Lecture 7 RF Front-End Design LNA Mixer - Auburn University

RFIC Design and Testing for Wireless Communications

A PragaTI (TI India Technical University) CourseJuly 18, 21, 22, 2008

Lecture 7: RF front-end design – LNA, mixer

BBy

Vishwani D. AgrawalFa Foster DaiFa Foster Dai

200 Broun Hall, Auburn University200 Broun Hall, Auburn UniversityAuburn, AL 36849-5201, USA

1

RFIC Design and Testing for Wireless Communications

TopicsMonday, July 21, 2008

9:00 – 10:30 Introduction – Semiconductor history, RF characteristics

11:00 – 12:30 Basic Concepts – Linearity, noise figure, dynamic range2:00 – 3:30 RF front-end design – LNA, mixer4:00 – 5:30 Frequency synthesizer design I (PLL)

T d J l 22 2008Tuesday, July 22, 2008

9:00 – 10:30 Frequency synthesizer design II (VCO)

11:00 – 12:30 RFIC design for wireless communications2:00 – 3:30 Analog and mixed signal testing

RF front-end design – LNA, mixer, FDAI, 2008 2

LNA Design Challenges(1) Amplify extremely low signals without adding much

noise.

(2) Amplify large signals without distortions.

(3) Variable gain to compensate large input signal variation.

(4) Input matching and flat gain over wide bandwidth for muti-mode transceivers.

(5) Input dynamic range of a WLAN LAN from -80dBm to -20dBm

Parameters for Microwave and RFIC DesignPeak-to peak voltage: Vpp

Root-mean-square voltage:

VV 2222

pprms

VV =

Power in Watt :

⎞⎛ WP tt ][

RV

RVPwatt pprms

8

2

==

Power in dBm : ⎟⎠⎞

⎜⎝⎛=

mWmWPwattPdBm 1

][log10 10

RZRefection coefficient :

Voltage standing wave ratio (VSWR):

Sin

Sin

RZRZ

S+−

==Γ 11 Γ−= log20lossReturn

Voltage standing wave ratio (VSWR):

Γ−

Γ+==

11

min

max

VV

VSWR


Basic Amplifiers• The common emitter amplifier is often used as a drive for an LNA.• The common-collector, with high input impedance and low output

impedance, makes an excellent buffer between stages or before the p , goutput driver.

• The common-base is often used as a cascode in combination with the common-emitter to form a LNA stage with gain to high frequency.g g g q y

VCC VCC

VCC

vout

vinvout

voutvin

vin

VEE VEEVEE

Common-Emitter(LNA Driver) Common-Collector

(Buffer)Common-Base

(Cascode)


Common-Emitter Amplifier

vi

ZL

vo

gmvπv Cπ

rb

r

Cμ

r Lgmvπvπ π rπ ro

• Voltage gain

e

LLm

bi

ovo r

ZZgrr

rvvA ≈

+−==

π

π

• Note that rπ=βre and gm=1/re. for low frequencies, the parasitic capacitances have been ignored and rb << rπ.

• Input impedance at low frequenciesInput impedance at low frequencies

πrrZ bin +=


Miller Capacitance in Common-Emitter Amplifier

Cμ is replaced with two equivalent capacitors CA and CB

μμπ

μ ZgCZgCvvCC LmLm

oA ≈+=⎟⎟

⎠

⎞⎜⎜⎝

⎛−= )1(1Cμvπ vo

μμπ

μ

π

CZg

CvvCC

LmoB ≈⎟⎟

⎠

⎞⎜⎜⎝

⎛+=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

⎠⎝

111

⇓vπ vo • Two RC time constants or two poles: one consisting of CA+ Cπ, and the

CA CB

g A π,other consisting CB.


Miller Capacitance in Common-Emitter Amplifier• The dominant pole is one formed by CA and Cπ:

[ ]f =1

( )[ ] [ ]AsbP CCRrr

f+⋅+⋅

=πππ21

• Recall Ft calculation, the output is loaded with a short circuit removes Miller multiplication, 3db current gain bandwidth:

1βf =

)(2 μππβ π CCr

f+⋅

The unity current gain frequency:The unity current gain frequency:

)(2 μππ CCgf m

T +⋅=


)( μπ

Common-Base Amplifierrb

Cμ

Cπ r g v Z

iout

vππ rπ gmvπ ZL

iin

Current gain (ignoring Cu and ro)T

ein

out

jrCjii

ωωω π +

≈+

≈1

11

1

Tω

At l f i th t i 1

( )CSLeS

Lv CCRjCrjR

RA++

⋅+

⋅≈μπ ωω

α1

11

10

At low frequencies, the current gain = 1.The pole in this equation is usually at much higher frequency than the one in the common-emitter amplifier Sbe Rrr +<

Cascode LNA R

VCC

Cascode LNA

Cmio Rgvv −≈/ Cascode Q2

vout

VCbias

RC

vi

vc1

Driver Q1

1Common emitter dominant pole

VEE

• Current ic1 through Q1 is about the same as the current ic2 through Q2

2/1 me gr ≈( )[ ] [ ]usbP CCRrr

f22

1

111 +⋅+⋅=

πππ

• Current ic1 through Q1 is about the same as the current ic2 through Q2current gain ~1 Gain is the same as for the common-emitter amplifier.

• The cascode transistor reduces the feedback of Cu1 (why?) increased high frequency gain.

• Cascode has good isolation with reduced S12.• Disadvantage: cascode transistor uses voltage headroom reduced

linearity; add another pole to the amp -12dB/oct roll-off; add little extra noise (to the 1st order approximation, cascode NF = common emitter NF);


( pp , );common base may cause noise and oscillation.

Bipolar Transistor Noise Model

C

rb

icn

cb’

ibn

vbb

4kTrb

Cμ

Cπ gmvb’erπcn

e

ibf

2qIB

ro

2qIC

e1/f noise Base Collector eBase

Shot Noise

CShot Noise

bbn kTrv 42 =

gmVπ1

Baserb

Zπ

vbn Collector

222 rπ Cπro icnibn

Emitter

ccn qIi 22 =Bbn qIi 22 =


Noise Figure versus Bias Current

2 40)

Lmbrno RgkTrvb

⋅≈ 4,

Output signal Lmsiso Rgvv ⋅≈

Base thermal noise

2.20

2.40

e Fi

gure

(dB

)

LCIno RqIvc

2, ≈

C RgRqIv 2≈

Collector shot noise

Base shot noise

1.80

2.00

nim

um N

oise

base th l

collector shot noise

base shot

LmsIno RgRvB β, ≈Base shot noise

1.001.60

Collector Current (mA)

Min

2.0 3.0 4.0 5.0 6.0

thermal noise

shot noise (correlated)

shot noise

2222111

ββSmSmbeq RgRg

RgRr

RR

NF ++++=+=


0 222 ββSmSS RgRR

Noise Figure of A Two Stage LNA

Ω11rGHzft 5=

Ω=11br

800 =β

GHzfin 1=

5=β

RgRgRR

rNF SmSmb

2211 2++++=

β

11.0 −Ω=mg

NF dominated

dB

RgR SmS

621551111

222 20

=++++=

ββ NF increases at high frequency

NF dominated by base resistance


dB62.1501601050

1 ++++

Minimum Noise Figure of Common Emitter LNA

SS

SmSm

SmS

b RbR

aRgRg

RgRr

NF ⋅++=++++=11

22211 2

0 ββ

012 =+−= b

Ra

dRdNF

SS

m

bTbm

moptS g

rffrg

gbaR

211

211, ≈

+

+==

RS=50 Ohm choose bias (gm) and emitter length to

hi imm gfg2

0

+ββ

⎞⎛

achieve noise matching

( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+++=+= 2

0min

1121121ββbmrgabNF


More on LNA Noise Figure2

( ) ( )2,2

2

min2

,min 2 optSSST

moptSS

S

RRRf

gfNFRR

RbNFNF −+≈−+=

m

bToptS g

rffR ,

2

2 frequency,High

β

≈ min

2

21 ωπ

m

b

gr

CNF +≈

m

boptS g

rR 0

,2

frequency, Lowβ

≈0

min2

1β

bmrgNF +≈

• For a given technology, NFmin is a strong function of bias current.• For low operation frequency, NFmin can be reduced by increasing emitter

length.• For high operation frequency, NFmin is a weak function of emitter length.

Increase device size does reduce rb, yet capacitance also increase.• For high operation frequency, NFmin degrades as frequency increases.


Input Matching of LNA Noise

Power matching:Q1RFin

Lb

• Input impedance (assuming Cuand rπ is not significant):

ππ

ωω

ωC

LgLj

CjrLjZ em

ebbin ++−+=Le

and rπ is not significant):

• Power matching:Real part=Rs Sb

em RrC

Lg=+

π T

S

m

bSe

Rg

CrRL

ωπ ≈

−=

)(

Imaginarypart=0

πω CLL be 2

1=+

( )T

bS

m

T

m

bSb

rRgg

CrRC

Lωω

ωω

π

π

−−≈

−−= 22

1

• If Cu is considered, Cπreplaced by Cπ + CA, and therefore a larger inductor is required for matching.

LmLmA ZgCZgCC μμ ≈+= )1(


LmLmA gg μμ )(

LNA Design StepsL Q1

Le

RFinLb(1) Noise matching: sizing the transistor (emitter length)

and adjusting bias current to achieve minimum NF

Ω=+

= 50211 bmrgR Ω=+

= 50112

0

,

ββm

optS gR

( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+++= 2

0min

11211ββbmrgNF

(2) Power matching: adjusting Le such that the real part of the LNA input impedance equals to 50 Ohm. For 5AM, Le is about 0.2nH Use multiple downbonds to reduce the package effect

TT

Se

RLωω50

==

to reduce the package effect.

(3) Power matching: adding Lb such that the imaginary part of the LNA input impedance equals to zero 2ω

ω

m

Tb g

L ≈

(4) G i /b d idth Ch i l d t k t t i d

(5) Using SPICE sim to fine tune the component values, it ti t t d ff th i t t d

(4) Gain/bandwidth: Choosing load tank to meet gain and bandwidth requirements.


iterations to trade off the various parameters are expected.

Mixing with Nonlinearity

• Mixer is to convert a signal from one frequency to another intrinsically needs a nonlinear transfer function. A diode or a transistor can be used as a nonlinear device.ca be used as a o ea de ce

• Two inputs at ω1 and ω2 , which are passed through a nonlinearity multiplier will produce mixing terms at ω1±ω2 with other terms (harmonics, feed-through, intermodulation) that need to be filtered out.

• Mixers (multiplier) can be made from an amplifier with a controlled• Mixers (multiplier) can be made from an amplifier with a controlled switch.

R R

VCCVCC

Rc Rc

vout +

v2

vout -

switch

v1 i(v1)


Controlled Transconductance Mixer

Th t i l t d t th i t lt b th t d t• The current is related to the input voltage v2 by the transconductance of the input transistors Q1 and Q2. The transconductance is controlled by the current I0, which in turn is controlled by the input voltage v1.

i1 i2 2Io

io

v2

Q1 Q2+

i0=i1-i2o

TvvO

eI

i /1 21+= −

2Io

-

-2Io

v2

v1 TvvO

eI

i /2 21+=


Controlled Transconductance Mixer

Tovv

Ovv

Ooo v

vIeI

eI

IiiiTT 2

tanh11

2//21 22

=⎟⎠

⎞⎜⎝

⎛+

−+

=−= −

• If v2<<vT

Too v

vIi2

2≈

• Current source is modulated by small v1 Io is replaced with Io+gmcv1, where gmc is transconductance of the current source:

44 344 21434212

tanh2

tanh2

tanh)( 21

221 v

vvgvvI

vvvgIi

Tmc

To

Tmcoo +=+=

)(2 mixingtionmultiplicahfeedthrougV

not appear in differential output


not appear in differential output voltage double balanced mixer

Double-balanced MixerVCC

• Use switching quad to eliminate the v2 feedthrough

vo1 vo2

RC1 RC2

i3 i4 i5 i6

Q3 Q4

v1 -v12I 2I

v2

Q5 Q6

vv

v1 -v12Io 2Io

Tmc

Too v

vvgvvIiii

2tanh

2tanh 2

12

56' −=−=• 2nd pair current:

• Total differential current:T

mcooob vvvgiii

2tanh2 2

1' =−=


Double-balanced Mixer⎞⎛⎞⎛ A i( ) ( ) ( )

EeTT Rrv

vvii

vviiii

+⎟⎟⎠

⎞⎜⎜⎝

⎛=−⎟⎟

⎠

⎞⎜⎜⎝

⎛=+−+ 12

212

6453 2tanh

2tanh

Assuming small signal for V1

RC1 RC2

VCC

TT vvvv

iiii

eii

eii

22

/1

4/1

3 22 11 −

==

+=

+=

Q3 Q4 Q5 Q6

i3 i4i5 i6

v2

vo1 vo2

Eeo Rr

vIi+

+≈1

21

1

TT vvvv ei

ei /6/5 22 11 −+

=+

=

Q1 Q2

i1 i2

RE RE

Eo

Ee

RrvIi

and

+−=

121

2

v1

2Io


Ee Rr +2VEE

⎞⎛

Double-balanced Mixer• Output differential voltage

CEeT

o RRr

vvvv

+⎟⎟⎠

⎞⎜⎜⎝

⎛−= 12

2tanh

• Conversion gain relative to v1Co

RrR

vv

vv

+⎟⎟⎠

⎞⎜⎜⎝

⎛−=

2tanh 2

EeT Rrvv +⎟⎠

⎜⎝ 21

• With RE=0, a general large-signal expression for the output:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−=

TToCo v

vvvIRv

2tanh

2tanh2 21


LO Level at Upper Quad TransistorsTh diff i l i d i l i f b 4 f h i• The differential pair needs an input voltage swing of about 4 to 5 vT for the transistors to be hard-switched one way or the other.

• LO input to the mixer should be at least 100mV peak for complete switching. At 50Ω, 100mV peak is -10 dBm.

• -10 to 0 dBm (100~300 mVpp = 200~600mVpp diff) is a reasonable compromise-10 to 0 dBm (100 300 mVpp = 200 600mVpp diff) is a reasonable compromise between noise figure, gain and required LO power. This is also the reasonable level for all switching circuits

• If the LO voltage is too large, large current has to be moved into and out of the bases of the transistors during transition lead to spikes in the signals and reduce the switching speed cause an increase in LO feed throughswitching speed cause an increase in LO feed-through.

• Large LO also pushes switching transistor into saturation loose switching speed and inject mixer noise into substrate.

Va) b)Va) b)

Rc Rc

Vc

c

VLO+ VLO-

Vin+ Vin-

a) b)

Rc Rc

Vc

c

VLO+ VLO-

Vin+ Vin-

a) b)

Ibias

LOQ3 Q4 VdVd

Ibias

LOQ3 Q4 VdVd


w1

Slide 24

w1 weishen, 7/16/2003

Noise Contributions

total

Mixer Noise10

8

6

4

top transistors

bottom t i t

total

Noi

se P

ower

ve v

alue

s)

sourceNN

NF tot

11)(0

log10 0=

4

2

0-0.1 0 0.1

transistors

source resistance

VLO (instantaneous)

Out

put N

(Rel

ativdB65.8

5.111log10 ==

• Top transistor contributes significant noise during transition and contributes ignorable noise when fully switched, either in cutoff or saturation (without gain).

• Gain from RF input is maximum when top transistors are fully switched (cascode)

VLO (instantaneous)

• Gain from RF input is maximum when top transistors are fully switched (cascode).• need sharp transition buffer for LO large LO such that minimal time is spent around 0V.• Mixer noise figure can be approximately analyzed using a lowly swept dc voltage at the LO

input or with an actual LO signal.• With a slowly swept dc voltage, the mixer becomes equivalent to a cascode amplifier and the

LO input served as a gain-controlling signal.• For mixer, any noise (or signal) is mixed to two output frequencies, thus reducing the output

level mixer having less gain than the equivalent differential pair.


• However, both RF and image is mixed to IF doubling noise power at output.

Mixer with Simultaneous Noise and Power MatchUse inductor degeneration and inductor input achieving simultaneous noise and• Use inductor degeneration and inductor input achieving simultaneous noise and power matching similar to that of a typical LNA.

ZLO j t

VCC

R R

TE f

ZLπ2

0=

LO

IF- IF+

LO rejectRL RL

LO

RF

VLE LE

Q1 Q2

V T

m

fZgIIP

πω2

3 0≈VBB VBB

Tf

Single-to-differentialFilter harmonics

• Noise matching: sizing LE, and RF transistor, and operating the RF transistors at the current required for minimum NF.

• The quad switching transistors are sized for maximum fT, (typically about five to


q g fT, ( yp yten times smaller than the RF transistors.)

Mixer Design IssuesSizing Transistors

• The RF differential pair is basically an LNA stage, and the transistors and associated passives can be optimized using the LNA design techniques.

• The switching quad transistors are sized so that they operate close to their

Sizing Transistors

g q y ppeak fT at the bias current that is optimal for the differential pair transistors are biased at their minimum noise current, then the switching transistors end up being about one-eighth the size.

Increasing Gain

R2

Increasing Gain

• Voltage gain without matching and assuming full switching of the upper quad:

inEe

Co v

RrRv+

=π2

• To increase the gain increase the load resistance RC, to reduce degeneration resistance RE, or to increase the bias current IB.

• Make sure that increasing output voltage swing will not cause the switching transistors to become saturated. Enough headroom.


g

Increasing IP3Mixer Design Issues

• Identify which part of the circuit is compressing. Compression can be due to overdriving of the lower differential pair, clipping at the output, or the LO bias voltage being too low, causing clipping at the collectors of the bottom differential pair. Adjust the bias and voltage swing to avoid clipping.p j g g pp g

• 1. If the compression is due to the bottom differential pair (RF input), then linearity can be improved by increasing RE or by increasing bias current.

• 2. Compression caused by clipping at the output is typically due to the quad transistors going into saturation. Saturation can be avoided by reducing the g g y gload resistance or adjust the quad transistor bias. Too large LO will also cause saturation.

• 3. If compression is caused by clipping at the collector of the RF input differential pair, then increasing the LO bias voltage will improve linearity; h hi l i li i hhowever, this may result in clipping at the output.

Improving Noise Figure• NF will be largely determined by the choice of topology• NF will be largely determined by the choice of topology.• Use the simultaneous matched design technique. • To minimize noise, the emitter degeneration resistor should be kept as small

as possible. Use inductor as degeneration to achieve low noise.


• Make top transistors switching fast.

M t hi Bi R i t d G i

Mixer Design Issues

Matching, Bias Resistors, and Gain

• Use resistive matching to achieve broad band. For a resistively degenerated mixer, the RF input impedance will be fairly high; for example, with RE=100 Ω, Z b f th d f Kil Oh i f LNA t t t t d i thZin can be of the order of a Kilo Ohm easier for LNA output stage to drive the mixer.

• At the output, if matched, the load resistor Ro is equal to the collector resistor Rc. Furthermore, to convert from voltage gain Av to power gain Po/Pi, one must consider the output resistance Ri and load resistance Ro=Rc as follows:

ov2

2

C

i

E

C

o

iv

o

i

i

o

i

i

o

i

o

RR

RR

RR

ARR

vv

RvR

PP

22

2

2

2

2/2⎟⎟⎠

⎞⎜⎜⎝

⎛≈===

π


Documents

Lecture 7 RF Front-End Design LNA Mixer - Auburn University