO and RZ by VZ VZ 0 RZ i Z A zener diode can be seen as offering a variable resistance whose value changes with current so that the voltage across the terminals is constant. The zener is therefore known as the voltage reference diode. Since RZ is very small it means that the zener voltage V Z is almost independent of the reverse diode current. The reverse region offers a constant voltage this makes the zener diode suitable for voltage regulation. A voltage regulator maintains a fairly constant output even when supply voltage and the load current vary over a wide range. A zener regulator is also known as a shunt regulator. Figure 3.1.8 shows a shunt regulator. The value of R S is chosen such that the zener operates in the reverse region over the entire range of input voltages. The equivalent circuit is represented by a piecewise model, figure 3.1.8(b). when v s varies the current i Z will vary because of RZ causing a variation in the output voltage. This defined by the line voltage given by 8 Electronic Engineering, La Trobe University ELE5PRA Engineering Practice 2007 v0 RZ Line regulation v S RZ RS If the load current i L increases then i Z ↓ because of RZ causing V out to↓. This variation of V out is load regulation. iS RS iS RS iL D1 D1 iL iZ VZO VZ VTD RL VZ vO vS RL RD RZ Figure 3.1.8 : a Circuit b Equivalent circuit v0 RZ || RS Load regulation i L A change in the zener voltage causes an increase in the output voltage. The variation is caused by zener regulation. v0 Rs Zener regulation VZ 0 RZ RS By superposition the effective voltage is v0 v v v0 VZ 0 0 v s 0 i L VZ 0 v S i L Rs RZ VZ 0 v S RZ || RS i L RZ RS RZ RS 2.1.8 Design of a Regulator The regulator is designed so that the zener can operate in the break down region under worst case scenario. For this to happen the following conditions should be met VS (min) VZ 0 RZ iZ (min ) 1. RS iZ (min) i L (max) VS (max) VZ 0 RZ iZ (max) 2. RS iZ (max) i L (min) The maximum zener current in terms of the variations in VS and iL is V S m in VZO RZ i Z m in i Z m ax i L m in VS m ax VZO RZ i Z m ax i Z m in i L m ax As a rule of thumb the minimum zener current i is limited to 10% of the maximum Z m in zener current i .That is i 0.1 i . Z m ax Z m in Z m ax 9 Electronic Engineering, La Trobe University