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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.

2

Amplifier Transmission or Transfer Function

3

• 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)

4

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

5

• 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

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.

7

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.

8

Differential Half-circuit.

Frequency Response: Differential Gain

Frequency Response is the same as studied earlier for common source amplifier.

Microelectronic Circuits - Fifth Edition Sedra/Smith

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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

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Figure 6.23 Analysis of the CS high-frequency equivalent circuit.

Microelectronic Circuits - Fifth Edition Sedra/Smith

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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.

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.

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Common-mode half-circuit.

15

Common-mode half-circuit.

D

D

SS

Dcm R

R

R

RA

2

SSSSD

D

SS

D

D

D

SS

Dcm RsC

R

R

R

R

R

R

Z

RA

1

22

SSSS

SSSSSSSS RsC

RCRZ

1||

Acm has a zero on the negative real-axis of the s-plan with frequency ωz

SSSSz

SSSSz CR

fCR

2

11

16

Figure 7.37 Variation of (a) common-mode gain, (b) differential gain, and (c) common-mode rejection ratio with frequency.

SSSSSS

D

SS

Dcm RsC

R

R

Z

RA 1

22

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Figure 7.37 Variation of (a) common-mode gain, (b) differential gain, and (c) common-mode rejection ratio with frequency.

SSSSSS

D

SS

Dcm RsC

R

R

Z

RA 1

22

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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.

Exercise 7.15

Microelectronic Circuits - Fifth Edition Sedra/Smith

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Figure 6.22 Application of the open-circuit time-constants method to the CS equivalent circuit of Fig. 6.20.

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Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential amplifier.

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22

Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential amplifier.

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Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential amplifier.

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idm

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2

3

3

4

344

1

22

m

m

idm

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idmm

gmd

gCs

vg

sCg

vggVgI

21

2

3

240id

m

m

m

idm

ddvg

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Lo

o

Lout

Lout CsR

R

sCRR

sCrrR

1

1||

1|||| 00402

Lo

m

m

idom CsR

gCs

vRgV

1

1

1

12

3

0

3

3

1

21

1

1

m

m

m

m

Loomd

gCs

gC

s

CsRRgA

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.

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0201 & rrNeglect

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idm

g sCg

vgV

33

2

3

3

4

344

1

22

m

m

idm

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idmm

gmd

gCs

vg

sCg

vggVgI

21

2

3

2440id

m

m

m

idm

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Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential amplifier. (b) The overall transconductance Gm as a function of frequency.

Lo

o

Lout

Lout CsR

R

sCRR

sCrrR

1

1||

1|||| 00402

21

2

3

0id

m

m

m

idm vg

gCs

vgI

Lo

m

m

idom CsR

gCs

vRgV

1

1

1

12

3

0

3

3

1

21

1

1

m

m

m

m

Loomd

gCs

gC

s

CsRRgA

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Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential amplifier. (b) The overall transconductance Gm as a function of frequency.

3

3

1

21

1

1

m

m

m

m

Loomd

gCs

gC

s

CsRRgA

L1 C of valuelarge todue poleDominanat 2

1

Lop CRf

omRgGainMidband

m

mp C

gf

23

2

m

mz C

gf

2

2 3

The zero frequency (fz) is twice that of the pole (fp2)

28

Figure 7.39 (a) Frequency-response analysis of the active-loaded MOS differential amplifier. (b) The overall transconductance Gm as a function of frequency.

Lop CRf

2

11

omRgGainMidband

m

mp C

gf

23

2

m

mz C

gf

2

2 3

Assignment # 4

• Carry out detailed frequency response analysis of the current-mirror-loaded MOS differential pair circuit.

• Due date: 2 Dec 2011