3.4. Operation in the Reverse Breakdown

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Abner Melton
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1 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 Provide a constant dc voltage between its output terminals To remain output as constant as possible in spite of changes in dc power supply voltage and load current V = r z I Figure 3.18 Circuit symbol for a zener diode. 1

2 V z = V z0 + r z I z I Z > I ZK, V Z > V Z0 2 Figure 3.20 Model for the zener diode.

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

4.5. 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

4 4.5. 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 Power transformer: Step down voltage: primary winding (N1) - Secondary winding (N2) Electrical isolation Diode rectifier: produce pulsating waveform Rectifier filter: constant + ripple 4

5 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 4.20: Block diagram of a dc power supply 5

6 3.5.1 Half-Wave Rectifier Half-wave rectifier: utilizes only alternate half-cycles of the input sinusoid Employ constant voltage drop diode model v = 0, v S < V D v = v S V D, v S V D Selecting a diode Current-handling capability (largest current to be conduct) Peak inverse voltage (PIV) (largest reverse voltage without breakdown) Figure 4.21: (a) Half-wave rectifier (b) Transfer characteristic of the rectifier circuit (c) Input and output waveforms 6

7 3.5.1 Half-Wave Rectifier Current-handling capability: maximum forward current diode expected to conduct Peak inverse voltage (PIV): maximum reverse voltage it is expected to block without breakdown Use of exponential model: It is possible to use the diode exponential model in describing rectifier operation; however, this requires too much work Apply small inputs: the rectifier will not operate properly when input voltage is small (< 1V). Require a precision rectifier 7

8 3.5.2 Full-Wave Rectifier Utilize both halves of the input sinusoid Provide a unipolar output Current through R always flows in the same direction 8 Figure 4.22: Full-wave rectifier utilizing a transformer with a center-tapped secondary winding

9 The key here is center-tapping of the transformer, allowing reversal of certain currents Figure 4.22: 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 3.5.2 Full-Wave Rectifier The most important observation The direction of current flowing across load never changes (both halves of AC wave are rectified) Produces a more energetic waveform than half-wave PIV for full-wave: PIV = 2V s V D 12

13 3.5.3 Bridge Rectifier Advantage No need for center-tapped transformer PIV is half of the full-wave rectifier with a center-tapped transformer Disadvantage: Used 4 diodes Series connection of two diodes will reduce output voltage Current through R always flows in the same direction PIV = V s V D 13 Figure 4.23: The bridge rectifier circuit.

14 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. 14

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

16 3.5.4 Rectifier with Filter Capacitor Pulsating nature of rectifier output makes unreliable dc supply Employed a filter capacitor to remove ripple 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) 16 Figure 4.24: (a) A simple circuit used to illustrate the effect of a filter capacitor. (b) input and output waveforms assuming an ideal diode.

17 Practical Situation When load resistor is placed in series with capacitor Consider the discharging of capacitor across load 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 circuit state #2 17

18 output voltage for state #1 v t v t v t V e t RC output voltage for state #2 I peak Figure 4.25: Voltage and Current Waveforms in the Peak Rectifier Circuit WITH RC >> T. The diode is assumed ideal. 18

19 bservations The diode conducts for a brief interval ( t) near the peak of the input sinusoid and supplies the capacitor with charge equal to that lost during the much longer discharge interval (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 setting of I D = 0) 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 = V p -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 P ). the average output voltage may be defined as below 1 (eq4.27) avgv Vpeak Vr Vpeak if Vr is small 19 2

20 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 Step 3: Define output voltage for state #1 output voltage for state #1 v v v I D 20 i L v R i i i D C L action: define capacitor current differentially dvi id C i dt circuit state #1 L

21 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 Step 6: Use combination of circuit and Laplace Analysis to solve for v (t) in terms of initial condition and time circuit state #2 21

22 3.5.4 Rectifier with Filter Capacitor Use Laplace transform 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 22

23 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 circuit state #2 23

24 3.5.4 Rectifier with 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 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 v t V e T is discharge interval V V v ( T) (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 24

25 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 = V p /R). Q: How is conduction interval ( t) defined? A: See following slides (eq4.29) V r V peak frc V peak I R L fc 25 expression to define ripple voltage (V r )

26 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 ω t cos(0 ) cos ω t (ω t)2 peak V cos t V V note that peak of vi represents cos(0 ), therefore cost represents variation around this value peak r (eq 4.30) t 2 V / V r peak 26 as assumed, conduction interval t will be small when V V r peak

27 3.5.5 Precision HW Rectifier Precision rectifier is a device which facilitates rectification of lowvoltage input waveforms Figure 4.27: The Superdiode Precision Half-Wave Rectifier and its almost-ideal transfer characteristic. 27

28 3.6 Limiting and Clamping Circuits Limiter circuit: limits voltage output Passive limiter circuit (K < 1) has linear range has nonlinear range Examples include v over linear range KvI constant value(s) Single limiter operate in unipolar manner outside linear range Double limiter operate in bipolar manner v over linear range KvI constant value(s) outside linear range L L - v I L K L v L KvI L L - K v I v v I I L K L K 28 L K Figure 3.30: General transfer characteristic for a limiter circuit

29 3.6 Limiting and Clamping Circuits Soft vs. Hard limiter Figure 3.32: Hard vs. Soft Limiting. How are limiter circuits applied? A: Signal processing, used to prevent breakdown of transistors within various devices 29

30 single limiters employ one diode double limiters employ two diodes of opposite polarity linear range may be controlled via string of diodes and dc sources zener diodes may be used to implement soft limiting Figure 3.33: Variety of basic limiting circuits. 30

31 3.6.2 Clamped Capacitor or DC Restorer DC restorer: Circuit which removes the dc component of an AC wave v C will charge equal to the magnitude of the most negative peak of the input signal v = v I + v C 31 Figure 3.34: The clamped capacitor or dc restorer with a square-wave input and no load

32 3.6.3 Voltage Doubler Clamped capacitor + peak rectifier utput voltage = double the input peak Figure 3.36: Voltage doubler: (a) circuit; (b) waveform of the voltage across D 1. 32

33 Summary (1) In the forward direction, the ideal diode conducts any current forced by the external circuit while displaying a zerovoltage drop. The ideal diode does not conduct in reverse direction; any applied voltage appears as reverse bias across the diode. The unidirectional current flow property makes the diode useful in the design of rectifier circuits. The forward conduction of practical silicon-junction diodes is accurately characterized by the relationship i = I S e V/VT. 33

34 Summary (2) A silicon diode conducts a negligible current until the forward voltage is at least 0.5V. Then, the current increases rapidly with the voltage drop increasing by 60mV for every decade of current change. In the reverse direction, a silicon diode conducts a current on the order of 10-9 A. This current is much greater than I S and increases with the magnitude of reverse voltage. 34

35 Summary (3) Beyond a certain value of reverse voltage (that depends on the diode itself), breakdown occurs and current increases rapidly with a small corresponding increase in voltage. Diodes designed to operate in the breakdown region are called zener diodes. They are employed in the design of voltage regulators whose function is to provide a constant dc voltage that varies little with variations in power supply voltage and / or load current. 35

36 Summary (4) In many applications, a conducting diode is modeled as having a constant voltage drop usually with value of approximately 0.7V. A diode biased to operate at a dc current I D has small signal resistance r d = V T /I D. Rectifiers covert ac voltage into unipolar voltages. Halfwave rectifiers do this by passing the voltage in half of each cycle and blocking the opposite-polarity voltage in the other half of the cycle. 36

37 Summary (5) The bridge-rectifier circuit is the preferred full-wave rectifier configuration. The variation of the output waveform of the rectifier is reduced considerably by connecting a capacitor C across the output load resistance R. The resulting circuit is the peak rectifier. The output waveform then consists of a dc voltage almost equal to the peak of the input sine wave, V p, on which is superimposed a ripple component of frequency 2f (in the full-wave case) and of peak-to-peak amplitude V r = V p /2fRC. 37

38 Summary (6) Combination of diodes, resistors, and possible reference voltage can be used to design voltage limiters that prevent one or both extremities of the output waveform from going beyond predetermined values the limiting levels. Applying a time-varying waveform to a circuit consisting of a capacitor in series with a diode and taking the output across the diode provides a clamping function. By cascading a clamping circuit with a peak-rectifier circuit, a voltage doubler is realized. 38

39 Summary (6) Beyond a certain value of reverse voltage (that depends on the diode itself), breakdown occurs and current increases rapidly with a small corresponding increase in voltage. Diodes designed to operate in the breakdown region are called zener diodes. They are employed in the design of voltage regulators whose function is to provide a constant dc voltage that varies little with variations in power supply voltage and / or load current. 39

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

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