전자회로전자회로Ch9 Cascode Stages and Current Mirrors

김 영 석

충북대학교 전자정보대학

2012.3.1

E il ki @ b kEmail: kimys@cbu.ac.kr

Ch9-1

Ch9 Cascode Stages and Current Mirrors

9.1 Cascode Stages

9.2 Current Mirrors

Ch9-2

9.1 Cascode Stage9.1.1 Cascode as a Current Source: Boosted Output Impedances

[ ] EOmOout rRrgrR ++= )||(11 π

( ) SOmOout RrgrR ++= 12

Ch9-3

Bipolar Cascode Stage

)||](1[ rrrgrR ++=( )1211

1211

|| )||](1[

π

π

rrrgrrrgrR

OOm

OOmOout

≈++=

Ch9-4

PNP Cascode Stage

12111 )||](1[ rrrgrR OOOt ++=( )1211

12111

|| )||](1[

π

π

rrrgrrrgrR

OOm

OOmOout

≈++=

Ch9-5

MOS Cascode Stage

( ) 2111 1 OOmOout rrgrR ++=

211 OOm rrg≈

Ch9-6

9.1.2 Cascode as an Amplifier: Short-Circuit Transconductance and Voltage Gain

= outm v

iG0=outvinv

outinmoutoutout

RGvvRvGRiv

−=−=−=

The short-circuit transconductance of a circuit measures its strength in converting input voltage to output current.

outminout RGvv −=

strength in converting input voltage to output current.

By representing a linear circuit with its Norton equivalent, the relationship between Vout and Vin can be expressed by the

d t f G d R

Ch9-7

product of Gm and Rout.

Bipolar Cascode Amplifier

G)]||([ 21221

1

πrrrggAgG

OOmmv

mm

−≈≈

Since rO is much larger than 1/gm, most of IC,Q1 flows into the diode-connected Q2. Using Rout as before, AV is easily

2

Ch9-8

calculated.

Alternate View of Cascode Amplifier

A bipolar cascode amplifier is also a CE stage in series with a CB stage.

Ch9-9

Practical Cascode Stage

321223 )]||([|| OOOmOout rrrrgrR ≈≈ π

Since no current source can be ideal, the output impedance drops.

Ch9-10

Improved Cascode Stage

)||(||)||( 21223433 ππ rrrgrrrgR OOmOOmout ≈

In order to preserve the high output impedance a cascodeIn order to preserve the high output impedance, a cascode PNP current source is used.

Ch9-11

CMOS Cascode Amplifier

RGA −=[ ]21221 )1( OOOmmv

outmv

rrrggARGA

++−≈−=

2211 OmOmv rgrgA −≈

Ch9-12

Improved MOS Cascode Amplifier

OOmon rrgR 122≈

OOmop

OOmon

rrgRg

433

122

≈

oponout RRR ||=

Similar to its bipolar counterpart, the output impedance of a MOS cascode amplifier can be improved by using a

Ch9-13

PMOS cascode current source.

9.2 Current Mirrors: Why? Temperature and Supply Dependence of Bias Current

1212 )ln()( =+ STCC IIVRRVR2

21

1212

21

)ln()(

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=

+

THDDoxn

STCC

VVRR

RLWCI

IIVRRVR

μ

Since VT, IS, μn, and VTH all depend on temperature, I1 for

212 ⎟⎠

⎜⎝ + RRL

Ch9-14

T S n TH 1 both bipolar and MOS depends on temperature and supply.

Concept of Current Mirror

To solve for the problem, 1) Temperature-Independent Voltages and Currents are generated by “Bandgap Reference Circuit”Circuit”

2) Sense the current from a “golden current source (Temp-Independent)” and duplicate this “golden current” to other

Ch9-15

locations.

9.2.2 Bipolar Current Mirror

S III 1= REFREFS

copy II

I,

=

The diode-connected QREF produces an output voltage V1 that forces Icopy1 = IREF, if Q1 = QREF.

Ch9-16

Multiple Copies of IREF and Current Scaling

jSI IIREF

REFS

jSjcopy I

II

I,

,, = REFjcopy nII =,

Multiple copies of IREF can be generated at different locations by simply applying the idea of current mirror to more transistorsmore transistors.

By scaling the emitter area of Qj n times with respect to QREF, Icopy,j is also n times larger than IREF. This is equivalent to placing n unit size transistors in parallel

Ch9-17

to placing n unit-size transistors in parallel.

Mirroring Error Due to Base Currents

=nII REF

( )111 ++=

nIcopy

βCh9-18

β

Improved Mirroring Accuracy

nII REF

( )111 2 ++=

nI REF

copy

ββ

Because of QF, the base currents of QREF and Q1 are mostly supplied by Q rather than I Mirroring error is reduced βsupplied by QF rather than IREF. Mirroring error is reduced βtimes.

Ch9-19

MOS Current Mirror

The same concept of current mirror can be applied to MOS transistors as well.

Ch9-20

Example: Current Scaling

Similar to their bipolar counterpart, MOS current mirrors can also scale IREF up or down (I1 = 0.2mA, I2 = 0.5mA).

Ch9-21

CMOS Current Mirror

The idea of combining NMOS and PMOS to produce CMOS

Ch9-22

g p current mirror is shown above.