Câu hỏi về bài giảng có thể được gửi trong phần thảo luận Q&A được lập trên website https://courses.uet.vnu.edu.vn/ References 1) ELECTRONIC DEVICES, 9th edition, Thomas L. Floyd, Prentice Hall 2) Semiconductor Physics And Devices, 3rd ed. - J. Neamen 3) Robert L. Boylestad, Louis Nashelsky, Electronic Devices and Circuit Prentice Hall 4) Linh kiện bán dẫn và vi mạch, Hồ Văn Sung, NXB Giáo Dục, 2007 5) Giáo trình linh kiện điện tử, Trương Văn Tám, ĐH Cần Thơ, 2003. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Theory, 8th Edition, Linh kiện Điện tử Electronic Devices The invention of the bipolar transistor in 1948 ushered in a revolution in electronics The bipolar junction transistor (BJT) is constructed with three doped semiconductor regions separated by two pn junctions Regions are called emitter, base and collector Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU TS. Phạm Ngọc Thảo Linh kiện Điện tử Electronic Devices2 TRANSFER+ RESISTOR → TRANSISTOR Vi = 200 mV VL = 50V Increase x250 times AMPLIFIER (KHUẾCH ĐẠI) Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU TS. Phạm Ngọc Thảo Linh kiện Điện tử Electronic Devices3 General-purpose/ small-signal Multipletransistor packages Power transistors and packages. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU TS. Phạm Ngọc Thảo Linh kiện Điện tử Electronic Devices4 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU TS. Phạm Ngọc Thảo Linh kiện Điện tử Electronic Devices5 pnp Common-Base CB Configuration Common-Collector CC Configuration Common-Emitter CE Configuration Input signal Input signal Input signal Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU TS. Phạm Ngọc Thảo npn Output signal Output signal Output signal Input signal Output signal Input signal Output signal Input signal Output signal Linh kiện Điện tử Electronic Devices6 E The base–emitter and collector–base junctions of a transistor are both reverse-biased. The base–emitter and collector–base junctions are forward-biased. The base–emitter junction is forward-biased, whereas the collector– base junction is reverse-biased. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices7 Cutoff mode The base–emitter and collector–base junctions of a transistor are both reverse-biased. VCE ≈ VCC Saturation mode The base–emitter and collector–base junctions of a transistor are both forward-biased. VCE ≈ 0 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện bán dẫn và vi mạch Linh kiện Điện tử Electronic Devices8 Active mode The base–emitter junction is forward-biased, whereas the collector– base junction is reverse-biased. (npn) UC>UB>UE Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU (pnp) UC<UB<UE Linh kiện bán dẫn và vi mạch Linh kiện Điện tử Electronic Devices9 Active mode The base–emitter junction is forward-biased, whereas the collector– base junction is reverse-biased. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 10 n p n Chuyển tiếp P-N giữa cực Base và cực Emitter được phân cực thuận bởi nguồn VEE. Chuyển tiếp P-N giữa cực Base và cực Collector được phân cực nghịch bởi nguồn VCC. Điện tử từ cực âm của nguồn VEE di chuyển vào vùng Emitter qua vùng Base, đáng lẽ trở về cực dương của nguồn VEE nhưng vì: + Vì vùng Base rất hẹp với 2 vùng kia + Nguồn VCC >> VEE cho nên đa số điện tử bị hấp dẫn về nó Dòng đi vào cực Base dgl dòng IB; Dòng đi vào cực Collector dgl dòng IC; Dòng đi vào cực Emitter dgl dòng IE. Do đó, số lượng điện tử từ vùng Base vào vùng thu tới cực dương của nguồn VCC rất nhiều so với số lượng điện tử từ vùng Base tới cực dương của nguồn VEE. Sự dịch chuyển của điện tử tạo thành dòng điện. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 11 Quy ước về chiều dòng điện là chiều từ cực dương đi qua dây dẫn và các linh kiện tiêu thụ điện tới cực âm của nguồn điện. Trong trường hợp npn, dòng dịch chuyển của các electron tích điện âm dịch chuyển ngược chiều với chiều của dòng điện npn còn được gọi là đèn (bóng) bán dẫn, BJT, ngược. Trong trường hợp pnp, dòng dịch chuyển của các lỗ trống tích điện dương dịch chuyển cùng chiều chiều với chiều của dòng điện pnp còn được gọi là đèn (bóng) bán dẫn, BJT, thuận. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 12 We have (1) IE = IB + IC (2) IC = α IE where α ≈ 0.95~0.99 Replace (2) into (1) Take α, β: Current gains (Current amplification factors) The collector current is comprised of two currents: Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 13 Using empirical methods, measure the parameters of the circuit to draw BJT characteristic curves. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU TS. Phạm Ngọc Thảo Linh kiện Điện tử Electronic Devices 14 Đặc tuyến ngõ vào IB (VBE) Đặc tuyến truyền dẫn IC (VBE) Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 15 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 16 Common-Emitter Configuration IB = f (VBE)|V CE =const Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU TS. Phạm Ngọc Thảo IC = f (VCE)|I B =const Linh kiện Điện tử Electronic Devices 17 Common-Collector Configuration Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU TS. Phạm Ngọc Thảo Linh kiện Điện tử Electronic Devices 18 Common-Collector Configuration IB = f (VCB)|V CE =const Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU TS. Phạm Ngọc Thảo IE = f (VCE)|I B =const Linh kiện Điện tử Electronic Devices 19 BJT as a switch A BJT can be used as a switching device in logic circuits to turn on or off current to a load. As a switch, the transistor is normally in either cutoff (load is OFF) or saturation (load is ON) Switching action of an ideal transistor Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 20 BJT as an amplifier Signal amplification can be understood as linearly increasing the signal amplitude electrical signal. BJT can be used for signal amplification. Let BJT amplify the signal the signal requires the BJT bias so that Base-Emitter is forward biased and Collector-Base is reverse biased. In the amplifier circuit exists both direct (dc) and alternating components (ac). One-dimensional quantities denoted according to the primary index rule are capital letters Indexes are also uppercase (example: IB). Alternating quantities are denoted according the main index rule is the lower case sub-index is the lower case (eg Ib) The BJT is able to amplify signals due to the Collector current approximately times the Base current. (IC = βIB) Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 21 The transistor can be employed as an amplifying device There is an “exchange” of dc power to the ac domain that permits establishing a higher output ac power. A conversion efficiencyis defined by η=Po(ac)/Pi(dc) , where Po(ac) is the ac power to the load and Pi(dc) is the dc power supplied. The factor missing from the discussion above that permits an ac power output greater than the input ac power is the applied dc power. It is the principal contributor to the total output power even though part of it is dissipated by the device and resistive elements. In other words, there is an “exchange” of dc power to the ac domain that permits establishing a higher output ac power. In fact, a conversion efficiencyis defined by h=Po(ac)/Pi(dc), where Po(ac) is the ac power to the load and Pi(dc) is the dc power supplied Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 22 Transistors as a Small Signal Amplifier There are 2 analysis; dc analysis and ac analysis. The purpose of dc analysis is to determine the initial operating values of IC, IB and VCE (Q-point). The goal is to set the Q-point such that it does not go into saturation or cutoff when an ac signal is applied. If the Q-point is in active region, the transistor can operate as an amplifier. The purpose of ac analysis is to obtain the gain. An amplifier is a system that has a gaining ability to amplify where a small electrical signal will be converted into a strong one. Amplifiers are classified as small signal amplifiers (preamplifiers) and strong signal amplifiers (power amplifiers). Amplifiers are able to amplify current, voltage and/or power. In other words, only amplifiers are able to produce power gain where as other devices such as transformer are only able to produce voltage and current gain Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 23 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 24 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 25 For saturation mode and cutoff mode, we just provide a sufficiently large (small) bias voltage so that the junction Base-Emitter , the junction Collector-Base are both forward (reverse) biasses. For active mode, in order to obtain the amplified signal without distorting, a steady voltage dc must be supplied to the terminals of the transistor (so that when adding an AC signal , the transistor does not work into saturation or cutoff modes) Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 26 β: increases with increase in temperature |VBE|: decreases about 2.5 mV per degree Celsius (°C) increase in temperature ICO(reverse saturation current): doubles in value for every 10°C increase in temperature A stability factor (S) is defined for each of the parameters affecting bias stability as follows: When the temperature changes, the trasistor parameters will change because IC = αIE + ICB0, so when the temperature changes, the Q-point will change Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 27 Fixed-bias Configuration (Mạch định thiên cố định) Voltagedivider bias configuration (Mạch định thiên phân áp) Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Emitter-bias configuration (Mạch định thiên Emitter) Collector feedback configura tion (Mạch định thiên hồi tiếp) Linh kiện Điện tử Electronic Devices 28 With dc supply, f = 0 Hz, dung kháng của tụ điện XC = 1/ (2πfC) = 1/(2π0C) = ∝ Ω Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 29 Forward Bias of Base–Emitter Writing Kirchhoff’s voltage equation for the loop Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 30 Collector–Emitter Loop Applying Kirchhoff’s voltage law around the indicated closed loop In the other words, we have The magnitude of the collector current is related directly to IB through Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Because VE = 0V, so that Linh kiện Điện tử Electronic Devices 31 Load-Line Analysis The network of an output equation that relates the variables IC and VCE in the following manner: (y = ax +b) Load-line analysis: (Left) the network; (Right) the device characteristics The load line established by Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 32 Movement of the Q-point with increasing level of IB Effect of an increasing level of RC on the load line and the Q-point Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Effect of lower values of VCC on the load line and the Q-point Linh kiện Điện tử Electronic Devices 33 = IC x RC Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 34 BJT bias circuit with emitter resistor Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU dc equivalent Linh kiện Điện tử Electronic Devices 35 Base–Emitter Loop Writing Kirchhoff’s voltage law around the indicated loop where Fixed-bias Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 36 Collector–Emitter Loop Writing Kirchhoff’s voltage law for the indicated loop where VE is the voltage from emitter to ground and is determined by VC is the voltage from collector to ground can be determined from OR Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 37 Load-Line Analysis The collector–emitter loop equation that defines the load line is The load line established by Load line for the emitter-bias configuration Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 38 Voltage-divider bias configuration Exact Analysis Defining the Q-point for the voltage-divider bias configuration Approximate Analysis Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 39 Exact Analysis Redrawing the input side of the network Determining RTh DC components of the voltage-divider configuration Định lý Thevenin https://3ce.vn/dinh-ly-thevenin/ Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 40 Exact Analysis The voltage source VCC is returned to the network and the open-circuit Thévenin voltage of determined as follows by applying the voltage-divider rule: Determining ETh IBQ can be determined by first applying Kirchhoff’s voltage law in the clockwise direction for the loop indicated: Inserting the Thévenin equivalent circuit Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 41 Approximate Analysis The resistance Ri is the equivalent resistance between base and ground The voltage across R2, which is actually the base voltage determined using the voltage-divider rule (hence the name for the configuration) Because Ri =(β +1)RE ≈ βRE the condition that will define whether the approximate approach can be applied is Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 42 Approximate Analysis The level of VE can be calculated from The emitter current can be determined from The collector-to-emitter voltage is determined by The Q-point (as determined by IC(Q) and VCE(Q)) is independent of β Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 43 Load-Line Analysis The similarities with the output circuit of the emitter-biased configuration result in the same intersections for the load line of the voltage-divider configuration The level of IB is of course determined by a different equation for the voltage-divider bias and the emitter-bias configurations. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 44 Base–Emitter Loop DC bias circuit with voltage feedback Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Base–emitter the network loop for Linh kiện Điện tử Electronic Devices 45 Base–Emitter Loop Writing Kirchhoff’s voltage law around the indicated loop IC’ = IC + IB IC = β IB Substituting IE = IC + IB In general, the equation for IB has the following format For the fixed-bias configuration, βR does not exist. For the emitter-bias setup (with β+1 ≈ β), R’=RE IC = β IB Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices Collector–Emitter Loop Applying Kirchhoff’s voltage law around the indicated loop which is exactly as obtained for the emitterbias and voltage-divider bias configurations Collector–emitter loop for the network Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 47 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 48 The key to transistor small-signal analysis is the use of the equivalent circuits (models) The re model became the more desirable approach because an important parameter of the equivalent circuit was determined by the actual operating conditions The re model is really a reduced version of the hybrid π model used almost exclusively for high-frequency analysis. This model also includes a connection between output and sinput to include the feedback effect of the output voltage and the input quantities. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 49 Transistor circuit Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU The network of next figure following removal of the dc supply and insertion of the short-circuit equivalent for the capacitors. Linh kiện Điện tử Electronic Devices 50 Defining the important parameters of any system Demonstrating the reason for the defined directions and polarities For all the analysis to follow here, the directions of the currents, the polarities of the voltages, and the direction of interest for the impedance levels are as appearing in the left figure. For example, in the right figure the input and output impedances for a particular system are both resistive. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 51 Current gain Circuit of a small figure redrawn for small-signal ac analysis Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 52 The ac equivalent of a transistor network is obtained by: 1. Setting all dc sources to zero and replacing them by a shortcircuit equivalent 2. Replacing all capacitors by a short-circuit equivalent 3. Removing all elements bypassed by the short-circuit equivalents introduced by steps 1 and 2 4. Redrawing the network in a more convenient and logical form Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 53 Common-Emitter Configuration Finding the input equivalent circuit for a BJT transistor Equivalent circuit for the input side of a BJT transistor Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU BJT equivalent circuit Linh kiện Điện tử Electronic Devices 54 Common-Emitter Configuration Now, for the input side: Solving for Vbe: and Dynamic resistance Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 55 Common-Emitter Configuration Improved BJT equivalent circuit BJT equivalent circuit re model for the common-emitter transistor configuration including effects of ro Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 56 Common-Base Configuration No phase shift between the input and output voltages Common-base BJT transistor Equivalent circuit for configuration Of the above figure Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 57 Common-Collector Configuration For the common-collector configuration, the model defined for the common-emitter configu-ration is normally applied rather than defining a model for the common-collector configuration npn versus pnp The dc analysis of npn and pnp configurations is quite different in the sense that the currents will have opposite directions and the voltages opposite polarities. However, for an ac analysis where the signal will progress between positive and negative values, the ac equivalent circuit will be the same. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 58 Common-emitter fixed-bias configuration Network of the left figure following the removal of the effects of VCC, C1, and C2 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 59 The re model Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 60 The re model Note the explicit absence of β in the equation, although we recognize that must be utilized to determine re. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 61 Phase Relationship The negative sign in the resulting equation for Av reveals that a 180°phase shift occurs between the input and output signals, as shown in the figure Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 62 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 63 Substituting the re equivalent circuit into the ac equivalent network of voltagedivider bias configuration Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 64 From the figure with Vi set to 0V, resulting in Ib =0 mA and βIb =0 mA, Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 65 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 66 The re model has the advantage that the parameters are defined by the actual operating conditions, whereas the parameters of the hybrid equivalent circuit are defined in general terms for any operating conditions. The description of the hybrid equivalent model will begin with the general two-port system Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 67 Complete hybrid equivalent circuit The re transistor model h11 input resistance hi h12 reverse transfer voltage ratio hr h21 forward transfer current ratio hf h22 output conductance ho Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 68 Common-emitter configuration Hybrid equivalent circuit Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Common-base configuration Hybrid equivalent circuit Linh kiện Điện tử Electronic Devices 69 Effect of removing hre and hoe from the hybird equivalent circuit Approximate hybrid equivalent model hrVo= 0 Because hr is normally a relatively small quantity, its removal is approximated by hr = 0 and hrVo =0, resulting in a short-circuit equivalent for the feedback element as shown in the left right. The resistance determined by 1/ho is often large enough to be ignored in comparison to a parallel load, permitting its replacement by an opencircuit equivalent for the CE and CB models. The right figure is quite similar to the general structure of the commonbase and common-emitter equivalent circuits obtained with the re model. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 70 Hybrid versus re model: common-emitter configuration Hybrid versus re model: common-base configuration Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 71 The analysis using the approximate hybrid equivalent circuit of the common-emitter configuration and of the common-base configuration is very similar eto that just performed using the re model. Approximate common-emitter hybrid equivalent circuit Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Approximate common-base hybrid equivalent circuit Linh kiện Điện tử Electronic Devices 72 Fixed-Bias Configuration Substituting the approximate hybrid equivalent circuit into the ac equivalent network of the next figure Using R’ =1/h Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU oe||RC, we obtain Linh kiện Điện tử Electronic Devices 73 Fixed-Bias Configuration Voltage Gain: Assuming that RB>>h ie and 1/hoe ≥10RC, we find Ib ≅Ii and Io=Ic=h Ib =hfeIi , and so Current Gain: Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 74 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 75 Two-port system Substituting the complete hybrid equivalent circuit into the two-port system Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 76 Current Gain, Ai = Io/ Ii Applying Kirchhoff’s current law to the output circuit yields Substituting Rewriting the equation above, we have Note that the current gain reduces to the familiar result of Ai =hf if the factor hoRL is sufficiently small compared to 1 Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 77 Voltage Gain, Ai = Vo/ Vi Applying Kirchhoff’s voltage law to the input circuit results in Substituting and Solving for the ratio Vo/ V i yields In this case, the familiar form of Av =-hfRL /hi returns if the factor (h iho–hf hr)RL is sufficiently small compared to hi. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 78 Input impedance, Zi = Zo/ Zi For the input circuit The familiar form of Zi =hi is obtained if the second factor in the denominator (hoRL) is sufficiently smaller than one. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 79 Output Impedance, Zo=Vo/Io The output impedance of an amplifier is defined to be the ratio of the output voltage to the output current with the signal Vs set to zero. For the input circuit with Vs = 0, In this case, the output impedance is reduced to the familiar form Zo=1/ho for the transis-tor when the second factor in the denominator is sufficiently smaller than the first. Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 80 Includes parameters that do not appear in the other two models primarily to provide a more accurate model for high-frequency effects. hybrid π high-frequency transistor small-signal ac equivalent circuit Faculty of Electronics and Telecommunication University of Engineering and Technology - VNU Linh kiện Điện tử Electronic Devices 81