Chapter 10 Analog Systems Microelectronic Circuit Design Richard

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

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 Mc. Graw-Hill Chap 10 - 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 Mc. Graw-Hill Chap 10 - 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 m. V and frequency w. S 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 Mc. Graw-Hill Chap 10 - 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 Mc. Graw-Hill Chap 10 - 5

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 Mc. Graw-Hill Chap 10 - 6

Amplification: Gain (contd. ) • Power Gain: For our example, On decibel scale, i. e. in d. B Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 7

Amplifier Biasing for Linear Operation VI = dc value of v. I, vi = time-varying component For linear amplification- v. I 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 Mc. Graw-Hill Chap 10 - 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 Mc. Graw-Hill Chap 10 - 9

Amplifier Biasing for Linear Operation (contd. ) Output signals for 1 k. HZ sinusoidal input signal of amplitude 50 m. V biased at VI= 0. 3 V and 0. 5 V: For VI =0. 3 V: Gain is 20, output varies about dc level of 4 V. For VI =0. 5 V: Gain is 40, output varies about dc level of 10 V. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 10

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 Mc. Graw-Hill Chap 10 - 11

Total Harmonic Distortion dc desired output 2 nd harmonic distortion 3 rd harmonic distortion Numerator= sum of rms amplitudes of distortion terms, Denominator= desired component Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 12

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. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 13

g-parameters Using open-circuit (i=0) and shortcircuit (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 Mc. Graw-Hill Chap 10 - 14

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. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 15

Hybrid or h-parameters Using open-circuit (i=0) and shortcircuit (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 Mc. Graw-Hill Chap 10 - 16

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. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 17

Admittance or y-parameters Using open-circuit (i=0) and shortcircuit (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 Mc. Graw-Hill Chap 10 - 18

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. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 19

Impedance or z-parameters Using open-circuit (i=0) and shortcircuit (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 Mc. Graw-Hill Chap 10 - 20

z-parameters: Example Problem: Find z-parameters for the same network (used in g-parameters example). Approach: Apply specified boundary conditions for each zparameter, 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. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 21

Mismatched Source and Load Resistances: Voltage Amplifier g-parameter representation (g 12=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 Mc. Graw-Hill Chap 10 - 22

Mismatched Source and Load Resistances: Current Amplifier h-parameter representation (h 12=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 Mc. Graw-Hill Chap 10 - 23

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) (-z 1, -z 2, …-zm)=zeros (frequencies for which transfer function is zero) (-p 1, -p 2, …-pm)=poles (frequencies for which transfer function is infinite) (In polar form) Bode plots display magnitude of the transfer function in d. B and the phase in degrees (or radians) on a logarithmic frequency scale. . Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 24

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 w. H = upper cutoff frequency or upper half-power point of amplifier. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 25

Low-pass Amplifier: Magnitude Response For w<<w. H : For w>>w. H : For w=w. H : • Gain is unity (0 d. B) at w=Aow. H , called gain-bandwidth product • Bandwidth (frequency range with constant amplification )= w. H (rad/s) Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 26

Low-pass Amplifier: Phase Response If Ao positive: phase angle = 00 If Ao negative: phase angle = 1800 At w. C: phase =450 One decade below w. C: phase =5. 70 One decade above w. C: phase =84. 30 Two decades below w. C: phase =00 Two decades above w. C: phase =900 Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 27

RC Low-pass Filter Problem: Find voltage transfer function Approach: Impedance of the capacitor is 1/s. C, use voltage division Jaeger/Blalock 7/1/03 where Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 28

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 w. H = lower cutoff frequency or lower half-power point of amplifier. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 29

High-pass Amplifier: Magnitude and Phase Response For w>>w. L : For w<<w. L : For w=w. L : • Bandwidth (frequency range with constant amplification ) is infinite • Phase response is given by Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 30

RC High-pass Filter Problem: Find voltage transfer function Approach: Impedance of the capacitor is 1/s. C, use voltage division Jaeger/Blalock 7/1/03 where Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 31

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 Mc. Graw-Hill Chap 10 - 32

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 Mc. Graw-Hill Chap 10 - 33

Band-pass Amplifier: Magnitude and Phase Response (contd. ) At both w. H and w. L, assuming w. L<<w. H, Bandwidth = w. H - w. L. The phase response is given by Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 34

Narrow-band or High-Q Band-pass Amplifiers • Gain maximum at center frequency wo and decreases rapidly by 3 d. B at w. H and w. L. • Bandwidth defined as w. H - w. L, 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 Mc. Graw-Hill Chap 10 - 35

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 Mc. Graw-Hill Chap 10 - 36

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 Mc. Graw-Hill Chap 10 - 37

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 w. H = w 4 and w. L = w 3, Jaeger/Blalock 7/1/03 Microelectronic Circuit Design Mc. Graw-Hill Chap 10 - 38

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 w. H yields w. H =0. 644 w 1. 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 Mc. Graw-Hill Chap 10 - 39