Frequency Response of Amplifier
• Input signal of an amplifier can always be
expressed as the sum of sinusoidal signals.
• The amplifier performance can be
characterized by its frequency response.
1
Amplifier Transmission or
Transfer Function
2
• The figure indicates that the gain is almost constant over a wide range of
frequency range ω1 to ω2 .
• The band of frequencies over which the gain of the amplifier is within 3dB
is called the amplifier bandwidth.
• The amplifier is always designed so that its bandwidth coincides with
spectrum of the input signal (Distortion less amplification)
3
Amplifier Transfer Function
• Amplifier Types
– Direct Coupled or dc amplifier
– Capacitively Coupled or ac amplifier
• Difference
– Gain of the ac amplifier falls off at low frequencies
• Amplifier gain is constant over a wide range of
frequencies, called Mid-band
4
• Evaluate the circuit in Frequency Domain by carrying out the
circuit analysis in the usual way but with inductance and
capacitance represented by their reactances
– An inductance L has a reactance or impedance jωL and Capacitance C
has a reactance or impedance 1/jωC
• The circuit analysis to determine the frequency response can
be in complex frequency domain by using complex frequency
variable ‘s’
– An inductance L has a reactance or impedance sL and Capacitance C
has a reactance or impedance 1/sC
5
Frequency Response of DC Amplifier
Figure 6.12 Frequency response of a direct-coupled (dc) amplifier. Observe that the gain does
not fall off at low frequencies, and the midband gain AM extends down to zero frequency.
A resistively loaded MOS differential pair
It is assumed that the total impedance between node S and ground is ZSS,
consisting of a resistance RSS in parallel with a capacitance CSS.
CSS includes Cbd & Cgd of QS as well as Csb1 & Csb2.
7
Differential Half-circuit.
Frequency Response: Differential Gain
Frequency Response is the same as studied earlier
for common source amplifier.
8
Figure 6.20 High-frequency equivalent-circuit model of the common-source amplifier. For the common-emitter amplifier, the
values of Vsig and Rsig are modified to include the effects of rp and rx; Cgs is replaced by Cp, Vgs by Vp, and Cgd by Cm.
Microelectronic Circuits - Fifth
Edition Sedra/Smith
9
Figure 6.23 Analysis of the CS high-frequency equivalent circuit.
Microelectronic Circuits - Fifth
Edition Sedra/Smith
10
Figure 6.24 The CS circuit at s 5 sZ. The output voltage Vo 5 0, enabling us to determine sZ from a node equation at D.
Microelectronic Circuits - Fifth
Edition Sedra/Smith
11
Quiz # 3 (Syn A)
Determine the
short circuit
transconductance
(Gm) of the given
circuit.
Quiz # 3 (Syn B)
Determine the
short circuit
transconductance
(Gm) of the given
circuit.
Common-mode half-circuit.
14
Common-mode half-circuit.
Acm 
Acm
RD RD
2 RSS RD


RSS

Z SS  RSS || CSS  
 1  sCSS RSS 
R RD
R RD
1  sCSS RSS 
 D
 D
2Z SS RD
2 RSS RD
Acm has a zero on the negative real-axis
of the s-plan with frequency ωz
z 
1
1
 f z 
RSS CSS
2pRSS CSS
15
Figure 7.37 Variation of (a) common-mode gain, (b) differential gain, and (c)
common-mode rejection ratio with frequency.
Acm 
RD
R
 D 1  sCSS RSS 
2Z SS 2RSS
16
Figure 7.37 Variation of (a) common-mode gain, (b) differential gain, and (c)
common-mode rejection ratio with frequency.
Acm 
RD
R
 D 1  sCSS RSS 
2Z SS 2RSS
17
Figure 7.38 The second stage in a differential amplifier is relied on to suppress
high-frequency noise injected by the power supply of the first stage, and therefore
must maintain a high CMRR at higher frequencies.
18
Exercise 7.15
Figure 6.22 Application of the open-circuit time-constants method to the CS equivalent circuit of Fig. 6.20.
Microelectronic Circuits - Fifth
Edition Sedra/Smith
20
Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential
amplifier.
Cm  Cgd1  Cdb1  Cdb3  Cgs 3  Cgs 4
CL  Cgd 2  Cdb 2  Cgb 4  Cdb3  Cx
21
Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential
amplifier.
Cm  Cgd1  Cdb1  Cdb3  Cgs 3  Cgs 4
CL  Cgd 2  Cdb 2  Cgb 4  Cdb3  Cx
22
Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential
amplifier.
Vg 3
gm
vid
2

g m3  sCm
I d 4   g m 4Vg 3 
gm4 gm
vid
2 
g m3  sC m
I0  Id 4  Id 2 
gm
vid
gm
Rout  r02 || r04 ||
vid
2
C
1 s m
g m3
2  g vid
m
2
Cm
1 s
g m3
Ro
1
1
 Rout  R0 ||

sC L
sCL 1  sRoCL

1
vid 
V0  g m Ro
2
C
1 s m

g m3


1

 1  sRoCL

Cm

1

s


2 g m3
1
 
Ad  g m Ro 
 1  sRoC L   1  s Cm

g m3





23
Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential
amplifier. (b) The overall transconductance Gm as a function of frequency.
Cm  Cgd1  Cdb1  Cdb3  Cgs 3  Cgs 4
CL  Cgd 2  Cdb 2  Cgb 4  Cdb3  Cx
Neglect r01 & r02
Vg 3 
I d 4   g m 4Vg 3 
gm
vid
2
g m3  sCm
gm4 gm
vid
2 
g m3  sC m
I 0  I d 4  I d 24 
gm
gm
vid
2
C
1 s m
g m3
vid
2  g vid
m
2
Cm
1 s
g m3
25
Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential
amplifier. (b) The overall transconductance Gm as a function of frequency.
I0 
Rout  r02 || r04 ||
gm
vid
2  g vid
m
2
Cm
1 s
g m3
Ro
1
1
 Rout  R0 ||

sC L
sCL 1  sRoCL

1
vid 
V0  g m Ro
2
C
1 s m

g m3


1

 1  sRoCL

Cm

1

s


2 g m3
1

 
Ad  g m Ro 
 1  sRoC L   1  s Cm

g m3





26
Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential
amplifier. (b) The overall transconductance Gm as a function of frequency.
Cm

1

s


2 g m3
1

 
Ad  g m Ro 
 1  sRoC L   1  s Cm

g m3





Midband Gain  gm Ro
f p1 
1
 Dominanatpoledue to large value of CL
2pRoCL
f p2 
g m3
2pCm
fz 
2 g m3
2pCm
The zero frequency (fz) is twice that of the pole (fp2)
27
Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential
amplifier. (b) The overall transconductance Gm as a function of frequency.
Midband Gain  gm Ro
f p1
1

2pRoC L
f p2
g m3

2pCm
2 g m3
fz 
2pCm
28
Assignment # 4
• Carry out detailed frequency response analysis
of the current-mirror-loaded MOS differential
pair circuit.
• Due date: 2 Dec 2011