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Chapter 3-1 Semiconductor Devices Diode MEMS1082 Mechatronics Chapter 3-1 Semiconductor devices Diode Department of Mechanical Engineering Semiconductor: Si Department of Mechanical Engineering Semiconductor Department of Mechanical Engineering N-type and P-type Semiconductors There are two types of impurities: N-type - In N-type doping, phosphorus or arsenic is added to the silicon in small quantities. Phosphorus and arsenic each have five outer electrons, so they're out of place when they get into the silicon lattice. The fifth electron has nothing to bond to, so it's free to move around. It takes only a very small quantity of the impurity to create enough free electrons to allow an electric current to flow through the silicon. N-type silicon is a good conductor. Electrons have a negative charge, hence the name N-type. P-type - In P-type doping, boron or gallium is the dopant. Boron and gallium each have only three outer electrons. When mixed into the silicon lattice, they form "holes" in the lattice where a silicon electron has nothing to bond to. The absence of an electron creates the effect of a positive charge, hence the name P-type. Holes can conduct current. A hole happily accepts an electron from a neighbor, moving the hole over a space. P-type silicon is a good conductor. Department of Mechanical Engineering N-type and P-type Semiconductors Department of Mechanical Engineering Semiconductor device-diode A diode is the simplest possible semiconductor device. A diode allows current to flow in one direction but not the other. You may have seen turnstiles at a stadium or a subway station that let people go through in only one direction. A diode is a one- way turnstile for electrons. When you put N-type and P-type silicon together as shown in this diagram, you get a very interesting phenomenon that gives a diode its unique properties. Department of Mechanical Engineering Diodes Department of Mechanical Engineering Diode Electron flow direction Current direction Department of Mechanical Engineering Diode depletion region Department of Mechanical Engineering pn junction PN Junction Department of Mechanical Engineering Diode depletion region Department of Mechanical Engineering Diode forward and reverse bias Department of Mechanical Engineering Shockley diode equation Department of Mechanical Engineering Diode current and voltage Department of Mechanical Engineering Diode Characteristic Department of Mechanical Engineering Diode Characteristic Department of Mechanical Engineering Diode Characteristic at different scale Department of Mechanical Engineering Diode Characteristic at different scale Department of Mechanical Engineering Diode measurement Meter with a “Diode check” function displays the forward voltage drop of 0.548 volts instead of a low resistance Department of Mechanical Engineering Measurement of a diode Measuring forward voltage of a diode without “diode check” meter function: (a) Schematic diagram. (b) Pictorial diagram Department of Mechanical Engineering Load line of diode A circuit with a diode Department of Mechanical Engineering Example For circuit, determine the current i Department of Mechanical Engineering Example Circuit reduction to Thévenin equivalent circuit Department of Mechanical Engineering Example Thévenin equivalent circuit Department of Mechanical Engineering Example Draw load line to determine the diode voltage and current Department of Mechanical Engineering Example Determine current i Department of Mechanical Engineering Example Determine the current and voltage of the diode in the circuit. The diode characteristic is given in the right figure. Department of Mechanical Engineering Example Department of Mechanical Engineering Piecewise-linear approximation and small signal analysis Diode is nonlinear resistor Department of Mechanical Engineering Piecewise-linear approximation and small signal analysis Diode piecewise-linear approximation Department of Mechanical Engineering Piecewise-linear approximation and small signal analysis Department of Mechanical Engineering Piecewise-linear approximation and small signal analysis Department of Mechanical Engineering Piecewise-linear approximation and small signal analysis Department of Mechanical Engineering Piecewise-linear approximation and small signal analysis Small signal analysis Department of Mechanical Engineering Piecewise-linear approximation and small signal analysis Small signal analysis Department of Mechanical Engineering Piecewise-linear approximation and small signal analysis If we are only interested in the portion due to vs(t), we may set Es=0, and Ef =0, then Often, for practical purpose, we can assume Ef =0 in small signal equivalent circuit of a diode. For typical diodes, the value of Rf is quite small, between 1Ω and 100Ω. Thus Rf can be neglected. Department of Mechanical Engineering Piecewise-linear approximation and small signal analysis Department of Mechanical Engineering The ideal diodes Department of Mechanical Engineering The piecewise- linear model of a diode, using an ideal diode Ideal diode Department of Mechanical Engineering Example Nonlinear resistors with a wide range of characteristics can be obtained, approximately, with circuit containing diodes, for example, a square-law device is two-terminal nonlinear resistor whose terminal voltage-current characteristic obey i = kv2 where k is normalization constant. The ideal characteristic is shown Department of Mechanical Engineering Example This device may be used in modulator, e.g., to attain a voice signal to high-frequency carrier wave, as is done in amplitude modulation (AM) radio transmission. Design a square-law device to approximate the ideal characteristics for 0 ≤ v ≤ 5V with a normalization constant k=0.001 Department of Mechanical Engineering Example A circuit using ideal diodes D1 and D2 and voltage sources E1 and E2 Use V=5V; E1 < E2 Initially 0≤v≤ E1,the diodes are reverse biased and open, the curve will have slope 1/R3 For E1 ≤v≤ E2,D1 closes, and D2 open, the input resistance will be R3llR1 For E2 ≤v≤ 5V,D1 and D2 close, the input resistance will be R3llR1llR2 Suppose E1 =2.0V and E2=3.5V 2 I1 = kE1 = 4mA 2 I2 = kE2 =12.25mA 2 I = kV = 25mA Department of Mechanical Engineering Example Noting the slope of each portion, we obtain E E − E R = 1 = 500Ω R R = 2 1 =182Ω R = 286Ω 3 1 2 − 1 I1 I2 I1 V − E2 R1 R2 R3 = =118Ω R2 = 333Ω I − I2 Replacing the actual diode with their piecewise-linear approximation using R f =10Ω, E f = 0.5V R1 = 276Ω R2 = 323Ω R3 = 500Ω E1 =1.5V and E2=3.0V Department of Mechanical Engineering Ideal transformer Department of Mechanical Engineering Rectifiers Half-Wave Rectifier The transformer isolates the load from the source Department of Mechanical Engineering Rectifiers Half-Wave Rectifier The average dc value of vL vL = Vs sinωt 0 ≤ ωt ≤ π π = π ≤ ω ≤ π 1 vL 0 t 2 VL = Vs sinωt d(ωt) 2π ∫0 V = s π Department of Mechanical Engineering Rectifiers Representing the Half-Wave Rectifier voltage by Fourier series vL = VL + a1 sinωt + a2 sin 2ωt +......+ b1 cosωt + b2 cos 2ωt +......... The Fourier coefficients can be determined as 2 T 2 T an = vL (t)sin nωt dt; bn = vL (t)cos nωt dt T ∫0 T ∫0 For the Half-Wave Rectified voltage T π 2 1 Vs a1 = vL (t)sinωt dt = Vs sinωt sinωt d(ωt) = T ∫0 π ∫0 2 2 T 1 π an = vL (t)sin nωt dt = Vs sinωt sin nωt d(ωt) = 0 T ∫0 π ∫0 Department of Mechanical Engineering Rectifiers 2V 2V b = 0; b = − s , b = 0; b = − s ; b = 0 1 2 3π 3 4 15π 5 Thus the Fourier series for the Half-Wave Rectified signal V V 2V 2V v (t) = s + s sinωt − s cos 2ωt − s cos 4ωt +..... L π 2 3π 15π Department of Mechanical Engineering Rectifiers Filtering the Half-Wave Rectifier Capacitor has lower impedance to higher frequencies Department of Mechanical Engineering Rectifiers Filtering the Half-Wave Rectifier Larger C can be used to increase the time constant RC Department of Mechanical Engineering Rectifiers Effects of actual diodes Department of Mechanical Engineering Rectifiers Effects of actual diodes Department of Mechanical Engineering The Full-Wave Rectifiers The full-wave rectifier Department of Mechanical Engineering The Full-Wave Rectifiers The full-wave rectifier The average dc value of vL 1 π VL = Vs sinωt d(ωt) π ∫0 2V = s π Thus the Fourier series for the Full-Wave Rectified signal 2V 4V 4V v (t) = s − s cos 2ωt − s cos 4ωt +..... L π 3π 15π Department of Mechanical Engineering The Full-Wave Rectifiers Effect of actual diodes Department of Mechanical Engineering The Full-Wave Bridge Rectifier A bridge rectifier makes use of four diodes in a bridge arrangement to achieve full-wave rectification. This is a widely used configuration, both with individual diodes wired as shown and with single component bridges where the diode bridge is wired internally. Department of Mechanical Engineering Bridge Rectifiers Various types of Bridge Rectifiers Note that some have a hole through their centre for attaching to a heat sink Department of Mechanical Engineering The Full-Wave Bridge Rectifier Bridge Rectifier Department of Mechanical Engineering The Full-Wave Bridge Rectifier Bridge Rectifier with RC Filter and LC filter Department of Mechanical Engineering The Voltage Limiter Limiter using ideal diodes and batteries Department of Mechanical Engineering The Voltage Limiter Limiter using ideal diodes and batteries Department of Mechanical Engineering The Voltage Limiter Limiter using ideal diode and batteries Department of Mechanical Engineering The Voltage Limiter Limiter using ideal diode and batteries Load voltage is limited for source voltage RL + Rs RL + Rs − V2 < vs (t) < V1 RL RL Department of Mechanical Engineering The Voltage Limiter Limiter using ideal diode and batteries Department of Mechanical Engineering Example For a limiter shown below, assume identical piecewise- linear diodes with Rf=100Ω, Ef=0.5V, V1=V2=10V, RL=100Ω, Rs=100Ω, and vs(t)=50sinωt V, sketch vL(t) Department of Mechanical Engineering Zener Diodes A Zener diode is a type of diode that permits current not only in the forward direction like a normal diode, but also in the reverse direction if the voltage is larger than the breakdown voltage known as "Zener knee voltage" or "Zener voltage".
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