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TRANSCRIPT
Chapter 9:
BJT and FET
Frequency Response
Brief Lecture Note/PPT
of
Analog Electronics
B.Tech.- Computer Science Engineering , Semester-IV, Session- 2018/19-22
Topic: Frequency Response of BJT and FET
By:
Amar Choudhary, Assistant Professor,
Dr. APJ Abdul Kalam Women's Institute of Technology, Darbhanga, Bihar
Research Scholar, Amity School of Engineering and Technology, Amity University
(Lucknow Campus), Noida, Uttar Pradesh- 226010
mail: [email protected]: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
General Frequency Considerations
2Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
The frequency response of an amplifier refers to the frequency range in which the
amplifier will operate with negligible effects from capacitors and device internal
capacitance. This range of frequencies can be called the mid-range.
• At frequencies above and below the midrange, capacitance and any
inductance will affect the gain of the amplifier.
• At low frequencies the coupling and bypass capacitors lower the gain.
• At high frequencies stray capacitances associated with the active device lower
the gain.
• Also, cascading amplifiers limits the gain at high and low frequencies.
Bode Plot
3Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
A Bode plot indicates the
frequency response of an
amplifier.
The horizontal scale
indicates the frequency (in
Hz) and the vertical scale
indicates the gain (in dB).
Cutoff Frequencies
4Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
The mid-range frequency
range of an amplifier is
called the bandwidth of
the amplifier.
The bandwidth is defined
by the lower and upper
cutoff frequencies.
Cutoff – any frequency at
which the gain has
dropped by 3 dB.
BJT Amplifier Low-Frequency Response
5Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
At low frequencies, coupling
capacitor (CS, CC) and bypass
capacitor (CE) reactances
affect the circuit impedances.
Coupling Capacitor (CS)
The cutoff frequency due to CS can be calculated by
2(Rs Ri )CsLs
1f
where
R i R 1 || R 2 ||βre
6Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
2π(Ro RL )CcLC
1f
where
Ro RC || ro
Coupling Capacitor (CC)
The cutoff frequency due to CC can be calculated with
7Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Bypass Capacitor (CE)
2πReCELE
1f
βe E e
RsR R || ( r )
and
Rs Rs || R1 || R 2
The cutoff frequency due to CE can be calculated with
where
8Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
BJT Amplifier Low-Frequency Response
9Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
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
frequency response of the
amplifier.
Roll-Off of Gain in the Bode Plot
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
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 amount of attenuation
is sometimes referred to as
roll-off.
The roll-off is described as
dB loss-per-octave or dB
loss-per-decade.
Roll-off Rate (-dB/Decade)
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
-dB/decade refers to the
attenuation for every 10-fold
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.
In this example:
fLS = 9kHz gain is 0dB
fLS/10 = .9kHz gain is –20dB
Thus the roll-off is 20dB/decade
The gain decreases by –20dB/decade
Roll-Off Rate (–dB/Octave)
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
-dB/octave refers to the
attenuation for every 2-fold
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.
In this example:
fLS = 9kHz gain is 0dB
fLS / 2 = 4.5kHz gain is –6dB
Therefore the roll-off is 6dB/octave.
This is a little difficult to see on this graph because
the horizontal scale is a logarithmic scale.
BJT Low Frequency Example
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
BJT Low Frequency Example
-b) Sketch the frequency response using Bode plot
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
FET Amplifier Low-Frequency Response
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
At low frequencies,
coupling capacitor (CG,
CC) and bypass capacitor
(CS) reactances affect the
circuit impedances.
Coupling Capacitor (CG)
2π(Rsig Ri )CGLC
1f
where
Ri RG
The cutoff frequency due to
CG can be calculated with
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Coupling Capacitor (CC)
2π(RoRL)CCLC
1f
where
Ro RD || rd
The cutoff frequency due to
CC can be calculated with
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Bypass Capacitor (CS)
2πReqCSLS
1f
rd Ωgm
Seq1
R ||R
The cutoff frequency due to
CS can be calculated with
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
where
FET Amplifier Low-Frequency Response
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
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.
FET Low Frequency Example
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
FET Low Frequency Example
-b) Sketch the frequency response using Bode plot
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Miller Capacitance
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Any p-n junction can develop capacitance. In a BJT amplifier,
this capacitance becomes noticeable across:
• The base-collector junction at high frequencies in
common-emitter BJT amplifier configurations
• The gate-drain junction at high frequencies in common-
source FET amplifier configurations.
These capacitances are represented as separate input and output
capacitances, called the Miller Capacitances.
Miller Input Capacitance (CMi)
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
CMi (1 A v )Cf
Note that the amount of
Miller capacitance is
dependent on inter-
electrode capacitance
from input to output (Cf)
and the gain (Av).
Miller Output Capacitance (CMo)
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
If the gain (Av) is
considerably greater
than 1, then
CMo Cf
BJT Amplifier High-Frequency Response
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Capacitances that affect the
high-frequency response are
• Junction
capacitances Cbe,
Cbc, Cce
• Wiring
capacitances
Cwi, Cwo
• Coupling
capacitors CS,
CC
• Bypass
capacitor CE
Input Network (fHi) High-Frequency Cutoff
2πRThiCiHi
1f
where
RThi Rs || R1 || R 2 || Ri
Ci CWi Cbe CMi
CWi Cbe (1 Av )Cbc
and
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Output Network (fHo) High-Frequency Cutoff
where
RTho RC || RL || ro
and
Co CWo Cce CMo
2πRThoCoHo
1f
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
hfe (or )Variation
The hfe parameter (or ) of a
transistor varies with
frequency
bc
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
mid e be
1fβ
2πβ r (C C )
BJT High Frequency Example
For the following circuit parameters,
a)Determine †H i and †Ho
†H i = 738.24 KHz, †Ho
=8.6MHz
b) Determine †Q and †T
†Q = 2. 52MHz
†T = 252 MHz
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
BJT Amplifier Frequency Response
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Note the highest lower cutoff frequency (fL) and the lowest upper cutoff
frequency (fH) are closest to the actual response of the amplifier.
FET Amplifier High-Frequency Response
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Capacitances that affect the
high-frequency response are
• Junction
capacitances Cgs,
Cgd, Cds
• Wiring
capacitances
Cwi, Cwo
• Coupling
capacitors CG,
CC
• Bypass
capacitor CS
Input Network (fHi) High-Frequency Cutoff
2πRThiCiHi
1f
Ci CWi Cgs CMi
CMi (1 A v )Cgd
RThi Rsig || RG
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Output Network (fHo) High-Frequency Cutoff
2πRThoCoHo
1f
RTho R D || RL || rd
Co CWo Cds CMo
MoA
1CgdC 1
v
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
For the following circuit parameters,
a)Determine †H i and †Ho
†H i = 945.67 KHz, †Ho
=11.57MHz
FET High Frequency Example
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Multistage Frequency Effects
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Each stage will have its own frequency response,
but the output of one stage will be affected by
capacitances in the subsequent stage. This is
especially so when determining the high frequency
response. For example, the output capacitance(Co)
will be affected by the input Miller Capacitance
(CMi) of the next stage.
Multistage Amplifier Frequency Response
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
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.
Multistage Amplifier Frequency Response
The total voltage gain for multistage with identical stages in low frequency is
given by
Av Av1n
= =Av,mid Av1,mid
1
1– j†1n
Which is equal to 1/sqrt(2) at cutoff so
The low cutoff frequency for the multistage can be derived as
1†u =
†1
21/n —1In similar way the high cutoff frequency for the multistage is given by
2†u = †1 21/n —1
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Square Wave Testing
In order to determine the frequency response of an amplifier by experimentation,
you must apply a wide range of frequencies to the amplifier.
One way to accomplish this is to apply a square wave. A square wave consists of
multiple frequencies (by Fourier analysis: it consists of odd harmonics).
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Square Wave Response Waveforms
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
If the output of the
amplifier is not a perfect
square wave then the
amplifier is ‘cutting’ off
certain frequency
components of the square
wave.
Square Wave Response Waveforms
Rising time vr is time needed by the signal to
raise from 10% to 90% from the maximum
value.
fs
The bandwidth is given by
BW = †H =0.35
vr
The low cutoff frequency is given byP
†L = g†s
V s
F
Where P =V–V
and † is the square wave
frequency.
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Square Wave Response Waveforms
Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky