Chapter 10 Analog Systems Microelectronic Circuit Design Richard C. Jaeger Travis N. Blalock Microelectronic Circuit Design, 3E McGraw-Hill

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). Microelectronic Circuit Design, 3E McGraw-Hill

Amplifier Biasing for Linear Operation (cont.) Voltage gain depends on the choice of 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. Microelectronic Circuit Design, 3E McGraw-Hill

Amplifier Biasing for Linear Operation (cont.) Output signals for 1 kHz sinusoidal input signal of amplitude 50 mV biased at VI = 0.3 V and VI = 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. Microelectronic Circuit Design, 3E 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. Microelectronic Circuit Design, 3E McGraw-Hill

Total Harmonic Distortion dc desired output 2nd harmonic distortion 3rd harmonic distortion Numerator = rms amplitude of distortion terms, Denominator = desired component Microelectronic Circuit Design, 3E McGraw-Hill

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.. Microelectronic Circuit Design, 3E 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 Ao = low-frequency gain or mid-band gain wH = upper cutoff frequency or upper half-power point of amplifier. Microelectronic Circuit Design, 3E McGraw-Hill

Low-pass Amplifier: Magnitude Response Low-pass filter symbol Gain is unity (0 dB) at w = AowH = wT called gain-bandwidth product Bandwidth (frequency range with constant amplification ) = wH (rad/s) Microelectronic Circuit Design, 3E McGraw-Hill

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 Microelectronic Circuit Design, 3E McGraw-Hill

Microelectronic Circuit Design, 3E RC Low-pass Filter Problem: Find voltage transfer function Approach: Impedance of the where capacitor is 1/sC, use voltage division Microelectronic Circuit Design, 3E McGraw-Hill