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Chapter 9

Decibel (dB)
◦ Level of gain
◦ Relates input to output
◦ Unless noted, log
is assumed
= 10
= log
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FIG. 21.1 Semilog graph
paper.
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FIG. 21.2 Frequency log
scale.
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

1 Bel= 10 Decibels (dB)
Power
◦

=
log
Voltage
◦
=
log
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TABLE 21.1
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Frequency Response: The frequency range in which an amplifier
will operate with negligible effects from capacitors and device
internal capacitances; often called the mid-range.
• At frequencies below mid-range, the coupling and bypass capacitors
lower the gain.
• At frequencies above mid-range, stray capacitances associated with
the active device lower the gain.
Also, cascading amplifiers limits the gain at high and low frequencies.
=
ECET 257 Consumer Power Electronics, PNC

Frequency where
near max
◦ -3 dB
◦ −
◦ At 7
is
 0.707
 0.707

FIG. 20.14 I versus frequency for
the series resonant circuit.
ECET 207 AC Circuit Analysis, PNC
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A Bode plot illustrates
the frequency response
of an amplifier.
The horizontal scale
indicates the frequency
(in Hz) and the vertical
scale indicates the gain
(in dB).
Fig. 9.8
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The Bode plot not only
indicates the cutoff
frequencies of the
various capacitors it also
indicates the amount of
attenuation (loss in gain)
at these frequencies.
The rate of attenuation
is sometimes referred to
as roll-off.
The roll-off is measured in dB-per-octave or dB-per-decade.
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-dB/decade refers to the
attenuation for every 10fold change in frequency.
For attenuations at the
low-frequency end, it
refers to the loss in gain
from the lower cutoff
frequency to a frequency
that is one-tenth the
cutoff value.
fLS = 9kHz gain is 0dB
fLS/10 = .9kHz gain is –20dB
Thus the roll-off is −20dB/decade
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-dB/octave refers to the
attenuation for every 2fold change in frequency.
For attenuations at the
low-frequency end, it
refers to the loss in gain
from the lower cutoff
frequency to a frequency
one-half the cutoff value.
fLS = 9kHz gain is 0dB
fLS / 2 = 4.5kHz gain is –6dB
Therefore the roll-off is 6dB/octave.
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The mid-range of an
amplifier is called the
bandwidth of the
amplifier.
The bandwidth is defined
by the lower and upper
cutoff frequencies.
Cutoff frequency – any
frequency at which the
gain has dropped by 3 dB
(70.7%) from its midrange value
Fig. 9.8
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At low frequencies, the
reactances of the coupling
capacitors (CS, CC) and the
bypass capacitor (CE) affect
the circuit impedances.
=
1
2
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The cutoff frequency due to CS can be calculated
using
where
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The cutoff frequency due to CC can be calculated using
where
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The cutoff frequency due to CE can be calculated with
where
and
Re is the resistance as seen from CE
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Find the equivalent formulas
◦ Zi – assume CE / CS are acting as bypasses
◦ Ex – Re for Emitter stabilized (
∥
)
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The Bode plot indicates
that each capacitor may
have a different cutoff
frequency.
It is the device that has
the highest lower cutoff
frequency (fL) that
dominates the overall
low-frequency response
of the amplifier.
ECET 257 Consumer Power Electronics, PNC

Phase shift
◦
= − tan
◦
= tan
=
19
1
2
 -45 at
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
Find
◦
◦
◦
◦
◦
◦
re
Zi
fLS
fLC
fLE
Low cut-off frequency
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At low frequencies, the
reactances of the
coupling capacitors (CG,
CC) and the bypass
capacitor (CS) affect the
circuit impedances.
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The cutoff frequency due to CG can be calculated with
where
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The cutoff frequency due to CC can be calculated with
where
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The cutoff frequency due to CS can be calculated with
where
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The Bode plot indicates that
each capacitor may have a
different cutoff frequency.
The capacitor that has the
highest lower cutoff
frequency (fL) is closest to
the actual cutoff frequency
of the amplifier.
ECET 257 Consumer Power Electronics, PNC

27
Find
◦
◦
◦
◦
◦
◦
◦
VGSQ and IDQ
gmo and gm
AVMID
Zi
AVS
fLG, fLC, and fLS
Low cut-off frequency
rd = ∞Ω
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Any p-n junction can develop capacitance. This capacitance
becomes noticeable across:
• The BJT base-collector junction in a common-emitter
amplifier operating at high frequencies
• The FET gate-drain junction in a common-source
amplifier at high frequencies
These capacitances are represented as separate input and
output capacitances, called the Miller capacitances.
THESE ARE NOT ACTUAL COMPONENTS, BUT
A PHENOMENON THAT OCCURS IN THE
CIRCUIT
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Feedback
Capacitance
Note that the amount of
Miller capacitance is
dependent on interelectrode capacitance
from input to output (Cf)
and the gain (Av).
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If the gain (Av) is
considerably
greater than 1,
then

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Junction capacitances
◦ Cbe, Cbc, Cce

Wiring capacitances
◦ Cwi, Cwo

Coupling capacitors
◦ CS , CC

Bypass capacitor
◦ CE
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where
and
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where
and
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The hfe parameter (or  )
of a transistor varies with
frequency
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Note the highest lower cutoff frequency (fL) and the lowest upper cutoff
frequency (fH) are closest to the actual response of the amplifier.

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Junction capacitances
◦ Cgs, Cgd, Cds

Wiring capacitances
◦ Cwi, Cwo

Coupling capacitors
◦ CG, CC

Bypass capacitor
◦ CS
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

= tan
= tan
=
1
2
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
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Find
◦ fHI, fHO
◦ High cut-off frequency
◦ Gain Bandwidth
rd = ∞Ω
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Each stage has its own frequency response,
but the output of each stage is affected by
capacitances in the subsequent stage. For
example, the output capacitance (Co) is
affected by the input Miller Capacitance (CMi)
of the next stage.
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Once the cutoff frequencies have been determined for each stage
(taking into account the shared capacitances), they can be plotted.
Note the highest lower cutoff frequency (fL) and the lowest upper cutoff
frequency (fH) are closest to the actual response of the amplifier.
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