Frequency Effects Chapter 16

The cutoff frequencies Also called the half-power frequencies The frequency response curve of an ac amplifier A Amid 0.707 Amid f f1 10f1 0.1f2 f2 The cutoff frequencies The midband 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

A logarithmic scale compresses large values 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

Cutoff (-3dB) frequencies* 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 Unity gain frequency *also called corner or break frequencies

( ) Amplitude response of RC lag circuit R 1 f2 = C 2pRC 1 A = f 1+ f2 ( ) 2 1+ 1 A = f2 10f2 100f2 1000f2 0 dB -20 dB -40 dB -60 dB

Angular response of RC lag circuit 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

C Inverting amplifier A vin vout Inverting amplifier with feedback capacitor Inverting amplifier A vin Cin Cout vout Miller equivalent circuit Cout = C A+1 A 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

Square-wave response of a circuit with limited bandwidth V C V 0.9V TR = 2.2RC fcutoff = 0.35 TR 0.1V TR

Cutoff frequency of input coupling capacitor zin(stage) = R1 R2 bre’ +VCC A f1 = 2p(RG + zin(stage))C 1 f RC f1 R1 RG RL C vG R2 RE

Cutoff frequency of output coupling capacitor +VCC A 1 f1 = f RC f1 2p(RC + RL)C R1 RG C RL vG R2 RE

( ) Cutoff frequency of emitter bypass capacitor re’ + R1 R2 RG b zout = RE +VCC A f f1 = 2p zoutC 1 RC f1 R1 RG RL vG R2 RE 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 CMiller Cstray 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.