# Chapter 10 Analog Systems

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

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

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

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: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap10 - 4

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. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap10 - 5

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

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

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). Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap10 - 8

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. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap10 - 9

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

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

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

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

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

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

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

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

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

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

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

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 i2 to output port and open circuit input port. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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