Digitally-Controlled Gm-C Band-pass Filter

G .Jin, H. Chen, C. Gao, Y. Zhang H. Kobayashi, N. Takai, K. Niitsu

（Gunma University） K. Hadidi (Urmia University)

2012 IEEE Asia Pacific Conference on Circuits and Systems

Paper No. 7036

Supported by STARC

Gunma University Kobayashi-Lab

Presented by Guanglei Jin (靳 光磊)

• Research Objective

• Switched Gm-C Band-pass Filter

• Center Frequency Tuning

• Q-Value Tuning

• Conclusion

3

Outline

• Research Objective

• Switched Gm-C Band-pass Filter

• Center Frequency Tuning

• Q-Value Tuning

• Conclusion

4

Outline

Wireless LAN, Bluetooth, etc. IF Receiver

5

Background

Gm-C filters are needed

Center frequency & Q-value adjustment is a challenge

6

Research Objective

Fine CMOS process Low voltage

Analog band-pass filter

• Switched Gm-C integrator

• Digital schemes

Center Frequency

Q-value

• Research Objective

• Switched Gm-C Band-pass Filter

• Center Frequency Tuning

• Q-Value Tuning

• Conclusion

7

Outline

Proposed Switched Gm-C Integrator

)( iiooo VVgmIII

)(2

iio

o VVsC

gm

sC

IV

)(2

iio

o VVsC

gm

sC

IV

iooo VsC

gmVVV

8

Input Voltage Output Current

Gm Cell (OTA)

Gm-C Integrator

Proposed Switched Gm-C Integrator

9

Gm

Ibias

Conventional approach

Proposed method

Analog adjustment of Gm using Ibias

Difficult for fine CMOS with low voltage

Gm

Digital adjustment of Gm by switch

low voltage control

Continuous Adjustment of Switched Gm-C Integrator

10

Noise characteristics C → Constant

Gm → Adjustable

Switched Gm-C Integrator • Low-voltage • Digital control

Continuous Adjustment

Integral Part Adjusting

Switched Gm-C Integrator

11

0

2Gｍ

Adjust Fractional Part by PWM

12

offon

on

TT

TD

GmDVin

Iout

PWM control

Tr ON

OFF

TON

Switched Gm-C Integrator

1bit ΔΣ converter for high accuracy

Adjust Fractional Part by ΔΣ

1bit ΔΣ converter

13

Switched Gm-C Integrator

Vin

Iout

Input and Output Waveforms of Switched Gm-C Integrator

14

mVVin 500

kHzf 598

pFC 1

SGm 6102/1

Input Voltage Amplitude and Pulse Density with ΔΣ Adjustment

15

0

10

20

30

40

50

60

70

80

0.0 0.2 0.4 0.6 0.8 1.0

Vre

f (m

V)

Pulse Density (×100%)

432221

2

21)(GmGmGmsCCCs

sCGmsH

2

002

0)(

sQ

s

sKsH

21

430

CC

GmGm

2

22

431

GmC

GmGmCQ

431

2

12

GmGmC

GmCK

Gm-C Second-order BPF

16

Gm-C Second-order LPF

432221

2

31" )(GmGmGmsCCCs

GmGm

V

VsH

in

m

2

002

0)(

sQ

s

KsH

21

430

CC

GmGm

2

22

431

GmC

GmGmCQ

421

3

2

1

GmCC

GmGmK

17

Vm

Another node of the filter

VLP

VBP

C

gm

MM

NN

21

430

2

22

431

NM

NNMQ

431

2

12

NNM

NMK

Proposed Digitally-controllable BPF and LPF

18

gmNGm 11

gmNGm 22

gmNGm 33

gmNGm 44

CMC 11

CMC 22

• Research Objective

• Switched Gm-C Band-pass Filter

• Center Frequency Tuning

• Q-Value Tuning

• Conclusion

19

Outline

Whole Tuning Scheme

20

• Suitable for digital low voltage implement • Require a reference frequency

VLPF

Center Frequency Tuning Part

21

VLPF

Proposed Center Frequency Tuning Method

)(arctan

2 22

0

0

i

i

Q

432221

2

21)(GmGmGmsCCCs

sCGmsH

22

Magnitude characteristics

Phase characteristics

θ＝0 Center frequency tuning is done

ω0: Center Frequency ωi: Input Frequency

Principle for Using Phase Characteristics

)(arctan

222

0

0

iQ

i 00①

i 00③

i 00② Done

ω0 is adjusted bigger

ω0 is adjusted smaller

21

430

CC

GmGm

23

Gm3, Gm4 bigger

Gm3, Gm4 smaller

4

Vref = sin(ωot)

Signals of PFD

PFD(Phase Frequency Detector)

24

ω0 is desired center frequency

Comparator

Charge pump

4bitADC

Comparator

BPF

Operation of Charge Pump

Adjust the Gm3, Gm4

values

25

Input and Output Waves of BPF

Vout

Vref

Transient state Adjusted state

26

Phase is aligned

Center Frequency Tuning Simulation Result of BPF

pF59.1CSGm 5105 Simulation parameters

221 NN 121 MM 150 43 NN

27

100kHz 500kHz 300kHz

Center Frequency Tuning Simulation Results of LPF

pF59.1CSGm 5105 Simulation parameters

221 NN 121 MM 150 43 NN

28

• Research Objective

• Switched Gm-C Band-pass Filter

• Center Frequency Tuning

• Q-Value Tuning

• Conclusion

29

Outline

Q-value Tuning Part

30

VLPF

KQCGm

CGmGm

CGmGm

CGm

Gm

GmH

2

2

2

143

143

2

2

1

2

10 )(proposed method

Fix Center frequency and K

QKjH )( 0

Q-value Tuning Method

31

Q-value is proportional to gain

ω0: Center frequency

ω0 determined by Gm3, Gm4

K determined by Gm1, Gm3, Gm4

21

430

CC

GmGm

2

22

431

GmC

GmGmCQ

421

3

2

1

GmCC

GmGmK

In Case Q is Smaller than Desired Value

32

V1>V2 Vcp is tuned bigger Gm2 is tuned smaller

Q∝（1/Gm2） Q → bigger

ω0 has been adjusted

2

22

431

GmC

GmGmCQ

ω0 has been adjusted

Output of Comparator

33

COMPUP

COMPDOWN

ω0 has been adjusted

Output of Charge pump

34

VCP

ω0 has been adjusted

Output of ADC

35

S1

S2

S3

S4 Q∝（1/Gm2）

In Case Q is Bigger than the Desired Value

36

V1<V2 Vcp is tuned smaller

Q∝（1/Gm2） Q →smaller

ω0 has been adjusted

2

22

431

GmC

GmGmCQ

Gm2 is tuned bigger

AKVQV ref /2 refVV 1

When V1 = V2 A

KQVAKVQ refref

1/

Q → Determined by A

Algorithm of Q-value Tuning

37

K is fixed

ω0 has been adjusted

KQjH )( 0

Input and Output Waves of BPF

Vout

Vref

38

Transient state adjusted state Phase is aligned

Q-value Tuning Simulation Result of BPF

Simulation parameters

pF59.1CSGm 5105

121 MMkHzf 6000

39

Q=6

Q=3

Q=1

Q-value Tuning Simulation Result of LPF

Simulation parameters

pF59.1CSGm 5105

121 MMkHzf 6000

40

Q=6

Q=2

Q=1

• Research Objective

• Switched Gm-C Band-pass Filter

• Center Frequency Tuning

• Q-Value Tuning

• Conclusion

41

Outline

Conclusion

42

• Propose a digitally-controlled Gm-C band-pass filter using switched Gm arrays

Fine CMOS Low voltage

• Digital tuning schemes

Center Frequency Phase property

Q-value Gain property (Center frequency has been adjusted)

• Present SPICE simulation results

Determined by Gm3，Gm4

Determined by Gm2

Orthogonal