Chapter

Chapter 7:
7:
BJT
Frequency Response

Sem I 0809/rosdiyana
 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
 Logarithms
relationship between the variables of a logarithmic function :
a  bx , x  log b a Formula 9.1

Common logarithm : x  log10 a Formula 9.2

Natural logarithm : y  log e a Formula 9.3

The two are related by:

log e a  2.3log10 a Formula 9.4

 Logarithms

log101  0 Formula 9.5

a
log10  log10 a  log10 b Formula 9.6
b

1
log10  log10 b Formula 9.7
b

log10ab  log10a  log10 b Formula 9.8

Semilog graph paper.
Identifying the numerical values of the tic marks on a log scale.
 Semilog

• Vertical scale- linear scale with equal divisions

• The distance from log10 1=0 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.
 Decibels
P2 Formula 9.9
G  log10 (bel)
P1

P2
G dB  10log10 (dB)
P1 Formula 9.10
* *10 dB  1 bel

P2 Formula 9.11
G dBm  10log10
1mW 600Ω

V2 Formula 9.12
G dB  20log10 (dB)
V1

Formula 9.15
G dBT  G dB 1  G dB2  G dB 3  ........  G dB n
 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.
Gain versus Frequency
 Low Frequency Analysis

RC combination that will define a low-cutoff frequency.

RC circuit at very high frequencies.

1
XC   0Ω
2 πfC

RC circuit at f = 0 Hz.

1 1
XC    Ω
2 πfC 2 π(0) C
 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

Low Frequency Analysis

Bode plot for the low-frequency region.

 Low Frequency Analysis
1. Determine the break frequency. f  1
1
2. Plot f1 point on the log scale. 2RC
3. Draw straight-line segment (slope) from f1 point to -20dB at linear scale.
4. In the same figure, draw straight-line for the condition of 0dB.
5. When f= f1 , there is a 3dB drop from the mid-band level. Plot this point.
6. Find the 3dB point corresponding to f1 and sketch the curve.

2 4

6 5
 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.
 Coupling Capacitor - CS

Determining the effect of CS on the low-frequency response.

1
Cutoff frequency: f Ls 
2 (R s  R i )Cs

R i Vs
Voltage Vi: Vi 
Ri  Rs
Coupling Capacitor - CS

Localized ac equivalent for CS.

R i  R 1 || R 2 || βre
 Coupling Capacitor - CC

Determining the effect of CC on the low-frequency response.

1
Cutoff frequency: f LC 
2π (R o  R L )CC
Coupling Capacitor - CC

Localized ac equivalent for CC with Vi = 0 V.

R o  R C || ro
 Bypass Capacitor - CE

Determining the effect of CE on the low-frequency response.

1
Cutoff frequency: f LE 
2πReC E
Bypass Capacitor - CE

Localized ac equivalent of CE.

R s
Re  RE || (  re)
β

R s  R s || R 1 || R 2
 Example
a. Determine the lower cutoff freq. for the network of
Fig. 1 using the following parameters:
Cs = 10μF, CE = 20μF, Cc = 1μF
Rs = 1KΩ, R1= 40KΩ, R2 = 10KΩ,
RE = 2kΩ, Rc = 4kΩ, RL = 2.2KΩ,
β = 100, r0 = ∞Ω, Vcc = 20V

b. Sketch the frequency response using a Bode plot

 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).
 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.

 -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.
 -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.
 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.
 Miller Input Capacitance (CMi)

It can be calculated: C Mi  (1  Av) C f [Formula 9.42]

Note that the amount of Miller Capacitance is dependent on

interelectrode capacitance from input to output (C f) and the gain
(Av).
 Miller Output Capacitance (CMo)

1
It can be calculated: CMo  (1  )Cf [Formula 9.43]
Av
If the gain (Av) is considerably greater than 1:

CMo  Cf [Formula 9.44]

 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
High-Frequency Response – BJT Amplifiers

High-frequency ac equivalent model for the network

1
C Mi  (1  A v )C f C Mo  (1  )C f
Av
 High-Frequency Response – BJT Amplifiers
Thevenin equivalent circuit for the input circuits.

 CWi  Cbe  CMi

 CWi  Cbe  (1  Av )Cbc

Thevenin equivalent circuits for the output circuits.

 CWo  Cce  CMo

 High-Frequency Cutoff

Cut-off frequency for input circuits:

1
f Hi 
2πR Thi Ci

Cut-off frequency for output circuits:

1
f Ho 
2πR Tho C o
 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.
Example
• Use the network for high frequency response with the
parameters as given
Cs = 10μF, CE = 20μF, Cc = 1μF
Rs = 1KΩ, R1= 40KΩ, R2 = 10KΩ,
RE = 2kΩ, Rc = 4kΩ, RL = 2.2KΩ,
β = 100, r0 = ∞Ω, Vcc = 20V
Cbe = 36 pF, Cbc = 4 pF, Cce = 1 pF, Cwi = 6 pF, Cwo = 8
pF
1. Determine fHi and fHo
2. Sketch the high-frequency response using bode plot.
Full frequency response for the BJT amplifier network
 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:
1. Each stage has a different lower critical frequency and a
different upper critical frequency.
2. 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 f’Lequals 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 f’H equals the
critical frequency of the stage with the lowest fH.
– Overal Band Width : BW= fH-fL
 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 1:2
fL
f 'L 
21 n  1
• When the upper critical frequencies of each stage are all the same, the
dominant upper critical frequency is reduced by a factor of 2  1
1n

f ' H  f H 21 n  1

• * n – is the number of stages in the multistage amplifier.

 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.