+VCC A 1 f1 = f RC f1 2p(RC + RL)C R1 RG C RL vG R2 REġ9 ( ) Cutoff frequency of emitter bypass capacitor re’ + R1 R2 RG b Zin(stage) = R1 R2 bre’ +VCC A f1 = 2p(RG + zin(stage))C 1 f RC f1 R1 RG RL C vG R2 REġ8 Cutoff frequency of output coupling capacitor V C V 0.9V TR = 2.2RC fcutoff = 0.35 TR 0.1V TRġ7 Cutoff frequency of input coupling capacitor 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 capacitorġ6 Square-wave response of a circuit with limited bandwidth ( ) 2 1+ 1 A = f2 10f2 100f2 1000f2 0 dB -20 dB -40 dB -60 dBġ3 Ideal Bode plot of a dc amplifier with two break frequencies.ĥ0 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 fb2ġ4 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) 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 frequenciesġ1 ( ) Amplitude response of RC lag circuit R 1 f2 = C 2pRC 1 A = f 1+ f2 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/20Ĩ A logarithmic scale compresses large valuesġ 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.ĩ 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 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 + A2dBħ More on the decibel GdB = AdB only if impedance matched If G = 2, GdB = +3 if G = 0.5, GdB = -3 if G = 10, GdB = +10 if G = 0.1, GdB = -10Ħ Definition of AdB A = vout/vin Adb = 20 log A Memorize: 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 = -3ĥ Definition of GdB G = pout/pin GdB = 10 log G Memorize: Also called the half-power frequenciesĤ Review of logarithms A logarithm is an exponent 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.
1 MALVINO Electronic PRINCIPLES SIXTH EDITIONģ The cutoff frequencies Also called the half-power frequencies