Chapter 16

Frequency Effects

0.707 Amid

A

f

Amid

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.

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

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.

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

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

Midbandgain

Cutoff (-3dB) frequencies*

20 dB/decaderolloff

*also called corner or break frequencies

Unity gainfrequency

Unity gainfrequency

R

C

Amplitude responseof RC lag circuit

0 dB

-20 dB

-40 dB

-60 dB

10f2f2 100f2 1000f2

f2 = 2pRC1

f2

f( )2

1+

1A =

0o

0.1f2 f2 10f2

Angular responseof RC lag circuit

-90o

-45o

R

C

f2

ff = -arctan

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

Invertingamplifier

Avin vout

Invertingamplifier

Avin vout

C

Cin Cout

Miller equivalent circuit

Inverting amplifier with feedback capacitor

Cin = C(A+1) Cout = C A+1A

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

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

+VCC

RER2

RC

R1

RL

vG

Cutoff frequency of input coupling capacitor

RG

zin(stage) = R1 R2 bre’

C

f1 = 2p(RG + zin(stage))C

1f1

A

f

+VCC

RER2

RC

R1

RL

vG

Cutoff frequency of output coupling capacitor

RG C

f1

A

ff1 = 2p(RC + RL)C

1

+VCC

RER2

RC

R1

RL

vG

Cutoff frequency of emitter bypass capacitor

RG

C

f1

A

ff1 =

2 p zoutC1

re’ +

R1 R2 RG

b( )zout = RE

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’e

f2

A

f

CMiller Cstray

CMiller

C’e

C’c

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.