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MALVINO & BATES
SEVENTH EDITION
Electronic
PRINCIPLES
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Frequency Effects
ChapterChapter1616
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Topics Covered in Chapter 16
• Frequency response of an amplifier
• Decibel power gain
• Decibel voltage gain
• Impedance matching
• Decibels above a reference
• Bode plots
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Topics Covered in Chapter 16
(Continued)
• More bode plots
• The Miller effect
• Rise-time bandwidth relationship
• Frequency analysis of BJT stages
• Frequency analysis of FET stages
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Frequency response
• A graph of voltage gain vs. input
frequency
• An ac amplifier has a lower and upper
cutoff frequency
• A dc amplifier has only an upper cutoff
frequency
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Frequency response
(Continued)
• Coupling and bypass capacitors produce
the lower cutoff frequency
• Internal transistor capacitance and stray
wiring capacitance produce the upper
cutoff frequency
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0.707 AV(mid)
AV
f
AV(mid)
The frequency response curve of an ac amplifier
f1 f210f1 0.1f2
The cutoff frequenciesAlso called the half-power frequencies
The midband
The gain is maximum in the midband.
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Decibel power gain
• Defined as 10 times the common logarithm of the power gain
• When power gain increases by a factor of 2, the decibel power gain increases by 3 dB
• When power gain increases by a factor of 10, the decibel power gain increases by 10 dB
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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
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Definition of AP(dB)
• AP = pout/pin
• AP(dB) = 10 log AP
• Memorize:
– if AP = 2, AP(dB) = +3
– if AP = 0.5, AP(dB) = -3
– if AP = 10, AP(dB) = +10
– if AP = 0.1, AP(dB) = -10
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Decibel voltage gain
• Defined as 20 times the common
logarithm of the voltage gain
• When voltage gain increases by a factor
of 2, the decibel voltage gain increases by
6 dB
• Total dB voltage gain of cascaded stages
equals the sum of decibels of each stage
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Definition of AV(dB)
• AV = vout/vin
• AV(db) = 20 log A
• Memorize:
> if AV = 2, AV(dB) = +6
> if AV = 0.5, AV(dB) = -6
> if AV = 10, AV(dB) = +20
> if AV = 0.1, AV(dB) = -20
• Cascade:
AV = (AV1)(AV2), A V(dB) = AV1(dB) + AV2(dB)
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Impedance matching
• Produces maximum power transfer
• In an impedance-matched system, the
decibel power gain and the decibel
voltage gain are equal
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More on the decibel
• AP(dB) = AV(dB) only if impedance matched
• AP = antilog AP(dB)/10
• AV = antilog AV(dB)/20
• PdBm = 10 log P/1 mW
• P = antilog PdBm/10
• VdBV = 20 log V
• V = antilog VdBV/20
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Decibels above a reference
• Two popular references are the milliwatt
and the volt
• Decibels with the 1 milliwatt reference
are labeled dBm
• Decibels with the 1 volt reference are
labeled dBv
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1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 100
Logarithmic scale
Linear scale
A logarithmic scale compresses large values
and allows a large range to be covered
without losing resolution for the smaller values.
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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
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10 Hz 100 Hz 1 kHz 10 kHz 100 kHz 1 MHz 10 MHz
50 dB
40 dB
30 dB
20 dB
10 dB
0 dB
Ideal Bode plot of an ac amplifier
Midband
gain
Cutoff (-3dB) frequencies*
20 dB/decade
rolloff
*also called corner or
break frequenciesUnity gain
frequency
Unity gain
frequency
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R
C
Amplitude response
of RC lag circuit
0 dB
-20 dB
-40 dB
-60 dB
10f2f2 100f2 1000f2
f2 =2π2π2π2πRC
1
f2
f( )2222
1+
1AV =
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0o
0.1f2 f2 10f2
Angular response
of RC lag circuit
-90o
-45o
R
C
f2
fφφφφ = -arctan
Phase angle is between 0 and 90 degrees
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10 Hz 100 Hz 1 kHz 10 kHz 100 kHz
50 dB
40 dB
30 dB
20 dB
10 dB
0 dB
Ideal Bode plot of a dc amplifier
with two break frequencies.
20 dB/decade
40 dB/decade
fb1 fb2
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The Miller effect
• A feedback capacitor from the output to
the input of an inverting amplifier is
equivalent to two capacitors
• Refers to the input capacitance being
(inverting amp) AV + 1 times the
feedback capacitance
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Inverting
amplifier
AV
vin vout
Inverting
amplifier
AV
vin vout
C
Cin Cout
Miller equivalent circuit
Inverting amplifier with feedback capacitor
Cin = C(AV+1) Cout = CAV+1
AV
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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
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R
C
Square-wave response of a circuit with limited bandwidth
0
V0.9V
0.1V
TR
TR = 2.2RC
fcutoff = 0.35
TR
0
V
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Risetime-bandwidth relationship
• When a voltage step is used as the input to a dc amplifier, the risetime of the output is the time between the 10 and 90percent points
• The upper cutoff frequency equals 0.35divided by the risetime
• Provides an easy way to measure bandwidth of a dc amplifier
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+VCC
RER2
RC
R1
RL
vG
Cutoff frequency of an input coupling capacitor
RG
zin(stage) = R1 R2 ββββre’
C
f1 = 2ππππ(RG + zin(stage))C
1f1
AV
f
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+VCC
RER2
RC
R1
RL
vG
Cutoff frequency of an output coupling capacitor
RG C
f1
AV
ff1 = 2ππππ(RC + RL)C
1
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+VCC
RER2
RC
R1
RL
vG
Cutoff frequency of an emitter bypass capacitor
RG
C
f1
AV
f
f1 = 2π π π π zoutC
1
re’ +
R1 R2 RG
ββββ( )zout = RE
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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.
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Frequency analysis of FET stages
• Input and output coupling capacitors
produce low cutoff frequencies
• Drain bypass capacitance, gate
capacitance, and Miller capacitance
produce high cutoff frequencies
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Base and collector bypass circuits
C’e
f2
AV
f
CMiller Cstray
CMiller
C’e
C’c
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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.