複素アナログフィルタの基礎

計測制御工学 第 6 回講義

複素アナログフィルタの基礎

小林春夫

群馬大学大学院理工学府 電子情報部門

[email protected]

下記から講義使用

pdf

出席・講義感想もここから入力してください。

2021

5

24

(

)

/19 1

欧州のアナログ集積回路 研究教育事情

群馬大学 小林春夫

2020/5/11

Disclaimer:

１５年前に訪問した時の情報もあり、

一部は最新情報ではない

/19

欧州地図 2

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意外な欧州 3

● 日本は面積も人口も少ない？

欧州で面積＆人口が日本より大の国なし

● 欧州は人口少ない、大都市少ない アジアは多い

「アジアは米、欧州は小麦が主食のため」の説 米は何年も備蓄可、小麦は不可

● 「イギリス（ブリテン島）と欧州大陸は別」

の意識が双方にあり (?)

/19

米国と欧州は異なる 4

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欧州 2000 年以上の西洋科学の伝統の底力 5

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オランダ 6

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ベルギー（大学） 7

/19

ベルギー（研究所） 8

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イタリア 9

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イギリス、アイルランド 10

イギリス： 海外では UK を使う

England, Scotland, Wales, Northern Ireland

United Kingdom

サッカー ワールドカップにも独立

4

/19

ドイツ 11

/19

スイス 12

/19

北欧 13

/19

ロシア 14

半導体メーカ技術者より

/19

ポルトガル、イスラエル 15

/19

スペイン バルセロナ市 雑景 16

サグラダファミリア(Sagrada Familia) 聖家族 贖罪教会

/19

フランス 17

/19

フランス パリ 雑景 18

パリ第

6

/19

日本企業への売り込み 19

/19

関係ファイル 20

https://kobaweb.ei.st.gunma-u.ac.jp/news/pdf/2019/oldrepo_NapoliUniv.pdf https://kobaweb.ei.st.gunma-u.ac.jp/news/pdf/2019/oldrepo_Europe.pdf

https://kobaweb.ei.st.gunma-u.ac.jp/warehouse/20160722am9IMSTW.pdf

https://kobaweb.ei.st.gunma-u.ac.jp/warehouse/IMSTW20150703.pdf

Complex Signal Processing

in Analog / Mixed-Signal Circuits

Haruo Kobayashi

Minh Tri Tran, Koji Asami Anna Kuwana, Hao San

Division of Electronics and Informatics Gunma University

IPS04 Analog and Power

3rd International Conference on Technology and Social Science

May 8, 2019

Keynote Lecture 03

Full Body

Outline

● Motivation for Complex Signal Processing Research

● RC Polyphase Filter: Transfer Function

● RC Polyphase Filter: Flat Passband Gain Algorithm

● RC Polyphase Filter and Hilbert Filter

● Active Complex Bandpass Filters

● Conclusion

Outline

● Motivation for Complex Signal Processing Research

● RC Polyphase Filter: Transfer Function

● RC Polyphase Filter: Flat Passband Gain Algorithm

● RC Polyphase Filter and Hilbert Filter

● Active Complex Bandpass Filters

● Conclusion

Why My Research for Complex Signal Processing ?

About 15 years ago

at IEEE International Solid-State Circuits Conference San Francisco, CA

The most prestigious conference in IC design

Katholieke Universiteit Leuven (KU Leuven), Belgium

World top research group in analog IC design

Some simple circuit

with curious characteristics presentation

However,

I could not understand its principle

Basics of Complex Signal

2 real signals: I, Q

V ^signal = I + jQ Complex Signal

V ^image = I – jQ Image

I = [V ^signal + V ^image ]/2

Q = [V ^signal – V ^image ]/(2 j)

j ・ j = -1

Basic complex signal processing blocks

Outline

● Motivation for Complex Signal Processing Research

● RC Polyphase Filter: Transfer Function

● RC Polyphase Filter: Flat Passband Gain Algorithm

● RC Polyphase Filter and Hilbert Filter

● Active Complex Bandpass Filters

● Conclusion

Research Goal of First Research

• To establish systematic design and analysis methods of RC polyphase filters.

• As its first step,

to derive explicit transfer functions of the 1st-, 2nd- and 3rd-order

RC polyphase filters.

Features of RC Polyphase Filter

• Its input and output are complex signal.

• Passive RC analog filter

• One of key components in wireless transceiver analog front-end

- I, Q signal generation - Image rejection

• Its explicit transfer function

has not been derived yet.

First-order RC Polyphase Filter

R ¹ C ¹

I ⁱⁿ⁺

Q ⁱⁿ⁺

I ^in- Q in ^-

I ^out+

Q ^out+

I out-

Q ^out-

C ¹ C ¹

C ¹

R ¹ R ¹ R ¹

I: In-Phase, Q: Quadrature-Phase

Differential Complex Input: V in = I in + j Q in

Differential Complex Output: V out = I out + j Q out

I, Q Signal Generation

-2.5 -2 -1.5

-1 -0.5

0 0.5 1 1.5 2 2.5

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4

voltage [V]

time [us]

I out Q out

1 1

1 C

LO = R



Polyphase Filter

Qin = 0

I in = cos (ω

t)

I out = A cos (ω

t+θ)

Q out = A sin (ω

t+θ)

Single cosine Cosine, Sine signals

Cosine, Sine Signals in Receiver

IF ^Analog _Bandpass

Filter

cos(ω

t)

I

Q

AD Converter

- sin(ω

t)

analog digital AD

Converter

Problem when ω ^LO ≠ １ /R ¹ C ¹

-3 -2 -1 0 1 2 3

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4

voltage [V]

time [us]

Q out I out

1 1

2 C

LO = R



-2.5 -2 -1.5 -1 -0.5 0 0.5

1 1.5

2 2.5

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4

voltage [V]

time [us]

I out Q out

1 1

1 C

LO = R



2 ^nd -order RC Polyphase Filter

I out Q out

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4

voltage [V]

time [us]

1 1

2 C

LO = R



The problem of large difference between I ^out , Q ^out amplitudes can be alleviated

R1

R1 R1

R1 C1

C1

C1

C1 C2 C2

C2

C2

R2

R2 R2

R2

Iin+

Qin+

Iin- Qin-

Iout+

Qout+

Iout-

Qout-

3 ^rd -order RC Polyphase Filter

1 1

2 C

LO = R



I out Q out

The amplitude

difference problem is further alleviated.

R1

R1 R1

R1 C1

C1

C1

C1 C2

C2 C2

C2

R2 R2 R2 R2

C3 R3 C3 R3

R3

C3

R3

C3

Iin+

Qin+

Iin- Qin-

Iout+

Qout+

Iout-

Qout-

Pure I, Q Signal Generation

With

3 ^rd -order harmonics.

Without

3 ^rd -order harmonics.

Simulation of 3 ^rd -order Harmonics Rejection

-8 -6 -4 -2 0 2 4 6 8

20 22 24 26 28 30 32 34 36 38 40

voltage [V]

time [ns]

Iout Qout

) (

sin )

sin(

) (

) (

cos )

cos(

) (

3 3

t a

t t

Q

t a

t t

I

LO LO

in

LO LO

in









+

=

+

=

) sin(

) (

) cos(

) (









+

=

+

=

t A

t Q

t A

t I

LO out

LO out

-8 -6 -4 -2 0 2 4 6 8

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4

voltage [V]

time [us]

Iin Qin

1 1

3 1

C

LO = R



Image Rejection Filter

Polyphase Filter

I in =

(A + ^{B) cos(ωt)}

Q in =

(A - ^{B) sin(ωt)}

I out = Acos(ωt) Q out =

Asin(ωt)

t j t

j Be

Ae ^ + ^{−  Ae j  t}

image

Approach (1)

Complex Input: V in = I in + j Q in Complex Output: V out = I out + j Q out Complex Signal Processing

There is NO physical complex signal.

It is only defined mathematically.

Complex Signal Processing is NOT Complex.

Gauss plane

Complex Transfer Function

• Complex Signal Theory

• Complex input

• Complex output

• Complex

Transfer Function

) (

) ) (

( 

 

j V

j j V

G

in

= out

out out

out

in in

in

Q j

I j

V

Q j

I j

V

 +

=

 +

= ) (

) (





Signals in RC Polyphase Filter

) ( )

( )

(

) ( )

( )

(

) ( )

( )

(

) ( )

( )

(

) ( )

( )

(

) ( )

( )

(

t jQ

t I

t V

t jQ t

I t

V

t Q

t Q

t Q

t I

t I

t I

t Q

t Q

t Q

t I

t I

t I

out out

out

in in

in

out out

out

out out

out

in in

in

in in

in

+

=

+

=

−

=

−

=

−

=

−

=

− +

− +

− +

− +

Differential signal

Complex signal

R 1

C 1

I in+

Q in+

I in-

Q in-

I out+

Q out+

I out-

Q out-

C 1

C 1

R 1

R 1

R 1

C 1

Transfer Function of RC Polyphase Filter

1 2 1

) (

1 ) 1

(

. 1

) 1 (

RC j RC

G

RC j

j RC G



 



 

+

= + +

= +

•Transfer Function

•Gain

RC

− 1

Asymmetric

Explanation of I, Q Signal Generation by G ¹ ( jω)

𝑄 _𝑖𝑛 𝑡 ≡ 0, 𝐼 _𝑖𝑛 𝑡 = cos 𝜔𝑡 𝑉 _𝑖𝑛 𝑡 = 𝐼 _𝑖𝑛 𝑡 + 𝑗 𝑄 _𝑖𝑛 𝑡 = cos 𝜔𝑡 = 1

2 [𝑒 ^𝑗𝜔𝑡 + 𝑒 ^{−𝑗𝜔𝑡} ]

𝐺 ₁ 𝑗𝜔

𝜔= 1 𝑅𝐶

= 0 , 𝐺 ₁ 𝑗𝜔

𝜔= 1 𝑅𝐶

= 2 , ∠𝐺 ₁ 𝑗𝜔 = − 𝜋 4 𝑉 _𝑜𝑢𝑡 𝑡 = 1

2 [ 𝐺 ₁ 𝑗𝜔 𝑒 ^{𝑗 𝜔𝑡+∠𝐺 1 𝑗𝜔} + 𝐺 ₁ −𝑗𝜔 𝑒 ^{𝑗(−𝜔𝑡+∠𝐺 1 (−𝑗𝜔))} ]

= ²

2 cos 𝜔𝑡 − ^𝜋

4 + ^{𝑗 2}

2 sin(𝜔𝑡 − ^𝜋

4 )

Here ^{𝑮 𝟏 −𝒋𝝎 𝒆}

𝒋(−𝝎𝒕+∠𝑮

(−𝒋𝝎)) ] = 𝟎

Outline

● Motivation for Complex Signal Processing Research

● RC Polyphase Filter: Transfer Function

● RC Polyphase Filter: Flat Passband Gain Algorithm

● RC Polyphase Filter and Hilbert Filter

● Active Complex Bandpass Filters

● Conclusion

Transfer Function of 2 ^nd -order RC Polyphase Filter

Transfer Function

Derivation is very complicated, so we used “Mathematica.”

Gain |G2(jω)|

characteristics

𝐺 ₂ 𝑗𝜔 = (1 + 𝜔𝑅 ₁ 𝐶 ₁ )(1 + 𝜔𝑅 ₂ 𝐶 ₂ )

1 − 𝜔 ² 𝑅 ₁ 𝐶 ₁ 𝑅 ₂ 𝐶 ₂ + 𝑗𝜔(𝐶 ₁ 𝑅 ₁ + 𝐶 ₂ 𝑅 ₂ + 2𝑅 ₁ 𝐶 ₂ )

Gain of 3 ^rd -order RC Polyphase Filter

Gain:

Phase:

Gain characteristics

) (

) )) (

( tan(

) (

) (

) ) (

(

3 3 3

2 3

2 3

3 3



 





 

j D

j j D

G

j D

j D

j j N

G

R I

I R

−

=



= +

Need for Flat Passband Gain Algorithm

Transfer Function

Gain |G2( jω)|

characteristics

𝐺 ₂ 𝑗𝜔 = (1 + 𝜔𝑅 ₁ 𝐶 ₁ )(1 + 𝜔𝑅 ₂ 𝐶 ₂ )

1 − 𝜔 ² 𝑅 ₁ 𝐶 ₁ 𝑅 ₂ 𝐶 ₂ + 𝑗𝜔(𝐶 ₁ 𝑅 ₁ + 𝐶 ₂ 𝑅 ₂ + 2𝑅 ₁ 𝐶 ₂ )

We need flat passband gain

Four Design Parameters

4 parameters : 𝑅 ₁ , 𝑅 ₂ , 𝐶 ₁ , 𝐶 ₂

𝜔 ₁ = 1

𝑅 ₁ 𝐶 ₁ , 𝜔 ₂ = 1

𝑅 ₂ 𝐶 ₂ , 𝑋 = 1

𝑅 ₂ 𝐶 ₁ , 𝑌 = 1 𝑅 ₁ 𝐶 ₂

4 constraints

Two Constraints from Filter Spec.

● 2 zeros : − 𝜔 ₁ = ^{− 1}

𝑅 ₁ 𝐶 ₁ , − 𝜔 ₂ = ⁻¹

𝑅 ₂ 𝐶 ₂

are given from the filter specification.

Proposed Algorithm Uses Third Constraint

● We use the third constraint 𝑋 = ¹

𝑅 ₂ 𝐶 ₁

for passpand gain flattening.

Nyquist Chart of G ² ( jω)

|G

(jω

)|

|G

(jω

)|

Gain characteristics |G ² (jω)| Nyquist chart of G ² (jω)=X(ω)+j Y(ω)

Y( ω)

X(ω)

|G ² (jω ¹ )|=|G ² (jω ² )|

But in general |G ² (jω ¹ )|=|G ² (jω ² )|=|G ² (j√ω ¹ ω ² )|

|G2(j√ω1ω2)|

Our Idea for Flat Passband Gain Algorithm

If we make|G ² (jω ¹ )| =|G ² (jω ² )| =|G ² (𝑗 𝜔 ¹ 𝜔 ² )|, Passband gain becomes flat from ω ¹ to ω ^2.

Gain characteristics |G ² (jω)| Nyquist chart of G ² (jω)=X(ω)+j Y(ω)

|G

(jω

)|

|G

(jω

)|

|G2(j√ω1ω2)|

Outline

● Motivation for Complex Signal Processing Research

● RC Polyphase Filter: Transfer Function

● RC Polyphase Filter: Flat Passband Gain Algorithm

● RC Polyphase Filter and Hilbert Filter

● Active Complex Bandpass Filters

● Conclusion

Research Objective

Analyze RC polyphase filter

We found that relevance between

RC Polyphase Filter Analog

Complex (I, Q) input

Hilbert Filter Digital

Real part (Vin) input

Vin

Iout+

Qout+

Hilbert Filter

◼ Characteristics

・ Hilbert transform

・ 1 input and 2 outputs

・ It is often implemented in digital filter

Phase

Cosine, Sine Generation with Hilbert Filter

Gain

cos(ωt)+jsin(ωt)

cos(ωt)-jsin(ωt)

cos(ωt)+jsin(ωt)

2 cos(ωt)

cos(ωt) sin(ωt)

x

-ω ω ω component

-ω component

ω component

Hilbert filter

Hilbert Transform

Complex signal from real signal 𝑥 (𝑡) 𝑥 𝑡 → 𝑥 𝑡 + 𝑗𝑦 𝑡

Hilbert transform

𝑦 𝑡 = ¹

𝜋 න

−∞

∞ 𝑥(𝜏)

𝑡 − 𝜏 𝑑𝜏 = 𝑥 𝑡 ∗ 1 𝜋𝑡

Impulse response Fourier Transform

ℎ 𝑡 = 1

𝜋𝑡 𝑯 𝝎 = ቊ −𝒋 (𝝎 ≥ 𝟎) 𝒋 (𝝎 < 𝟎)

Frequency characteristic 𝐻 (ω)

𝒀 𝝎 = 𝑯 𝝎 𝑿(𝝎) = ቊ −𝒋𝑿 𝝎 (𝝎 ≥ 𝟎) 𝒋𝑿 𝝎 (𝝎 < 𝟎)

𝐹𝑜𝑢𝑟𝑖𝑒𝑟

David Hilbert 1862-1943

Phase

余弦波の複素平面での解釈

「現世」と「あの世」

ヒルベルトフィルタで負周波数成分のカット

ヒルベルトフィルタで負周波数が見える

1 ^st order RC Polyphase Filter ： Analysis

R1

R1

R1

R1 C1

C1

C1

C1

Iin+

Qin+

Iin-

Qin-

Iout+

Qout+

Iout-

Qout-

Pass band Stop band

: Transfer function

𝐻 ₁ 𝑗𝜔 = 1 + 𝜔𝑅 ₁ 𝐶 ₁ 1 + 𝑗𝜔𝑅 ₁ 𝐶 ₁

1

1 ^st order RC Polyphase Filter : Gain and Phase

H _1re − H _1im H _1re + H _1im

π

2 phase lag

π

2 phase lead 𝐻 _1𝑟𝑒 𝑗𝜔 = 𝐻 ₁ 𝑗𝜔 + 𝐻 ₁ ^∗ (−𝑗𝜔)

2 = 1

1 + 𝑗𝜔𝑅 ₁ 𝐶 ₁ 𝐻 _1𝑖𝑚 𝑗𝜔 = 𝐻 ₁ 𝑗𝜔 − 𝐻 ₁ ^∗ (−𝑗𝜔)

2 = −𝑗 𝜔𝑅 ₁ 𝐶 ₁ 1 + 𝑗𝜔𝑅 ₁ 𝐶 ₁

𝐻 ₁ 𝑗𝜔 = 𝐻 _1𝑟𝑒 𝑗𝜔 + 𝑗𝐻 _1𝑖𝑚 (𝑗𝜔)

ー H _1re

ー H _1im

ー H ₁

1 ^st order case Analysis Results

Gain : Hilbert filter only at zero Phase : Completely Hilbert filter

Hilbert filter

RC Polyphase Filter

Results ： 2 ^nd to 4 ^th RC Polyphase Filter

Gain Phase

2 ^nd

3 ^rd

4 ^th

ー H

ー H

ー H

Analysis Results and Consideration

1 ^st to 4 ^th order RC Polyphase Filter Analysis results

Prove for general n-th order case (n = 1, 2, 3, 4, 5, ...)

Gain : Hilbert filter only at zero

Phase : Completely Hilbert filter

Order and Gain

-20 -10 0 10 20

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

相対角周波数 [rad/s] (RC=1/(2π))

|H|

-20 -10 0 10 20

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

相対角周波数 [rad/s] (RC=1/(2π))

|H|

-20 -10 0 10 20

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

相対角周波数 [rad/s] (RC=1/(2π))

|H|

-20 -10 0 10 20

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

相対角周波数 [rad/s] (RC=1/(2π))

|H|

1

2

3

4

The higher orders,

Increase number of zeros

|𝐻𝑟𝑒| and |𝐻𝑖𝑚| becomes close in wide range

Close to ideal Hilbert transform

Order and Phase

Phase characteristic is not changed

There is always 90 ° phase difference

1

2

3

4

Fulfill Hilbert transform in full range

-20 -10 0 10 20

-π π/2 0 π/2 π

相対角周波数 [rad/s] (RC=1/(2π))

∠H

-20 -10 0 10 20

-π π/2 0 π/2 π

相対角周波数 [rad/s] (RC=1/(2π))

∠H

-20 -10 0 10 20

-π π/2 0 π/2 π

相対角周波数 [rad/s] (RC=1/(2π))

∠H

-20 -10 0 10 20

-π π/2 0 π/2 π

相対角周波数 [rad/s] (RC=1/(2π))

∠H

Conclusion

RC polyphase filter is approximation of ideal Hilbert filter for complex input signal

-20 -10 0 10 20

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

相対角周波数 [rad/s] (RC=1/(2π))

|H|

RC Polyphase Filter Hilbert Filter

Phase

Gain Gain Phase

-20 -10 0 10 20

-π π/2 0 π/2 π

相対角周波数 [rad/s] (RC=1/(2π))

∠H

Outline

● Motivation for Complex Signal Processing Research

● RC Polyphase Filter: Transfer Function

● RC Polyphase Filter: Flat Passband Gain Algorithm

● RC Polyphase Filter and Hilbert Filter

● Active Complex Bandpass Filters

● Conclusion

Gm : Transconductance

Input voltage: V _in

Output current : I _out I _out =g _m V _in

V _in g _m I _out I ₊ I _-

I _b V _in

+ -

dimension of g m

R 1

I _out =I ₊ -I _-

=g _m V _in

Complex Bandpass Gm-C Filter

I ⁱⁿ

Q in

C

C

g _m

- +

V _Iout

V _Qout g ₀

g ₀

C s g C

s g

g

jg sc

g jQin Iin

jV V

m

m

Qout Iout

2 0 2 2

0 2

0

+ 2 +

+

−

= +

+

+

+

Gain of Complex Bandpass Gm-C Filter

0 ω

C gm C

g C

gm +

C g C

gm −

0

1 2 1

g

0

1 g

Center Freq.

C gm

g 0

Q = gm

Gain

Complex Bandpass Active RC Filter

I _out+

Q _out- I _in

I _out-

Q _out+

Q _in

+ -

+ -

g

g

g

g

g

g

C

C

3 2

1

) ) (

(

g g

g C g

j g j g

H

=

=

= +

− +

= −







 

Our Investigation Results

● Transfer functions of

complex bandpass Gm-C and active RC filters are the same.

● Both complex bandpass filters are NOT close to Hilbert filter

Phase characteristics are far from Hilbert.

● RC polyphase filter is close to Hilbert filter.

Outline

● Motivation for Complex Signal Processing Research

● RC Polyphase Filter: Transfer Function

● RC Polyphase Filter: Flat Passband Gain Algorithm

● RC Polyphase Filter and Hilbert Filter

● Active Complex Bandpass Filters

● Conclusion

Conclusion

RC polyphase filter is simple, but very interesting

Even somewhat mysterious !

To understand its principle, we use its complex transfer function and

Hilbert transfer form.

These are useful for filter design as well as analysis

Final Statement

Complex Signal Processing is NOT Complex.

Quadrature Signals: Complex, But Not Complicated.

Our World is in Complex Domain.

Real Imaginary

付録： スイッチトキャパシタ回路

スイッチトキャパシタ回路の動作原理

スッチト・キャパシタ積分回路

H. San, Y. Jingu, H. Wada, H. Hagiwara, A. Hayakawa, J. Kudoh ² , K. Yahagi ² ,

T. Matsuura ² , H. Nakane ² , H. Kobayashi,

M. Hotta ³ , T. Tsukada ² , K.Mashiko ⁴ , A.Wada ⁵

1) Gunma University

2) Renesas Technology Corp.

3) Musashi Institute of Technology

A Multibit Complex

Bandpass ∆ΣAD Modulator with I,Q Dynamic Matching

and DWA Algorithm

 Motivation

 Complex Bandpass Delta-Sigma AD Modulator

 Proposed Architecture

 I, Q Dynamic Matching

 Complex DWA Algorithm

 Measured Results

 Conclusion

Outline

 Motivation

 Complex Bandpass Delta-Sigma AD Modulator

 Proposed Architecture

 I, Q Dynamic Matching

 Complex DWA Algorithm

 Measured Results

 Conclusion

Outline

Low power ADC in low-IF receiver

targeted for bluetooth, wireless LAN.

Motivation

Complex bandpass delta-sigma

AD modulator

f

Zero-IF

DC Frequency

Signal offset 1/f noise

f

Signal offset 1/f noise

DC Frequency

Low-IF Image

f

Low-IF offset 1/f noise

RF → Baseband Zero-IF

⇒ No mage

Problem of DC offset, flicker noise RF → Low-IF

No problem of DC offset, flicker noise.

Image as well as signal are

AD converted ⇒ Power is wasted Image is not AD converted.

Direct conversion receiver

Low-IF receiver Conventional

Receiver Architecture Comparison

Quadrature-IF

 Motivation

 Complex Bandpass Delta-Sigma AD Modulator

 Proposed Architecture

 I,Q Dynamic Matching

 Complex DWA Algorithm

 Measured Results

 Conclusion

Outline

H(z)

Complex Banpass Filter

ADC

ADC

DAC

DAC

+ +

Iin

Qin

Iout

Qout Analog

Input

Digital Output E

E

- -

) jE E

H ( 1

) 1 jQ I

H ( 1

H jQ I

q i

in in

out out

 



 





Complex Bandpass Delta-Sigma Modulator

 Motivation

 Complex Bandpass Delta-Sigma AD Modulator

 Proposed Architecture

 I,Q Dynamic Matching

 Complex DWA Algorithm

 Measured Results

 Conclusion

Outline

Proposed Architecture

• New complex bandpass filter

• Multi-bit ADCs/DACs

• Complex DWA algorithm

Proposed Structure

Conventional complex filter I &Q crossing paths

I,Q Dynamic Matching of Complex Filter

Proposed complex filter Upper, lower separated paths

 I,Q mismatch reduction.

Operation of Proposed Complex Filter

Iout(n) = Iin(n-1) - Qout(n-1)

Qout(n) = Qin(n-1) + Iout(n-1)

Complex BPDSM with Low-power

• 2 ^nd order ---- low power

• 9-level ADCs/DACs

• Stability improvement

• Low quantization error

• Power reduction of amplifiers I,Q mismatch

• Solved by dynamic matching Nonlinearities of multibit DAC

• Solved by complex DWA

Complex DWA (1)

j z

) 1 z ( H ₁

  H ₂ ( z )  z  j

Digital bandpass filter Analog band elimination filter

Complex DWA (2)

 Motivation

 Complex Bandpass Delta-Sigma AD Modulator

 Proposed Architecture

 I,Q Dynamic Matching

 Complex DWA Algorithm

 Measured Results

 Conclusion

Outline

Chip Implementation

• 1P6M 0.18µm CMOS Process

•

Measured Output Power Spectrum

Effect of Complex DWA

Summary of Modulator Performance

Technology 0.18-µm CMOS 1P6M

Supply voltage 2.8V

Sampling Frequency 20MHz

SNDR 64.5dB @ BW=78kHz

Power consumption 28.4mw

Active area 1.4mm*1.3mm

 Motivation

 Complex Bandpass Delta-Sigma AD Modulator

 Proposed Architecture

 I,Q Dynamic Matching

 Complex DWA Algorithm

 Measured Results

 Conclusion

Outline

• A 2 ^nd -order multi-bit complex bandpass delta-sigma modulator

Low power

• Complex filter with dynamic matching

– I,Q mismatch reduction – Layout simplification

• Complex DWA

– Suppression of multibit DACs nonlinearities

• Chip measurements demonstrated these

Conclusion