Electronic Devices and Electronic Devices and

CircuitsCircuits

Frequency responseFrequency response

Cascode amplifiersCascode amplifiers

2/14

medium frequency :– coupling capacitors coupling capacitors →→ shortshort--circuitscircuits

–– internal parasitic capacitances internal parasitic capacitances →→ openopen--circuitscircuits

low frequency:- coupling capacitors coupling capacitors →→ equivalent impedancesequivalent impedances

-- internal parasitic capacitances internal parasitic capacitances →→ openopen--circuitscircuits

high frequency : - coupling capacitors coupling capacitors →→ shortshort--circuitscircuits

-- internal parasitic capacitances internal parasitic capacitances →→ equivalent impedancesequivalent impedances

• must be taken inmust be taken intoto considerationconsideration::- output resistance of the signal sourceoutput resistance of the signal source

-- load resistanceload resistance

Frequency response of the CS and CE amplifiers

3/14

PS

( )( )ω

ωω

jv

jvjA

i

ov =)(

CS amplifier

vo(jω)=Fo(jω)⋅id(jω);

id(jω)=Fs(jω)⋅vg(jω);

vg(jω)=Fi(jω)⋅vi(jω);

( ) ( ) ( )ωωω jFjFjFA osiv ⋅⋅=

Analysis in the low-frequency range

4/14

( )( )( ) ( ) i

i

i

g

iCRRj

CRj

jv

jvjF

G

G

++==

ω

ω

ω

ωω

1

( ) ( ) CiiCi

LiCRRCRR

fG

+=

+=

ππ 2

1

2

1

HPF, introduces a pole at

the frequency of the pole:CCi multiplied by the total resistance seen by CCi

( )( )( )ω

ωω

jv

jijF

g

ds =

SS

m

Ls

CRg

f

=

||1

2

1

π

( )( )( )ω

ωω

ji

jvjF

d

oo =

( ) ( ) CoLoCoLD

LoCRRCRR

f+

=+

=ππ 2

1

2

1

• the dominant pole: the greater break frequency between fLi, fLs, fLo if the nearest pole or zero will be at least a decade away.

• usally given by fLs, for equal coupling capacitances

5/14

Analysis in the high-frequency range

CCgdgd is reflected to the input according to

MillerMiller’’s theorems theorem ( ) gdLmgsi CRgCC '1++=

( )( )( ) ( ) iG

Lm

G

G

i

ov

CRRjRg

RR

R

jv

jvjA

||1

1'

ωω

ωω

+⋅⋅

+−==

Lm

G

Gvo Rg

RR

RA '⋅

+−=

( ) ( ) iiiG

HCRRCRR

f||2

1

||2

1

ππ==

Cds is not shown here because it generates a pole at a much higher frequency that the one generated by Cgs

and Cgd

6/14

Numerical example

CCi=CCo=Cs=10µF, R=20KΩ, RG=2MΩ, RD=10kΩ, RL=20kΩ,

Rs=10KΩ, I=400µA.

K=100µA/V2, (W/L)=18, VA=100V. Cgs=Cgd= 1pF @ I=400µA

mS2.1=mgSolution: KΩ250=or

( )mHz8

1010102000202

163

≅⋅⋅+

=−π

Lif

Hz21

10101010||2.1

12

1

63

≅

⋅⋅

=

−πLsf

( )Hz5.0

10101020102

163

≅⋅⋅+

=−π

Lof

fL=21Hz

The output resistance of the signal source R does not affect fLi but affects fH

7/14

( )[ ] ( )[ ] pF8.9120||10||2502.111||||1 ≅⋅++=++= gdLDomgsi CRRrgCC

( )KHz820

108.9102000||202

1123

=⋅⋅⋅

=−π

Hf

7.17)7.7log(20dB

==voA

7.75.62.1202.0

2−=⋅⋅

+−=voA

8/14

The effect of each capacitor is found considering the othertwo capacitors with infinite capacity (zero equivalent impedance)

CE amplifier

Analysis in the low-frequency range

CibeB

LiCrRR

f)||(π2

1

+=

;π2

1

EE

LeCR

f′

=

1

||||

+

+=′

β

RRrRR Bbe

EE

CoLC

LoCRR

f)(π2

1

+=

21 || BBB RRR =

9/14

Analysis in the high-frequency range

bcLmbei CRgCC )1( ′++=

ii

LCm

beB

beBv

CRRRg

rRR

rRA

′++=

ωω

j1

1)||(

||

||)j(

RRrR Bbei ||||=′

iBbe

HCRRr

f)||||π(2

1=)||(

||

||LCm

beB

beBvo RRg

rRR

rRA

+=

10/13

Cascode amplifiers

for the CS and CE amplifiers the absolute value of the gain and the bandwidth in inverse ratio due to Miller’s effect

when the gain increases, the parasitic capacitance reflected to the input also increases so the high cutoff frequency decreases

a technique to build wideband amplifiers

to reduce the multiplication effect of the parasitic capacitanceit is often use the cascodecascode configurationconfiguration::

- connection of a CS (CE) amplifier followed by aCG (CB) amplifier

Lm

G

Gvo Rg

RR

RA '

+−=

( ) )'1)(||||π(2

1

gdLmgsBbe

HCRgCRRr

f++

=

11/14

The cascode configuration with MOSFET

−==

2

211

1

1||

m

om

i

ov

grg

v

vA

1

2

1o

m

rg

<< same current through T1, T2

medium frequency

21 mmm ggg == 11 −≅vA

CG

DmDm

o

ov RgRg

v

vA =≈= 22

1

21 vvv AAA ⋅=

Dmv RgA −=

GGGi RRRR == 21 ||

DoomooDo RrrgrrRR ≈++= )(|| 21221

CS

12/14

High frequency

11111 2)1( gdgsgdvgsi CCCACC +=−+=

The multiplication factor of Cgd1 is 2, considerable smaller that the one in CS configuration . The value for Ci results much more reduced, that leads to a much higher value of the high cutoff frequency:

)1( 2Rgm′+

iG

HCRR

f)||(π2

1=

the other two poles due to Cgs2 and Cgd2 results to considerable higher frequency than fH

CCii introduces the dominant pole at high frequency and determines introduces the dominant pole at high frequency and determines the passthe pass--band of the amplifierband of the amplifier

13/14

Numerical illustration

MΩ421 == GG RR Ω= K10DR

µA400=I

KΩ20=R KΩ20=LR

18)/( =LW V100=AV

2V

µA100=K

pF1== gdgs CC

mS 1,2µS 12004001810022 ==⋅⋅⋅== IL

WKgm

Ω=== M 24||4|| 21 GGG RRR

[ ] 9,7)20||10(2,1200020

20)||( −=⋅⋅

+−=−

+= LDm

G

v RRgRR

RA

pF 31212 =⋅+=+= gdgsi CCC

MHz 7,210310)2000||20(2

1

)||(2

1123

≅⋅⋅⋅

==−ππ iG

HCRR

f

14/14

The cascode configuration with BJT

)||(1

||

||2

2

1

1

1LCm

m

m

beB

beB

i

ov RRg

gg

rRR

rR

v

vA

−

+==

21 || BBB RRR =

21 bebebe rrr ==

21 mmm ggg ==

)||(||

||LCm

beB

beBv RRg

rRR

rRA

+−=

)2)(||||(2

1

bcbeBbe

HCCRRr

f+

=π

For identical T1 and T2 transistors