# 一个理想的线性放大器

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1.NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 1 Topic 6 Analog Circuits Ideal Operational Amplifiers One Transistor Amplifier ECE 271 Electronic Circuits I

2.NJIT ECE 271 Dr. Serhiy Levkov Example of Analog Electronic System: FM Stereo Receiver Linear functions: Radio and audio frequency amplification, frequency selection (tuning), impedance matching, local oscillator Nonlinear functions: DC power supply(rectification), frequency conversion (mixing), detection/demodulation The characteristics of signals are most often manipulated with linear amplifiers . Much information in the world (temperature, pressure, light intensity, sound, etc.) is analog in nature. In electric form those signals are transformed by different linear and nonlinear functions. Topic 6 - 2

3.NJIT ECE 271 Dr. Serhiy Levkov Amplification: Introduction A complex periodic signal can be represented as the sum of many individual sine waves, one component of which has amplitude V i = 1 mV and frequency w s with 0 phase (signal is used as reference): After amplification, linear amplifier output is sinusoidal with same frequency but different amplitude V O and phase : Example: Audio amplifier. The input is a form of complicated periodic signal. Topic 6 - 3

4.NJIT ECE 271 Dr. Serhiy Levkov Amplification: Introduction (cont.) Amplifier output power is: If we need to deliver P O = 100 W and have R L = 8 W, then This power results in output current: where Input current is given by ( V i = 1 mV ) and the phase is zero because circuit is purely resistive. Topic 6 - 4

5.NJIT ECE 271 Dr. Serhiy Levkov Amplification: Gain The main parameter of an amplifier is the gain. Using phasor representation , we can introduce three types of gain. Voltage Gain (complex number): Magnitude and phase of voltage gain are given by and For our example, Current Gain : Magnitude of current gain is given by Topic 6 - 5

6.NJIT ECE 271 Dr. Serhiy Levkov Amplification: Gain (cont.) Power Gain : For our example, The gain is often expressed in decibel scale: Topic 6 - 6

7.NJIT ECE 271 Dr. Serhiy Levkov Two-port Model for Amplifier Simplifies amplifier-behavior modeling in complex systems. Two-port (four terminal) models are linear network models, valid only under small-signal conditions. Represented by g- , h- , y- and z- parameters. ( v 1 , i 1 ) and ( v 2 , i 2 ) represent signal components of voltages and currents at the network ports. Type of input-output model, black box that relates outputs to inputs. input output x 1 x 2 Amplifier Topic 6 - 7

8.NJIT ECE 271 Dr. Serhiy Levkov Two-port Model Parameters Theoretically, two-port model could be described fully by a 4x4 matrix or 16 parameters. In practice, several sets of 4 parameters are used. Topic 6 - 8

9.NJIT ECE 271 Dr. Serhiy Levkov Two-port Model Parameters Impedance (z)-parameters Admittance (y)-parameters Theoretically, two-port model could be described fully by a 4x4 matrix or 16 parameters. In practice, several sets of 4 parameters are used. Topic 6 - 9

10.NJIT ECE 271 Dr. Serhiy Levkov Two-port Model Parameters Impedance (z)-parameters Admittance (y)-parameters Theoretically, two-port model could be described fully by a 4x4 matrix or 16 parameters. In practice, several sets of 4 parameters are used. Hybrid (h)-parameters Inverse hybrid (g)-parameters Topic 6 - 10

11.NJIT ECE 271 Dr. Serhiy Levkov Two-port Model Parameters Impedance (z)-parameters Admittance (y)-parameters Theoretically, two-port model could be described fully by a 4x4 matrix or 16 parameters. In practice, several sets of 4 parameters are used. Hybrid (h)-parameters Inverse hybrid (g)-parameters Transfer (A,B,C,D) -parameters Topic 6 - 11

12.NJIT ECE 271 Dr. Serhiy Levkov g -parameters Use open-circuit ( i = 0) and short-circuit ( v = 0) terminal conditions Open-circuit input conductance Reverse short-circuit current gain Forward open-circuit voltage gain Short-circuit output resistance Topic 6 - 12

13.NJIT ECE 271 Dr. Serhiy Levkov g -parameters Use open-circuit ( i = 0) and short-circuit ( v = 0) terminal conditions Open-circuit input conductance Reverse short-circuit current gain Forward open-circuit voltage gain Short-circuit output resistance If g 12 = 0 Norton transformation Topic 6 - 13

14.NJIT ECE 271 Dr. Serhiy Levkov g -parameters: Example Problem : Find g -parameters. Approach: Apply specified boundary conditions for each g -parameter, use circuit analysis. For g 11 and g 21 : apply voltage v 1 to input port and open circuit output port. For g 12 and g 22 : apply current i 2 to output port and short circuit input port. Topic 6 - 14

15.NJIT ECE 271 Dr. Serhiy Levkov g -parameters: Example Problem : Find g -parameters. Approach: Apply specified boundary conditions for each g -parameter, use circuit analysis. For g 11 and g 21 : apply voltage v 1 to input port and open circuit output port. For g 12 and g 22 : apply current i 2 to output port and short circuit input port. Topic 6 - 15

16.Ideal Voltage Amplifier Consider amplifier with g 12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 16

17.Ideal Voltage Amplifier Consider amplifier with g 12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 17

18.Ideal Voltage Amplifier Consider amplifier with g 12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 18

19.Ideal Voltage Amplifier Consider amplifier with g 12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 19 Conclusion: full gain depends on source and load parameters.

20.Ideal Voltage Amplifier Consider amplifier with g 12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 20 Conclusion: full gain depends on source and load parameters. How to make it non- dependent?

21.Ideal Voltage Amplifier R in >> R s and R out << R L , Ideal voltage amplifier : R out = 0, Consider amplifier with g 12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 21 Conclusion: full gain depends on source and load parameters. How to make it non- dependent?

22.Ideal Voltage Amplifier R in >> R s and R out << R L , Ideal voltage amplifier : R out = 0, Consider amplifier with g 12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 22 Conclusion: full gain depends on source and load parameters. For current: How to make it non- dependent?

23.Other Amplifier Types NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 23 Voltage amplifier Current amplifier Transconductance amplifier Transresistance amplifier

24.Other Amplifier Types NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 24 Voltage amplifier Current amplifier Transconductance amplifier Transresistance amplifier

25.Other Amplifier Types NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 25 Voltage amplifier Current amplifier Transconductance amplifier Transresistance amplifier

26.Other Amplifier Types NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 26 Voltage amplifier Current amplifier Transconductance amplifier Transresistance amplifier

27.Other Amplifier Types NJIT ECE 271 Dr. Serhiy Levkov Topic 6 - 27 Voltage amplifier Current amplifier Transconductance amplifier Transresistance amplifier

28.Operational Amplifier (Op Amp) NJIT ECE 271 Dr. Serhiy Levkov Op amp is a fundamental building block in electronic design. They are cheap mass produced IC and can be used to build many different types of electronic devices like instrumentation amplifiers, active filters, rectifiers, A/D and D/A converters, and others. Typical integrated circuit amplifier: LM386N ( ~ $1.00 each) The practical op amp is a form of differential amplifier : responds to a difference of two input signals. Typically: V CC > 0, V EE < 0 – so the voltages are symmetric 5V, 10V, 18V. Topic 6 - 28

29.NJIT ECE 271 Dr. Serhiy Levkov Differential Amplifier – Signal Amplification A - open-circuit voltage gain, A =10, A db =20log(10) = 20 db v ID = ( v + -v -- ) - differential input signal v ID = V ID + v id = 1 + 0.25sin t , where V ID – dc value, v id – signal component v O = V O + v o = 5 + 2.5sin t The typical voltage transfer characteristic for a differential amplifier biased by two symmetric power supplies: Topic 6 - 29