3.4. Reverse Breakdown Region Zener Diodes In the breakdown region Very steep i-v curve Almost constant voltage drop Used for voltage regulator

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1 3.4. Reverse Breakdown Region Zener Diodes In the breakdown region Very steep i-v curve Almost constant voltage drop Used for voltage regulator Voltage regulator Provide a constant dc output voltage If changing their load current and power supply voltage Under certain circumstances, diodes may be intentionally used in the reverse breakdown region Referred to as zener diodes / breakdown diodes 1

2 3.4.1 Specifying and Modeling the Zener Fig 3.17 Knee current/knee voltage V Z at a specified test current, I ZT V = r Z I r Z (few ohms ~ few tens of ohms) Inverse of the slop of almost linear i-v curve at point Q Incremental resistance at operating point Q Dynamic resistance of Zener V Z = V Z0 + r Z I Z Temperature effects operating current Low temperature coefficient: connect a Zener diode with positive temco of 2mV/C in series with a forward-conducting diode (V Z + 0.7) 2

3 3.5. Rectifier Circuits ne important application of diode is the rectifier Electrical device which converts alternating current (AC) to direct current (DC) ne important application of rectifier is dc power supply. 3 Figure 3.20: Block diagram of a dc power supply

4 step #1: increase / decrease rms magnitude of AC wave via power transformer step #2: convert full-wave AC to half-wave DC (still time-varying and periodic) step #3: employ low-pass filter to reduce wave amplitude by > 90% step #4: employ voltage regulator to eliminate ripple step #5: supply dc load. Figure 3.20: Block diagram of a dc power supply 4

5 The Half-Wave Rectifier half-wave rectifier utilizes only alternate half-cycles of the input sinusoid Constant voltage drop diode model is employed Figure 3.21: (a) Half-wave rectifier (b) Transfer characteristic of the rectifier circuit (c) Input and output waveforms 5

6 The Half-Wave Rectifier current-handling capability what is maximum forward current diode is expected to conduct? peak inverse voltage (PIV) what is maximum reverse voltage it is expected to block w/o breakdown? (PIV = V S ) Usually 50% greater than expected PIV 6

7 The Half-Wave Rectifier exponential model? It is possible to use the diode exponential model in describing rectifier operation; however, this requires too much work. small inputs? Regardless of the model employed, one should note that the rectifier will not operate properly when input voltage is small (< 100mV). Those cases require a precision rectifier. 7

8 The Full-Wave Rectifier Q: How does fullwave rectifier differ from halfwave? A: It utilizes both halves of the input ne potential is shown to right. Figure 3.22: Full-wave rectifier utilizing a transformer with a centertapped secondary winding. 8

9 The key here is center-tapping of the transformer, allowing reversal of certain currents Figure 3.22: full-wave rectifier utilizing a transformer with a centertapped secondary winding: (a) circuit; (b) transfer characteristic assuming a constant-voltage-drop model for the diodes; (c) input and output waveforms. 9

10 When instantaneous source voltage is positive, D 1 conducts while D 2 blocks 10

11 when instantaneous source voltage is negative, D 2 conducts while D 1 blocks 11

12 The Full-Wave Rectifier Q: What are most important observation(s) from this operation? A: The direction of current flowing across load never changes (both halves of AC wave are rectified). The full-wave rectifier produces a more energetic waveform than half-wave. PIV for full-wave = 2V S V D 12

13 The Bridge Rectifier An alternative implementation of the full-wave rectifier is bridge rectifier. Shown to right. Figure 3.23: The bridge rectifier circuit. 13

14 when instantaneous source voltage is positive, D 1 and D 2 conduct while D 3 and D 4 block Figure 3.23: The bridge rectifier circuit. 14

15 when instantaneous source voltage is positive, D 1 and D 2 conduct while D 3 and D 4 block Figure 4.23: The bridge rectifier circuit. 15

16 3.5.3: The Bridge Rectifier (BR) Q: What is the main advantage of BR? A: No need for center-tapped transformer. Q: What is main disadvantage? A: Series connection of TW diodes will reduce output voltage. PIV = V S V D The most popular rectifier circuit configuration 16

17 The Rectifier with a Filter Capacitor Pulsating nature of rectifier output makes unreliable dc supply As such, a filter capacitor is employed to remove ripple Figure 3.24: (a) A simple circuit used to illustrate the effect of a filter capacitor. (b) input and output waveforms assuming an ideal diode. 17

18 The Rectifier with a Filter Capacitor step #1: source voltage is positive, diode is forward biased, capacitor charges. step #2: source voltage is reverse, diode is reverse-biased (blocking), capacitor cannot discharge. step #3: source voltage is positive, diode is forward biased, capacitor charges (maintains voltage). Figure 3.24 (a) A simple circuit used to illustrate the effect 18

19 The Rectifier with a Filter Capacitor Q: Why is this example unrealistic? A: Because for any practical application, the converter would supply a load (which in turn provides a path for capacitor discharging). 19

20 The Rectifier with a Filter Capacitor Q: What happens when load resistor is placed in series with capacitor? A: ne must now consider the discharging of capacitor across load. 20

21 The Rectifier with a Filter Capacitor The textbook outlines how Laplace Transform may be used to define behavior below. circuit state #1 output voltage for state #1 v t v t v I D v t V e peak t RC output voltage for state #2 xford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith ( ) 21 circuit state #2

22 Q: What happens when load resistor is placed in series with capacitor? circuit state #1 step #1: Analyze circuit state #1. When diode is forward biased and conducting. step #2: Input voltage (v I ) will be applied to output (v ), minus 0.7V drop across diode. 22 i L v R i i i D C L action: define capacitor current differentially dvi id C i dt L

23 Q: What happens when load resistor is placed in series with capacitor? step #3: Define output voltage for state #1. output voltage for state #1 v v v I D circuit state #1 23

24 Q: What happens when load resistor is placed in series with capacitor? step #4: Analyze circuit state #2. When diode is blocking and capacitor is discharging. step #5: Define KVL and KCL for this circuit. v = Ri L i L = i C circuit state #2 24

25 Q: What happens when load resistor is placed in series with capacitor? step #6: Use combination of circuit and Laplace Analysis to solve for v (t) in terms of initial condition and time 25

26 The Rectifier with a Filter Capacitor action: replace i with -i action: define i differentially action: change sides action: take Laplace transform dv v Ri L Lv RC 0 dt L v v v C Ri C dv R C dt dv RC dt i C C 0 action: take Laplace transform V s RC sv s V 0 0 dv transform of dt action: seperate disalike / collect alike terms 1 RCs V ( s) V s RCsV s RCV action: pull out RC 0 initial condition 1RCsV s RCV 0 1 RCs V ( s) RC 1 action: eliminate RC from both sides 1 RC s V s RCV RC action: solve for V V s V L 0 V s V 0 s 1 1 s RC action: take inverse Laplace action: solve 0 v t V e 1 s 1/ t RC 0 RC 26

27 The Rectifier with a Filter Capacitor Q: What is V (0)? A: Peak of v I, because the transition between state #1 and state #2 (aka. diode begins blocking) approximately as v I drops below v C. 27

28 The Rectifier with a Filter Capacitor step #7: Define output voltage for states #1 and #2. circuit state #1 output voltage for state #1 v t v t v I D v t V e peak t RC output voltage for state #2 xford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith ( ) 28 circuit state #2

29 output voltage for state #1 v t v t v t V e t RC output voltage for state #2 I peak Figure 3.25: Voltage and Current Waveforms in the Peak Rectifier Circuit WITH RC >> T. The diode is assumed ideal. 29

30 A Couple of bservations The diode conducts for a brief interval (Dt) near the peak of the input sinusoid and supplies the capacitor with charge equal to that lost during the much longer discharge interval. The latter is approximately equal to T. Assuming an ideal diode, the diode conduction begins at time t 1 (at which the input v I equals the exponentially decaying output v ). Diode conduction stops at time t 2 shortly after the peak of v I (the exact value of t 2 is determined by settling of I D ). xford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. 30

31 A Couple of bservations During the diode off-interval, the capacitor C discharges through R causing an exponential decay in the output voltage (v ). At the end of the discharge interval, which lasts for almost the entire period T, voltage output is defined as follows v (T) = V peak V r. When the ripple voltage (V r ) is small, the output (v ) is almost constant and equal to the peak of the input (v I ). the average output voltage may be defined as below 1 (eq4.27) (Eq3.27) avgv Vpeak Vr Vpeak if Vr is small 2 31

32 The Rectifier with a Filter Capacitor Q: How is ripple voltage (V r ) defined? step #1: Begin with transient response of output during off interval. step #2: Note T is discharge interval. step #3: Simplify using assumption that RC >> T. step #4: Solve for ripple voltage V r. 32 v t V e T is discharge interval V V v ( T) (Eq3.28) (eq4.28) peak peak r r t RC T RC Vpeak Vr Vpeak e V action: solve for ripple voltage V because RCT, we can assume... e T RC T 1 RC Vpeak r T RC T 1 1 RC

33 The Rectifier with a Filter Capacitor step #5: Put expression in terms of frequency (f = 1/T). bserve that, as long as V r << V peak, the capacitor discharges as constant current source (I L ). Q: How is conduction interval (Dt) defined? A: See following slides 33 (eq4.29) (Eq3.29) V r V peak frc peak expression to define ripple voltage (V r ) V I R L fc

34 Q: How is conduction interval (Dt) defined? cos(0 ) step #1: Assume that diode conduction stops (very close to when) v I approaches its peak. step #2: With this assumption, one may define expression to the right. step #3: Solve for wdt. cos ω t (ω t)2 34 peak V cos wdt V V note that peak of vi represents cos(0 ), therefore coswdt represents variation around this value (eq (Eq3.30) 4.30) wdt 2 V / V peak as assumed, conduction interval Dt will be small when V V r r peak r peak

35 The Rectifier with a Filter Capacitor Q: How is peak-to-peak ripple (V r ) defined? A: (3.29) Q: How is the conduction interval (Dt) defined? A: (3.30) (Eq3.29) (eq4.29) V r V peak frc V peak I R L fc (Eq3.30) (eq4 wdt 2 V / V r peak as assumed, conduction interval Dt will be small when V V r peak 35

36 Precision Half-wave Rectifier - Superdiode precision rectifier is a device which facilitates rectification of low-voltage input waveforms. Figure 3.27: The Superdiode Precision Half-Wave Rectifier and its almost-ideal transfer characteristic. 36

37 Limiter Circuits Fig. 3.28: transfer characteristic for a limiter circuit Double limiter (vs. single limiter : Fig.3.29) Hard limiter (vs. soft limiting : Fig.3.30) L /K v I L + /K K 1 as passive limiters Ex) Fig.3.31 Control thresholds and saturation levels of diode limiters by using strings of diodes and/or by connecting a dc voltage in series with the diode Double-anode zener 37

38 3.6.2 Clamped Capacitor or DC Restorer Fig v = v I + v C Fig.3.33 Fig.3.34 Schottky-Barrier Diode (SBD): metal + n-type semiconductor No minority-carrier charge-storage effects due to majority carrier(electron) Fast switch 0.3V-0.5V forward voltage drop Varactors: voltage variable capacitors using a charge storage effect in depletion layer or junction capacitance in the reverse-biased Photodiodes Light-Emitting Diodes (LEDs) 38

3.4. Operation in the Reverse Breakdown

3.4. Operation in the Reverse Breakdown 3.4. peration in the Reverse Breakdown Under certain circumstances, diodes may be intentionally used in the reverse breakdown region These are referred to as Zener Diode or Breakdown Diode Voltage regulator