1 / 39

Chapter 10 Analog Systems

Chapter 10 Analog Systems. Microelectronic Circuit Design Richard C. Jaeger Travis N. Blalock. Chap10 - 1. Chapter Goals. Develop understanding of linear amplification concepts such as: Voltage gain, current gain, and power gain, Gain conversion to decibel representation,

cheri
Download Presentation

Chapter 10 Analog Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 10Analog Systems Microelectronic Circuit Design Richard C. Jaeger Travis N. Blalock Microelectronic Circuit Design McGraw-Hill Chap10 - 1

  2. Chapter Goals • Develop understanding of linear amplification concepts such as: • Voltage gain, current gain, and power gain, • Gain conversion to decibel representation, • Input and output resistances, • Transfer functions and Bode plots, • Cutoff frequencies and bandwidth, • Low-pass, high-pass, band-pass, and band-reject amplifiers, • Biasing for linear amplification, • Distortion in amplifiers, • Two-port representations of amplifiers, • g-, h-, y-, and z-parameters, • Use of transfer function analysis in SPICE. Microelectronic Circuit Design McGraw-Hill Chap10 - 2

  3. Example of Analog Electronic System: FM Stereo Receiver • Linear functions: Radio and audio frequency amplification, frequency selection (tuning), impedance matching(75-W input, tailoring audio frequency response, local oscillator • Nonlinear functions: DC power supply(rectification), frequency conversion (mixing), detection/demodulation Microelectronic Circuit Design McGraw-Hill Chap10 - 3

  4. Amplification: Introduction A complex periodic signal can be represented as the sum of many individual sine waves. We consider only one component with amplitude VS =1 mV and frequency wS with 0 phase (signal is used as reference): Amplifier output is sinusoidal with same frequency but different amplitude VO and phase θ: Microelectronic Circuit Design McGraw-Hill Chap10 - 4

  5. Amplification: Introduction (contd.) Amplifier output power is: Here, PO = 100 W and RL=8 W Output power also requires output current which is: Input current is given by phase is zero because circuit is purely resistive. Microelectronic Circuit Design McGraw-Hill Chap10 - 5

  6. Amplification: Gain • Voltage Gain: Magnitude and phase of voltage gain are given by and For our example, • Current Gain: Magnitude of current gain is given by Microelectronic Circuit Design McGraw-Hill Chap10 - 6

  7. Amplification: Gain (contd.) • Power Gain: For our example, On decibel scale, i.e. in dB Microelectronic Circuit Design McGraw-Hill Chap10 - 7

  8. Amplifier Biasing for Linear Operation VI = dc value of vI, vi = time-varying component For linear amplification- vI must be biased in desired region of output characteristic by VI. If slope of output characteristic is positive, input and output are in phase (amplifier is non-inverting). If slope of output characteristic is negative, input and output signals are 1800 out of phase (amplifier is inverting). Microelectronic Circuit Design McGraw-Hill Chap10 - 8

  9. Amplifier Biasing for Linear Operation (contd.) Voltage gain depends on bias point. Eg: if amplifier is biased at VI = 0.5 V, voltage gain will be +40 for input signals satisfying If input exceeds this value, output is distorted due to change in amplifier slope. Microelectronic Circuit Design McGraw-Hill Chap10 - 9

  10. Amplifier Biasing for Linear Operation (contd.) Output signals for 1 kHZ sinusoidal input signal of amplitude 50 mV biased at VI= 0.3 V and 0.5V: For VI =0.3V: Gain is 20, output varies about dc level of 4 V. For VI =0.5V: Gain is 40, output varies about dc level of 10 V. Microelectronic Circuit Design McGraw-Hill Chap10 - 10

  11. Distortion in Amplifiers • Different gains for positive and negative values of input cause distortion in output. • Total Harmonic Distortion (THD) is a measure of signal distortion that compares undesired harmonic content of a signal to the desired component. Microelectronic Circuit Design McGraw-Hill Chap10 - 11

  12. Total Harmonic Distortion dc desired output 2nd harmonic distortion 3rd harmonic distortion Numerator= sum of rms amplitudes of distortion terms, Denominator= desired component Microelectronic Circuit Design McGraw-Hill Chap10 - 12

  13. Two-port Models for Amplifiers • Simplifies amplifier-behavior modeling in complex systems. • Two-port models are linear network models, valid only under small-signal conditions. • Represented by g-, h-, y- and z-parameters. • (v1, i1) and (v2, i2) represent signal components of voltages and currents at the network ports. Microelectronic Circuit Design McGraw-Hill Chap10 - 13

  14. g-parameters Using open-circuit (i=0) and short-circuit (v=0) termination conditions, Open-circuit input conductance Reverse short-circuit current gain Forward open-circuit voltage gain Short-circuit output resistance Microelectronic Circuit Design McGraw-Hill Chap10 - 14

  15. g-parameters:Example Problem:Find g-parameters. Approach: Apply specified boundary conditions for each g-parameter, use circuit analysis. For g11 and g21: apply voltage v1 to input port and open circuit output port. For g12 and g22: apply current i2 to output port and short circuit input port. Microelectronic Circuit Design McGraw-Hill Chap10 - 15

  16. Hybrid or h-parameters Using open-circuit (i=0) and short-circuit (v=0) termination conditions, Short-circuit input resistance Reverse open-circuit voltage gain Forward short-circuit current gain Open-circuit output conductance Microelectronic Circuit Design McGraw-Hill Chap10 - 16

  17. h-parameters:Example Problem:Find h-parameters for the same network (used in g-parameters example). Approach: Apply specified boundary conditions for each h-parameter, use circuit analysis. For h11 and h21: apply current i1 to input port and short circuit output port. For h12 and h22: apply voltage v2 to output port and open circuit input port. Microelectronic Circuit Design McGraw-Hill Chap10 - 17

  18. Admittance or y-parameters Using open-circuit (i=0) and short-circuit (v=0) termination conditions, Short-circuit input conductance Reverse short-circuit transconductance Forward short-circuit transconductance Short-circuit output conductance Microelectronic Circuit Design McGraw-Hill Chap10 - 18

  19. y-parameters:Example Problem:Find y-parameters for the same network (used in g-parameters example). Approach: Apply specified boundary conditions for each y-parameter, use circuit analysis. For y11 and y21: apply voltage v1 to input port and short circuit output port. For y12 and y22: apply voltage v2 to output port and short circuit input port. Microelectronic Circuit Design McGraw-Hill Chap10 - 19

  20. Impedance or z-parameters Using open-circuit (i=0) and short-circuit (v=0) termination conditions, Open-circuit input resistance Reverse open-circuit transresistance Forward open-circuit transresistance Open-circuit output resistance Microelectronic Circuit Design McGraw-Hill Chap10 - 20

  21. z-parameters:Example Problem:Find z-parameters for the same network (used in g-parameters example). Approach: Apply specified boundary conditions for each z-parameter, use circuit analysis. For z11 and z21: apply current i1 to input port and open circuit output port. For z12 and z22: apply current i2to output port and open circuit input port. Microelectronic Circuit Design McGraw-Hill Chap10 - 21

  22. Mismatched Source and Load Resistances: Voltage Amplifier g-parameter representation (g12=0) with Thevenin equivalent of input source: If Rin >> Rs and Rout<< RL, In an ideal voltage amplifier, and Rout=0 Microelectronic Circuit Design McGraw-Hill Chap10 - 22

  23. Mismatched Source and Load Resistances: Current Amplifier h-parameter representation (h12=0) with Norton equivalent of input source: If Rs >> Rin and Rout>> RL, In an ideal current amplifier, and Rin=0 Microelectronic Circuit Design McGraw-Hill Chap10 - 23

  24. Amplifier Transfer Functions Av(s)=Frequency-dependent voltage gain Vo(s) and Vs(s) = Laplace Transforms of input and output voltages of amplifier, (In factorized form) (-z1, -z2,…-zm)=zeros (frequencies for which transfer function is zero) (-p1, -p2,…-pm)=poles (frequencies for which transfer function is infinite) (In polar form) Bode plots display magnitude of the transfer function in dB and the phase in degrees (or radians) on a logarithmic frequency scale.. Microelectronic Circuit Design McGraw-Hill Chap10 - 24

  25. Low-pass Amplifier: Description • Amplifies signals over a range of frequencies including dc. • Most operational amplifiers are designed as low pass amplifiers. • Simplest (single-pole) low-pass amplifier is described by Ao = low-frequency gain or mid-band gain wH = upper cutoff frequency or upper half-power point of amplifier. Microelectronic Circuit Design McGraw-Hill Chap10 - 25

  26. Low-pass Amplifier: Magnitude Response For w<<wH : For w>>wH : For w=wH : • Gain is unity (0 dB) atw=AowH , called gain-bandwidth product • Bandwidth (frequency range with constant amplification )= wH (rad/s) Microelectronic Circuit Design McGraw-Hill Chap10 - 26

  27. Low-pass Amplifier: Phase Response If Ao positive: phase angle = 00 If Ao negative: phase angle = 1800 At wC: phase =450 One decade below wC: phase =5.70 One decade above wC: phase =84.30 Two decades below wC: phase =00 Two decades above wC: phase =900 Microelectronic Circuit Design McGraw-Hill Chap10 - 27

  28. RC Low-pass Filter Problem: Find voltage transfer function Approach: Impedance of the where capacitor is 1/sC, use voltage division Microelectronic Circuit Design McGraw-Hill Chap10 - 28

  29. High-pass Amplifier: Description • True high-pass characteristic impossible to obtain as it requires infinite bandwidth. • Combines a single pole with a zero at origin. • Simplest high-pass amplifier is described by wH = lower cutoff frequency or lower half-power point of amplifier. Microelectronic Circuit Design McGraw-Hill Chap10 - 29

  30. High-pass Amplifier: Magnitude and Phase Response For w>>wL : For w<<wL : For w=wL : • Bandwidth(frequency range with constant amplification ) is infinite • Phase response is given by Microelectronic Circuit Design McGraw-Hill Chap10 - 30

  31. RC High-pass Filter Problem: Find voltage transfer function Approach: Impedance of the where capacitor is 1/sC, use voltage division Microelectronic Circuit Design McGraw-Hill Chap10 - 31

  32. Band-pass Amplifier: Description • Band-pass characteristic obtained by combining highpass and low-pass characteristics. • Transfer function of a band-pass amplifier is given by • Ac-coupled amplifier has a band-pass characteristic: • Capacitors added to circuit cause low frequency roll-off • Inherent frequency limitations of solid-state devices cause high-frequency roll-off. Microelectronic Circuit Design McGraw-Hill Chap10 - 32

  33. Band-pass Amplifier: Magnitude and Phase Response • The frequency response shows a wide band of operation. • Mid-band range of frequencies given by , where Microelectronic Circuit Design McGraw-Hill Chap10 - 33

  34. Band-pass Amplifier: Magnitude and Phase Response (contd.) At both wHand wL, assumingwL<<wH, Bandwidth =wH - wL. The phase response is given by Microelectronic Circuit Design McGraw-Hill Chap10 - 34

  35. Narrow-band or High-Q Band-pass Amplifiers • Gain maximum at center frequency wo and decreases rapidly by 3 dB at wHand wL. • Bandwidth defined aswH - wL, is a small fraction ofwowith width determined by: • For high Q, poles will be complex and • Phase response is given by: Microelectronic Circuit Design McGraw-Hill Chap10 - 35

  36. Band-Rejection Amplifier or Notch Filter • Gain maximum at frequencies far from wo and exhibits a sharp null at wo. • To achieve sharp null, transfer function has a pair of zeros on jw axis at notch frequency wo , and poles are complex. • Phase response is given by: Microelectronic Circuit Design McGraw-Hill Chap10 - 36

  37. All-pass Function • Uniform magnitude response at all frequencies. • Can be used to tailor phase characteristics of a signal • Transfer function is given by: • For positive Ao, Microelectronic Circuit Design McGraw-Hill Chap10 - 37

  38. Complex Transfer Functions Amplifier has 2 frequency ranges with constant gain. Midband region is always defined as region of highest gain and cutoff frequencies are defined in terms of midband gain. Since wH = w4 and wL = w3, Microelectronic Circuit Design McGraw-Hill Chap10 - 38

  39. Bandwidth Shrinkage • If critical frequencies aren’t widely spaced, the poles and zeros interact and cutoff frequency determination becomes complicated. • Example : for which , Av(0) = Ao Upper cutoff frequency is defined by or Solving for wH yields wH =0.644w1.The cutoff frequency of two-pole function is only 64% that of a single-pole function. This is known as bandwidth shrinkage. Microelectronic Circuit Design McGraw-Hill Chap10 - 39

More Related