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11

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ファイルをダウンロードしてください。

出席・講義感想もここから入力してください。

https://kobaweb.ei.st.gunma-u.ac.jp/lecture/lecture.html

2020年6月1日(月)

/191

Kobayashi Lab.

Gunma University

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

/192

欧州地図

/193

意外な欧州

● 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 (?)

/194

米国と欧州は異なる

/195

欧州 2000年以上の西洋科学の伝統の底力

/196

オランダ

/197

ベルギー（大学）

/198

ベルギー（研究所）

/199

イタリア

/1910

イギリス、アイルランド

イギリス：海外では UK を使う

England, Scotland, Wales, Northern Ireland の連合王国 United Kingdom

サッカーワールドカップにも独立4チーム出場

https://www.google.co.jp/url?sa=i&url=https%3A%2F%2Fmars-speed.co.jp%2Funited-kingdom%2F&psig=AOvVaw0seSQ2lQ5qOjHQ5dlf0q5o&ust=1589266162619000&source=images&cd=vfe&ved=0CAIQjRxqFwoTCNiIqPybq-kCFQAAAAAdAAAAABAI

https://www.google.co.jp/url?sa=i&url=https%3A%2F%2Fwww.internationalstudent.com%2Fstudy_uk%2Fliving_uk%2Fmap_climate%2F&psig=AOvVaw0seSQ2lQ5qOjHQ5dlf0q5o&ust=1589266162619000&source=images&cd=vfe&ved=0CAIQjRxqFwoTCNiIqPybq-kCFQAAAAAdAAAAABAO

/1911

ドイツ

/1912

スイス

/1913

北欧

/1914

ロシア

半導体メーカ技術者より

/1915

ポルトガル、イスラエル

/1916

スペインバルセロナ市雑景

サグラダファミリア(Sagrada Familia)

聖家族贖罪教会

/1917

フランス

● グルノーブル(Grenoble)：フランスのシリコンバレー

/1918

フランスパリ雑景

パリ第6大学セーヌ川エッフェル塔凱旋門

/1919

日本企業への売り込み

/1920

関係ファイル

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

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

Gunma University Kobayashi Lab

Complex Signal Processingin Analog / Mixed-Signal Circuits

Haruo Kobayashi

Minh Tri Tran, Koji Asami

Anna Kuwana, Hao San

Division of Electronics and InformaticsGunma University

IPS04 Analog and Power

3rd International Conference on Technology and Social Science

May 8, 2019Keynote Lecture 03

Full Body

http://www.google.co.jp/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=XxicGsaDCzsPuM&tbnid=2cjxvii7O6Y6aM:&ved=0CAcQjRw&url=http://sophie-in-tokio.blogspot.com/2010/01/owari.html&ei=S7I5VOTZIYSa8QXs8oHQCQ&bvm=bv.77161500,d.dGc&psig=AFQjCNHYkkS5Xy28Z2VuOcAl2KzQaLEzPA&ust=1413153670218700

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

2/57

Outline






● Conclusion

3/57

Why My Research for Complex Signal Processing ?

About 15 years ago

at IEEE International Solid-State Circuits ConferenceSan Francisco, CAThe most prestigious conference in IC design

Katholieke Universiteit Leuven (KU Leuven), BelgiumWorld top research group in analog IC design

Some simple circuit with curious characteristics

presentation

However, I could not understand its principle

4/57

Basics of Complex Signal

2 real signals: I, Q

Vsignal = I + jQ Complex Signal

Vimage= I – jQ Image

I = [Vsignal + Vimage]/2

Q = [Vsignal – Vimage]/(2 j)

j・ j = -1

Basic complex signal processing blocks

5/57

Outline






● Conclusion

6/57

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.

7/57

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.

8/57

First-order RC Polyphase Filter

R1C1

Iin+

Qin+

Iin-

Qin-

Iout+

Qout+

Iout-

Qout-

C1

C1

C1

R1

R1

R1

I: In-Phase, Q: Quadrature-Phase

Differential Complex Input: Vin = Iin + j Qin

Differential Complex Output: Vout = Iout + j Qout

9/57

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

vo

lta

ge

[V

]

time [us]

Iout Qout

11

1

CRLO =

Polyphase

FilterQin = 0

Iin = cos (ωLO t)Iout = A cos (ωLO t+θ)

Qout = A sin (ωLO t+θ)

Single cosine Cosine, Sine signals

10/57

Cosine, Sine Signals in Receiver

IF Analog

Bandpass

Filter

cos(ω0 t)

I

Q

AD

Converter

- sin(ω0 t)

analog digital

AD

Converter

They are used for down conversion

11/57

Problem when ωLO≠１/R1C1

-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

vo

lta

ge

[V

]

time [us]

QoutIout

11

2

CRLO=

-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]

Iout Qout

11

1

CRLO =

12/57

2nd-order RC Polyphase Filter

Iout Qout

-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]

11

2

CRLO=

The problem of large

difference between

Iout, Qout 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-

13/57

3rd-order RC Polyphase Filter

11

2

CRLO=

Iout Qout

The amplitude

difference problem

is further alleviated.

R1

R1

R1

R1

C1

C1

C1

C1C2

C2

C2

C2

R2

R2

R2

R2

R3C3

R3C3

R3C3

R3

C3

Iin+

Qin+

Iin-

Qin-

Iout+

Qout+

Iout-

Qout-

14/57

Pure I, Q Signal Generation

With3rd-order harmonics.

Without3rd-order harmonics.

15/57

Simulation of 3rd-order Harmonics Rejection

-8

-6

-4

-2

0

2

4

6

8

20 22 24 26 28 30 32 34 36 38 40

vo

lta

ge

[V

]

time [ns]

Iout Qout

)(sin)sin()(

)(cos)cos()(

3

3

tattQ

tattI

LOLOin

LOLOin

+=

+=

)sin()(

)cos()(

+=

+=

tAtQ

tAtI

LOout

LOout

-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

11

13

CRLO=

16/57

Image Rejection Filter

Polyphase

Filter

Iin =

(A+B) cos(ωt)

Qin =

(A-B) sin(ωt)

Iout =

Acos(ωt)

Qout =

Asin(ωt)

tjtj BeAe −+tjAe

signal image

17/57

Approach (1)

Complex Input: Vin = Iin + j Qin

Complex Output: Vout = Iout + j Qout

Complex Signal Processing

There is NO physical complex signal.

It is only defined mathematically.

Complex Signal Processing is NOT Complex.

Gauss plane

18/57

Complex Transfer Function

• Complex Signal Theory

• Complex input

• Complex output

• Complex

Transfer Function

)(

)()(

jV

jVjG

in

out=

outoutout

ininin

QjIjV

QjIjV

+=

+=

)(

)(

19/57

Signals in RC Polyphase Filter

)()()(

)()()(

)()()(

)()()(

)()()(

)()()(

tjQtItV

tjQtItV

tQtQtQ

tItItI

tQtQtQ

tItItI

outoutout

ininin

outoutout

outoutout

ininin

ininin

+=

+=

−=

−=

−=

−=

−+

−+

−+

−+

Differential signal

Complex signal

R1

C1

Iin+

Qin+

Iin-

Qin-

Iout+

Qout+

Iout-

Qout-

C1

C1

R1

R1

R1C1

20/57

Transfer Function of RC Polyphase Filter

21

1

)(1

1)(

.1

1)(

RC

RCjG

RCj

RCjG

+

+=

+

+=

•Transfer Function

•Gain

RC

1−

Asymmetric

21/57

Explanation of I, Q Signal Generation by G1(jω)

𝑄𝑖𝑛 𝑡 ≡ 0, 𝐼𝑖𝑛 𝑡 = cos 𝜔𝑡

𝑉𝑖𝑛 𝑡 = 𝐼𝑖𝑛 𝑡 + 𝑗 𝑄𝑖𝑛 𝑡 = cos 𝜔𝑡 =1

2[𝑒𝑗𝜔𝑡 + 𝑒−𝑗𝜔𝑡]

𝐺1 𝑗𝜔𝜔=

1𝑅𝐶

= 0 , 𝐺1 𝑗𝜔𝜔=

1𝑅𝐶= 2 , ∠𝐺1 𝑗𝜔 = −

𝜋

4

𝑉𝑜𝑢𝑡 𝑡 =1

2[ 𝐺1 𝑗𝜔 𝑒𝑗 𝜔𝑡+∠𝐺1 𝑗𝜔 + 𝐺1 −𝑗𝜔 𝑒𝑗(−𝜔𝑡+∠𝐺1(−𝑗𝜔))]

=2

2cos 𝜔𝑡 −

𝜋

4+

𝑗 2

2sin(𝜔𝑡 −

𝜋

4)

Here𝑮𝟏 −𝒋𝝎 𝒆𝒋(−𝝎𝒕+∠𝑮𝟏(−𝒋𝝎))] = 𝟎

22/57

Outline






● Conclusion

23/57

Transfer Function of 2nd-order RC Polyphase Filter

Transfer Function

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

Gain |G2(jω)| characteristics

𝐺2 𝑗𝜔 =(1 + 𝜔𝑅1𝐶1)(1 + 𝜔𝑅2𝐶2)

1 − 𝜔2𝑅1𝐶1𝑅2𝐶2 + 𝑗𝜔(𝐶1𝑅1 + 𝐶2𝑅2 + 2𝑅1𝐶2)

24/57

Gain of 3rd-order RC Polyphase Filter

Gain:

Phase:

11

1

CR−

22

1

CR−

33

1

CR−

Gain characteristics

)(

)())(tan(

)()(

)()(

3

33

23

23

33

jD

jDjG

jDjD

jNjG

R

I

IR

−=

+=

25/57

Need for Flat Passband Gain Algorithm

Transfer Function

Gain |G2(jω)| characteristics

𝐺2 𝑗𝜔 =(1 + 𝜔𝑅1𝐶1)(1 + 𝜔𝑅2𝐶2)

1 − 𝜔2𝑅1𝐶1𝑅2𝐶2 + 𝑗𝜔(𝐶1𝑅1 + 𝐶2𝑅2 + 2𝑅1𝐶2)

We need flat passband gain

26/57

Four Design Parameters

4 parameters : 𝑅1, 𝑅2, 𝐶1, 𝐶2

𝜔1 =1

𝑅1𝐶1, 𝜔2 =

1

𝑅2𝐶2, 𝑋 =

1

𝑅2𝐶1, 𝑌 =

1

𝑅1𝐶2

4 constraints

27/57

Two Constraints from Filter Spec.

● 2 zeros : −𝜔1=− 1

𝑅1𝐶1, − 𝜔2=

−1

𝑅2𝐶2

are given from the filter specification.

28/57

Proposed Algorithm Uses Third Constraint

● We use the third constraint 𝑋 =1

𝑅2𝐶1

for passpand gain flattening.

● The fourth constraint is left for ease of IC realization.29/57

Nyquist Chart of G2(jω)

|G2(jω1)||G2(jω2)|

Gain characteristics |G2(jω)| Nyquist chart of G2(jω)=X(ω)+j Y(ω)

Y(ω

)X(ω)

|G2(jω1)|=|G2(jω2)|

But in general |G2(jω1)|=|G2(jω2)|=|G2(j√ω1ω2)|

|G2(j√ω1ω2)|

30/57

Our Idea for Flat Passband Gain Algorithm

If we make|G2(jω1)| =|G2(jω2)| =|G2(𝑗 𝜔1𝜔2)|,Passband gain becomes flat from ω1 to ω2.

Gain characteristics |G2(jω)| Nyquist chart of G2(jω)=X(ω)+j Y(ω)

|G2(jω1)||G2(jω2)|

|G2(j√ω1ω2)|

31/57

Outline






● Conclusion

32/57

Research Objective

Analyze RC polyphase filter

We found that relevance between

RC polyphase filter and Hilbert filter

RC Polyphase Filter

Analog

Complex (I, Q) input

Hilbert Filter

Digital

Real part (Vin) input

Vin

Iout+

Qout+

33/57

Hilbert Filter

◼ Characteristics・Hilbert transform・1 input and 2 outputs・It is often implemented in digital filter

Gain

Phase

34/57

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)

xω-ω

ω component

-ω component

ω component

Hilbert filter

35/57

Hilbert Transform

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

Hilbert transform

𝑦 𝑡 =1

𝜋න

−∞

∞𝑥(𝜏)

𝑡 − 𝜏𝑑𝜏 = 𝑥 𝑡 ∗

1

𝜋𝑡

Impulse response Fourier Transform

ℎ 𝑡 =1

𝜋𝑡𝑯 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 Hilbert1862-1943

Phase

36/57

余弦波の複素平面での解釈

37/57

「現世」と「あの世」

38/57

ヒルベルトフィルタで負周波数成分のカット

39/57

ヒルベルトフィルタで負周波数が見える

40/57

1st order RC Polyphase Filter：Analysis

R1

R1

R1

R1

C1

C1

C1

C1

Iin+

Qin+

Iin-

Qin-

Iout+

Qout+

Iout-

Qout-

Zero:

Pass bandStop band

: Transfer function𝐻1 𝑗𝜔 =1 + 𝜔𝑅1𝐶11 + 𝑗𝜔𝑅1𝐶1

ωk =1

𝑅𝑘𝐶𝑘41/57

1st order RC Polyphase Filter : Gain and Phase

H1re − H1im H1re + H1im

H1re = H1im

π

2phase lag

π

2phase lead

Gain Phase

𝐻1𝑟𝑒 𝑗𝜔 =𝐻1 𝑗𝜔 + 𝐻1

∗(−𝑗𝜔)

2=

1

1 + 𝑗𝜔𝑅1𝐶1

𝐻1𝑖𝑚 𝑗𝜔 =𝐻1 𝑗𝜔 − 𝐻1

∗(−𝑗𝜔)

2= −𝑗

𝜔𝑅1𝐶11 + 𝑗𝜔𝑅1𝐶1

𝐻1 𝑗𝜔 = 𝐻1𝑟𝑒 𝑗𝜔 + 𝑗𝐻1𝑖𝑚(𝑗𝜔)

ー H1reー H1imー H1

42/57

1st order case Analysis Results

Gain : Hilbert filter only at zero

Phase : Completely Hilbert filter

Gain Phase

Hilbert filter

RC Polyphase Filter

43/57

Results：2nd to 4th RC Polyphase Filter

Gain Phase

2nd

3rd

4th

ー H1reー H1imー H1

44/57

Analysis Results and Consideration

1st to 4th 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

45/57

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


|H|

-20 -10 0 10 20

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6


|H|

-20 -10 0 10 20

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6


|H|

1st 2nd 3rd 4th

The higher orders,Increase number of zeros|𝐻𝑟𝑒| and |𝐻𝑖𝑚| becomes close in wide range

Close to ideal Hilbert transform

46/57

Order and Phase

Phase characteristic is not

changed

There is always 90° phase

difference

1st 2nd 3rd 4th

Fulfill Hilbert transform in full range

-20 -10 0 10 20-π

π/2

0

π/2

π


∠H

-20 -10 0 10 20-π

π/2

0

π/2

π


∠H

-20 -10 0 10 20-π

π/2

0

π/2

π


∠H

-20 -10 0 10 20-π

π/2

0

π/2

π


∠H

47/57

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


|H|

RC Polyphase Filter Hilbert Filter

PhaseGain Gain Phase

-20 -10 0 10 20-π

π/2

0

π/2

π


∠H

48/57

Outline






● Conclusion

49/57

Gm : Transconductance

Input voltage: Vin

Output current : Iout Iout=gmVin

Vin

Ioutgm

I+ I-

Ib

Vin

+

-

dimension of gmR

1

Iout=I+-I-=gmVin

50/57

Complex Bandpass Gm-C Filter

Iin

Qin

C

C

gm

-

+

VIout

VQout

g0

g0

CsgCsgg

jgscg

jQinIin

jVV

m

m

QoutIout

02222

0

0

2+++

−+=

+

+

+

51/57

Gain of Complex Bandpass Gm-C Filter

ω0

C

gm

C

g

C

gm 0+C

g

C

gm 0−

0

1

2

1

g

0

1

g

Center Freq.C

gm

0g

gmQ =

Gain

52/57

Complex Bandpass Active RC Filter

Iout+

Qout-

Iin

Iout-

Qout+

Qin

+

-

+

-

g2

g2 g3

g3

g1

g1

C

C

2

1

2

3300

32

1

|)(|2

)()(

g

gjH

g

gQQ

C

g

Cgjg

gjH

===

+−+

−=

　ゲイン値　　　中心周波数Center freq. Gain

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Our Investigation Results

● Transfer functions of complex bandpass Gm-C and active RC filtersare the same.

● Both complex bandpass filters are NOTclose to Hilbert filter

Phase characteristics are far from Hilbert.

● RC polyphase filter is close to Hilbert filter.

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Outline






● Conclusion

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Conclusion

RC polyphase filter is simple, but very interesting

Even somewhat mysterious !

To understand its principle, we useits complex transfer function and

Hilbert transfer form.

These are useful for filter design as well as analysis

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Final Statement

Complex Signal Processing is NOT Complex.

Quadrature Signals: Complex, But Not Complicated.

Our World is in Complex Domain.

Real Imaginary

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付録：スイッチトキャパシタ回路

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スイッチトキャパシタ回路の動作原理

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スッチト・キャパシタ積分回路

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H. San, Y. Jingu, H. Wada, H. Hagiwara,

A. Hayakawa, J. Kudoh2, K. Yahagi2,

T. Matsuura2, H. Nakane2, H. Kobayashi,

M. Hotta3, T. Tsukada2, K.Mashiko4, A.Wada5 1) Gunma University

2) Renesas Technology Corp.

3) Musashi Institute of Technology

4) STARC

5) Sanyo Electric Co., Ltd.

A Multibit Complex

Bandpass ∆ΣAD Modulator

with I,Q Dynamic Matching

and DWA Algorithm

2006/11/14 A-SSCC 2006 2

Motivation

Complex Bandpass Delta-Sigma

AD Modulator

Proposed Architecture

I, Q Dynamic Matching

Complex DWA Algorithm

Measured Results

Conclusion

Outline

2006/11/14 A-SSCC 2006 3

Motivation


AD Modulator


I, Q Dynamic Matching


Measured Results

Conclusion

Outline

2006/11/14 A-SSCC 2006 4

Low power ADC in low-IF receiver

targeted for bluetooth, wireless LAN.

Motivation

Complex bandpass delta-sigma

AD modulator

2006/11/14 A-SSCC 2006 5

fLOZero-IF

DC Frequency

Signaloffset

1/f noise

fLO

Signal

offset1/f noise

DC Frequency

Low-IFImage

fLO

Signal

DC Frequency

Low-IF

offset1/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

2006/11/14 A-SSCC 2006 6

Motivation


AD Modulator


I,Q Dynamic Matching


Measured Results

Conclusion

Outline

2006/11/14 A-SSCC 2006 7

H(z)

Complex

Banpass Filter

ADCI

ADCQ

DACI

DACQ

+

+

Iin

Qin

Iout

Qout

Analog

Input

Digital

Output

Ei

Eq

-

-

)jEE(H1

1)jQI(

H1

H

jQI

qiinin

outout

Complex bandpass noise-shaping

Complex Bandpass Delta-Sigma Modulator

2006/11/14 A-SSCC 2006 8

Motivation


AD Modulator




Measured Results

Conclusion

Outline

2006/11/14 A-SSCC 2006 9


• New complex bandpass filter

• Multi-bit ADCs/DACs

• Complex DWA algorithm

2006/11/14 A-SSCC 2006 10

Proposed Structure

2006/11/14 A-SSCC 2006 11

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.

Layout simplification.

2006/11/14 A-SSCC 2006 12

Operation of Proposed Complex Filter

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

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

2006/11/14 A-SSCC 2006 13

Complex BPDSM with Low-power

• 2nd 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

2006/11/14 A-SSCC 2006 14

Complex DWA (1)

jz

1)z(H1

jz)z(H2

Digital bandpass filter Analog band elimination filter

2006/11/14 A-SSCC 2006 15

Complex DWA (2)

2006/11/14 A-SSCC 2006 16

Motivation


AD Modulator




Measured Results

Conclusion

Outline

2006/11/14 A-SSCC 2006 17

Chip Implementation

• 1P6M 0.18µm CMOS Process

• Core size 1.4 *1.3mm2.

2006/11/14 A-SSCC 2006 18

Measured Output Power Spectrum

2006/11/14 A-SSCC 2006 19

Effect of Complex DWA

2006/11/14 A-SSCC 2006 20

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

2006/11/14 A-SSCC 2006 21

Motivation


AD Modulator




Measured Results

Conclusion

Outline

2006/11/14 A-SSCC 2006 22

• A 2nd-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

複素アナログフィルタの基礎 - koba lab official … › lecture › mce2020_06.pdf1...

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