1. Microelectronic Circuits Zhou Lingling
Chapter 1 Diodes
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2. Outline of Chapter 1 1.1 Introduction 1.2 Basic Semiconductor Concepts
1.3 The pn Junction
1.4 Analysis of diode circuits
1.5 Applications of diode circuits
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3. 1.1 Introduction
The diode is the simplest and most fundamental nonlinear circuit element.
Just like resistor, it has two terminals.
Unlike resistor, it has a nonlinear current-voltage characteristics.
Its use in rectifiers is the most common application.
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4. Physical Structure
The most important region, which is called pn junction, is the boundary between n-type and p-type semiconductor.
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5. Symbol and Characteristic for the Ideal Diode
(a) diode circuit symbol; (b) i–v characteristic; (c) equivalent circuit in the reverse direction; (d) equivalent circuit in the forward direction.
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6. Characteristics
Conducting in one direction and not in the other is the I-V characteristic of the diode.
The arrowlike circuit symbol shows the direction of conducting current.
Forward biasing voltage makes it turn on.
Reverse biasing voltage makes it turn off.
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7. 1.2 Basic Semiconductor Concepts
Intrinsic Semiconductor
Doped Semiconductor
Carriers movement
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8. Intrinsic Semiconductor
Definition
A crystal of pure and regular lattice structure is called intrinsic semiconductor.
Materials
Silicon---today’s IC technology is based entirely on silicon
Germanium---early used
Gallium arsenide---used for microwave circuits
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9. Intrinsic Semiconductor(cont’d)
Two-dimensional representation of the silicon crystal. The circles represent the inner core of silicon atoms, with +4 indicating its positive charge of +4q, which is neutralized by the charge of the four valence electrons. Observe how the covalent bonds are formed by sharing of the valence electrons. At 0 K, all bonds are intact and no free electrons are available for current conduction.
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10. Intrinsic Semiconductor(cont’d)
At room temperature, some of the covalent bonds are broken by thermal ionization. Each broken bond gives rise to a free electron and a hole, both of which become available for current conduction.
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11. Intrinsic Semiconductor(cont’d)
Thermal ionization
Valence electron---each silicon atom has four valence electrons
Covalent bond---two valence electrons from different two silicon atoms form the covalent bond
Be intact at sufficiently low temperature
Be broken at room temperature
Free electron---produced by thermal ionization, move freely in the lattice structure.
Hole---empty position in broken covalent bond,can be filled by free electron, positive charge
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12. Intrinsic Semiconductor(cont’d)
Carriers
A free electron is negative charge and a hole is positive charge. Both of them can move in the crystal structure. They can conduct electric circuit.
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13. Intrinsic Semiconductor(cont’d)
Recombination
Some free electrons filling the holes results in the disappearance of free electrons and holes.
Thermal equilibrium
At a certain temperature, the recombination rate is equal to the ionization rate. So the concentration of the carriers is able to be calculated.
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14. Intrinsic Semiconductor(cont’d)
Carrier concentration in thermal equilibrium
At room temperature(T=300K)
carriers/cm3
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15. Intrinsic Semiconductor(cont’d)
Important notes:
has a strong function of temperature. The high the temperature is, the dramatically great the carrier concentration is.
At room temperature only one of every billion atoms is ionized.
Silicon’s conductivity is between that of conductors and insulators. Actually the characteristic of intrinsic silicon approaches to insulators.
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16. Doped Semiconductor
Doped semiconductors are materials in which carriers of one kind predominate.
Only two types of doped semiconductors are available.
Conductivity of doped semiconductor is much greater than the one of intrinsic semiconductor.
The pn junction is formed by doped semiconductor.
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17. Doped Semiconductor(cont’d)
n type semiconductor
Concept
Doped silicon in which the majority of charge carriers are the negatively charged electrons is called n type semiconductor.
Terminology
Donor---impurity provides free electrons, usually entirely ionized.
Positive bound charge---impurity atom donating electron gives rise to positive bound charge
carriers
Free electron---majority, generated mostly by ionized and slightly by thermal ionization.
Hole---minority, only generated by thermal ionization.
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18. Doped Semiconductor(cont’d)
A silicon crystal doped by a pentavalent element. Each dopant atom donates a free electron and is thus called a donor. The doped semiconductor becomes n type.
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19. Doped Semiconductor(cont’d)
p type semiconductor
Concept
Doped silicon in which the majority of charge carriers are the positively charged holes is called p type semiconductor.
Terminology
acceptor---impurity provides holes, usually entirely ionized.
negatively bound charge---impurity atom accepting hole give rise to negative bound charge
carriers
Hole---majority, generated generated mostly by ionized and slightly by thermal ionization.
Free electron---minority, only generated by thermal ionization.
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20. Doped Semiconductor(cont’d)
A silicon crystal doped with a trivalent impurity. Each dopant atom gives rise to a hole, and the semiconductor becomes p type.
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21. Doped Semiconductor(cont’d)
Carrier concentration for n type
Thermal equilibrium equation
Electric neutral equation
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22. Doped Semiconductor(cont’d)
Carrier concentration for p type
Thermal equilibrium equation
Electric neutral equation
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23. Doped Semiconductor(cont’d)
Because the majority is much great than the minority, we can get the approximate equations shown below:
for n type for p type
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24. Doped Semiconductor(cont’d)
Conclusion
Majority carrier is only determined by the impurity, but independent of temperature.
Minority carrier is strongly affected by temperature.
If the temperature is high enough, characteristics of doped semiconductor will decline to the one of intrinsic semiconductor.
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25. Doped Semiconductor(cont’d)
Doping compensation
n type semiconductor is generated by donor diffusion, then injecting acceptor into the specific area(assuming ) forms p type semiconductor. The boundary between n and p type semiconductor is the pn junction. This is the basic step for VLSI fabrication technology. NA ND
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26. Carriers Movement
There are two mechanisms by which holes and free electrons move through a silicon crystal.
Drift--- The carrier motion is generated by the electrical field across a piece of silicon. This motion will produce drift current.
Diffusion--- The carrier motion is generated by the different concentration of carrier in a piece of silicon. The diffused motion, usually carriers diffuse from high concentration to low concentration, will give rise to diffusion current.
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27. Drift and Drift Current
Drift velocities
Drift current densities
Where are the constants called mobility of holes and electrons respectively.
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28. Drift and Drift Current
Total drift current density
Resistivity
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29. Drift and Drift Current
Resistivities for doped semiconductor
* Resistivities are inversely proportional to the concentration of doped impurities.
Temperature coefficient(TC)
TC for resistivity of doped semiconductor is positive due to negative TC of mobility
For n type
For p type
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30. Drift and Drift Current
Resistivity for intrinsic semiconductor
* Resistivity is inversely proportional to the carrier concentration of intrinsic semiconductor.
Temperature coefficient(TC)
TC for resistivity of intrinsic semiconductor is negative due to positive TC of
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31. Diffusion and Diffusion Current
A bar of intrinsic silicon (a) in which the hole concentration profile shown in (b) has been created along the x-axis by some unspecified mechanism.
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32. Diffusion and Diffusion Current
where are the diffusion constants or diffusivities for hole and electron respectively.
* The diffusion current density is proportional to the slope of the the concentration curve, or the concentration gradient.
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33. Einstein Relationship
Einstein relationship exists between the carrier diffusivity and mobility:
Where VT is Thermal voltage.
At room temperature，
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34. 1.3 pn Junction The pn junction under open-circuit condition
I-V characteristic of pn junction
Terminal characteristic of junction diode.
Physical operation of diode.
Junction capacitance
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35. pn Junction Under Open-Circuit Condition
Usually the pn junction is asymmetric, there are p+n and pn+.
The superscript “+” denotes the region is more heavily doped than the other region.
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36. pn Junction Under Open-Circuit Condition
Fig (a) shows the pn junction with no applied voltage (open-circuited terminals).
Fig.(b) shows the potential distribution along an axis perpendicular to the junction.
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37. Procedure of Forming pn Junction
The procedure of forming pn the dynamic equilibrium of drift and diffusion movements for carriers in the silicon. In detail, there are 4 steps:
Diffusion
Space charge region
Drift
Equilibrium
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38. Procedure of Forming pn Junction
diffusion
Both the majority carriers diffuse across the boundary between p-type and n-type semiconductor.
The direction of diffusion current is from p side to n side.
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39. Procedure of Forming pn Junction
Space charge region
Majority carriers recombining with minority carriers results in the disappearance of majority carriers.
Bound charges, which will no longer be neutralized by majority carriers are uncovered.
There is a region close to the junction that is depleted of majority carriers and contains uncovered bound charges.
This region is called carrier-depletion region or space charge region.
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40. Procedure of Forming pn Junction
Drift
Electric field is established across the space charge region.
Direction of electronic field is from n side to p side.
It helps minority carriers drift through the junction. The direction of drift current is from n side to p side.
It acts as a barrier for majority carriers to diffusion.
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41. Procedure of Forming pn Junction
Equilibrium
Two opposite currents across the junction is equal in magnitude.
No net current flows across the pn junction.
Equilibrium conduction is maintained by the barrier voltage.
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42. Junction Built-In Voltage
The Junction Built-In Voltage
It depends on doping concentration and temperature
Its TC is negative.
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43. Width of the Depletion Region
Depletion region exists almost entirely on the slightly doped side.
Width depends on the voltage across the junction.
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44. I-V Characteristics
The diode i–v relationship with some scales expanded and others compressed in order to reveal details
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45. I-V Characteristic Curve
Terminal Characteristic of Junction Diodes
The Forward-Bias Region, determined by
The Reverse-Bias Region, determined by
The Breakdown Region, determined by
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46. The pn Junction Under Forward-Bias Conditions
The pn junction excited by a constant-current source supplying a current I in the forward direction.
The depletion layer narrows and the barrier voltage decreases by V volts, which appears as an external voltage in the forward direction.
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47. The pn Junction Under Forward-Bias Conditions
Minority-carrier distribution in a forward-biased pn junction. It is assumed that the p region is more heavily doped than the n region; NA >>ND.
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48. The pn Junction Under Forward-Bias Conditions
Excess minority carrier concentration:
Exponential relationship
Small voltage incremental give rise to great incremental of excess minority carrier concentration.
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49. The pn Junction Under Forward-Bias Conditions
Distribution of excess minority concentration:
Where
are called excess-minority-carrier lifetime.
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50. The pn Junction Under Forward-Bias Conditions
The total current can be obtained by the diffusion current of majority carriers.
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51. The pn Junction Under Forward-Bias Conditions
The saturation current is given by :
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52. The pn Junction Under Forward-Bias Conditions
I-V characteristic equation:
Exponential relationship, nonlinear.
Is is called saturation current, strongly depends on temperature.
or 2， in general
VT is thermal voltage.
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53. The pn Junction Under Forward-Bias Conditions
assuming V1 at I1 and V2 at I2
then:
* For a decade changes in current, the diode voltage drop changes by 60mv (for n=1) or 120mv (for n=2).
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54. The pn Junction Under Forward-Bias Conditions
Turn-on voltage
A conduction diode has approximately a constant voltage drop across it. It’s called turn-on voltage.
Diodes with different current rating will exhibit the turn-on voltage at different currents.
Negative TC,
For silicon
For germanium
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55. The pn Junction Under Reverse-Bias Conditions
The pn junction excited by a constant-current source I in the reverse direction.
To avoid breakdown, I is kept smaller than IS.
Note that the depletion layer widens and the barrier voltage increases by VR volts, which appears between the terminals as a reverse voltage.
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56. The pn Junction Under Reverse-Bias Conditions
I-V characteristic equation:
Where Is is the saturation current, it is proportional to ni2 which is a strong function of temperature.
Independent of voltage。
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57. The pn Junction In the Breakdown Region
The pn junction excited by a reverse-current source I, where I > IS. The junction breaks down, and a voltage VZ , with the polarity indicated, develops across the junction.
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58. The pn Junction In the Breakdown Region
Supposing , the current source will move holes from p to n through the external circuit.
The free electrons move through opposite direction.
This result in the increase of barrier voltage and decrease almost zero of diffusion current.
To achieved the equilibrium, a new mechanism sets in to supply the charge carriers needed to support the current I.
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59. Breakdown Mechanisms Zener effect Avalanche effect.
Occurs in heavily doping semiconductor
Breakdown voltage is less than 5v.
Carriers generated by electric field---field ionization.
TC is negative.
Avalanche effect.
Occurs in slightly doping semiconductor
Breakdown voltage is more than 7v.
Carriers generated by collision.
TC is positive.
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60. Breakdown Mechanisms Remember:
pn junction breakdown is not a destructive process, provided that the maximum specified power dissipation is not exceeded.
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61. Zener Diode Circuit symbol
The diode i–v characteristic with the breakdown region shown in some detail.
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62. Junction Capacitance Diffusion Capacitance Depletion capacitance
Charge stored in bulk region changes with the change of voltage across pn junction gives rise to capacitive effect.
Small-signal diffusion capacitance
Depletion capacitance
Charge stored in depletion layer changes with the change of voltage across pn junction gives rise to capacitive effect.
Small-signal depletion capacitance
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63. Diffusion Capacitance
According to the definition:
The charge stored in bulk region is obtained from below equations:
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64. Diffusion Capacitance
The expression for diffusion capacitance:
Forward-bias, linear relationship
Reverse-bias, almost inexistence
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65. Depletion Capacitance
According to the definition:
Actually this capacitance is similar to parallel plate capacitance.
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66. Depletion Capacitance
A more general formula for depletion capacitance is :
Where m is called grading coefficient.
If the concentration changes sharply,
Forward-bias condition,
Reverse-bias condition,
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67. Junction Capacitance Remember:
Diffusion and depletion capacitances are incremental capacitances, only are applied under the small-signal circuit condition.
They are not constants, they have relationship with the voltage across the pn junction.
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68. 1.4 Analysis of Diode Circuit
Models
Mathematic model
Circuit model
Methods of analysis
Graphical analysis
Iterative analysis
Modeling analysis
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69. The Diode Models Mathematic Model：
The circuit models are derived from approximating the curve into piecewise-line.
Forward biased
Reverse biased
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70. The Diode Models Circuit Model Simplified diode model
The constant-voltage-drop model
Small-signal model
High-frequency model
Zener Diode Model
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71. Simplified Diode Model
Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation.
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72. The Constant-Voltage-Drop Model
The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation.
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73. Small-Signal Model Symbol convention:
Lowercase symbol, uppercase subscript stands for total instantaneous qualities.
Uppercase symbol, uppercase subscript stands for dc component.
Lowercase symbol, lowercase subscript stands for ac component or incremental signal qualities.
Uppercase symbol, lowercase subscript stands for the rms(root-mean-square) of ac.
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74. Small-Signal Model
Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.
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75. Small-Signal Model(cont’d)
Incremental resistance:
*The signal amplitude sufficiently small such that the excursion at Q along the i-v curve is limited to a short, almost linear segment.
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76. High-Frequency Model
High frequency model
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77. Zener Diode Model
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78. Method of Analysis Load line Diode characteristic
Q is the intersect point
Visualization
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79. Method of Analysis Iterative analysis Model Analysis
Refer to example 3.4
Model Analysis
Refer to example 3.6 and 3.7
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80. 1.5 The Application of Diode Circuits
Rectifier circuits
Half-wave rectifier
Full-wave rectifier
Transformer with a center-tapped secondary winding
Bridge rectifier
The peak rectifier
Voltage regulator
Limiter
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81. Half-Wave Rectifier Half-wave rectifier.
Equivalent circuit of the half-wave rectifier with the diode replaced with its battery-plus-resistance model.
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82. Half-Wave Rectifier
(c) Transfer characteristic of the rectifier circuit.
(d) Input and output waveforms, assuming that
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83. Full-Wave Rectifier circuit
transfer characteristic assuming a constant-voltage-drop model for the diodes
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84. Full-Wave Rectifier
(c) input and output waveforms.
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85. The Bridge Rectifier
(a) circuit
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86. The Bridge Rectifier
(b) input and output waveforms
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87. Peak Rectifier
Voltage and current waveforms in the peak rectifier circuit with
The diode is assumed ideal.
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88. Voltage Regulator
We define:
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89. Limiter
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90. Limiter
Applying a sine wave to a limiter can result in clipping off its two peaks.
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91. Soft Limiting
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