856 Feedback Networks: Theory and Circuit Applications. Butterworth MFM response, 767 Butterworth response, 767

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1 Index I/O transfer admittance, 448 N stage cascade, 732, 734 S-parameter characterization, 226 ω max, 204 π-type, 148 π-type network model, 137 c-parameter, 151, 153 c-parameter matrix, 154 g-parameter modeling, 128 h-parameter, 118, 119 h-parameter equivalent circuit, 119 h-parameter model, 119 m-port multiport, 260 y-parameters, 135, 469 z-parameters, 146 scattered current, 227 dbm,51 dbm Power Measure, 50 3-dB bandwidth, 66, 286, 289, 318, 342, 345, 536, cycle hum, 58 active divider, 692 adjustable resistance, 679 amplifier bandwidth, 793 available load power, 195 available power, 194 available power gain, 191 average power, 258 balanced circuit, 636 balanced differential amplifiers, 206, 651 balanced differential configuration, 207 balanced differential realization, 207 bandpass, 265 bandpass amplifiers, 51 bandpass architecture, 819 bandpass feedback amplifier, 816 bandpass frequency responses, 51 bandpass units, 58 bandwidth, 66 Barkhausen criterion, 292 Battjes f T -doubler, 850 Bessel, 261 biasing, 115, 116 bilateral, 122 bilateral circuit element, 670 bilateral linear network, 252 bilateral two-port network, 137 bilinear coefficient, 230 bilinear transformation, 230 biquadratic filters, 57, 540, 591 Blackman s formula, 457, 486 Blackman s impedance formula, 476, 484 Blecher s procedure, 469 Boltzmann voltage, 507 Boltzmann s constant, 506 bond wire, 778, 801 bridging capacitance, 776 broadbanded dominant pole, 301 buffered capacitive compensation, 676 buffered capacitive feedback, 670 buffers, 32 bulk induced modulation of threshold voltage, 655 bulk source capacitance, 737 bulk transconductance factor, 737 bulk-drain capacitance, 737 Butterworth, 261 Butterworth filter, 847 Butterworth MFM,

2 856 Feedback Networks: Theory and Circuit Applications Butterworth MFM response, 767 Butterworth response, 767 capacitance density of the oxide-channel, 655 carrier frequency, 817 cascade interconnection, 154 cascaded 3-dB bandwidth, 733 center frequency, 51, 816 chain matrix, 155 chain parameters, 151 channel length, 502, 655 channel length modulation voltage, 510, 655 channel pinch off, 512 channel resistance, 737 characteristic impedance, 241, 271, 817 characteristic polynomial, 282 circuit instability, 292 circuit partitioning, 337 circuit quality factor, 754 circuit stability, 293 closed loop, 181 closed loop bandwidth, 286 closed loop characteristic polynomial, 298 closed loop current gain, 188, 361 closed loop damping factor, 290, 297, 311 closed loop gain, 161, 169, 176, 178, 279, 337 closed loop input impedance, 190 closed loop instability, 291 closed loop output impedance, 191 closed loop pole, 286 closed loop stability, 300 closed loop system, 178 closed loop transadmittance, 171, 190 closed loop transfer function, 286 closed loop transimpedance, 170, 188 closed loop undamped natural frequency, 290 closed loop voltage gain, 332 CMOS amplifier, 550 Colpitts oscillator, 316 column vectors, 259 common drain amplifier, 498, 552 common gate amplifier, 498, 499, 568 common gate cascode, 841 common gate I/O characteristics, 571 common mode excitation, 640, 645 common mode gain, 713 common mode input signal, 634 common mode model, 641 common mode Norton transconductance, 641 common mode output resistance, 642, 713 common mode rejection ratio, 637, 642, 647, 650, 713 common mode signal rejection, 636 common mode transconductance, 636 common mode voltage gain, 646 common source amplifier, 498, 524, 535 common source RF amplifier, 821 common source-common gate cascode, 569, 575, 753 compensated operational amplifier, 673 compensated source follower, 617 compensation, 300 compensation pole, 303 complex conjugate poles, 76 constant reactance circles, 233 constant resistance criteria, 778 constant resistance networks, 847 continued fraction expansion, 261 controlled vector, 477 controlling parameter, 448 controlling vector, 477 coupled inductor load, 776 coupling coefficient, 777 Cramer s rule, 446 critical damping, 78, 85 critical feedback parameter, 331, 409 critical frequencies, 75, 289 critical frequency parameter, 294, 295 critical parameter, 324, 326, 338, 341, 448 crucial parameter, 448 current amplifier, 30, 122, 348 current buffer, 34, 40 current buffering, 576 current controlled voltage source, 149 current extracting node, 447 current feedback amplifier, 360 current gain, 448, 456

3 Index 857 current injecting node, 447 current mirror, 652 cutoff, 505 damping factor, 62, 83, 288, 298, 309 Darlington configuration, 812 decibel, 15 decibel value, 64 decoupling capacitance, 525, 621 degenerative RC broadbanding, 736 delay, 69 depletion mode, 500 desensitization, 279 dielectric constant, 507 differential input signal, 631, 634 differential mode, 644 differential mode excitation, 645 differential mode gain, 713 differential mode half circuit, 640 differential mode Norton transconductance, 641 differential mode output resistance, 713 differential mode transconductance, 636 differential mode voltage gain, 646 differential mode, half circuit schematic, 715 differential to single ended conversion, 634 differential to single ended converter, 638, 642 diode-connected transistor, 651 distributed transmission line, 231, 772 dominant, 77 dominant energy storage element, 106 dominant open circuit time constant, 577 dominant pole, 78, 528, 680 dominant pole amplifiers, 731 dominant pole open loop, 287 dominant pole response, 84, 533, 681 dominant pole, approximation, 285 double series peaking, 776 drain saturation current, 512 drain saturation voltage, 512 driving point, 118 driving point function matrix, 477 driving point impedance, 445, 446, 457, 473 driving point input impedance, 19, 120, 123, 132, 194, , 342 driving point input resistance, 343, 361, 789 driving point null output resistance, 343 driving point output impedance, 123, 132, 195, driving point output resistance, 345, 361, 789 dual loop, 787 dual loop feedback, 385, 387, 401 Early resistance, 381 effective forward transconductance, 174 effective loop gain, 248 electrical noise, 55 electron mobility, 504 electronic potentiometer, 511 emitter degeneration resistance, 209, 380 energy incidence, 241, 242 enhanced common gate cell, 581 enhancement mode, 500 envelope delay, 72, 273, 732, 762, 763 equicofactor matrix, 443, 446 equivalent input noise voltage, 797 error signal, 278, 326 f T -doubler, 812 feedback, 246, 285, 456 feedback admittance, 206 feedback branch admittance, 366 feedback branch impedance, 377 feedback current amplifier, 357 feedback factor, 136, 278, 284, 286, 314, 324, 394 feedback network, 177 feedback parameter, 177, 327, 332 feedback signal flow path, 188 feedback transimpedance, 147 feedback voltage amplifier, 354 feedback voltage gain, 244 Fermi potential, 505 final value theorem, 309 first order cofactor, 443

4 858 Feedback Networks: Theory and Circuit Applications flatband potential, 505 folded current mirror, 717 forward current gain, 122 forward gain, 120, 136, 147, 162, 250 forward network gain, 339 forward short circuit current gain, 120 forward transadmittance, 249 forward transconductance, 516, 737 forward transimpedance, 162, 526 forward, signal path, 187 frequency response, 16, 63, 285 frequency response transformation, 265 front-end, 816 full power bandwidth, 690 fundamental matrix feedback flow graph, 478, 492 gain bandwidth product, 90, 287 gain margin, 292, 295, 297, 299, 300 gain-bandwidth product, 732 gate aspect ratio, 509, 654 gate impedance, 825 gate oxide overlap, 518 gate-drain capacitance, 518, 737 gate-source capacitance, 518, 737 gate-source threshold voltage, 655 global architecture, 178 global feedback, 178, 277, 348 gyrator, 267 h-parameters, 250, 252 half circuit analysis, 637 Hartley oscillator, 317 headroom, 295 highpass, 58, 265 hole mobility, 504 hybrid, 119 hybrid g-parameters, 128 hybrid h-parameters, 118 ideal current buffer, 40 ideal current source, 123 ideal feedback model, 464 ideal transadmittance amplifier, 27 ideal transconductor, 141 ideal transimpedance amplifier, 29 ideal transresistor, 149 ideal voltage amplification, 181, 182 ideal voltage amplifier, 24, 132, 181 ideal voltage buffer, 34 ideal voltage source, 149 identity matrix, 260, 479 immittance, 176, 449 impedance measurements, 472 impulse response, 79 impulsive source, 79 incident component of load current, 229 incident component of load voltage, 229 incident current, 227, 228 incident energy variable, 258 incident energy wave, 240 incident power, 229 incident voltage, 228 indefinite admittance matrix, 142, 144, 442, 449, 453, 455 indirect measurement of return difference, 486 inductive load port, 841 information passband, 817 input admittance, 136 input impedance, 147, 176, 448 input noise voltage, 748 input port reflection coefficient, 241, 245, 246 instability, 164, 200 integrator, 591, 592 intermodulation, 255 intrinsic carrier concentration, 506 Kron s network partitioning theorem, 322 lateral field, 695 linear feedback circuit, 326 linear phase, 71 linear phase response, 71 linear transconductor, 26 linear two-port network, 239 linear two-port systems, 226 linearized network, 116 Llewellyn constraint, 199 Llewellyn stability factor, 199, 202

5 Index 859 loop gain, , 168, 170, 171, 176, 188, 279, , 289, 314, 361, 527, 667 loop gain phase response, 539 loop transmission, 452 loop transmission matrix, 481, 491 lossless two-port filter, 261 lossless two-port network, 255 lossless, passive two-port network, 260 lowpass network, 14 lowpass response, 58 magnitude response peaking, 783 match terminated, 49, 195, 377, 789, 793 match terminated I/O ports, 376 match terminated condition, 792 match terminated design condition, 50 match termination, 172 matching filter, 797 matrix signal flow graph, 478 matrix singularity, 131 matrix transposition, 258 maximal flatness, 756 maximally flat delay (MFD), 74, 77, 763, 765, 845 maximally flat delay response, 762 maximally flat magnitude (MFM), 66, 77, 756, 765 maximally flat magnitude frequency, 759 maximally flat magnitude frequency response, 289, 782 maximally flat magnitude network, 784 maximally flat magnitude response, 756, 757, 761, 767, 782 maximally flat response, 784 maximum load power, 49 maximum possible transducer power gain, 202 maximum power, 195 maximum power transfer, 48 maximum signal source power, 230 maximum transducer gain, 201, 203 memoryless, 15 microwave amplifiers, 226 Miller capacitance multiplication, 633 Miller effect, 530, 561, 633, 661 Miller multiplication, 577, 598, 741, 751, 752 Miller multiplier, 794, 829, 841 Miller time, 750, 804, 829 Miller-limited frequency response, 532 mixed signal, 498 mixed signal integrated circuits, 630 mobility degradation, 695, 696 mobility of electrons, 510 model, 119 monic polynomials, 301 multi-parameter sensitivity, 492 multiloop feedback, 475 multiloop feedback circuits and systems, 322 multiparameter sensitivity function, 493 multiple feedback paths, 322 multiple loop feedback amplifiers, 476 mutual inductance, 777 N-channel, 500 N-channel driver transconductor, 634 narrow banding, 306 narrowband, 820 narrowband, amplifiers, 816 natural frequencies, 467 negative, 285 negative feedback, 164, 282, 286, 394 network I/O gain metric, 137 network block diagram, 325 network functions, 456 network power gain, 194 network stability, 286 network time delay, 762 NMOS, 500 noise, 256 noise floor, 255, 797 nondominant network pole, 78 nondominant open loop pole, 299 nondominant pole, 301, 680 nondominant pole frequency, 298 normalized loop gain, 386 normalized null return ratio, 325, 327, 331, 334, , 346, 347, 386, 789, 791, 826

6 860 Feedback Networks: Theory and Circuit Applications normalized return ratio, 325, 327, 328, 331, 334, 335, , 341, 342, 346, 347, 349, 789, 791, 826 normalizing inductance, 263 Norton current, 5, 9 Norton current gain, 10, 152 Norton equivalent network, 470 Norton forward transadmittance, 152 Norton impedance, 5 Norton transadmittance, 10 Norton s theorem, 3, 4 notch, 265 notch filter, 58, 97, 210 notch frequency, 97, 210 null driving point input resistance, 343 null feedback parameter, 790 null forward gain, 339 null forward transadmittance, 354 null impedance, 340 null input impedance, 338, 339 null output impedance, 341, 342 null output response, 340 null parameter gain, 325, 327, 386 null parameter voltage gain, 334, 356, 789 null return difference, 454, 482 null return difference matrix, 476, 482, 483 null return ratio, 325, 331, 344, 454, 609 null return ratio matrix, 483 null signal flow metric, 327 null Thévenin admittance, 380 null Thévenin impedance, 369 null Thévenin resistance, 374 null transadmittance, 352 null transimpedance, 348 ohmic regime, 509, 513 ohmmeter method, 8 one-port linear network, 239 one-stage operational amplifier, 631 op-amp, 629 open circuit, 122, 151 open circuit forward voltage gain, 128 open circuit impedance parameters, 146 open circuit impedances, 146 open circuit input impedance, 147, 253 open circuit input port admittance, 128 open circuit output impedance, 147 open circuit time, 531 open circuit time constant, 529, 531, 557, 732 open circuit transimpedance, 10, 147 open circuit voltage gain, 10 open circuit z-parameters, 146 open circuit, open loop voltage gain, 632 open loop, 284, 287, 526 open loop current gain, 168, 361, 363, 609 open loop dominant pole, 299 open loop gain, 35, 134, 160, 161, 176, 248, 278, 314, 356 open loop gain function, 318 open loop input impedance, 165 open loop network transimpedance, 350 open loop pole dominance, 293 open loop response, 680 open loop self-resonant frequency, 298 open loop transadmittance, 352 open loop transfer function, 286 open loop transimpedance, 170 open loop voltage gain, 410, 790 open-circuited capacitive time constants, 371 operational amplifier, 281, 629 operational transconductance amplifier-capacitor (OTA-C) integrator, 540 operational transconductor amplifier, 25 oscillation, 196 oscillator, 282 OTA, 25 output admittance, 122 output impedance, 4, 129, 176 output port reflection coefficient, 245 output port time constant, 540 overdamped, 77 overdamped network, 83 overshoot, 86 oxide capacitance, 510 P-channel, 500 P-channel driver transconductor, 634 P-channel transconductor, 635, 638

7 Index 861 passive highpass feedback, 670 passive highpass frequency compensation, 677, 678 peak overshoot, 308 phase, 69 phase distortion, 71 phase margin, 292, 294, 297, 299, 311, 539, 680 phase response, 762, 763 phasor formats, 257 pi topology, 519 PMOS, 500 PMOS load, 548 pole splitting capacitance, 661 poles, 75 polysilicon, 502 port current vector, 258 port voltage gain, 132, 154 port voltage vector, 258 positive feedback, 163, 282 positive loop gain, 164 positive real functions, 196, 197 potential instability, 164, 200 potential stability, 196 potentially unstable, 164, 197, 282 power busses, 525 power gain, 191 power scattering, 229 prototype lowpass filter, 265 quality factor, 53, 62, 288, 749, 818 quiescent, 113 quiescent operating conditions, 515 radio frequency (RF) amplifier, 816 reference impedance, 227, 241, 243 reference impedances, 239 reflected current, 227 reflected energy variable, 258 reflected energy wave, 240 reflected load current, 229 reflected load voltage, 229 reflected power, 229 reflected voltage, 228 reflection coefficient, 227, 228, 230, 239, 243, 246 reflection coefficient plane, 231, 232 reflection plane, 230, 232 response peaking, response sensitivity, 448 return difference, 290, 291, 448, 449, 452, 457, 459, 461, 464, 468, 472, 475 return difference function, 487 return difference matrix, 476, 480, 481, 485, 491 return ratio, 325, 331, 343, 349, 451, 609 return ratio matrix, 481, 491 returned signal, 482 returned voltage, 459 reverse gain, 162 reverse transadmittance, 162 reverse voltage gain, 121, 122, 243, 252 root mean square (RMS), 46, 257 S-Parameters, 250 Säckinger circuit, 426 saturated domain, 513 saturation, 514 saturation regime, 512 scalar sensitivity function, 492 scattering, 226 scattering analysis, 244 scattering parameter, 226, 228, 239, 240, 252 second order circuits, 57 second order closed loop network, 309 second order compensated response, 767 second order filters, 58 second order model, 285 second order network, 319 second-order cofactor, 444, 454 self-resonant, frequency, 824 sensitivity, 463 sensitivity function, 463, 491 sensitivity matrix, 488, 490 sensitivity metric, 464 series peaked amplifier, 765 series peaked common source amplifier, 770 series peaked compensation, 765 series peaking, 768 series peaking element, 772

8 862 Feedback Networks: Theory and Circuit Applications series peaking inductance, 769 series-series architecture, 399 series-series feedback, 178, 189, 380 series-series/shunt-shunt, 388 series-series/shunt-shunt dual loop feedback, 405 series-series/shunt-shunt feedback, 388 series-series/shunt-shunt feedback pair, 398 series-shunt feedback, 178, 405, 460 series-shunt feedback amplifier, 452, 455, 462, 481 series-shunt peaked amplifier, 771 series-shunt peaked compensation, 771 series-shunt/shunt-series dual loop feedback amplifier, 411 series-shunt/shunt-series feedback, 405 settling time, 82, 308, 309 sgn, 444 short circuit, 136 short circuit admittance parameters, 135 short circuit current, 9 short circuit current gain, 10, 123, 140, 253, 813 short circuit input admittance, 136, 137 short circuit input impedance, 137 short circuit output admittance, 136 short circuit output impedance, 129 short circuit transadmittance, 136 short circuit transconductance, 631 short circuit transfer admittance, 10 short circuit unity gain frequency, 204 short circuit, common base current gain, 362 shunt peaked amplifier, 753, 755 shunt peaked compensation, 748 shunt peaking, 748 shunt peaking element, 772 shunt peaking inductor, 757 shunt-antiphase shunt, 204, 207 shunt-antiphase shunt compensation, shunt-series feedback, 178, 360, 405 shunt-series feedback amplifier, 186, 787, 790 shunt-series topology, 187 shunt-series/series-shunt, 388 shunt-shunt feedback, 178, 188 shunt-shunt global feedback, 427 shunt-shunt loop, 399 signal flow parameters, 326 signal flow theory, 322 signal incidence, 241 signal reflection, 241 silicon dioxide, 502 single ended output voltage, 631 single loop feedback amplifier, 457 single stage op-amp, 630, 632 sinusoidal oscillator, 164 slew rate, slew rate limitations, 685 small signal drain-source conductance, 511 small signal model, 518 small signal MOS equivalent circuit, 517 Smith chart, 231 source follower, 499, 552 source follower I/O impedances, 560 source follower transfer function, 555 spiral inductor, 778, 824 spiral metallization, 822 stability, 62, 164, 195 stability headroom, 293 stable network, 467 standby, 113 step response, 82 subcircuits, 498 substrate, 502 subthreshold regime, 608 superposition theory, 8 supply independent biasing, 702, 703 Tchebyschev, 261 tee-type, 148 tee-type network model, 148 Thévenin equivalent model, 345 Thévenin impedance, 4 Thévenin input impedance, 19 Thévenin transimpedance, 10 Thévenin voltage, 4, 9 Thévenin voltage gain, 10, 151, 195 Thévenin s theorem, 3

9 Index 863 Thévenin, forward transimpedance, 151 thermal gradient, 639 third order compensated response, 768 threshold voltage, 505 time constant, 14, 528, 536 time domain response, 306 transadmittance, 171 transadmittance amplifier, 20, 189, 278, 348 transadmittance feedback amplifier, 352 transconductance amplifier, 141 transconductance coefficient, 509 transconductance parameter, 654 transconductor, 20, 25, 141, 381 transducer power gain, 191, 194, 196, 243, 260 transfer admittance, 448 transfer function matrix, 476, 477, 479, 480, 484 transfer impedance, 445 transient response, 79 transimpedance, 188, 445 transimpedance amplifier, 20, 27, 278, 348 transimpedance feedback amplifier, 348 transimpedance network, 526 transition capacitance, 519 transmission matrix, 155 transmission parameters, 151 transresistance amplifier, 149 transresistor, 20, 27, 149 transverse cutoff frequency, 613 tuned amplifiers, 51 tuned center frequency, 818, 824 tuned frequency, 816 two-port networks, 111 two-port parameters, 112 two-port scattering parameters, 239 two-stage op-amp, 632 two-stage operational amplifier, 633 unconditional stability, unconditionally stable, 188, 197, 202, 282 undamped natural frequency, 81, 288, 297, 754 undamped natural frequency of oscillation, 62 undamped self-resonant frequency, 62 underdamped, 76 underdamped network, 86 underdamping, 77 undershoot, 86 unilateral, 206 unilateral amplifier, 204 unilateral capacitive feedback, 670 unilateral feedback, 670 unilateral network, 122 unilateral two-port system, 205 unilateralization, 204 unit step response, 306 unity gain frequency, 299, 305, 310, 311, 318, 522, 523, 534, 535, 680, 732, 813, 815 unity loop gain frequency, 293 unity power gain frequency, 204 unstable, 282 vertical field mobility degradation, 695 virtual dominant pole, 304 virtual short circuit, 281 voltage amplifier, 20, 21, 185, 348 voltage buffer, 34 voltage controlled current source, 141 voltage controlled voltage source, 132 voltage gain, 446, 448, 453 voltage measurement node, 447 voltage reference node, 447 voltage scattering, 228 voltage transfer function, 154, 247 voltage-series feedback amplifier, 483, 494 Wien bridge oscillator, 316 Wilson amplifier, 619 Wilson current amplifier, 618, 720 winding resistance, 749 zero feedback parameter gain, 325 zero frequency gain, 528

Index. Small-Signal Models, 14 saturation current, 3, 5 Transistor Cutoff Frequency, 18 transconductance, 16, 22 transit time, 10

Index. Small-Signal Models, 14 saturation current, 3, 5 Transistor Cutoff Frequency, 18 transconductance, 16, 22 transit time, 10 Index A absolute value, 308 additional pole, 271 analog multiplier, 190 B BiCMOS,107 Bode plot, 266 base-emitter voltage, 16, 50 base-emitter voltages, 296 bias current, 111, 124, 133, 137, 166, 185 bipolar