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Sem I 0809/rosdiyana
Chapter 7:Chapter 7:Chapter 7:Chapter 7:
BJTBJT
Frequency ResponseFrequency Response
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
alog x,ba
:function clogarithmi a of variablesebetween th iprelationsh
bx
alog x:logarithmCommon 10
alogy : logarithm Natural e
a2.3logalog 10e
The two are related by:
Formula 9.1
Formula 9.2
Formula 9.3
Formula 9.4
blogalogablog
blogb
1log
blogalogb
alog
01log
101010
1010
101010
10
Formula 9.5
Formula 9.6
Formula 9.7
Formula 9.8
Logarithms
Semilog graph paper.
Identifying the numerical values of the tic marks on a log scale.
• 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.
Semilog
Decibels
ndBdBdBdBdB
1
210dB
600Ω
210dBm
1
210dB
1
210
G........GGGG
(dB) V
V20logG
1mW
P10logG
bel 1 dB *10*
(dB) P
P10logG
(bel) P
PlogG
321T
Formula 9.9
Formula 9.10
Formula 9.11
Formula 9.12
Formula 9.15
• 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.
Decibels
Gain versus Frequency
Low Frequency Analysis
0ΩπfC2
1XC
RC combination that will define a low-cutoff frequency.
ΩCπ(0)2
1
πfC2
1XC
RC circuit at f = 0 Hz.
RC circuit at very high frequencies.
Low-frequency response for the RC circuit
• 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 andmore of the input voltage appears across the output terminals.
Low Frequency Analysis
Low Frequency Analysis
Bode plot for the low-frequency region.
1. Determine the break frequency.
2. Plot f1 point on the log scale.
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.
RCf
2
11
Low Frequency Analysis
2
3
4
56
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
sisLs )CR(R2
1f
Determining the effect of CS on the low-frequency response.
Cutoff frequency:
Voltage Vi:si
sii RR
VRV
βre||R||RR 21i
Localized ac equivalent for CS.
Coupling Capacitor - CS
Coupling Capacitor - CC
CLoLC )CRR(2
1f
π
Cutoff frequency:
Determining the effect of CC on the low-frequency response.
oCo r||RR
Localized ac equivalent for CC with Vi = 0 V.
Coupling Capacitor - CC
Bypass Capacitor - CE
EeL CR2
1f
E π
Determining the effect of CE on the low-frequency response.
Cutoff frequency:
)rβ
R(||RR e
sEe
21ss R||R||RR
Localized ac equivalent of CE.
Bypass Capacitor - CE
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
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
-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: [Formula 9.42]
Note that the amount of Miller Capacitance is dependent on interelectrode capacitance from input to output (Cf) and the gain
(Av).
fMi CAv)(1C
Miller Output Capacitance (CMo)
It can be calculated: [Formula 9.43]
If the gain (Av) is considerably greater than 1:
[Formula 9.44]
fMo )CAv
1(1C
fMo CC
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 ac equivalent model for the network
High-Frequency Response – BJT Amplifiers
fvMi )CA(1C fv
Mo )CA
1(1C
Thevenin equivalent circuit for the input circuits.
Thevenin equivalent circuits for the output circuits.
High-Frequency Response – BJT Amplifiers
bcvbeWi
MibeWi
CACC
CCC
)1(
MoceWo CCC
High-Frequency Cutoff
iThiHi CR2
1f
π
Cut-off frequency for input circuits:
Cut-off frequency for output circuits:
oThoHo CR2
1f
π
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 fHo2. Sketch the high-frequency response using bode plot.
Full frequency response for the BJT amplifier network
• 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
• 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.
12'
1
n
LL
ff
Multistage Frequency Effects
121 n
12' 1 nHH ff
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.