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ELECTRONIC CIRCUITS II
Typical Frequency Response
• Amplifier gain is affected by the frequency because
of the imput and output of impedences and
capacitors used in amplifiers.
CHAPTER 7.
FREQUENCY RESPONSE OF
BJT AND JFET
Typical Frequency Response
• The frequency region below the fL cutoff frequency is
called the low frequency region and above fH is
called high frequency region.
• There is a band of frequencies in which the
magnitude of the gain is either equal or relatively
close to the midband value which is 0,707Avmid.
• The corresponding frequencies fL and fH are
generally called the cutoff, or half-power
frequencies.
NORMALIZATION PROCESS
• The plot of an amplifier will typically be of dB versus
frequency rather than gain versus frequency.
• To obtain such a dB plot, the curve is first normalized
by a process whereby the vertical parameter is
divided by a specific level or quantity sensitive.
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NORMALIZATION PROCESS
Low-Frequency Analysis
• The curve is normalized by dividing the output voltage gain at
each frequency by the midband level.
The reactance of the capacitor is:
• Note that the curve has the same shape but the band
frequencies are now defined by simply the 0.707 level and not
linked to the actual midband level.
At high frequencies,
the reactance is:
(Short circuit eqv.)
At f = 0, the reactance is:
(Open circuit eqv.)
Low-Frequency Analysis
By the voltage-divider rule
Low-Frequency Analysis
The magnitude of Vo is
found as follows:
For the special case where XC = R
When f = ∞
 Xc = 0

Vo / Vi = 1
When f = 0
 Xc = ∞

Vo / Vi = 0
At the frequency for
which XC = R , the
output will be 70.7% of
the input for the
network.
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Low-Frequency Analysis
The frequency at which this occurs is determined from
In terms of logs
• There is a 3-dB drop in
gain from the midband
level when f = fL where fL
is the the low-frequency
cutoff frequency for a BJT
transistor.
Low-Frequency Analysis
Low-Frequency Analysis
• If the gain equation is written as
using
we obtain
Low-Frequency Analysis
The magnitude
and phase form:
Phase angle is:
Verifying when f = fL
The gain in dB is
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Low-Frequency Analysis –
Bode Plot
Low-Frequency Response
of BJT w/ RL
The cutoff frequency defined by Cs:
Graph is called a Bode plot of the
magnitude versus frequency.
Low-Frequency Response of BJT
w/ RL
Low-Frequency Response
of BJT w/ RL
The cutoff frequency defined by CE:
• The cutoff frequency defined by Cc:
RTh
• The cutoff frequency due to
CE can be determined using
• The total series resistance is now Ro+ RL, and the cutoff
frequency due to Cc is determined by:
• The value of Re is therefore
determined by
• If the frequencies fC , fE, and fLe are relatively far apart, the
highest cutoff frequency will essentially determine the lower
cutoff frequency for the entire system.
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EXERCISE
Determine the cutoff frequencies of the circuit.
EXERCISE Cont’d
EXERCISE
To determine r e for dc conditions, we first apply
the test equation:
Impact of RS on The BJT
Low-frequency Response
When RS is present the
equivalent circuit is then:
The cutoff frequency
defined by Cs
The cutoff frequency
defined by CE :
Since fLE >> fLC or fLS the bypass capacitor CE is determines the
lower cutoff frequency of the amplifier.
where
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Low-Frequency Response of JFET
Low-Frequency Response of JFET
CG :
For the coupling capacitor between the source and the
active device, the ac equivalent network is as shown. The
cutoff frequency determined by CG:
Low-Frequency Response of JFET
CC:
For the coupling capacitor between the active device and the
load the network is as shown. The resulting cutoff frequency
Low-Frequency Response of JFET
CS:
For the source capacitor CS , the resistance level of importance
is shown. The cutoff frequency is defined by
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Miller Effect Capacitance
• For any inverting amplifier, the input capacitance will be
increased by a Miller effect capacitance sensitive to the gain of
the amplifier and the interelectrode (parasitic) capacitance
between the input and output terminals of the active device.
Miller Effect Capacitance
Applying Kirchhoff’s current law:
Since XCf =
Miller Effect Capacitance
Using the equation establishesthe equivalent network as:
𝟏
𝟐𝝅𝒇𝑪𝒇
Miller Effect Capacitance
• To determine the output
Miller effect are in place.
Applying Kirchhoff’s current
law results in
the Miller effect input
capacitance is defined by:
• The resistance Ro is usually sufficiently large to permit ignoring I1
compared to I2 resulting:
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Miller Effect Capacitance
High-Frequency Response
• At the high-frequency end, there are two factors that define the
-3 dB cutoff point at the BJTs:
• The network capacitance (parasitic and introduced)
• The frequency dependence of hfe(β).
The Miller output capacitance:
High-Frequency Response of BJT
Amplifier
High-Frequency Response of BJT
Amplifier
• In the high-frequency equivalent model for the circuit, Cs , Cc ,
and Ce are not present due to being short-circuit state in high
frequency.
• The various parasitic capacitances (Cbe, Cbc, Cce) of the
transistor are included with the wiring capacitances ( CWi,
CWo) introduced during construction.
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High-Frequency Response of BJT
Amplifier
• Using the Thévenin equivalent
of input circuit as shown
High-Frequency Response of BJT
Amplifier
Using the Thévenin equivalent
of output circuit as shown
EXERCISE
Using the given parameters of the circuit and the transistor;
a. Determine the fhi and fho
c. Sketch the frequency response for the low- and high-frequency regions
using the results of parts (a) and (b).
EXERCISE
Solution:
a. For the fhi
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EXERCISE
EXERCISE
High-Frequency Response Of The
FET Amplifier
High-Frequency Response Of The
FET Amplifier
For the fho
b. The fβ :
• The analysis of the high-frequency response of the FET
amplifier is very similar to the BJT amplifier.
• There are interelectrode and wiring capacitances that will
determine the high-frequency characteristics of the amplifier.
• The capacitors Cgs and Cgd typically vary from 1 pF to 10 pF,
whereas the capacitance Cds is usually quite a bit smaller,
ranging from 0.1 pF to 1 pF.
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High-Frequency Response Of The
FET Amplifier
• Using the Thévenin equivalent of input circuit as shown
Multistage Frequency Effects
• For a second transistor stage connected directly to the output
of a first stage, there will be a significant change in the overall
frequency response.
High-Frequency Response Of The
FET Amplifier
Using the Thévenin equivalent of output circuit as shown
Multistage Frequency Effects
• The input and output parasitic capacitances (Cwi1, Cwo2) does
not change but first stage output parasitic capacitance changes
in the following multistage amplifier configuration.
• In the high-frequency region, the output capacitance Co must
now include the wiring capacitance (CW1), parasitic
capacitance ( Cbe ), and Miller capacitance (CMi) of the
following stage.
• Furthermore, there will be additional low-frequency cutoff
levels due to the second stage, which will further reduce the
overall gain of the system in this region.
Output parasitic capacitance of the first stage will be:
Co1 = Cwo1 + Cce1 + CMo1 + CMi2 + Cwi2 + Cbe2
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Gain-Bandwidth Product
Gain-Bandwidth Product
• GBP is defined as:
• The Gain-Bandwidth Product (GBP) is commonly used to
initiate the design process of an amplifier.
• It provides information about the relationship between the
gain of the amplifier and the expected operating frequency
range.
• GBP is defined as:
At Av = Avmid = 100 the bandwidth as shown in the figure is
approximately 1 MHz.
Multistage Frequency Effects
• For each stage, the upper cutoff frequency will be
determined primarily by the lowest cutoff frequency.
• The low-frequency cutoff is primarily determined by the
highest low-frequency cutoff frequency.
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