EE265B: Communication Circuits II · 2016-03-27 · EE265B: Communication Circuits II •Device...

EE265B: Communication Circuits II

• Device Modeling (3 lectures)

– BJT (RF Device Model, RF Noise Model)

– MOS (RF Device Model, RF Noise Model)

– Passive Elements: Res., Cap. & Inductors

• LNA Design (5 Lectures)

→ Stability

• RF Circuit Biasing (1 lectures)

– Voltage and Current References

• Mixer Design (3 lectures)

– BJT mixers

– MOS mixers

• VCO Design (3 lectures)

• Systems and Architectures (3 lectures)

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.

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

• “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.

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.

Mixer Purpose

• Why do we need mixers?

• Key metrics:– Noise Figure

– Linearity

• What will we explore? – Practical designs for mixers and limits on noise

figure and linearity.

FOM MIX =IIP3×GC × ISLO-RF × f

FSSB -1( ) ×PDC ×PLO

Review: Homodyne versus Heterodyne

• Heterodyne

• Homodyne

©James Buckwalter

rf lo if

0rf lo

General Spurious Tones

• Many different frequencies can fall into the same intermediate frequency

©James Buckwalter

1cos cos

2rf lo rf lo rf lov V V t t

if rf lo

rf lov v v

if rf lom n

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

Mixer Noise

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

• For homodyne,

©James Buckwalter

kTDfGLNA

IM - IF

GRF-IF

ø÷ 1+

Nadded

GIM -IF

+ GRF- IF( )kTDf

RF- IF+ G

IM -IF

GRF- IF

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.

LO Waveform in Mixer

• Noise factor degraded by images around harmonics.

©James Buckwalter

1cosLO pk LO

V t V n tn

LO Waveform (cont)

• Now our minimum noise figure is 3.8 dB (or 0.8 dB for DSB)

• Nonetheless, the following slides will explain WHY we use square waves for mixing!

©James Buckwalter

12 2.4

o i MIX LO MIX LO MIX

o i MIX LO MIX i MIX LO MIX LO MIX

N N G n G Nn

N N G N N G G Nn

= 2.4 +N

= 2.4 + FMIX

= 1.2 +N

= 1.2 + FMIX

Mixer Types• Mixer Types:

– Multiplication through non-linearity

– Multiplication through switching

• Active mixers

• Passive mixers

Mixers Based On Non-linearity

Non-linear System S a S a S a S

b S b S b S

c S S c S S c S S

MIX RF RF RF

LO LO LO

RF LO RF LO RF LO

Mixers Based On Non-linearity

Cl earg

0.ds SQ GSQ TI K V V

ds SQ bias RF LO T

SQ bias T RF LO bias T RF LO

I K V V V V

K V V V V V V V V

ids wLO ±wRF( ) = KSQVRFVLO cos wLO -wRF( )t + cos wLO +wRF( )t{ }

Practical Square Law Mixers

Cl earg 2

Cl earg

ids wLO -wRF( ) = KSQVRFVLO cos wLO -wRF( )t

Transconductance conversion gain = Gc =ids w IF = w LO -w RF( )

VRF w RF( )

= KSQVLO =mCoxW

Practical Bipolar Mixer

Cl earg I I eC CO

Cl earg

Transconductance conversion gain = Gc =iC w IF = w LO -wRF( )

VRF w RF( )=

IC = ICQ .e

VRF -VLO

VT = ICQ . 1+VRF -VLO

èçö

VRF -VLO

èçö

+ ...ìíï

üýï

MOSFET Mixer (with impedance matching)• MOSFET mixer (with impedance matching):

Cl earg

Cmatch

IF Filter

Matching

Network

Features of Square Law Mixers• Noise Figure: The square law MOSFET mixer can be designed to have very low noise

figure.

• Linearity: By operating the square law MOSFET mixer in the square law region the linearity of the mixer can be improved considerably. Note that the corresponding BJT mixer produces a host of non-linear components due to the exponential nature of the BJT mixer.

• Power Dissipation: The square law mixer can be designed with very low power dissipation.

• Power Gain: Reasonable power gain can be achieved through the use of square law mixers.

• Isolation: Square law mixers offer poor isolation from LO to RF port. This is by far the biggest short coming of the square law mixers.

Mixers: Switching Operation

SRF wRF( )

LO Input

Sout = SRF cos wRFt( )Ä .........................................}{1

cos wRF

t( )Ä4

pcos w

LOt( ) -

3pcos 3w

LOt( ) +

5pcos 5w

LOt( ) - ...

ìíî

üýþ

SW t( )

Mixers: Multiplication Through Switching

Sout = SRF cos wRFt( )Ä .........................................}{1

cos wRF

t( )Ä4

pcos w

LOt( ) -

3pcos 3w

LOt( ) +

5pcos 5w

LOt( ) - ...

ìíî

üýþ

wLO -wRF

LO RF 3 LOwLO +wRF

3wLO -wRF

3wLO +wRF

IF( ) =2

One-Diode Mixer

• Attractive for very high frequency applications where transistors are slow.

• Poor gain

• Poor LO-RF isolation

• Poor LO-IF isolation

Two-Diode Mixer

• Poor gain

• Good LO-IF isolation

• Good LO-RF isolation

• Poor RF-IF isolation

Four-Diode Mixer

• Poor gain

• Good LO-IF isolation

• Good LO-RF isolation

• Good RF-IF isolation

VLOVRF

Simple Switching Mixer (Single Balanced Mixer)

• The transistor M1 converts the RF voltage signal to the current signal.

• Transistors M2 and M3 commute the current between the two branches.

I IDC RF

IF Filter

VOUT t

wLO -wRF

LO RF wLO +wRF

wLO -wRF

IF Filter

Single Balanced Mixer Analysis (Incl. Harmonics)

wLO -wRF

LO RF 2 LO

SLO wLO( )

SRF wRF( ) SMIX

Single Balanced Mixer Analysis (Incl. Impd. Match)• Single Balanced Mixer (Including impedance matching for RF port)

• In this architecture, without impedance matching for the LO port is very commonly used in many designs.

Cl earg G VM RF

Single Balanced Mixer Analysis (Incl. Impd. Match)• Single Balanced Mixer (Including impedance matching for LO port)

• In this architecture, with impedance matching for the LO port maximizes LO power utilization without wasting it.

1GGVLs

Cl earg G VM RF

Lm2 Lm3

Mixer Input Match

Cl earg

S g T SR R L 1

Mixer Gain

sig M RFI G V

0 : . .2

: . .2

LOout cc DC sig L cc DC sig L

LOLO out cc cc DC sig L DC sig L

TV V I I R V I I R

TT V V V I I R I I R

out DC sig LV I I R SW t

Mixer Gain

sig M RFI G V

RF´ SW t( )

Single Balanced Mixer Analysis: Linearity

• Linearity Consideration:

• Linearity of the Mixer primarily depends on the linearity of the transducer (I_tail=Gm*V_rf). Inductor Ls helps improve linearity of the transducer.

• The transducer transistor M1 can be biased in the linear law region to improve the linearity of the Mixer. Unfortunately this results in increasing the noise figure of the mixer (as discussed in LNA design).

GGV Ls

Cl eargG VM RF

Single Balanced Mixer Analysis: Linearity• Linearity Consideration cont...:

• Using the common gate or common base stage as the transducer improves the linearity of the mixer. Unfortunately the approach reduces the gain and increases the noise figure of the mixer.

VSIbias Cc

G VM RF

Single Balanced Mixer Analysis: Isolation• Isolation Consideration (LO-RF Feed through)

• The strong LO easily feeds through and ends up at the RF port in the above architecture if the LO does not have a 50% duty cycle. Why?

Cl earg G VM RF

LO-RF Feed through

0.5 LOT

Single Balanced Mixer Analysis: Isolation• Isolation Consideration (LO-RF Feed through)

• The amplified RF signal from the transducer is passed to the commuting switches through use of a common gate stage ensuring that the mixer operation is unaffected. Adding the common gate stage suppresses the LO-RF feed through.

VLO VLOM2 M3

Cl earg

Weak LO-RF Feed through

G VM RF

Single Balanced Mixer Analysis: Isolation• Isolation Consideration (LO-IF Feed through)

• The strong LO-IF feed-through may cause the mixer or the amplifier following the mixer to saturate. It is therefore important to minimize the LO-IF feed-through.

Cl earg G VM RF

LO-IF Feed through

Double Balanced Mixer• Double balanced mixer (also called Gilbert Cell):

• The strong LO-IF feed is suppressed using the double balanced mixer.

• All the even harmonics are also cancelled.

• All the odd harmonics are doubled (including the signal).

VLOM2 M3

I IDC RF I IDC RF

Double Balanced Mixer• Double balanced mixer (Gilbert Cell) cont...:

• The LO feed through cancels.

• The output voltage due to RF signal doubles.

VoutM2 M3

I IDC RF I IDC RF

Double Balanced Mixer: Linearity• Measuring Linearity of a double balanced mixer:

• Show that:

= 2IDC

3 + ...

þïIIP3 in - volts( ) =

VLOM2 M3

I IDC RF I IDC RF1M1M

Mixer Output Match• Output match for mixers:

– Heterodyne Mixer

– Homodyne Mixer

• Heterodyne Mixer: For IF frequencies of 100-200MHz (signal bandwidth of 4MHz) we do not do impedance matching due to the following reasons:

– The signal bandwidth is comparable to the IF frequency therefore the impedance matching would create gain and phase distortions

– Need large inductors and capacitors to impedance match at 200MHz

• The general approach taken is the following

– Case (1) Output goes to SAW: In this case we need to keep the VSWR close to 1. The output impedance of the mixer at IF (200MHz) tends very high (~5kOhms). Due to this, we stabilize the output impedance by putting a resistor across the collectors of the mixers.

– Case (2) Output goes to amplifier on chip. We don’t care about impedance matching and directly couple the output of the mixer to the IF amplifier. This generates the largest voltage at the input of the IF amplifier.

Mixer Output Match (Heterodyne)• Output match for a Heterodyne mixer:

3.0CCV V

2parL nH

Mixer Output Match (Homodyne)• Output match for a Homodyne mixer:

VoutM2 M3

Cl earg

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

,DC mix RF NoiseI I I

wLO -wRF

LO RF wLO +wRF

Instantaneous Switching

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.

M2 M3 VOUT

Finite Switching Time

• 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)

M on2 M off3 VOUT

• 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)

M off2 M on3VOUT

• 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.

M on2 M on3 VOUT

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.

M on2 M on3

...m DCg W fixed I 1

...T DCfixed IW

Mixer Noise Analysis• Noise Figure Calculation:

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

M on2 M on3VOUT

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

IF RF LO

2 4 2noise RL Lv kT R

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

inoise- M1-switch

= inoise- M1

t( )SW t( )

= inoise- M1

pcos w

LOt{ } -

3pcos 3w

LOt{ } +

5pcos 5w

LOt{ } - ...

èçö

t,DC mix RF NoiseI I I

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

inoise-M1

2 f( ) = 4kTg gdo,1

inoise- M1-switch

= inoise- M1

t( )SW t( )

= inoise- M1

pcos w

LOt{ } -

3pcos 3w

LOt{ } +

5pcos 5w

LOt{ } - ...

èçö

3 ...3

LO LOSW f

inoise- M1

2 wIF( ) = 2

èçö

52+ ..

ûú4kTg g

inoise-M1

2 wIF( ) = 4 ×4kTg g

n=1,odd

å =p 2

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

VLO VLOM on2 M on3id ,3

2id ,2

2 » 4kTg gm

2g vm gs g vm gs

2 =4kTg

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

• Show that:

out outi i

2 3 2,3

2. DC mix

m m m m

IG g g g

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

2,3n mv

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

Gm t( )

t( ) =DTG

/ 2( )2

sin kDTw

å cos kwpt( )

Gm f( )

p 2 p 3 p

2,3n mv f

p 2 p 3 p

vn-m2,3

2 = 24kTg

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

Gm f( )

p 2 p 3 p

2,3n mv f

p 2 p 3 p

vn-m2,3

2 = 24kTg

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

inoise- M 2,3

2 wIF( ) = v

n-m2,3

èçö

çççç

÷÷÷÷

+ 2vn-m2,3

èçö

çççç

÷÷÷÷

sinc kDTw

How do we solve this?

inoise- M 2,3

2 wIF( ) = v

n-m2,3

èçö

çççç

÷÷÷÷

+ 2vn-m2,3

èçö

çççç

÷÷÷÷

sinc kDTw

Heterodyne Mixer Noise Analysis: Switch Noise

inoise- M 2,3

2 wIF( ) = v

n-m2,3

èçö

çççç

÷÷÷÷

+ 2vn-m2,3

èçö

çççç

÷÷÷÷

inoise- M 2,3

2 wIF( ) = v

n-m2,3

èçö

çççç

÷÷÷÷

2DT= v

n-m2,3

èçö

sinc kDTw

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( ) =

èçö

2 DT vn-m2,3

inoise- M 2,3

2 wIF( ) =

èçö

2 DT vn-m2,3

2 DC mix

DV = SlopeDT LO LO LOV t A Cos t

LO LOt

dV tSlope A

m2,3»

2IDC ,mix

vn-m2,3

2 = 24kTg

inoise- M 2,3

2 wIF( ) =

n-m2,3

4kTg( ) =4DT

2IDC ,mix

DV4kTg( )

DC ,mix

DV4kTg( ) = 4

2IDC ,mix

4kTg( )

= 4 ×4kTgI

DC ,mix

Total Noise Contribution due to switches M2 and M3

2IDC ,mix

vn-m2,3

2 = 24kTg

inoise- M 2,3

2 wIF( ) =

èçö

2 DT vn-m2,3

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

inoise- M1

2 wIF( ) = 4 ×g 4kTg

m1= 4 ×g 4kT

IDC ,mix

-VT 0( )

inoise- M 2,3

2 wIF( ) = 4 ×g 4kT

IDC ,mix

2 4 2noise RL Lv kT R

vnoise- MIX

2 wIF( ) = 4kTR

L2 + 4g I

DC ,mixR

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

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

noise MIX IFv

1.6GSQV V

0.8GSQV V

vnoise- MIX

2 wIF( ) = 4kTR

L2 + 4g I

DC ,mixR

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.

1 11 1 4

noise MIX IF SDC mix L

L T LOGSQ Tnoise RS IF

v RNF I R

R AV Vv

2 1 416

T Tnoise Rs IF S

kTi kT R

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

m3( )gm3

a + 2g1G + R

LO+ 2r

g 2( )G2 +1

sin2 2

G2 = 4.64K

1/2IDC ,mix

2p ALO

Homodyne Mixers

• Issues– DC offsets: Mixing to DC means tolerance to

mismatch between devices and waveforms is tighter

– LO leakage: LO at RF frequency means it is difficult to distinguish between the two

– Noise: 1/f noise will play a prominent role in the homodyne mixer.

– Resistive load: Reduces voltage headroom and gain

Issues with Homodyne

• Homodyne seems so easy…there must be a catch.

– LO phase must track RF (need a PLL to lock to RF)

– LNA must be exceptionally linear (more on this soon)

– LO leakage must be controlled

©James Buckwalter

LO Leakage Issue

• Doesn’t my LNA have excellent return loss?

• Yes but your LO signal is strong…

• LO leakage back into RF port is

where PLO is LO power, ISMIX is the isolation of the LO-to-RF port, and RLLNA is the return loss of the LNA.

• A typical case

©James Buckwalter

,LO LEAKAGE LO MIX LNAP P IS RL

, 0 40 30 70LO LEAKAGEP dBm dB dB dBm

Homodyne Mixer Noise Analysis: Transducer Noise• Noise Analysis of Homodyne Mixer (noise from transducer M1):

Homodyne Mixer Noise Analysis: RL Noise• Noise Analysis of Homodyne Mixer (noise from RL):

Noise from RL

Homodyne Mixer Noise Analysis: non-50% duty LO• Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty cycle of

IM1( )Ä DC +

pcos w

LOt( ) -

3pcos 3w

LOt( ) + ...

èçö

IM1( )Ä DC +

pcos w

LOt( ) -

3pcos 3w

LOt( ) + ...

èçö

p t( ) =DTp

sin kDTp

å cos2p k

p t( ) = d + 4sin kdp( )

å cos 2pkfLO

LO)--{Noise from M1}:

M2 M3INoise M 1

INoise thermalINoise f1/

, 1/DC mix RF Noise thermal Noise fI I I I

LO)--{Noise from M1}:

IDC ,mix

+ INoise-thermal

+ INoise-1/ f( ). DC +

pcos w

LOt( ) -

3pcos 3w

LOt( ) + ...

èçö

DC-term of LO

LO)--{Noise from M2/M3}:

VLO VLOM on2 M on3id3id 2

i i id d thermal d f 1/

C WL f

g vm gs g vm gs

C WL f

1/gn fv

, 1/DC mix RF Noise thermal Noise fI I I I

1/gn fv

i i iout out no noise noise f 1/

1/gn fv t

T tSlope

Slope ALO LO 2

VLO1/gn fv

i i iout out no noise noise f 1/

v tT t

,max ,max

. . . .2 2 2

gn fLO LODC DC

k kLO LO

v tT TNoise Energy T t I t k I t k

,DC mixI

1/gn fv t

0.5 LOT

1/gn fv f

0.5 LOT

1/ ,max.2

noise f DC

v fi I

Increasing Headroom in DBM (Option 1)

2parL nH

2 1Q '

2 2Q bR

LOV LOV

cC cCinV

2parL nH

BQIBQI

10C nF 10C nF

2 1Q '

2 2Q bR bR bRbR

bVbV bV

LOV LOV

3.0CCV V

2parL nH

BQIBQI

10C nF 10C nF

2 1Q '

2 2Q bR bR bRbR

bVbV bV

LOV LOV

3.0CCV V

Homodyne Issues: Harmonic Mixers• The LO radiation problem can be partially overcome by the use of harmonic mixers.

A two-level mixing scheme can be employed, as shown in the figure below. The LO frequency is precisely one half the desired frequency, which is easily filtered by the duplex filter. Additionally, a full differential structure will exhibit extremely low second harmonic distortion of the LO. The harmonic mixers must be driven by LO outputs at 45 degrees phase shift to each other.

2LOV2LOV

1LOV1LOV

1LOVRFV

1LOV 2LOV

Passive FET Mixer• Passive FET Mixers:

• Alternative for Homodyne Mixers: Lower 1/f noise because no current through devices (This is not exactly true at high-frequency).

VLO VLOM1 M2

VLO M4 VLOM3

Passive FET Mixer• Passive FET Mixers (homodyne operation):

cos wRF

t( ) ×4

pcos w

LOt( ) -

3pcos 3w

LOt( ) +

5pcos 5w

LOt( ) - ...

èçö

2out IF

Passive FET Mixer• Passive homodyne FET Mixers (non-50% duty cycle of LO) result in no DC offsets!!

DC-term of LO

cos wRF

t( ) × DC +4

pcos w

LOt( ) -

3pcos 3w

LOt( ) +

5pcos 5w

LOt( ) - ...

èçö

Passive FET Mixer With Biasing

1biasC nF

1biasC nFggV

Passive FET Mixer• Passive Homodyne Mixers (Shahani & Lee):

Vo = Vi

R1 + R2

G1 + G2

• where:m t( ) =

g t( ) - g t - TLO / 2( )g t( ) + g t - TLO / 2( )

IF RF RF

g tV t V t

T Tg t g t g t g t

Tg t g t

V t V t V t m tT

g t g t

• where:

• The last expression is “approximate” under the consideration that the load is not actually a conductance but a capacitance. Under this condition, the conductance is solved from the linear system and gives the final expression.

out RF

g tV t m t V t

gg tV t m t V t

time varying thevenin equivalent conductanceTg t

,max maximum of T Tg g t

average of T Tg g t

Tg t g t

V t V tT

G g t g t

g tV t V t

Passive FET Mixer (II)• Passive Homodyne Mixers (Shahani & Lee):

• Effect of LO waveforms

square wave

sine wave

break before make

make before break

1ideal passive mixerF Power conversion loss

Power Gain

Subharmonic Mixer

• Khatri and Larson, TMTT 2008

Mixer Noise Analysis (General Approach)• Determining Noise Figure of Mixers (General Approach)--{Hu & Mayaram}:

I IDC RF

Non-linear

Circuit

Filter

LNAVRF

I IDC RF

Mixer Noise Analysis (General Approach)• Determining Noise Figure of Mixers (General Approach--the recipe):

• Procedure:

– Step 1: Calculate the small signal gain g(t) for each noise source.

– Step 2: Calculate the Fourier coefficients Gn of g(t).

– Step 3: Calculate the transfer function of the output filter H(w).

– Step 4: Calculate the frequency response |H(w).Gn|.

– Step 5: Determine the output noise density at Wif.

– Step 6: Determine the noise figure.

Non-linear

Circuit

Filter

LNAVRF

Mixer Noise Analysis (General Approach)• Determining Noise Figure of Mixers (General Approach) cont…:

VLOM2 M3

im1irf Ibias

• Small signal gain from vb to delta_Ic:

• Small signal gain from ie to delta_Ic:

• Refer to paper by Hu and Mayaram for detail on calculating noise figure.

DIC = IBIAS tanhVLO

èçö

gvbt( ) =

dV V=VLO t( ),IC =IBIAS

=IBIAS

2eVLO t( )/VT

1+ eVLO t( )/VT( )

giet( ) =

dIee V=VLO t( ),IC =IBIAS

= tanhVLO t( )

èçö

VLOM2 M3

im1irf Ibias

Linearity• Measuring Linearity of a double balanced mixer:

= 2IDC

3 + ...

IIP3 in - volts( ) =8IDC

VLOM2 M3

I IDC RF I IDC RF1M1M

How about linearity of switching pair?

Distortion in Mixers

• Terrovitis and Gray (JSSC 2000)

• Switching of current through single-balance differential pair

• What does this function look like?

o= F V

rf( )IDC+irf

Io1 =ISS

2vid 1-

Io2 =ISS

2vid 1-

• Switching of current through single-balance differential pair

• Linearize expression in terms of mixing

• pk are the coefficients of a Taylor series describing the switching

• However, pk coefficients are a function of time since F depends on VLO

• Example: If M1 is on and M2 is off, p1 = 1, p2 = 0, p3 = 0

o= F V

t( ) × irf

2 + p3

t( ) × irf

where pk

IDC+irf

• We can simplify this by recognizing that we are primarily concerned about the conversion of tones through the 1st harmonic of the LO

t( ) × irf

2 + p3

t( ) × irf

3 where pk

= p1,k

× is+ p

2,k× i

2 + p3,k

3( )sin kwLO

IDC+irf

= p1,k

× is+ p

2,k× i

2 + p3,k

3( )sin kwLO

= b1× i

2 + b3× i

where bk

t( )sin wLO

t( )dt0

IDC+irf

• How can we use this polynomial series?

= b1× i

2 + b3× i

3 where bk

t( )sin wLO

t( )dt0

IDC+irf

• Minimizing b3 is good for the linearity of the mixer.

Ssin w

LO- D( )t( ) + sin w

LO+ D( )t( )( )

IM3 =3

Solving for LO swing

• If large amplitude swing, LO approaches “square-wave” and

• There is a period of time Δ during which the switches are both on and in during this time

• where λ is the slope of the p3 in this region and Vo is the maximum is the cut-off voltage.

b p t t dtT

3 32 2 0

LO LO LO

b p V V dVT

t( )sin wLO

t( )dt0

• Consider sine LO

• Coefficients of switching waveform are shown to the left

• Then the b1 component depends on the “switching threshold” Vx.

• where

• and

b1 »2

arcsinVx

ççç

÷÷÷

VX =IDCq

èçö

3 32 2 0

LO LO LO

b p V V dVT

• DC analysis shows that

– Lower current is more linear

– Higher swing is more linear (to a point)

IM3 =3

Cascaded IIP3

= b1× i

2 + b3× i

3 where bk

t( )sin wLO

t( )dt0

2 + a3×v

IM3 =3

ø÷ v

Frequency Dependent Effects

• Capacitances cause frequency dependence in switching pair

t, fa( ) i

b( ) irf

2 + P3

t, fa, f

c( ) irf

t, fa( ) = d

1t( ) H

b( ) = d1

t( ) H2

t, fa, f

b( ) + d2

t( ) H1

t, fa( ) H

t, fa, f

c( ) = d1

t( ) H3

t, fa, f

c( ) + 2d2

t( ) H1

t, fa( ) H

c( ) + d3

t( ) H1

t, fa( ) H

b( ) H1

t, fc( )

a( ) irf

t, fa, f

b( ) irf

2 + H3

t, fa, f

c( ) irf

t( ) =d

t( ) - f2

t( )( )

t( ) =1

dV 2f1

t( ) - f2

t( )( )

t( ) =1

dV 3f1

t( ) - f2

t( )( )

Frequency Dependent Effects

• Time-varying performance indicates some “ideal” bias and LO swing behavior.

• Does that make sense?

Measurement

• 0.8 um CMOS

• Low bias: Transconductordominates

• High bias: switching pair dominates

• High frequency effects evident in IIP3 versus Vo.

• Note IIP3 drops rather than increases with swing

EE265B: Communication Circuits II · 2016-03-27 · EE265B: Communication Circuits II •Device...

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