Transcript Slide 1 - UniMAP Portal

DMT 231/3 Electronic II
Lecture V
Low Frequency Response of
BJT Amplifiers
Effect of Coupling Capacitors
mid-band frequencies:
coupling & bypass capacitors
 shorts to ac
low frequencies:
capacitive reactance affect the gain & phase
shift of signals
 must be taken into account
FREQUENCY RESPONSE :
the change in gain or phase shift
over a specified range of input
signal frequencies
Effect of Coupling Capacitors
1
XC 
2fC
 capacitive reactance varies
inversely with frequency
Effect of Coupling Capacitors: Example
Figure 1
Effect of Coupling Capacitors:
Example
• At low freq (audio freq: 10 Hz)
 less voltage gain (then they have at
higher freq): Figure 1
More signal voltage is dropped across C1
& C3 (higher reactances : reduce voltage
gain)
Reactance of C2 becomes significant & the
emitter is no longer at ac ground.
Nonzero reactance of the bypass capacitor in parallel with RE
creates an emitter impedance, (Ze), which reduces the voltage
gain.
Figure 2
Effect of Internal Transistor
Capacitances
Internal transistor capacitances
reduce amplifier gain & introduce
phase shift as the signal frequency
increases
Cbe: base-emitter junction capacitance
Cbc: base-collector junction capacitance
Figure 3
AC equivalent circuit for a BJT amplifier showing effects of the internal
capacitances Cbe and Cbc.
Figure 4
Miller’s Theorem
General case of Miller input and output capacitances. C represents Cbc
Figure 5
Amplifier ac equivalent circuits showing internal capacitances and
effective Miller capacitances.
Figure 6
Decibel
• Logarithmic measurement of the ratio of
one power to another OR one voltage to
another
Ap(dB) = 10 log Ap
Ap = Pout / Pin
Av(dB) = 20 log Av
Av = Vout / Vin
O dB Reference
• Reference gain (no matter what its actual
value is)
 used as a reference with which compare
other values of gain
Midrange gain
• Maximum gain occurs for the range of freq
between the upper & lower critical freq
Normalized
• Midrange voltage gain is assigned a value
of 1 or 0 dB.
Normalized voltage gain versus frequency curve.
Figure 7
Critical Frequency
• Also known as cutoff frequency OR corner
frequency
Frequency at which the output drops to
one-half of its midrange value.
Corresponds to a 3 dB reduction in the
power gain:
Ap(dB) = 10 log (0.5) = - 3 dB
Power Measurement in dBm
• dBm : unit for measuring power levels
referenced to 1 mW
Low Frequency Amplifier Response
A capacitively coupled
amplifier
Figure 8
The low-frequency ac equivalent circuit of the amplifier consists of three
high-pass RC circuits.
Figure 9
Input RC circuit formed by the input coupling capacitor and the
amplifier’s input resistance.
Figure 10
Input RC Circuit
The base voltage for the input
RC circuit:


R
in
V
Vbase  
 R 2  X 2  in
in
C1 

when
Vbase

Rin


 R2  R2
in
in

X C1  Rin

 R
in
V  
 in  2 R 2
in



V   1 V  0.707V
in
 in  2  in

Lower critical frequency
Condition where the gain is down 3 dB: overall
gain is 3 dB less than at midrange freq
 a.k.a lower cutoff freq, lower corner freq, or
lower break freq.
X C1 
1
2f cl (input) C1
f cl (input)
Taking into account the
input source resistance
f cl ( input)
 Rin
1

2Rin C1
1

2 RS  Rin C1
Bode Plot
Decade: ten times change
in frequency
Bode Plot: a plot of dB
voltage gain versus
frequency on semilog
graph paper
Figure 11
dB voltage gain versus frequency for the input RC circuit
Phase angle versus frequency for the input RC circuit.
  tan
Phase angle in an input RC circuit
For midrange frequencies
At critical frequency
 X C1

 R
 in
X C1  0
X C1  Rin
 Rin 
  tan    45
 Rin 
X C1  10 Rin




 0 
  0
 Rin 
  tan 1 
At a decade below the critical frequency
Figure 12
1
1
 10 Rin 
  84.3
 Rin 
  tan 1 
The input RC circuit causes the base voltage to lead the input voltage
below midrange by an amount equal to the circuit phase angle, .
Figure 13
Development of the equivalent low-frequency output RC circuit.
Output RC Circuit
f cl ( output)
1

2 RC  R L C 3
 X C3
  tan 
 RC  RL
Phase Shift in
Output RC Circuit
1
Figure 14



At low frequencies, XC2 in parallel with RE creates an impedance that
reduces the voltage gain.
Figure 15
Development of the equivalent bypass RC circuit.
Figure 16
Total Low Frequency Response of Amplifier
Composite Bode plot of a BJT amplifier response for three lowfrequency RC circuits with different critical frequencies. Total response
is shown by the blue curve.
Figure 17
Composite Bode plot of an amplifier response where all RC circuits have
the same fc. (Blue is ideal; red is actual.)
Figure 18
High Frequency Response of
BJT Amplifiers
Coupling & bypass capacitors: effective shorts
Internal capacitance: significant ONLY at high
frequencies
Capacitively coupled amplifier and its high-frequency equivalent circuit.
Figure 19
High-frequency equivalent circuit after applying Miller’s theorem.
C in( Miller)  C bc  Av  1
Cout( Miller)
 Av  1 

 Cbc 
 Av 
Figure 20
Development of the equivalent high-frequency input RC circuit.
X Ctot  RS // R1 // R2 //  ac re'
1
2f cu (input) Ctot
f cu ( input) 
 RS // R1 // R2 //  ac re'
1
2 ( RS // R1 // R2 //  ac re' )C tot
Figure 21
Example: Derive the equivalent high-frequency input RC circuit for the
BJT Amplifier in Figure 22
Figure 22
Development of the equivalent high-frequency output RC circuit.
Figure 24
High-frequency Bode plots.
Figure 26
A BJT amplifier and its generalized ideal response curve (Bode plot).
Figure 27