BJT

1
Chapter 7

• BJT
• Frequency Response

2
Contents

• Logarithm and dB
• Low frequency analysis-Bode plot
• Low frequency response-BJT amplifiers
• Miller effect capacitance
• High frequency response-BJT amplifiers
• Multistage frequency effects
• Square wave testing

3
Logarithms
Formula 9.1
Formula 9.2
Formula 9.3
The two are related by
Formula 9.4
4
Logarithms
Formula 9.5
Formula 9.6
Formula 9.7
Formula 9.8
5
Semilog graph paper.
6
Identifying the numerical values of the tic
marks on a log scale.
7
Semilog

• Vertical scale- linear scale with equal divisions
• The distance from log10 10 to log10 2 is 30 of
  the span.
• Important to note the resulting numerical value
  and the spacing, since plots will typically only
  have the tic marks.
• Plotting a function on a log scale can change the
  general appearance of the waveform as compared to
  a plot on a linear scale.
• Straight line plot on a linear scale can develop
  a curve on a log scale.
• Nonlinear plot on a linear scale can take on the
  appearance of a straight line on a log plot.

8
Decibels
Formula 9.9
Formula 9.10
Formula 9.11
Formula 9.12
Formula 9.15
9
Decibels

• Term decibel-the fact that power and audio levels
  are related on a logarithmic basis.
• P1, P2 power levels
• Bel-too large unit of measurement for practical
  purpose.
• The terminal rating of electronic communication
  equipment is commonly in decibels.
• Decibels- is a measure of the difference in
  magnitude between two power levels.
• Advantages of the logarithmic relationship, it
  can be applied to cascade stages.

10
Gain versus Frequency
11
Low Frequency Analysis
RC combination that will define a low-cutoff
frequency.
RC circuit at very high frequencies.
RC circuit at f 0 Hz.
12
Low Frequency Analysis

• A low frequency, the reactance of the capacitive
  becomes very large, so a significant portion of a
  signal dropped across them.
• Then as the frequency approaches zero or at dc,
  the capacitive reactance approach infinity or
  become an open circuit.
• As the frequency increases, the capacitive
  reactance decreases and
• more of the input voltage appears across the
  output terminals.

Low-frequency response for the RC circuit
13
Low Frequency Analysis
Bode plot for the low-frequency region.
14
Low Frequency Analysis

• Determine the break frequency.
• Plot f1 point on the log scale.
• Draw straight-line segment (slope) from f1 point
  to -20dB at linear scale.
• In the same figure, draw straight-line for the
  condition of 0dB.
• When f f1 , there is a 3dB drop from the
  mid-band level. Plot this point.
• Find the 3dB point corresponding to f1 and sketch
  the curve.

2
4
3
6
5
15
Low Frequency Response BJT Amplifier
At low frequencies Coupling capacitors (Cs, CC)
and Bypass capacitors (CE) will have capacitive
reactance (XC) that affect the circuit impedances.
16
Coupling Capacitor - CS
Determining the effect of CS on the low-frequency
response.
Cutoff frequency
Voltage Vi
17
Coupling Capacitor - CS
Localized ac equivalent for CS.
18
Coupling Capacitor - CC
Determining the effect of CC on the low-frequency
response.
Cutoff frequency
19
Coupling Capacitor - CC
Localized ac equivalent for CC with Vi 0 V.
20
Bypass Capacitor - CE
Determining the effect of CE on the low-frequency
response.
Cutoff frequency
21
Bypass Capacitor - CE
Localized ac equivalent of CE.
22
Example

• Determine the lower cutoff freq. for the network
  of Fig. 1 using the following parameters
• Cs 10µF, CE 20µF, Cc 1µF
• Rs 1KO, R1 40KO, R2 10KO,
• RE 2kO, Rc 4kO, RL 2.2KO,
• ß 100, r0 8O, Vcc 20V
• Sketch the frequency response using a Bode plot

23
Bode Plot of Low Frequency Response BJT
Amplifier
The Bode plot indicates that each capacitor may
have a different cutoff frequency. It is the
device that has the highest of the low cutoff
frequency (fL) that dominates the overall
frequency response of the amplifier (fLE).
24
Roll-off of Gain in the Bode Plot
Roll-off
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.
25
-dB/Decade
-dB/Decade refers to the attenuation for every
10-fold change in frequency. For Low Frequency
Response attenuations it refers to the loss in
gain from the lower cutoff frequency to a
frequency 1/10th the lower cutoff frequency.
26
-dB/Octave
-dB/Octave refers to the attenuation for every
2-fold change in frequency. For Low Frequency
Response attenuations it refers to the loss in
gain from the lower cutoff frequency to a
frequency 1/2 the lower cutoff frequency.
27
Miller Effect Capacitance
Any P-N junction can develop capacitance. This
was mentioned in the chapter on diodes. In a BJT
amplifier this capacitance becomes noticeable
between the Base-Collector junction at high
frequencies in CE BJT amplifier configurations
and the Gate-Drain junction at high frequencies
in CS FET amplifier configurations. It is
called the Miller Capacitance. It effects the
input and output circuits.
28
Miller Input Capacitance (CMi)
It can be calculated Formula 9.42
Note that the amount of Miller
Capacitance is dependent on
interelectrode capacitance from input to output
(Cf) and the gain (Av).
29
Miller Output Capacitance (CMo)
It can be calculated
Formula 9.43 If the gain (Av) is
considerably greater than 1

Formula 9.44
30
High-Frequency Response BJT Amplifiers
Capacitances that will affect the high-frequency
response Cbe, Cbc, Cce internal
capacitances Cwi, Cwo wiring
capacitances CS, CC coupling
capacitors CE bypass capacitor
31
High-Frequency Response BJT Amplifiers
High-frequency ac equivalent model for the network
32
High-Frequency Response BJT Amplifiers

• Thevenin equivalent circuit for the input
  circuits.
• Thevenin equivalent circuits for the output
  circuits.

33
High-Frequency Cutoff
Cut-off frequency for input circuits
Cut-off frequency for output circuits
34
Total Amplifier Frequency Response

• fL produce by coupling bypass capacitor at
  low frequency.
• fH produce by interelectrode capacitance at
  high frequency
• Dominant frequencies are referred to as the lower
  critical frequency fL and the upper critical
  frequency fH
• fH and fL are sometimes called the half-power
  frequencies.

35
Example

• Use the network for high frequency response with
  the parameters as given
• Cs 10µF, CE 20µF, Cc 1µF
• Rs 1KO, R1 40KO, R2 10KO,
• RE 2kO, Rc 4kO, RL 2.2KO,
• ß 100, r0 8O, Vcc 20V
• Cbe 36 pF, Cbc 4 pF, Cce 1 pF, Cwi 6 pF,
  Cwo 8 pF
• Determine fHi and fHo
• Sketch the high-frequency response using bode
  plot.

36
Full frequency response for the BJT amplifier
network
37
Multistage Frequency Effects

• When amplifier stages are cascaded to form a
  multistage amplifier, the dominant frequency
  response is determined by the responses of the
  individual stages. There are two cases to
  consider
• Each stage has a different lower critical
  frequency and a different upper critical
  frequency.
• Each stage has the same lower critical frequency
  and the same upper critical frequency.
• Different critical frequencies
• When the lower critical frequency, fL of each
  amplifier stage is different, the dominant lower
  critical frequency fLequals the critical
  frequency of the stage with the highest fL.
• When the upper critical frequency fH, of each
  amplifier stage is different, the dominant upper
  critical frequency fH equals the critical
  frequency of the stage with the lowest fH.
• Overal Band Width BW fH-fL

38
Multistage Frequency Effects

• Equal Critical Frequencies
• When each amplifier stage in a multistage
  arrangement has equal critical frequencies, the
  dominant lower critical frequency is increased by
  a factor of 12
• When the upper critical frequencies of each stage
  are all the same, the dominant upper critical
  frequency is reduced by a factor of
• n is the number of stages in the multistage
  amplifier.

39
Total Frequency Response of a Multistage Amplifier
Once the cutoff frequencies have been determined
for each stage (taking into account the shared
capacitances), they can be plotted.
Again note the highest Lower
Cutoff Frequency (fL) and the
lowest Upper Cutoff Frequency (fH) are
closest to the actual response of the amplifier.