1. Frequency Effects
Chapter 16

2. 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

3. 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 = -3

4. 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

5. 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

6. 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

7. 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.

8. 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

9. 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

10. ( ) 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

11. Angular response of RC lag circuit
f = -arctan
0.1f2 f2
10f2 0o
-45o
-90o

12. 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

13. 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)

14. 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

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

16. 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

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

18. ( ) 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

19. 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.

20. Base and collector bypass circuits
C’c A f f2
C’e
CMiller
Cstray
CMiller
C’e

21. 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.