RFIC Design and Testing for Wireless Communications

RFIC Design and Testing for Wireless Communications

A PragaTI (TI India Technical University) Course

July 18, 21, 22, 2008

Lecture 6: Basic Concepts

– Linearity, noise figure, dynamic range

By

Vishwani D Agrawal

Vishwani D. Agrawal

Fa Foster Dai

200 Broun Hall, Auburn University

Auburn, AL 36849-5201, USA

RFIC Design and Testing for Wireless Communications

Topics

Monday, July 21, 2008

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

11:00 – 12:30 Basic Concepts – Linearity, noise figure, dynamic range

2:00 – 3:30 RF front-end design – LNA, mixer 4:00 – 5:30 Frequency synthesizer design I (PLL)

T

d

J l 22 2008

Tuesday, July 22, 2008

9:00 – 10:30 Frequency synthesizer design II (VCO) 11:00 – 12:30 RFIC design for wireless communications

Units for Microwave and RFIC Design

Peak-to peak voltage: V

_pp

Root-mean-square voltage:

2

2

pp rms

V

V

=

Power in Watt :

V

V

Pwatt

rms pp 2 2

=

=

2

2

Power in dBm :

R

R

Pwatt

8

=

=

⎟

⎠

⎞

⎜

⎝

⎛

=

mW

mW

Pwatt

P

_dBm

1

]

[

log

10

₁₀

On a 50Ohm load, 0dBm=1mW=224mV

_rms

=632mV

_pp

⎠

⎝

1

mW

Noise Figure

• In RF design, most of the front-end receiver blocks are

characterized in terms of “noise figure” rather than input

referred noise

referred noise.

• Noise factor F is defined as

N

N

N

N

N

N

S

SNR

_{in i i o} o total o source o added o added

1

F

( ) ( )

+

( )

+

( )

F

N

N

N

GN

N

S

SNR

_{i o source o source o source}

o o o i i out in 10

log

10

NF

Figure,

Noise

1

F

) ( ) ( ) ( ) ( ) ( ) ( ) (

=

+

=

=

=

=

=

=

• Noise figure measures how much the SNR degrades as the

signal passes through a system.

• For a noiseless system, SNRin = SNRout, namely, F=1,

y

,

,

y,

,

NF=0dB,

regardless of the gain. This is because both the

input signal and the input noise are amplified (or attenuated)

by the same factor and no additional noise is introduced.

Thermal Noise

Th

l

i

(J h

i )

d

t

d

th

l

ti

f

•

Thermal noise (Johnson noise)

– due to random thermal motion of

electrons and is generated by resistors, base and emitter resistance

r

_b

,r

_E

,and r

_c

. of bipolar devices, and channel resistance of MOSFETs.

Thermal noise is a white noise with Gaussian amplitude distribution.

•

Thermal noise floor:

K

Hz

dBm

mW

kT

0

290

at

/

174

1

log

10

⎟

=

−

⎠

⎞

⎜

⎝

⎛

2 nb

V

Q

r

b

M

_I

2

R

2

n

V

+

_

+

r

e

Q

M

n

I

n

_

2 ne

V

+

_{_}

f

kTR

V

_n2

= 4

Δ

f

g

kT

I

_{n m}

⎟

Δ

⎠

⎞

⎜

⎝

⎛

=

3

2

4

2

>2/3 for submirocn MOS

>2/3 for submirocn MOS

Shot Noise

•

Shot noise (Schottky noise)

– due to the particle-like nature of

charge carriers. Only the time-average flow of electrons and holes

appears as constant current. Any fluctuation in the number of

charge carriers produces a random noise current at that instant.

Shot noise is a Gaussian white process associated with the transfer

Shot noise is a Gaussian white process associated with the transfer

of charge across an energy barrier (e.g., a p-n junction). This

random process is called shot noise and is expressed in amperes

per root hertz.

2 ,b n

I

Q

2 ,c n

I

f

qI

I

_n2

= 2

Δ

B bn

qI

i

=

2

i

_cn

=

2

qI

_C

Flicker noise

•

Flicker noise (1/f noise)

– found in all active devices. In bipolar

transistors, it is caused by traps associated with contamination and

crystal defects in the emitter-base depletion layer. These traps capture

and release carriers in a random fashion with noise energy

and release carriers in a random fashion with noise energy

concentrated in low frequency. K depends on processing and may vary

by order of magnitude.

2

5

0

,

2

~

.

a

f

f

I

K

I

a C n

=

Δ

≈

•

In MOSFETs, 1/f noise arises from random trapping of charge at the

oxide-silicon interfaces. Represented as a voltage source in series with

the gate, the noise spectral density is given by

f

WLCox

K

Noise Power Spectral Density

z) -135 e Power (dBm /H z 10dB/Dec Total Noise -150 -145 -140 Nois e Thermal and Shot Noise Flicker Noise -160 -155 0.1 1 10 100 1000 Frequency (kHz)

The 1/f corner frequency

The 1/f corner frequency

can be significantly higher

for MOSFET

BJT Model with Noise Sources

r_{b c} b’ v_b b 4kT C_μ C_{π g} mvb’e r_π i_cn i_bn i_bf 2qI_B 4kTr_b r_o 2qI_C e e 1/f noise _Base Shot Noise Collector Shot Noise

c

a)

b)

c

r

_b

b

v

rb

4kTr

_b

b’

_i

cn

2qI

_C

i

_bn

a)

r

_b

b

b’

_i

cn

c

2qI

i

b)

4kTr

_b

base

shot noise

collector

shot noise

e

2qI

_B

2qI

_B

q

_C bn

4kT

r

e

2qI

_B

2qI

_B

2qI

_C

i

_bn

shot noise

r

CMOS Model with Noise Sources

Input-referred noise

v_gs C_GS CGD g_mv_gs r v_o I_nd

_V

2

=

8

kT

r_o

kT

2

8

m

g

V

3

n

=

⎟

⎠

⎞

⎜

⎝

⎛

=

kT

g

_m

I

3

2

4

2 nd m

g

Z

kT

I

₂ in 2 n

3

8

=

•

Gate resistance can be added to the noise model with gate resistivity ρ

L

W

R

_GATE

ρ

3

1

=

Linear vs. Nonlinear Systems

• A system is

linear

if for any inputs x

1

(t) and

x

2

(t), x

1

(t) Æ y

2

(t), x

2

(t) Æ y

2

(t) and for all

values of constants a and b, it satisfies

a x

1

(t)+bx

2

(t) Æ ay

1

(t)+by

2

(t)

a x

1

(t)+bx

2

(t) Æ ay

1

(t)+by

2

(t)

A

t

i

li

if it d

t

ti f

• A system is

nonlinear

if it does not satisfy

Effects of Nonlinearity

• Harmonic Distortion

Harmonic Distortion

• Gain Compression

• Desensitization

Desensitization

• Intermodulation

• For simplicity, we limit our analysis to

memoryless time invariant

system Thus

memoryless, time invariant

system. Thus,

...

)

(

)

(

)

(

)

(

t

=

₁

x

t

+

₂

x

2

t

+

₃

x

3

t

+

y

α

α

α

(3.1)

Effects of Nonlinearity -- Harmonics

If a single tone signal is applied to a nonlinear system, the

output generally exhibits fundamental and harmonic

frequencies with respect to the input frequency. In Eq. (3.1), if

t

A

t

A

t

A

t

y

(

)

α

cos

ω

+

α

2

cos

2

ω

+

α

3

cos

3

ω

frequencies with respect to the input frequency. In Eq. (3.1), if

x(t) = Acosωt

, then

t

t

A

t

A

t

A

t

A

t

A

t

A

t

y

ω

ω

α

ω

α

ω

α

ω

α

ω

α

ω

α

)

3

cos

cos

3

(

4

)

2

cos

1

(

2

cos

cos

cos

cos

)

(

3 3 2 2 1 3 2 1

+

+

+

+

=

+

+

=

t

A

t

A

t

A

A

A

ω

α

ω

α

ω

α

α

α

3

cos

4

2

cos

2

cos

)

4

3

(

2

3 3 2 2 3 3 1 2 2

+

+

+

+

=

Observations:

1. even order harmonics result from α

_j

with even j and vanish if the system

has odd symmetry, i.e., differential circuits.

Effects of Nonlinearity -- Gain Compression

t

A

t

A

t

A

A

A

t

y

α

α

α

ω

α

ω

α

cos

3

ω

4

2

cos

2

cos

)

4

3

(

2

)

(

3 3 2 2 3 3 1 2 2

+

+

+

+

=

(3.2)

• Under small-signal assumption, the system is

4

2

4

2

g

y

normally linear and harmonics are negligible. Thus,

α

1

A dominates Æ

small-signal gain = α

1

.

• For large signal nonlinearity becomes evident

• For large signal, nonlinearity becomes evident.

large-signal gain =

. The gain varies

when input level changes.

4

/

3

₃ 3 1

α

A

α

+

• If

α

₃

< 0

, the output is a “compressive” or

“saturating” function of the input Æ

the gain is

compressed when A increases

Output of Bipolar Differential Pair

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −

=

T id C EE F id od

V

V

R

I

V

V

2

tanh

α

( )

=

−

3

+

5

−

7

+

_K

315

7

15

2

3

1

tanh

x

x

x

x

x

Effects of Nonlinearity – 1dB Compression Point

(dBV)

20

log

α

1

A

₃

1−dB

=

1

dB

u

t V

o

ltage

_1dB

1 1 1 3 1 3 1 1

3808

0

145

0

4

3

α

α

α

α

=

=

+

₋ − dB dB dB

A

A

A

dB

A

₁

Outp

u

20logA

in 3 3 1−dB

0

.

145

α

0

.

3808

α

A

V

dB

10

l

pp

/

8

2 dB

A

₁₋

_20logA

in

• 1-dB compression point is defined as the input signal level that causes

small-signal gain to drop 1 dB It’s a measure of the maximum input

mW

dBm

pp

1

50

log

10

×

Ω

=

small signal gain to drop 1 dB. It s a measure of the maximum input

range.

Effects of Nonlinearity – Desensitization (Blocking)

• Desensitization

-- small signal experiences a vanishingly small gain when

co-exists with a large signal, even if the small signal itself does not drive the

system into nonlinear range.

A

l i

t

t

i

t

x(t) = A cosω t+ A cosω t

t E (3 1)

h

,

cos

2

3

4

3

)

(

_{1 1 3 1}3 _{3 1 2}2

⎟

₁

+

L

⎠

⎞

⎜

⎝

⎛

₊

₊

=

A

A

A

A

t

t

y

α

α

α

ω

Applying two-tone inputs

x(t) = A

1

cosω

1

t+ A

2

cosω

2

t

to Eq.(3.1), we have

gain of

desired

2

4

⎠

⎝

,

cos

2

3

)

(

_{1 3 2}2

⎟

_{1 1}

+

L

⎠

⎞

⎜

⎝

⎛

₊

=

A

A

t

t

y

α

α

ω

For A

1

<< A

2

, it reduces to

signal

2

⎠

⎝

Observations:

• Weak signal’s gain decreases as a function of A

Weak signal s gain decreases as a function of A

₂₂

if α

if α

₃₃

< 0. For sufficiently large

< 0. For sufficiently large

A

₂

, the gain drops to zero Æ the weak signal is “

blocked

” by the strong signal.

(Why cannot we see stars during day?)

• Many RF receivers must be able to withstand blocking signals 60 to 70 dB

t

th

th

t d i

l

greater than the wanted signals.

Effects of Nonlinearity – Intermodulation

• Harmonic distortion is due to

self-mixing

of a

single-t

i

l It

b

d b l

filt i

tone signal. It can be suppressed by low-pass filtering

the higher order harmonics.

• However there is another type of nonlinearity

• However, there is another type of nonlinearity

--intermodulation (IM) distortion,

which is normally

determined by a “

two tone test

”.

• When two signals with different frequencies applied to

a nonlinear system, the output in general exhibits some

components that are not harmonics of the input

frequencies. This phenomenon arises from

cross-mixing

(multiplication) of the two signals

Effects of Nonlinearity – Intermodulation

A

A

)

(

DC Term

+

+

=

+

=

A

A

t

y

A

t

A

t

x

)

(

2

1

)

(

cos

cos

)

(

2 2 2 1 2 2 2 1 1

α

ω

ω

1

st

_Order

Terms

⎥

⎤

⎢

⎡

+

⎥⎦

⎤

⎢⎣

⎡

₊

₊

t

A

A

A

A

t

A

A

A

A

)

2

(

3

cos

)

2

(

4

3

2 2 1 2 2 2 1 1 3 1 1

α

ω

α

2

nd

_Order

[

+

]

+

+

⎥⎦

⎤

⎢⎣

⎡

₊

₊

t

A

t

A

t

A

A

A

A

2

cos

2

cos

2

1

cos

)

2

(

4

2 2 2 1 2 1 2 2 2 2 2 1 2 3 2 1

ω

ω

α

ω

α

α

Terms

[

]

[

+

]

+

+

−

+

+

t

A

t

A

t

t

A

A

3

cos

3

cos

4

1

)

cos(

)

cos(

2

2 3 2 1 3 1 3 2 1 2 1 2 1 2

ω

ω

α

ω

ω

ω

ω

α

3

rd

_Order

terms

[

]

[

]

[

]

_⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

−

+

+

+

−

+

+

t

t

A

A

t

t

A

A

)

2

cos(

)

2

cos(

)

2

cos(

)

2

cos(

4

3

4

1 2 1 2 2 2 1 2 1 2 1 2 2 1 3

ω

ω

ω

ω

ω

ω

ω

ω

α

[

]

_⎭

⎩

1 2 2 1 2 1

Intermodulation – Why do we care about IM3 mostly?

In wireless communication system such as cellular handsets with narrow-band

operating frequencies (i.e., a few tens of MHz), only the IM3 spurious signals

(2w1 - w2) and (2w2 - w1) fall within the filter passband.

Intermodulation -- Third Order Intercept Point (IP3)

• Two-tone test:

A

₁

=A

₂

=A and A is sufficiently small

so that

higher-order nonlinear terms are negligible and the gain is relatively

constant and equal to α

1

.

constant and equal to α

1

.

• As A increases, the fundamentals increases in proportion to A,

whereas IM3 products increases in proportion to A³.

⎤

⎡

⎤

⎡

+

=

+

=

A

t

y

A

t

A

t

x

)

(

cos

cos

)

(

2 2 2 1

α

ω

ω

3 1 3 3 1 3 2 3 1

and

3

4

4

9

IIP

OIP

IIP

A

α

α

α

α

α

>>

→

=

=

dB

A

_dB

6

9

145

.

0

1

[

+

]

+

[

+

+

]

+

+

⎥⎦

⎤

⎢⎣

⎡ +

+

⎥⎦

⎤

⎢⎣

⎡ +

t

t

A

t

t

A

t

A

A

t

A

A

)

cos(

)

cos(

2

cos

2

cos

1

cos

4

9

cos

4

9

2 2 2 2 3 1 1 2 3 1

ω

ω

ω

ω

α

ω

ω

α

ω

α

α

ω

α

α

A

_IP

dB

dB

₉

_.

₆

3

/

4

3 1

=

≈

−

[

]

[

]

[

]

[

_[

]

_]

⎭

⎬

⎫

⎩

⎨

⎧

−

+

+

+

−

+

+

+

+

+

−

+

+

+

+

t

t

t

t

A

t

t

A

t

t

A

t

t

A

)

2

cos(

)

2

cos(

)

2

cos(

)

2

cos(

4

3

3

cos

3

cos

4

1

)

cos(

)

cos(

2

cos

2

cos

2

2 1 2 1 2 1 2 1 3 3 2 1 3 3 2 1 2 1 2 2 1 2

ω

ω

ω

ω

ω

ω

ω

ω

α

ω

ω

α

ω

ω

ω

ω

α

ω

ω

α

[

]

_⎭

⎩

cos(

2

+

)

t

+

cos(

2

)

t

4

4

ω

₁

ω

₂

ω

₁

ω

₂

Intermodulation – IP2 vs. IP3

20

40

IP2 Fundamental

α

1

A

α

₁

A

‰

A

1

=A

2

=A

‰

2

ND

_{Order IM Product:}

2 1 2

α

α

=

IP

A

20

0

20

Fundamental 2 2

A

α

1 2 2

A

α

-60

-40

-20

IP3 1 1 1 2 1

ω

ω

−

ω

₁

ω

₂

ω

₁

+

ω

₂

Freq

‰

3

RD

_{Order IM Product}

₄

_α

-80

3

-100

3rd_{Order IM} Product 2nd_Order IM Product 1

‰

3

Order IM Product

3 1 3

3

4

α

α

=

IP

A

P

Δ

A

1

α

α

₁

A

3

-60

-120

_IIP3 -40 0 20 40 IM Product 2 3 3

4

3

A

α

3 3

4

3

A

α

Calculate IIP3 without Extrapolation

1

A

A

A

1

P

Δ

A

1

α

α

₁

A

3

3

A

3

20logAi 3 3

A

P

Freq

3 3

4

α

A

3 3

4

3

A

α

20logAin

P/2

2 1

2

ω

−

ω

ω

₁

ω

₂

2

ω

2

−

ω

1

Freq

]

[

2

]

[

]

[

3

P

dBm

dB

P

dBm

IIP

=

Δ

+

_in

Relationship Between 1-dB Compression and IP3

1-dB compression point with single tone applied:

3 1 3

3

4

α

α

=

IP

A

3 1 1

0

.

145

α

α

=

−dB

A

dB

A

A

dB IP

₃

_.

₀₄

₉

_.

₆₆

1 3

=

=

1-dB compression point with two tones applied:

dB

A

_IP

4

14

25

5

3

2

3 1 3

α

α

dB

A

_dB IP

₅

_.

₂₅

₁₄

_.

₄

22

.

0

3 1 1 3

=

=

=

α

α

Determine IIP3 and 1-dB Compression Point from Measurement

•

An amplifier operates at 2 GHz with a gain of 10dB. Two-tone test with equal power

applied at the input, one is at 2.01 GHz. At the output, four tones are observed at 1.99,

2.0, 2.01, and 2.02GHz. The power levels of the tones are -70,-20,-20, and -70dBm.

Determine the IIP3 and 1-dB compression point for this amplifier.

•

Solution: 1.99 and 2.02 GHz are the IP3 tones.

(

)

[

]

[

]

dB

P

dBm

P

P

G

P

IIP

66

14

66

9

5

5

70

20

2

1

10

20

2

1

3

=

₁

−

+

₁

−

₃

=

−

−

+

−

+

=

−

OIP3

)

log(

20

₁

A

dBm

P

_1dB

=

−

5

−

9

.

66

=

−

14

.

66

3 3

4

3

log

20

A

P

]

[

2

]

[

]

[

3

P

dBm

dB

P

dBm

IIP

=

Δ

+

_in IIP3 20logAin

4

P/2

2

Intermodulation of Cascade Nonlinear Stages

...

)

(

)

(

)

(

)

(

...

)

(

)

(

)

(

)

(

3 1 3 2 1 2 1 1 2 3 3 2 2 1 1

+

+

+

=

+

+

+

=

t

y

t

y

t

y

t

y

t

x

t

x

t

x

t

y

β

β

β

α

α

α

L

)

(t

)

(t

)

(t

)

y

₁

(

t

)

y

₂

(

t

)

(t

x

A

_IP3,1

A

A

A

A

_IP

₃

_,

₂

A

IP

3

,

3

Linearity is more important for back-end stages.

K

+

+

+

≈

₂

1

2

2

1

2

2

1

2

2

1

1

A

A

A

A

β

α

α

Noise Figure of Cascade Stages

(

)

NF

−

1

NF

−

1

NF

−

1

(

)

G

G

G

NF

G

G

NF

G

NF

NF

NF

m p p p m p p p tot ) 1 ( ... 2 1 1 1 3 1 2 1

1

...

1

1

1

1

−

+

+

+

+

−

+

=

NF

_tot

– total equivalent Noise Figure

NF

_m

– Noise Figure of m

th

_stage

G

A il bl

i

f

th

_t

G

_pm

– Available power gain of m

th

_stage

Sensitivity

• Sensitivity

-- defined as the minimum signal level that the

system can detect with acceptable SNR.

OUT RS sig OUT in

SNR

P

P

SNR

SNR

NF

=

=

/

• The overall signal power is distributed across the channel

bandwidth, B, integrating over the bandwidth to obtain total

mean square power

B

SNR

NF

P

P

_sig

_,

_tot

=

_RS

•

•

_OUT

•

B

SNR

NF

P

P

dB

dB

Hz

dBm

RS

dBm

Maximum Input Power

OIP3

)

log(

20

₁

A

2

, 3 out IM out in IIP

P

P

P

P

=

+

−

20logA 3 3

4

3

log

20

A

P

2

3

2

, ,in in IM in IM in in

P

P

P

P

P

+

−

=

−

=

2

P

+

P

IIP3

20logAin

P/2

3

2

_{IIP3 IM,in} in

P

P

P

=

+

where P

_IM,out

denotes output-referred power of IM

₃

products, P

_out

=P

_in

+G,

P

_IM,OUT

= P

_IM,in

+G.

The input level for which the IM products become equal to

the noise floor F

is thus given by

3

log

10

174

2

3

2

P

₃

F

P

₃

dBm

NF

B

P

_in

=

IIP

+

=

IIP

−

+

+

Dynamic Range

• Dynamic Range (DR)

-- defined as the ratio of the maximum to

minimum input levels that the circuit provides a reasonable

signal quality.

• Spurious Free Dynamic Range (SFDR)

determine the upper

• Spurious-Free Dynamic Range (SFDR)

-- determine the upper

end of dynamic range on the intermodulation behavior and the

lower end on sensitivity.

• The upper end of the dynamic range is defined as the

e uppe e d o t e dy a

c a ge s de

ed as t e

maximum input power

in a two tone test for which the 3rd IM

products do not exceed the

noise floor F=-174dBm+NF+10logB

.

• The SFDR is thus given by

min 3 min 3 , max ,

3

)

(

2

)

(

3

2

SNR

F

P

SNR

F

F

P

P

P

SFDR

_{in in mim} IIP

⎟

−

+

=

IIP

−

−

⎠

⎞

⎜

⎝

⎛

+

=

−

=

• Example: NF=9dB, P

_IIP3

=-15dBm, B=100kHz, SNR

_min

=12dB Æ

SFDR=(-15-(-174+9+50))/1.5-12=54.7dB.