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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.