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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chapter 10 Analog Systems Microelectronic Circuit Design Richard C. Jaeger Travis N. Blalock Chap10 - 1

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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. Chap10 - 2

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 Chap10 - 3

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Amplification: Introduction A complex periodic signal can be represented as the sum of many individual sine waves. We consider only one component with amplitude V S =1 mV and frequency S with 0 phase (signal is used as reference): Amplifier output is sinusoidal with same frequency but different amplitude V O and phaseθ: Chap10 - 4

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Amplification: Introduction (contd.) Amplifier output power is: Here, P O = 100 W and R L =8 Output power also requires output current which is: Input current is given by phase is zero because circuit is purely resistive. Chap10 - 5

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 Chap10 - 6

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Amplification: Gain (contd.) Power Gain: For our example, On decibel scale, i.e. in dB Chap10 - 7

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Amplifier Biasing for Linear Operation V I = dc value of v I, v i = time-varying component For linear amplification- v I must be biased in desired region of output characteristic by V I. 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 out of phase (amplifier is inverting). Chap10 - 8

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Amplifier Biasing for Linear Operation (contd.) Voltage gain depends on bias point. Eg: if amplifier is biased at V I = 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. Chap10 - 9

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Amplifier Biasing for Linear Operation (contd.) Output signals for 1 kHZ sinusoidal input signal of amplitude 50 mV biased at V I = 0.3 V and 0.5V: For V I =0.3V: For V I =0.5V: Gain is 20, output varies about dc level of 4 V. Gain is 40, output varies about dc level of 10 V. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Total Harmonic Distortion dcdesired output 2nd harmonic distortion 3rd harmonic distortion Numerator= sum of rms amplitudes of distortion terms, Denominator= desired component Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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. (v 1, i 1 ) and (v 2, i 2 ) represent signal components of voltages and currents at the network ports. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 h 11 and h 21 : apply current i 1 to input port and short circuit output port. For h 12 and h 22 : apply voltage v 2 to output port and open circuit input port. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 y 11 and y 21 : apply voltage v 1 to input port and short circuit output port. For y 12 and y 22 : apply voltage v 2 to output port and short circuit input port. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 z 11 and z 21 : apply current i 1 to input port and open circuit output port. For z 12 and z 22 : apply current i 2 to output port and open circuit input port. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Mismatched Source and Load Resistances: Voltage Amplifier If R in >> R s and R out << R L, In an ideal voltage amplifier, and R out =0 g-parameter representation (g 12 =0) with Thevenin equivalent of input source: Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Mismatched Source and Load Resistances: Current Amplifier h-parameter representation (h 12 =0) with Norton equivalent of input source: If R s >> R in and R out >> R L, In an ideal current amplifier, and R in =0 Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Amplifier Transfer Functions A v (s)=Frequency-dependent voltage gain V o (s) and V s (s) = Laplace Transforms of input and output voltages of amplifier, (-z 1, -z 2,…-z m )=zeros (frequencies for which transfer function is zero) (-p 1, -p 2,…-p m )=poles (frequencies for which transfer function is infinite) Bode plots display magnitude of the transfer function in dB and the phase in degrees (or radians) on a logarithmic frequency scale.. (In factorized form) (In polar form) Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 A o = low-frequency gain or mid-band gain H = upper cutoff frequency or upper half-power point of amplifier. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Low-pass Amplifier: Magnitude Response For << H : For H : For H : Gain is unity (0 dB) at H, called gain-bandwidth product Bandwidth (frequency range with constant amplification )= H (rad/s) Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Low-pass Amplifier: Phase Response If A o positive: phase angle = 0 0 If A o negative: phase angle = At w C : phase =45 0 One decade below w C : phase =5.7 0 One decade above w C : phase = Two decades below w C : phase =0 0 Two decades above w C : phase =90 0 Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill RC Low-pass Filter Problem: Find voltage transfer function Approach: Impedance of the where capacitor is 1/sC, use voltage division Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 H = lower cutoff frequency or lower half-power point of amplifier. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill High-pass Amplifier: Magnitude and Phase Response For >> L : For L : For L : Bandwidth (frequency range with constant amplification ) is infinite Phase response is given by Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill RC High-pass Filter Problem: Find voltage transfer function Approach: Impedance of the where capacitor is 1/sC, use voltage division Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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. Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Band-pass Amplifier: Magnitude and Phase Response The frequency response shows a wide band of operation. Mid-band range of frequencies given by, where Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Band-pass Amplifier: Magnitude and Phase Response (contd.) At both and L, assuming L << H, Bandwidth = H - L. The phase response is given by Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Narrow-band or High-Q Band-pass Amplifiers Gain maximum at center frequency and decreases rapidly by 3 dB at and L. Bandwidth defined as H - L, is a small fraction of with width determined by: For high Q, poles will be complex and Phase response is given by: Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Band-Rejection Amplifier or Notch Filter Gain maximum at frequencies far from and exhibits a sharp null at o. To achieve sharp null, transfer function has a pair of zeros on j axis at notch frequency o, and poles are complex. Phase response is given by: Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 o, Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill 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 = and L = , Chap

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Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Bandwidth Shrinkage If critical frequencies aren’t widely spaced, the poles and zeros interact and cutoff frequency determination becomes complicated. Example : for which, A v (0) = A o Upper cutoff frequency is defined by or Solving for yields =0.644 .The cutoff frequency of two-pole function is only 64% that of a single-pole function. This is known as bandwidth shrinkage. Chap

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