mixer - ucsb · 2016-03-27 · mixers: switching operation s rf (w rf) 1 1 s out lo input s ... dc...

Mixer

©James Buckwalter

Mixer References• “Noise in RF-CMOS Mixers: A Simple Physical Model” by Darabi and Abidi, IEEE

Transactions on Solid-State Circuits, Vol. 35, No. 1, 2000.

• “Noise in Current-Commuting CMOS Mixers” by Terrovitis and Meyer, IEEE Journal of Solid-State Circuits, Vol. 34, No. 6, 1999.

• “Behavioral Models for Noise in Bipolar and MOSFET Mixers” by Hu and Mayaram, IEEE Transactions on Circuits and Systems II, Vol. 46, No. 10, 1999.

• “A Class AB Monolithic Mixer for 900MHz Applications” by Fong and et al, IEEE Journal of Solid-State Circuits, Vol. 32, No. 8, 1997.

• “Monolithic RF Active Mixer Design” by Fong and Meyer, IEEE Transactions on Circuits and Systems II, Vol. 46, No. 3, 1999.

• “A 12mW Wide Dynamic Range CMOS FrontEnd for a Portable GPS Receiver” by Shahani et al, IEEE Journal of Solid-State Circuits, Vol. , No. 12, 1997.

• “A Parallel Structure for CMOS Four-Quadrant Analog Multipliers and Its Application to a 2GHz Down-conversion Mixer” by Hsiao and Wu.

• “A Low Voltage Bulk Driven Down-conversion Mixer Core” by Kathiresan and Toumazou, 1999.

• “Low Voltage Mixer Biasing Using Monolithic Integrated Transformer De-coupling” by MacEachern and et.al, 1999.

©James Buckwalter

References• “A Charge-Injection Method for Gilbert Cell Biasing” by MacEachern and Manku,

1998.

• “Doubly Balanced Dual-Gate CMOS Mixer” by Sullivan and et al, IEEE Journal of Solid-State Circuits, Vol. 34, No. 6, 1999.

• “A 1.5GHz Highly Linear CMOS Down conversion Mixer” by Crols and Steyaert, IEEE Journal of Solid-State Circuits, Vol. 30, No. 7, 1995.

• “Micro-power CMOS RF Components for distributed wireless sensors” by Lin and et al, IEEE Radio Frequency Integrated Circuits Symposium, 1998.

• “A Zero DC-Power Low Distortion Mixer for Wireless Applications” by Kucera and Lott, IEEE Microwave and Guided Wave Letters, Vol. 9, No. 4, 1999.

• “A 900MHz/1.8GHz CMOS Receiver for Dual-Band Applications” by Wu and Razavi, IEEE Journal of Solid-State Circuits, Vol. 33, No. 12, 1998.

• “The MICROMIXER: A Highly Linear Variant of the Gilbert Mixer Using a BiSymmetric Class-AB Input Stage” by Gilbert, IEEE Journal of Solid-State Circuits, Vol. 32, No. 9, 1997.

• “A 2V, 1.9GHz Si Down-Conversion Mixer with an LC Phase Shifter” by Komurasaki and et al, IEEE Journal of Solid-State Circuits, Vol. 33, No. 5, 1998.

©James Buckwalter

References• “A Low Distortion Bipolar Mixer for Low Voltage Direct Up-Conversion and High IF

Systems” by Behbahani and et al, IEEE Journal of Solid-State Circuits, Vol. 32, No. 9, 1997.

• “A 2GHz Balanced Harmonic Mixer for Direct-Conversion Receivers” by Yamaji and Tanimoto, Custom Integrated Circuits Conference, 1997.

• “A Blocker-Tolerant, Noise-Cancelling Receiver Suitable for Wideband Wireless Applications,” David Murphy et al. JSSC 2012”

©James Buckwalter

Tradeoffs in RX

• Noise Figure(Sensitivity)

• Distortion (Linearity)

• Phase Noise (Aliasing)

©James Buckwalter

Review: Homodyne versus Heterodyne

• Heterodyne

• Homodyne

©James Buckwalter

rf lo if

0rf lo

Heterodyne: High-side injection

• LO is above the RF tone

• Image frequency (IM) is above the LO tone

©James Buckwalter

, , 1rf N lo N

, , 1im N lo N

Heterodyne: Low-side injection

• LO is below the RF tone

• Image frequency (IM) is below the LO tone

©James Buckwalter

, , 1rf N lo N

, , 1im N lo N

Differential Receiver

• N-path filtering translates the baseband impedance to higher frequency (more on this later)

• Impedance loads LNA and provides gain to desired band while blocking on out-of-band signals.

• Mixer is a “voltage-mode” operation. ©James Buckwalter

Gm Receiver

©James Buckwalter

• Gm cell produces an RF current to go through the mixer.

• Mixer is a “current-mode” operation.

• Avoids large voltage gain at RF and filters out-of-band at baseband.

Mixer-First Architecture

©James Buckwalter©James Buckwalter

• N-path filtering presents a high-impedance to the antenna

• Avoids linearity problems of LNA by putting mixer at front-end

• Costs is noise figure.

Mixer Noise

• How do we cascade the noise contribution of a mixer?

• For homodyne,

• For heterodyne,

©James Buckwalter

FDSB

= 1+N

added

kTDfGLNA

FSSB

= 1+G

IM - IF

GRF-IF

æ

èç

ö

ø÷ 1+

Nadded

GIM -IF

+ GRF- IF( )kTDf

æ

èç

ö

ø÷

=G

RF- IF+ G

IM -IF

GRF- IF

+N

added

GLNA

kTDf

Notes: This is the single sideband noise figure (SSB NF) and is at least 3dB.Please remember that SSB noise figure is generally 3 dB higher than double sideband (DSB) noise figure.

Pulse Waveform

• Spectral Components of LO waveform

VLO

= vLO

p t( )p t( ) = a

0+ a

kcos kw

LOt( )

k³1

å

a0

= Ad ak

=2A

kpsin kp d( )

VLO

tA

d

©James Buckwalter

LO Waveform in Mixer

• Noise factor degraded by images around harmonics.

©James Buckwalter

VLO

t( ) =Vpk

2sin npd( )np

n=1odd

¥

å cos nwLO

t( )

Pulse Waveform

• Some special cases…

• d = 1/2

• d = ¼

• d -> 0 we approach an infinite train of delta functions.

VLO

tA

d

p t( ) =

1

2+

2

pcos w

LOt( ) -

4

3pcos 3w

LOt( )+

4

5pcos 5w

LOt( ) - ...

p t( ) =

1

4+

2

pcos w

LOt( )+

2

3pcos 3w

LOt( ) -

2

5pcos 5w

LOt( ) -

2

7pcos 7w

LOt( )...

©James Buckwalter

Mixers: Switching Operation

SRF wRF( )

1

1

Sout

LO Input

Sout = SRF cos wRFt( )´ .........................................}{

1

1

Sout

= SRF

cos wRF

t( )Ä4

pcos w

LOt( ) -

4

3pcos 3w

LOt( ) +

4

5pcos 5w

LOt( ) - ...

ìíî

üýþ

SW t( )

Note that “S” is a generic signal. Could be voltage or current?

©James Buckwalter

Mixer Gain

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

sig M RFI G V

0®T

LO

2:V

out= V

cc- I

DC+ I

sig( ) RL

éë

ùû-V

cc= - I

DC+ I

sig( ) RL

TLO

2®T

LO:V

out=V

cc- V

cc- I

DC+ I

sig( ) RL

éë

ùû= I

DC+ I

sig( ) RL

Vout

= IDC

+ Isig( ) R

L´ SW t( )

1

2

TM

S

GR

©James Buckwalter

Mixer Noise Analysis• Noise analysis of a single balanced mixer:

VLO

RL RL

VLO

VRF

Vout

,DC mix RF NoiseI I I

M1

M2 M3

wLO -wRF

LO RF wLO +wRF

VOUT

t

Instantaneous Switching

©James Buckwalter

Mixer Noise Analysis• Noise analysis of a single balanced mixer cont...:

• If the switching is not instantaneous, additional noise from the switching pair will be added to the mixer output.

• Let us examine this in more detail.

VLO

RL RL

VLO

VRF

Vout


M1

M2 M3 VOUT

t

Finite Switching Time

©James Buckwalter


• When M2 is on and M3 is off:

– M2 does not contribute any additional noise (M2 acts as cascode)

– M3 does not contribute any additional noise (M3 is off)

VLO

RL RL

VLO

VRF

Vout

M1

M on2 M off3 VOUT

t



©James Buckwalter


• When M2 is off and M3 is on:

– M2 does not contribute any additional noise (M2 is off)

– M3 does not contribute any additional noise (M3 acts as cascode)

VLO

RL RL

VLO

VRF

Vout

M1

M off2 M on3VOUT

t



©James Buckwalter


• When VLO+ = VLO- (i.e. the LO is passing through zero), the noise contribution from the transducer (M1) is zero. Why?

• However, the noise contributed from M2 and M3 is not zero because both transistors are conducting and the noise in M2 and M3 are uncorrelated.

VLO

RL RL

VLO

VRF

Vout

M1

M on2 M on3 VOUT

t



©James Buckwalter

Mixer Noise Analysis• Optimizing the mixer (for noise figure):

• Design the transducer for minimum noise figure.

• Noise from M2 and M3 can be minimized through fast switching of M2/M3 by:

– making LO amplitude large

– making M2 and M3 small (i.e. increasing fT of M2 and M3)

• Noise from M2 and M3 can be increased by using large M2/M3 switches.

VLO

RL RL

VLO

VRF

Vout

M1

M on2 M on3

VOUT

t

Trise

...m DCg W fixed I 1

...T DCfixed IW


©James Buckwalter

Mixer Noise Analysis• Noise Figure Calculation:

• Let us calculate the noise figure including the contribution of M2/M3 during the switching process.

VLO

RL RL

VLO

VRF

Vout

M1

M on2 M on3VOUT

t

Trise


©James Buckwalter

Heterodyne Mixer Noise Analysis: RL Noise• Noise Analysis of Heterodyne Mixer (RL noise):

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

IF RF LO


2 4 2noise RL Lv kT R

©James Buckwalter

Heterodyne Mixer Noise Analysis: Transducer Noise• Noise Analysis of Heterodyne Mixer (Transducer noise):

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

inoise- M1-switch

= inoise- M1

t( )SW t( )

= inoise- M1

t( )4

pcos w

LOt{ } -

4

3pcos 3w

LOt{ } +

4

5pcos 5w

LOt{ } - ...

æ

èçö

ø÷

VLO

t,DC mix RF NoiseI I I

©James Buckwalter

Heterodyne Mixer Noise Analysis: Transducer Noise• Noise Analysis of Heterodyne Mixer (Trans-conductor noise):

IF LO

inoise-M1

2 f( ) = 4kTg gdo,1

inoise- M1-switch

= inoise- M1

t( )SW t( )

= inoise- M1

t( )4

pcos w

LOt{ } -

4

3pcos 3w

LOt{ } +

4

5pcos 5w

LOt{ } - ...

æ

èçö

ø÷

3 LO

SW f( ) =

4

pd f - f

LO( )+4

3pd f -3 f

LO( )+ ...

inoise- M1

2 wIF( ) = 2

4

p

æ

èçö

ø÷

2

1+1

32+

1

52+ ..

é

ëê

ù

ûú4kTg g

do1

5 LO

inoise-M1

2 wIF( ) = 4 ×4kTg g

do,1

1

n2

n=1,odd

¥

å =p 2

8

©James Buckwalter

Heterodyne Mixer Noise Analysis: Switch Noise• Noise Analysis of Heterodyne Mixer (switch noise):

VLO VLOM on2 M on3id ,3

2id ,2

2

id

2 » 4kTg gm

id

2g vm gs g vm gs

vgn

2 =4kTg

gm

©James Buckwalter

Heterodyne Mixer Noise Analysis: Switch Noise• Noise Analysis of Heterodyne Mixer (switch noise):

• Show that:

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

out outi i

VLO

Gm

VLO

G

m= g

m2= g

m3= g

m2,3»

2IDC ,mix

DV


0mG

©James Buckwalter

Heterodyne Mixer Noise Analysis: Switch Noise• Noise Analysis of Heterodyne Mixer (switch noise) cont...:

Gm

VLO

2,3n mv

iout

2,3.out m n mi t G t v t

2

LOT

T

©James Buckwalter


Gm t( )

Gm

t( ) =DTG

m0

TLO

/ 21+ 2

sin kDTw

p

2

æ

èçç

ö

ø÷÷

kDTw

p

2

æ

èçç

ö

ø÷÷

k=1

¥

å cos kwpt( )

é

ë

êêêêê

ù

û

úúúúú

Gm f( )

p 2 p 3 p

2,3n mv f

p 2 p 3 p

vn-m2,3

2 = 24kTg

gm2,3

2

/ 2p

LOT

2

LOT

T

2 2 2

2,3 2 3n m n m n mv v v

©James Buckwalter

VLO

= vLO

p t( )p t( ) = a

0+ a

kcos kw

LOt( )

k³1

å

a0

= Ad ak

=2A

kpsin kp d( )


Gm f( )

p 2 p 3 p

2,3n mv f

p 2 p 3 p

vn-m2,3

2 = 24kTg

gm2,3

iout

t( ) = Gm

t( )vn-m2,3

t( )

inoise- M 2,3

2 wIF( ) = v

n-m2,3

2 Gm0

DT

TLO

2

æ

èçö

ø÷

æ

è

çççç

ö

ø

÷÷÷÷

2

+ 2vn-m2,3

2 Gm0

DT

TLO

2

æ

èçö

ø÷

æ

è

çççç

ö

ø

÷÷÷÷

2

sinc kDTw

p

2

æ

èç

ö

ø÷

æ

èç

ö

ø÷

2

k=1

å

How do we solve this?©James Buckwalter

inoise- M 2,3

2 wIF( ) = v

n-m2,3

2 Gm0

DT

TLO

2

æ

èçö

ø÷

æ

è

çççç

ö

ø

÷÷÷÷

2

+ 2vn-m2,3

2 Gm0

DT

TLO

2

æ

èçö

ø÷

æ

è

çççç

ö

ø

÷÷÷÷

2

sinc kDTw

p

2

æ

èç

ö

ø÷

æ

èç

ö

ø÷

2

k=1

å

Heterodyne Mixer Noise Analysis: Switch Noise

inoise- M 2,3

2 wIF( ) = v

n-m2,3

2 Gm0

DT

TLO

2

æ

èçö

ø÷

æ

è

çççç

ö

ø

÷÷÷÷

2

+ 2vn-m2,3

2 Gm0

DT

TLO

2

æ

èçö

ø÷

æ

è

çççç

ö

ø

÷÷÷÷

2

-1+2p

DTwp

2

inoise- M 2,3

2 wIF( ) = v

n-m2,3

2 Gm0

DT

TLO

2

æ

èçö

ø÷

æ

è

çççç

ö

ø

÷÷÷÷

2

TLO

2DT= v

n-m2,3

2 Gm0

2 DT

TLO

2

æ

èçö

ø÷

sinc kDTw

p

2

æ

èç

ö

ø÷

æ

èç

ö

ø÷

2

k=1

å =

-1+2p

DTwp

2

©James Buckwalter


Gm f( )

p 2 p 3 p

2,3n mv f

Gm f( )

p 2 p 3 p

2,3n mv f

inoise- M 2,3

2 wIF( ) =

1

TLO

2

æ

èçö

ø÷

Gm0

2 DT vn-m2,3

2

©James Buckwalter


inoise- M 2,3

2 wIF( ) =

1

TLO

2

æ

èçö

ø÷

Gm0

2 DT vn-m2,3

2

,

0

2 DC mix

m

IG

V

DV = SlopeDT

V

LOt( ) = A

LOcos w

LOt( )

90

90LO

LO

LO

LO LOt

t

dV tSlope A

dt

G

m= g

m2= g

m3= g

m2,3»

2IDC ,mix

DV

vn-m2,3

2 = 24kTg

gm2,3

©James Buckwalter


inoise- M 2,3

2 wIF( ) =

Gm0

2 DT

TLO

/ 2v

n-m2,3

2 =G

m0

2 DT

TLO

/ 22

4kTg

gm2,3

æ

èç

ö

ø÷

= 4G

m0DT

TLO

4kTg( ) =4DT

TLO

2IDC ,mix

DV4kTg( )

= 42I

DC ,mix

TLO

DT

DV4kTg( ) = 4

2IDC ,mix

TLO

1

ALO

wLO

4kTg( )

= 4 ×4kTgI

DC ,mix

p ALO

æ

èç

ö

ø÷

Total Noise Contribution due to switches M2 and M3

G

m»

2IDC ,mix

DV

vn-m2,3

2 = 24kTg

gm2,3

inoise- M 2,3

2 wIF( ) =

1

TLO

2

æ

èçö

ø÷

Gm0

2 DT vn-m2,3

2

DV

DT= A

LOw

LO

©James Buckwalter

Heterodyne Mixer Noise Analysis: Total Noise• Noise Analysis of Heterodyne Mixer (total noise):

inoise-M1

2 wIF( ) = 4 ×g4kTg

m1= 4 ×g4kT

IDC ,mix

VGSQ

-VT 0( )

inoise- M 2,3

2 wIF( ) = 4 ×g 4kT

IDC ,mix

p ALO

æ

èç

ö

ø÷

2 4 2noise RL Lv kT R

vnoise- MIX

2 wIF( ) = 4kTR

L2 + 4g I

DC ,mixR

L

1

VGSQ

-VT 0

+1

p ALO

æ

èç

ö

ø÷

ì

íï

îï

ü

ýï

þï

0

1

2

DS short DS shortm short ox sat

GS GSQ T

dI Ig WC v

dV V V

2 2 2 2 2 2

1 2,3noise MIX IF noise RL L noise M L noise Mv v R i R i

©James Buckwalter

Heterodyne Mixer Noise Analysis: Total Noise• Noise Analysis of Heterodyne Mixer (total noise):

0 1 &GSQ TV V M linearity Noise

0... min 2 / 3GSQ T LOAs V V A to imize noise contribution from M M

2

noise MIX IFv

1.6GSQV V

0.8GSQV V

VLO

vnoise- MIX

2 wIF( ) = 4kTR

L2 + 4g I

DC ,mixR

L

1

VGSQ

-VT 0

+1

p ALO

æ

èç

ö

ø÷

ì

íï

îï

ü

ýï

þï

©James Buckwalter

Heterodyne Mixer Noise Analysis: Noise Figure

• This assumes that all of the “white noise” from Rs is folded down. In reality, there is some matching and filtering between the generator and mixer.

22

,20

1 11 1 4

noise MIX IF SDC mix L

L T LOGSQ Tnoise RS IF

v RNF I R

R AV Vv

2 2

2 1 416

2

T Tnoise Rs IF S

S S

kTi kT R

R R

©James Buckwalter

Load

No

ise

LO P

ort

No

ise

Heterodyne Mixer Noise Analysis: Total Noise• Noise Analysis of Heterodyne Mixer (total noise)--{Terrovitis and Meyer}:

F =a

c2+

g3+ r

g3g

m3( )gm3

a + 2g1G + R

LO+ 2r

g 2( )G2 +1

RL

c2gm3

2 Rs

sin2 2

2

LO

LO

T

cT

41

3LOTf

G =2I

p ALO

G2 = 4.64K

sq

1/2IDC ,mix

3/2

2p ALO

©James Buckwalter

Homodyne Mixer Noise Analysis: Transducer Noise• Noise Analysis of Heterodyne Mixer (Transducer noise):

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

inoise- M1-switch

= inoise- M1

t( )SW t( )

= inoise- M1

t( )4

pcos w

LOt{ } -

4

3pcos 3w

LOt{ } +

4

5pcos 5w

LOt{ } - ...

æ

èçö

ø÷

VLO

t,DC mix RF NoiseI I I

©James Buckwalter

Homodyne Mixer Noise Analysis: Transducer Noise• Noise Analysis of Heterodyne Mixer (Trans-conductor noise):

IF LO

inoise-M1

2 f( ) = 4kTggdo,1

inoise- M1-switch

= inoise- M1

t( )SW t( )

= inoise- M1

t( )4

pcos w

LOt{ } -

4

3pcos 3w

LOt{ } +

4

5pcos 5w

LOt{ } - ...

æ

èçö

ø÷

3 LO

SW f( ) =

4

pd f - f

LO( )+4

3pd f -3 f

LO( )+ ...

inoise-M1

2 0( ) =4

p

æ

èç

ö

ø÷

2

1+1

32+

1

52+ ..

é

ëê

ù

ûú4kTgg

do1

5 LO

inoise-M1

2 0( ) = 2 ×4kTggdo,1

1

n2

n=1,odd

¥

å =p 2

8

©James Buckwalter

Harmonic Rejection Mixers

• Harmonic aliases can be uniformly removed. Recall that we saw a duty cycle dependence on harmonic terms.

©James Buckwalter


• The LO can be synthesized to remove harmonic content.

©James Buckwalter

3 LOs separated by 45 degrees are weighted to generate desired spectral properties

sLO t( ) = ak p t - kT( )k=-N

N

å

T =1

fLO

p

2 N +1( )


• When the mixer is driven with the stepped waveform

and we eliminate any aliasing of the signal on to N-1 harmonics

©James Buckwalter

Harmonic Rejection Mixer Example

©James Buckwalter

LO Phase

Shift

No. of

Square

Waves

Square

Waves

Harmonics Can be

Cancelled

45o 3 √2*LO(t), LO(t-π/4), LO(t+π/4) 3rd, 5th

30o 5

2*LO(t), √3*LO(t-π/6),

√3*LO(t+π/6), LO(t-π/3),

LO(t+π/3)

3rd ,5th ,7th, 9th

22.5o 7

√2*LO(t)

√2*cos(π/8)*LO(t-π/8)

√2*cos(π/8)*LO(t+π/8)

LO(t-π/4), LO(t+π/4)

√2*sin(π/8)*LO(t-3π/8)

√2*sin(π/8)*LO(t+3π/8)

3rd, 5th, 7th, 9th,11th,13th

Harmonic Rejection Mixer Implementation

• Harmonic rejection can be realized as a set of parallel RF paths or through direct frequency synthesis techniques

©James Buckwalter

mixer - ucsb · 2016-03-27 · mixers: switching operation s rf (w rf) 1 1 s out lo input s ... dc...

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