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ESE 232 Introduction to Electronic Circuits Professor Paul Min [email protected] (314) 853-6200 Bryan Hall 302A Chapter 1. Signals and Amplifiers Microelectronics • Integrated circuit technology • Billions of components • Typically implement in silicon wafer < 100 mm2 • Examples: microprocessors, memories, logic chips ESE 232 • Study of microelectronics • Analysis and design • Functional circuits Copyright 2004 by Oxford University Press, Inc. Electrical circuits • Processes signals • Driven by power sources (voltage or current) • At every point in a circuit, voltage and current are defined. Signal (or power) represented in voltage (Thevenin form) vs(t) = Rs is(t) Signal (or power) Equivalent and represented in current translatable (Norton form) Copyright 2004 by Oxford University Press, Inc. Signals • • • • Contain time-varying information. Exist in various forms (mechanical, electrical, chemical, acoustical, etc.) Can be conveniently processed by electrical circuits. Converting non-electrical signal to electrical signal is done by transducer (or sensor). Copyright 2004 by Oxford University Press, Inc. Frequency Spectrum of Signals • • Often difficult to express signals in time (in mathematical form). Signals can be shown in frequency spectrum: Fourier series, Fourier transform, Z-transform, etc. → At what frequencies does the signal contain energy and by how much? Copyright 2004 by Oxford University Press, Inc. Fourier Series • Example: sine-wave va(t) = Va sin wt va(t) has all its energy at the angular frequency of w = 2πf. f is frequency in Hz. T = 1/f is period in seconds. Magnitude of this sine-wave at the angular frequency w is Va. Copyright 2004 by Oxford University Press, Inc. Example: square-wave Time expression w0= 2π/T Frequency expression Copyright 2004 by Oxford University Press, Inc. Frequency Allocations in the U.S.A. Copyright 2004 by Oxford University Press, Inc. Digital v. Analog • • Analog signal: continuous value, continuous time Digital signal: discrete value, discrete time Analog Signal Continuous time Continuous value Sample Digital Signal Quantize Discrete time Continuous value Discrete time Discrete value Copyright 2004 by Oxford University Press, Inc. Why Digital? • • • • • Less expensive circuits Privacy and security Small signals (less power) Converged multimedia Error correction and reduction Why Not Digital? • More bandwidth • Synchronization in electrical circuits • Approximated information Copyright 2004 by Oxford University Press, Inc. Notation • • • • • Total instantaneous quantities: lowercase symbols with uppercase subscripts (e.g., iC) dc quantities: uppercase symbols with upper case subscripts (e.g., IC) Power supply voltages: uppercase V’s with double letter uppercase subscripts (e.g., VEE) dc currents draw from power supply: uppercase I’s with double letter uppercase subscripts (e.g., ICC) Incremental signal quantities: lowercase symbols with lower case subscripts (e.g., ic) Copyright 2004 by Oxford University Press, Inc. Amplifiers • Amplification of input signal • Linear amplifier: vo(t) = Avi(t) (A: constant gain) • Voltage amplifier: changes input signal amplitude Av = voltage gain = vo / vi • Preamplifier: shaping in frequency (i.e., amplifies different frequency components differently). • Power amplifier: gains in voltage and current symbols Copyright 2004 by Oxford University Press, Inc. Transfer Characteristic Copyright 2004 by Oxford University Press, Inc. load power (PL ) vO iO Ap = power gain = input power (PI ) vI iI iO Ai = current gain iI Ap Av Ai voltage gain in decibels 20 log Av dB current gain in decibels 20 log Ai dB power gain in decibels 10 log Ap dB Copyright 2004 by Oxford University Press, Inc. Power Supplies dc power delivered to amplifer: Pdc V1 I1 V2 I 2 power drawn from sources: PI power delivered to load: PL power dissipated in amplifier: Pdissipated PL amplifier efficiency: 100 Pdc Copyright 2004 by Oxford University Press, Inc. Example. Amplifier with 10 V power supplies. Given: vI (t ) sin wt , vO (t ) 9sin wt , RL 1 k , IˆI 0.1 mA I1 I 2 9.5 mA 9 Av = = 9 V/V (or 19.1 dB) 1 ˆ ˆI 9 V 9 mA A I O 9 90 A/A (or 39.1 dB) O i 1 k IˆI 0.1 9 9 1 0.1 40.5 mW, PI Virms I irms 0.05 mW 2 2 2 2 Ap Av Ai 9 90 810 W/W (or 29.1 dB) PL Vorms I orms Pdc 10 9.5 10 9.5 190 mW Pdissipated Pdc PI PL 190 0.05 40.5 149.6 mW PL 100 21.3% Pdc Copyright 2004 by Oxford University Press, Inc. Amplifier Saturation maximum output minimum output To avoid saturation: L L vI Av Av Copyright 2004 by Oxford University Press, Inc. Nonlinear Transfer Characteristics and Biasing • • To avoid saturation, input signal should be shifted. → Biasing Input signals are biased to operate in the middle of linear region. quiescent point: Q instantaneous input: vi (t ) instantaneous output: vo (t ) input voltage is dc shifted by VI : vI (t ) VI vi (t ) output voltage: vO (t ) VO vo (t ) where vo (t ) Av vi (t ) and Av Copyright 2004 by Oxford University Press, Inc. dvO dvI at Q Example. transistor amplifier transfer characteristic: vO 10 1011 e 40vI for vI 0 V and vO 0.3 V L 0.3 V. At vO 0.3 V, vI 0.690 V. vO is highest when vI is lowest, i.e., vI 0 V. Therefore, L vO when vI 0 V. L 10 V. We want to find VI such that VO 5 V. VI 0.673 V Av = dvO dvI = -200 V/V vI 0.673 Copyright 2004 by Oxford University Press, Inc. Circuit Models for Voltage Amplifiers vo Avo vi RL v RL Av o Avo RL Ro vi RL Ro To make gain larger, make Ro smaller. This also decouples the effects of unknown value of RL . Ideal amplifiers have Ro 0. If R L , Av Avo . This decouples the voltage gain of the amplifer from the values of RL . If Ri , then vi vs Ri . Input is reduced by a voltage divider. Ri Rs We want Ri Rs . Ideally, Ri . v Ri RL Overall voltage gain: o Avo Ri Rs RL Ro vs Copyright 2004 by Oxford University Press, Inc. Cascaded Amplifiers Multiple stages of amplifiers put together. Each stage may serve different purpose (e. g., power gain, followed by voltage gain). High Ri with gain 10 (Signal may be small.) Modest Ri with gain 100 Small Ri with gain 1 (Provide gain.) (Buffer output for next stage.) Copyright 2004 by Oxford University Press, Inc. vi1 1M 0.909 V/V vs 1M 100k v 100k Av1 i 2 10 9.9 V/V 100k 1k vi1 v 10k Av 2 i 3 100 90.9 V/V 10k 1k vi 2 v 10 Av 3 L 1 0.909 V/V v 10 100 i3 v Av L Av1 Av 2 Av 3 818 V/V vi1 vL vs vL vi1 vi1 A 743.6 V/V v vi1 vs vs i v /100 6 Ai o L 8.18 10 A/A ii vi1 /1M P Ap L Pi vL io 8 66.9 10 W/W vi1i1 Copyright 2004 by Oxford University Press, Inc. Different Amplifier Types R R General Relationship: Avo Ais o Gm Ro m Ri Ri Copyright 2004 by Oxford University Press, Inc. Example 1.4. Small signal model for Bipolar Junction Transistor (BJT) Let Rs B: Base, E: Emitter, C: Collector Emitter as common (i.e., ground) Common Emitter Amplifier 5k , r = 2.5k , g m 40 m A/V, ro 100k , and RL 5k . BJT r vbe vs and vo g m vbe RL || ro r Rs vo r v g m RL || ro 63.5 V/V. If ro , o 66.7 V/V vs r Rs vs Copyright 2004 by Oxford University Press, Inc. Frequency Response With a sinusoidal input to a linear amplifier, the output is a sinusoid with the same frequency, but with different amplitude and phase shift. T ( w) : Transfer function of amplifier Vo T ( w) and T ( w) Vi Need to determine T ( w) and T ( w) for all frequencies. Copyright 2004 by Oxford University Press, Inc. Typically 3 dB Constant gain between w1 and w2 . Should operate in this region. Gain dropping away from w1 and w2 . Signals are distorted at frequencies away from w1 and w2 We say the amplifier has the bandwidth between w1 and w2 . Copyright 2004 by Oxford University Press, Inc. First Order Systems: systems with a single time constant RC circuits have a single time constant RC L RL circuits have a single time constant R General solution (during a time period: initial time t final time) x(t ) xFinal xInitial xFinal e t Frequency domain analysis (w : angular variable, s : Laplace variable) 1 1 R R, C or , L jwL or sL jwC sC Copyright 2004 by Oxford University Press, Inc. Copyright 2004 by Oxford University Press, Inc. Low pass RC circuit No distortion means constant amplitude gain and linear phase shift. Copyright 2004 by Oxford University Press, Inc. High pass RC circuit No distortion means constant amplitude gain and linear phase shift. Copyright 2004 by Oxford University Press, Inc. 1 Ri Zi sCi Example 1.5. Vi Vs and Zi Ri || Ci 1 Zi Rs Ri sCi Vo Vi RL RL Ro 1 Vo Vs 1 Rs Ri 1 1 Ro RL constant Vi 1 Vs 1 Rs sC R i s Ri 1 Rs Ri 1 sCi Rs Ri Function of s RR Time constant: Ci s i Ci Rs || Ri Rs Ri Copyright 2004 by Oxford University Press, Inc. Only the input circuit is a first order system (or single time constant circuit). Output circuit is a zero order system (i.e., no energy storing element). K K Overall transfer function T ( s ) (wo : 3 dB frequency) 1 s s 1 wo Vo K Vs s 0 1 1 Rs Ri 1 1 Ro RL Copyright 2004 by Oxford University Press, Inc. Different Shapes of Amplifier Frequency Response For all devices, the transfer function loses amplitude gain at high frequency because of internal capacitance. Simple low pass configuration. Direct coupled amplifier Amplifier can block low frequency components (including DC) by putting a capacity in series with input (i.e,. input circuit is a high pass circuit). Capacitively coupled amplifier Amplifier can "filter-in" only selective frequency components. Typically higher order circuits. Tuned amplifier Copyright 2004 by Oxford University Press, Inc. Logic Inverter Nonlinear (saturation) region for digital binary logic operation Circuit symbol • input 1 (high) → out put 0 (low) • input 0 (low) → out put 1 (high) Linear region for ordinary amplifier operation (transition region) Transfer function • high vi (> 0.690V) → low vo (≈ 0.3V) • low vi (≈ 0V) → high vo (≈ VDD) • linear region for mid value of vi Copyright 2004 by Oxford University Press, Inc. Noise Margin • For cascaded inverters • Noise margin for high input NMH = VOH - VIH • Noise margin for low input NML = VIL - VOL Copyright 2004 by Oxford University Press, Inc. Ideal Inverter NMH = NML =VDD / 2 Copyright 2004 by Oxford University Press, Inc. Abstract Implementation of Inverter voltage controlled switch. When vI is low, switch is open, leaving the vertical path disconnected. → vo = VDD is an open circuit voltage. When vI is high, switch connects the vertical path. → vo is a low level voltage determined largely by Voffset, a characteristic of the voltage controlled switch. Copyright 2004 by Oxford University (RonPress, is Inc. typically small.) Propagation Delay • Change of output after input change is not instantaneous. • Internal capacitance of devices causes the delay. Copyright 2004 by Oxford University Press, Inc. Copyright 2004 by Oxford University Press, Inc. When the switch is on (input high), it provides the vertical path with Voffset and Ron . The capacity is open circuit at steady state. Thus the steady state output value is low: VOL Voffset VDD Voffset Ron 0.55 V. R Ron When the switch becomes off (input becomes low), the vertical path is connected by the capacitor only. The final value of output is VDD because once again, the capacitor becomes an open circuit at steady state. Assuming the input changes at t 0, vo t vo (0 ) vo () vo (0 ) e 108 t t (where RC ) 108 t 5 (0.55 5)e 5 4.45e Define t PLH to be the time for output to go from low to the half way point to the final high output value. vo t PLH 1 1 V V OH OL 5 0.55 2 2 From this we get, t PLH =6.9 ns. Copyright 2004 by Oxford University Press, Inc.