SIXTH EDITION MALVINO Electronic PRINCIPLES
Frequency Effects Chapter 16
The midband The cutoff frequencies The frequency response curve of an ac amplifier A Amid 0.707 Amid f f1 10f1 f2 0.1f2 The gain is maximum in the midband. Also called the half-power frequencies
Review of logarithms • A logarithm is an exponent • If x = 10y, then y = log10x • y = log 10 = 1 • y = log 100 = 2 • y = log 1000 = 3 • y = log 0.1 = -1 • y = log 0.01 = -2 • y = log 0.001 = -3
Definition of GdB • G = pout/pin • GdB = 10 log G • Memorize: • if G = 2, GdB = +3 • if G = 0.5, GdB = -3 • if G = 10, GdB = +10 • if G = 0.1, GdB = -10
Definition of AdB • A = vout/vin • Adb = 20 log A • Memorize: • if A = 2, AdB = +6 • if A = 0.5, AdB = -6 • if A = 10, AdB = +20 • if A = 0.1, AdB = -20 • Cascade: A = A1A2, AdB = A1dB + A2dB
More on the decibel • GdB = AdB only if impedance matched • G = antilog GdB/10 • A = antilog AdB/20 • PdBm = 10 log P/1 mW • P = antilog PdBm/10 • VdBV = 20 log V • V = antilog VdBV/20
0 1 2 3 4 5 6 7 8 9 10 Linear scale 1 2 3 4 5 6 7 8 9 10 Logarithmic scale A logarithmic scale compresses large values and allows a large range to be covered without losing resolution for the smaller values.
Bode plots • Use semilogarithmic graph paper (the horizontal axis is logarithmic; the vertical is linear) • Plot dB voltage gain on the vertical axis • Plot frequency on the horizontal axis • An octave refers to a ratio of 2 • A decade refers to a ratio of 10
Unity gain frequency Unity gain frequency Ideal Bode plot of an ac amplifier Cutoff (-3dB) frequencies* 50 dB Midband gain 40 dB 30 dB 20 dB/decade rolloff 20 dB 10 dB 0 dB 10 Hz 100 Hz 1 kHz 10 kHz 100 kHz 1 MHz 10 MHz *also called corner or break frequencies
R 1 1 f2 = A = 2pRC ( ) 2 f 1+ f2 C Amplitude response of RC lag circuit f2 10f2 100f2 1000f2 0 dB -20 dB -40 dB -60 dB
f f2 R Angular response of RC lag circuit C f = -arctan 0.1f2 f2 10f2 0o -45o -90o
Ideal Bode plot of a dc amplifier with two break frequencies. 50 dB 40 dB 20 dB/decade 30 dB 20 dB 40 dB/decade 10 dB 0 dB 10 Hz 100 Hz 1 kHz 10 kHz 100 kHz fb1 fb2
A+1 Cout = C A C Inverting amplifier A vout vin Inverting amplifier with feedback capacitor Inverting amplifier A vout vin Cin Cout Miller equivalent circuit Cin = C(A+1)
Frequency compensation • Most op amps are internally compensated to prevent oscillations • One dominant internal compensation capacitor rolls off the gain at 20 dB/decade • IC capacitors are limited to the pF range • The Miller effect makes the internal compensation capacitor equivalent to a much larger capacitor
V 0 0.35 fcutoff = TR TR Square-wave response of a circuit with limited bandwidth R C V 0.9V TR = 2.2RC 0.1V 0
1 2p(RG + zin(stage))C zin(stage) = R1 R2 bre’ f1 = Cutoff frequency of input coupling capacitor +VCC A f RC f1 R1 RG RL C vG RE R2
Cutoff frequency of output coupling capacitor +VCC A 1 f f1 = RC f1 2p(RC + RL)C R1 RG C RL vG RE R2
1 re’+ f1 = 2p zoutC ) ( zout = RE R1 R2 RG b Cutoff frequency of emitter bypass capacitor +VCC A f RC f1 R1 RG RL vG RE R2 C
Combined frequency effects • The input coupling, output coupling, and emitter bypass capacitors each produce a cutoff frequency. • One is usually dominant (the highest frequency) and produces a rolloff of 20 dB/decade as frequency decreases. • When the next cutoff is reached, the gain rolloff increases to 40 dB/decade. • When the third is reached, it becomes 60 dB/decade.
Base and collector bypass circuits C’c A f f2 C’e Cstray CMiller CMiller C’e
Bypass circuits • The base bypass circuit contains the internal base-emitter capacitance (C’e) and the Miller capacitance due to the internal collector-base feedback capacitance (C’c) • The collector bypass circuit contains the Miller capacitance and the stray (wiring) capacitance.
