0 Chap. 3 Diodes Simplest semiconductor device Nonlinear Used in power supplies Voltage limiting circuits

1 3.1 Ideal Diodes Forward bias (on) Reverse bias (off)

2 I-V characteristics of an ideal diode

3 Ideal diode operation on off

4 Ideal diode operation diode on diode off

on off V in = 24 sin  t V out Ideal diode operation Diode conducts when 24 sin  t = 12 sin  t = 12/24  t = 30  30 

6 Exercise 3.4(a) 5V 2.5K  Find I and V Assume diode is on. V = 0, I = 5V/ 2.5K  I = 2mA, implies diode is on. Correct assumption 5V 2.5K  I +V-+V- I

7 Exercise 3.4(b) 5V 2.5K  Find I and V Assume diode is off. V D = - 5, I D = 0 implies diode is off. Correct assumption V = 5, I D = 0 5V 2.5K  I +V-+V-

8 Exercise 3.4(e) (Start with largest voltage) Assume D1 on, then D2 will be off, and D3 will be off V = 3V, and I = 3V/1K  mA. Check assumption, V D1 = 0, on V D2 = -1, off V D3 = -2, off Correct assumption (old-style OR gate) +V-+V- I Find I and V

9 3.6 Zener diodes Designed to break down at a specific voltage Used in power supplies and voltage regulators When a large reverse voltage is reached, the diode conducts. Vz is called the breakdown, or Zener voltage.

10 Typical use of Zener diode The Zener diode will not usually conduct, it needs Vs > 12.5V to break down Assume Vs fluctuates or is noisy If Vs exceeds 12.5V, the diode will conduct, protecting the load

11 Solving ideal diode problems (determining if the diode is on or off) Assume diodes are on or off. Perform circuit analysis, find I & V of each diode. Compare I & V of each diode with assumption. Repeat until assumption is true.

12 Prob. 3.9(b) Assume both diodes are on. 10V = (10K)I 1 I 1 = 10V/10K = I 1 = 1mA 0 = (5K)I V, I 2 = 2mA Current in D2 = I 2 = 2mA, on Current in D1 = I 1 - I 2 = -1mA, off Does not match assumption; start over. Are the diodes on or off? I1I1 I2I2

13 Prob. 3.9(b) Assume D1 off and D2 on. 10V = (10K)I + (5K)I -10V 20V = (15K)I I = 20V/15K = 1.33mA Current in D2 = I = 1.33mA, on Voltage across D1 10V - 10K(1.33mA) = -3.33V, off Matches assumption; done. Are the diodes on or off? I

14 I-V characteristics of an ideal diode

15 Solving ideal diode problems (determining if the diode is on or off) Assume diodes are on or off. Perform circuit analysis, find I & V of each diode. Compare I & V of each diode with assumption. Repeat until assumption is true.

16 Prob. 3.10(b) Assume diode on. 15V = (10K)I 1 + (10K)(I 1 - I 2 ) 15 = (20K)I 1 - (10K)I = (10K)(I 2 - I 1 ) + (10K)(I 2 - I 3 ) 0 = -(10K)I 1 + (20K)I 2 - (10K)I = (10K)( I 3 - I 2 ) + (10K)I = -(10K)I 2 + (20K)I 3 3 Is the diode on or off? I1I1 I3I3 I2I2 Put 3 into = -(10K)I 1 + (15K)I 2, Put 1 into this equation, solve for I 2. I 2 = 0.875mA, Current through diode is negative! Diode can’t be on.

17 Prob. 3.10(b) Assume diode off. 15V = (10K)I 1 + (10K)I 1 I 1 = 0.75mA I 2 = 0 0 = (10K)I 3 + (10K)I I 3 = -0.5mA I1I1 I3I3 I2I2 Find V 1. V 1 = (10K)I 1 = 7.5V Find V 2. V 2 = -(10K)I 3 = 5V Voltage across diode is V 2 - V 1 = -2.5V, diode is off V1V1 V2V2

Real diodes Characteristics of a real diode Forward biasReverse bias breakdown

19 Reverse bias region A small current flows when the diode is reversed bias, I S I S is called the saturation or leakage current I S  1nA -V Z is the reverse voltage at which the diode breaks down. V Z is the Zener voltage in a Zener diode (controlled breakdown). Otherwise, V Z is the peak inverse voltage (PIV) ISIS

20 Forward bias region For Silicon diodes, very little current flows until V  0.5V At V  0.7V, the diode characteristics are nearly vertical In the vicinity of V  0.7V, a wide range of current may flow. The forward voltage drop of a diode is often assumed to be V = 0.7V Diodes made of different materials have different voltage drops V  0.2V - 2.4V Almost all diodes are made of Silicon, LEDs are not and have V  1.4V - 2.4V

Analysis of diode circuits (Simplified diode models ) p Ideal diode Constant-voltage drop model Constant-voltage drop model with resistor All use assumptions because actual diode characteristics are too difficult to use in circuit analysis

22 Constant-voltage drop model I-V characteristics A straight line is used to represent the fast-rising characteristics. Resistance of diode when slope is vertical is zero.

23 Constant-voltage drop model I-V characteristics and equivalent circuit 0.7V + -

24 Constant-voltage drop with resistor model A straight line with a slope is used to represent the fast-rising characteristics. Resistance of diode is 1/slope. I-V characteristics

25 Constant-voltage drop with resistor model I-V characteristics and equivalent circuit 0.7V  50  + -

26 Prob. 3.9(b) (using constant voltage-drop model) Assume both diodes are on. 10V = (10K)I I 1 = 9.3V/10K = I 1 = 0.93mA 0 = (5K)I V, I 2 = 2mA Current in D2 = I 2 = 2mA, on Current in D1 = I 1 - I 2 = -1.07mA, off Does not match assumption; start over. Are the diodes on or off? I1I1 I2I2

27 Prob. 3.9(b) (using constant voltage-drop model) Assume D1 off and D2 on. 10V = (10K)I (5K)I -10V 19.3V = (15K)I I = 19.3V/15K = 1.29mA Current in D2 = I = 1.29mA, on Voltage across D1 10V - 10K(1.29mA) = -2.9V, off Matches assumption; done. Are the diodes on or off? I

28 Prob. 3.10(b) (using constant voltage-drop model) Assume diode on. 15V = (10K)I 1 + (10K)(I 1 - I 2 ) 15 = (20K)I 1 - (10K)I = (10K)(I 2 - I 1 ) (10K)(I 2 - I 3 ) 0.7 = -(10K)I 1 + (20K)I 2 - (10K)I = (10K)( I 3 - I 2 ) + (10K)I = -(10K)I 2 + (20K)I 3 3 Is the diode on or off? I1I1 I3I3 I2I2 Put 3 into = -(10K)I 1 + (15K)I 2, Put 1 into this equation, solve for I 2. I 2 = 0.91mA, Current through diode is negative! Diode can’t be on.

29 Prob. 3.10(b) (using constant voltage-drop model) Assume diode off. 15V = (10K)I 1 + (10K)I 1 I 1 = 0.75mA I 2 = 0 0 = (10K)I 3 + (10K)I I 3 = -0.5mA I1I1 I3I3 I2I2 Find V 1. V 1 = (10K)I 1 = 7.5V Find V 2. V 2 = -(10K)I 3 = 5V Voltage across diode is V 2 - V 1 = -2.5V, diode is off V1V1 V2V2

Rectifier circuits Block diagram of a dc power supply

31 Half-wave rectifier Simple Wastes half the input

32 Full-wave rectifier V S > 0 V S < 0 Current goes through load in same direction for + V S. V O is positive for + V S. Requires center-tap transformer

33 Full-wave rectifier Entire input waveform is used

34 Bridge rectifier A type of full-wave rectifier Center-tap not needed Most popular rectifier V S > 0 D 1, D 2 on; D 3, D 4 off V S < 0 D 3, D 4 on; D 1, D 2 off

35 Bridge rectifier V O is 2V D less than V S

36 Filter Capacitor acts as a filter. Vi charges capacitor as Vi increases. As Vi decreases, capacitor supplies current to load.

37 Filter Diode on Diode off When the diode is off, the capacitor discharges. V o = V p exp(-t/RC) Assuming t  T, and T=1/f V P - V r = V p exp(-1/fRC) half-wave rectifier (t  T) V P - V r = V p exp(-1/2fRC) full-wave rectifier (t  T/2)

38 Exercise 3.30 Bridge rectifier, given: V S = 12V(rms) f = 60 Hz V D = 0.8V R = 100  (a) Find C for a ripple voltage of 1V p-p V P - V r = V p exp(-1/2fRC) V P - V r = [12  2 - 2(0.8)] - 1= V P = [12  2 - 2(0.8)] = Solve for C. C = -T/[2R ln (V P - V r )/V P ] = 1280  F

39 Exercise 3.30 Bridge rectifier, given: V S = 12V(rms) f = 60 Hz V D = 0.8V R = 100  V o = V S - 2V D - 1/2Vr Vo = 12  2 - 2(0.8) = 14.87V (average voltage) (b) What is the DC voltage at the output? (c) What is the load current? I avg = V o /R = 14.87/100 = 0.15A

40 Exercise Diodes on Diode off V P - V r = V P cos(  t)  t = cos -1 (1-V r /V P )  t = radians = 20.7 degree Each diode is on for 20.7 degree and off for = 339.3degree The other 2 Diodes on (d) What is the diode’s conduction angle? (What fraction of the cycle is the diode on?)

41 Exercise 3.30 (e) What is the average diode current? VoVo VSVS IDID I avg(diodes) = 0.15*360/20.7=2.6 A I avg(each diode) = 1.3 A I max(each diode) = 2.6 A  t = radians using  = 2  f t=8.33*20.7/180 =0.96mS length of time diodes are on.

42 Prob Given a half-wave rectifier with: V S = 20Vp-p (triangular) V D = 0.7V, R = 100  C = 100  F, f = 1kHz (a) Find the average DC output voltage 20V V P - V r = V p exp(-1/fRC) V P - V r = 8.4V Average Vo  ( )/2 = 8.85 V P = V S - V D = 9.3V 8.4V

43 Prob (b) How long is the diode on? 20V Diode on Slope =  V/  t slope = 20V/0.5mS  V = V P -V r = Solve for  t  t = 0.022mS VPVP tt

44 Prob Charge supplied to capacitor = Charge released by capacitor (I diode )  t = I avg in load( 2  -  t ) 2 .0mS, I avg in load = Vo avg /R = 8.85/100 = 0.089A (I diode )0.022mS = 0.089A ( 1.0mS mS ) I diode  4A(average current) (c) What is the average diode current?

45 Fig A variety of basic limiting circuits.

46 Fig (a) A three-segment sine-wave shaper. (b) the input triangular waveform and the output approximately-sinusoidal waveform.

47 Fig (a) The bistable circuit of Fig with the negative input terminal of the op amp disconnected from ground and connected to an input signal v I. (b) The transfer characteristic of the circuit in (a) for increasing v I. (c) The transfer characteristic for increasing v I. (d) the complete transfer characteristics.

48 Fig (a) Connecting a bistable multivibrator with inverting transfer characteristic in a feedback loop with an RC circuit results in a square-wave generator. (b) The circuit obtained when the bistable multivibrator is implemented with the circuit of Fig (a). (c) Waveforms at the various nodes of the circuit in (b). This circuit is called an astable multivibrator.

49 Fig General scheme for generating triangular and square waveforms.

50 Fig (a) A three-segment sine-wave shaper. (b) the input triangular waveform and the output approximately-sinusoidal waveform.