10th International Conference on Information Science, Signal Processing and their Applications (ISSPA 2010)

SUBSAMPLING CONTINUOUS· TIME BANDPASS �L\ MODULATOR FOR RADIO FREQUENCY AID CONVERSION

DAD! Mohamed Bechir1,2, BOUALLEGUE Ridha2,3

1 National Engineering School of Tunis, ENIT. 2Research Unit of Telecommunication Systems, 6'Tel, Tunis - Tunisia

3Higher School of Communications of Tunis, Sup' Com. Mohamed.dadi @isimg.rnu.tn Ridha.Bouallegue@supcom.rnu.tn

ABSTRACT

This paper presents a fourth-order I-bit continuous time

bandpass �� modulator assigned for radio frequency ana­

log to digital conversion. The constraints imposed on the

sampling frequency found with conventional method can

be intensely reduced using subsampling process. A sin­

gle loop architecture with sine shaped feedback DAC is

chosen to compensate the subsampling continuous time

(CT) bandpass �� modulator non-idealities such as tim­

ing jitter. To demonstrate the efficiency of this approach,

simulation results for a single-carrier WCDMA signal at

2.14 GHz with 60 MHz band and a sampling frequency

of 778.18 MHz show that the maximum attainable SNDR

with the proposed modulator is about 44 dB.

1. INTRODUCTION

The continuous progress in wireless communication sys­

tems require the design a single RF sampling receiver ca­

pable of supporting the majority next generation standards.

One of the defiant amounts of these systems is the analog

to digital converter which would be placed as close to an­

tenna as possible. These requirements translate the need

for high speed and high resolution at the analog to digi­tal converter. Continuous-Time (CT) bandpass �� ND

structures are mostly preferred for high radio frequency

analog to digital conversion [1] due to their intrinsic anti­

aliasing filtering, lower sampling rate and lower power

consumption. In order to reduce the high sampling fre­

quency for these systems, a subsampling scheme [2] is

required. CT-bandpass �� modulators based on Interme­

diate Frequency (IF) or baseband subsampling scheme are

investigated in [3]. Nevertheless, direct digitization with

gigahertz carrier frequency is required for the next wire­

less communication standards. CT-bandpass �� mod­

ulation combined with subsampling technique can be a

promising method for RF analog to digital conversion for

wireless communication receiver.

An example of RF subsampling receiver based on CT­

bandpass �� modulator for radio frequency analog to

digital conversion is shown in figure 1. The received sig­

nal is first filtered by a RF bandpass filter. Then, it is am­

plified with a Low Noise Amplifier (LNA). After that, the

desired bandpass signal is injected into a RF subsampling

978-1-4244-7167-6/101$26.00 ©2010 IEEE 181

Fs

Fig. 1. RF subsampling �� receiver

stage based on CT-bandpass �� modulator to down con­

vert the signal an intermediate frequency. Finally, the

signal is decimated and donwconverted to baseband fre­

quency through an inphase (I) and quadrature (Q) paths.

A low pass filtering is needed to cancel the aliasing image

before moving on digital signal processing Blocks (DSP).

The CT-bandpass �� modulator can be modeled by figure

2. The modulator comprises a CT-bandpass filter, a Sam-

cr· Bandpass Filter

yen)

y(t)

Fig. 2. CT-Bandpass �� Modulator

pie and Hold circuit (5/ H), a quantizer and a feedback

Digital to Analog Converter (DAC). The sampling oper­

ation is accomplished before quantization process. Note

that, the pass band of the CT-bandpass �� filter is equal

to the frequency band of the pass band input signal[4].

The excess loop delay [5] in the CT-bandpass �� mod­

ulator, defined as the delay between the quantizer clock

edge and the outpout of the feedback DAC pulse, can be

modeled by (e-as ), where a is the time delay between the

ideal and real response of the DAC pulse. Besides, a can

be expressed as fraction of the sampling period, T, as :

a=pT (1)

where p is between 0 and 1.

In order to reduce the jitter sensitivity in CT-bandpass ��

modulator, a sine shaped feedback DAC is proposed in

[5][6].

In this paper, we propose a new fourth order RF sub­

sampling I-bit CT-bandpass �� modulator based on sine

shaped feedback DAC pulse. The presented modulator

is designed to receive a signal for different wireless stan­

dards in a carrier frequency range of gigahertz. Widespread

study and simulation results for single-carrier WCDMA

signal centered at 2.14 GHz within 60 MHz down-link

band show the ability of the modulator to relax the re­

quirements on design parameter such as timing jitter.

This paper is organized as fellows: section 2 presents the

architecture of the CT-bandpass-�� Modulator using RF

subsampling process with sine shaped feedback DAC. Per­

formance analysis of the proposed modulator for WCDMA

system with simulation results are detailed in the section

3. Some conclusions are drown in section 4.

2. PROPOSED RF SUBSAMPLING CT-BANDPASS

�� MODULATOR

2. 1. Subsampling and frequency synthesis

Consider an input signal x(t) with a frequency fin lo­

cated around frequency fRF passe through a continuous

bandpass filter of the modulator as shown in figure 2. For

conventional sampling scheme, it is preferable to choose

the sampling frequency of the �� modulator, Fs, equal

to four times the center frequency f RF in order to give

the maximum separation between the aliases in the out­

put spectrum of the modulator [1]. So, according to the

Nyquist theorem, we can find a problem for high freque­

ncy and low bandwidth signals. However, using bandpass

sampling, called also subsampling, the input RF bandpass

signal is sampled with a frequency fRF by an intentional

aliasing [7]. The signal band of interest at the output of the

modulator is downconverted to an intermediate frequency

!IF. The relation between Fs, fRF and !IF is given as

[7]:

he { rem(jRF, Fs) if L iRP J is even Fs/2

Fs - rem(jRF, Fs) if LlE.LJ �s odd Fs/2 (2)

where rem(a, b) denotes the remainder of a divided by b, and Lx J denotes the largest integer less than or equal to

x. According to the bandpass sampling theory [2] and in

order to avoid any destructive aliasing, the following three

conditions must be met:

Fs > 2B, B O<!IF - 2'

B Fs !IF + 2 < 2 (3)

where B is the signal bandwidth.

In this work, the sampling frequency Fs for a bandpass

�� modulator using bandpass sampling is selected as [8]:

4 Fs = 2N + 1 fRF, N» 0 (4)

where N is the subsampling ratio. Substituting (4) in (3) and (2), the intermediate frequency !IF is equal to Fs /4 and also (3) is satisfied. If we assume that the modulator

182

is designed to convert a 60 MHZ centered at 2.14 GHz for

WCDMA standard, the conventional sampling frequency

is equal to 8.56 GHz. However, if the modulated signal is

sampled with subsampling process and using (2)-(4), sev­

eral sampling frequencies can be selected without alias­

ing RF signal.In this work,we choose a subsampling ratio

N = 5 in (4). Therefore, a sampling frequency of 778.18 MHz is selected and the corresponding intermediate fre­

quency is equal to !I F= 194.54 MHz. As a result, the sub­

sampling scheme have reduced the sampling frequency.

As the same case, the OverSampling Ratio (OSR) of the

modulator is declined from 71 to 7.

2.2. Fourth-order proposed modulator architecture

As illustrated in figure 3, the linearized model of the pro­

posed fourth-order subsampling CT-bandpass �� modu­

lator, designed to receive single-carrier WCDMA signal,

is composed by a two second order continuous time res­

onators with a transfer functions respectively H 1 (s) and

H2(S). The subsampling process of the input RF signal

Xes) Yes)

Fig. 3. Fourth order subsampling CT-bandpass �� mod­

ulator

is achieved after the bandpass filter operation. The noise

aliasing, introduced by subsampling, will be reduced by

the loop filter. The chosen structure for the modulator

is monobit because of its higher linearity. The feedback

DAC can be designed by different pulse wave. As de­

tailed in [3], a NRZ pulse used in the feedback DAC cause

a strong attenuation of the input signal around the fre­

quency fRF. This problem can be resolved by translating

the spectrum of the signal in the Nyquist band around the

RF frequency f RF. This operation can be achieved by a

multiplying the signal of the output of the modulator by a

sinusoidal signal as proposed in [3]. As a results, the DAC

pulse is transformed to a sinusoidal pulse. Nevertheless, a

deficiency of synchronization between the sinusoidal sig­

nal and reference clock can improve the error in the DAC

and limit the performance approach.

As described in [6], a sine shaped DAC feedback pulse

can be used in order to reduce the jitter sensitivity in the

feedback DAC of a CT-bandpass �� modulator. For this

reason, we propose to use a sine shaped DAC pulse in the

present modulator. The sine shaped pulse signal, as shown

in figure 4, can be defined as :

(5)

Fig. 4. Sine shaped DAC signal

where fdac is input frequency of the sine shaped signal

and it is given by:

fdac = fRF + hF (6)

Then, the impulse response of the output of the sine shaped

DAC is defined as:

2 (1 -sT) H ( ) _ Wdac - e

dac S - ( 2 2 ) S S + Wdac (7)

where Wdac = 27r fdac. The frequency response of the

NRZ and sine shaped feedback DAC with a carrier fre­

quency of 2.14 GHz and a sampling frequency of 778.18 MHz is plotted in figure 5.

In order to simplify the implementation of the proposed

1 .4'-�-�-�-�-F=C::::::::::===il " ',.,' N RZ pulse

co " - 0.6 <1l " .3 .� 0.6 '" :;:

0.4

0.2

- Sine shaped pulse

o L-_L-L-L-_�_L-�L-����� o 500 1000 1500 2000 2500 3000 3500 4000

Fequency (MHz)

Fig. 5. Frequency spectrum of NRZ and sine shaped feed­

back DAC

modulator, we assume that the two bandpass filters are

identical:

where, A is a constant gain factor, Q is the quality factor

of the filter and w is equal to 27r f RF. According to figure 3, the s-domain transfer function of

the first and second open loop filter GHl(S) and GH2(S) can be written respectively as :

GH1(s) = klH(s)2 Hdac(s)e-as (9)

GH2(s) = k2 H(s)Hdac(s)e-as (10)

where Hdac(s) and H(s) are given respectively by (7) and

(8), kl and k2 are the coefficients feedback of the loop

filters. Then, the s-domain transform function of the open

loop filter of the proposed modulator can be written as :

(11)

183

Substituting from (7)-( 10) into (11), we give:

AWJac[klAs + k2(S2 + ZJS + w2)] T GH(s) - (l-e-S )(e-as) - (s2 + ZJS + w2)2(S2 + wJac) (12)

Using the impulse-invariant transformation technique, the

z-domain of the open loop filter is defined as:

GH(z) = Z[L-l{GH(s)}] (13)

So, the final expression of GH(z) can be obtained using

the modified z-transform technique and residue theorem

as described in [5]. If we suppose that the input signal and the loop filter are

band limited, we can write the loop transfer function in the

z-domain as:

(14)

From (13) and (14), the Noise and Signal Transfer Func­

tion, (NTF) and (STF), of the modulator can be derived

as: 1 NTF(z) = 1 + GH(z)

ST F(z) = G(z)

1 + GH(z)

3. PERFORMANCES ANALYSIS OF THE

PROPOSED MODULATOR

(15)

(16)

It is well known that stability of the proposed modula­

tor is assured when the poles/zeros of the noise transfer

function are inside of the unit circle on the complex plan.

However, excess loop delay can severely degrade the noise

transfer function of the modulator. From (1) a total de­

lay of a = O.IT is used within the proposed subsam­

piing CT-bandpass I;� modulator in order to make the

modulator stable. the NTF/STF frequency responses of

the proposed subsampling modulator deduced from (15) and (16) are depicted in figure 6 where f RF=2.14 GHz,

hF=194.54 MHz, Fs=778.18 MHz, Q=150, kl=k2=1. The NTF and STF are centered around the intermediate

frequency h F· In figure 7, the resulting Signal-to-Noise-and-Distortion

co -5 � Ql � -10

." C> � -15

-20

-25

.......... '.'" """'"

_30L-_L-_L-_L-_�_�_�_�-------' o 0.5 1.5 2 2.5

frequency (Hz) 3.5

Fig. 6. NTF and STF of the proposed Modulator

Ratio (SNDR) is plotted vs. the input amplitude. The

maximum achievable SNDR is 44 dB The limit of the

45 40 35 30 25 20

15 10

�·��--����-30�--�25---�2O�� -1�5 ---1� 0-- -�5� Amplitude (dB)

Fig. 7. SNDR versus input amplitude

SNDR is due to subsampling process.

Another important parameter which can affect the per­

formance of the modulator is called timing jitter. It is also

well known that CT-bandpass I:� modulator is very sen­

sitive to timing jitter than discrete modulators. However,

the timing jitter error introduced in the DAC is directly

additionned to the input signal and it has a dominant ef­

fects on the SNR output of the modulator. Subsampling

scheme can amplified the jitter effects. The final expres­

sions of the jitter limited SNR with NRZ and sine shaped

DAC pulse is defined respectively as[1][6]:

(VOSRASinC(7r'l"F)) (17) SNRNRZ = 2010glO 2 .F

s {}] s

SNRSine�shaped = 20l0glO (/�3) .37r s {}] (18)

where A is the amplitude of input signal and (}j is the

rms value of the jitter. (17)-( 18) are depicted in figure 8

for WCDMA systems where the SNR is plotted in func­

tion of the timing jitter( % of sampling period, T) with

OSR=7, Fs=778.18 MHz, frF=194.54 MHz, A=0.5. We

can conclude that the proposed modulator with subsam­

piing scheme is very sensitive to timing jitter. However,

a sine shaped feedback DAC can alleviate this attenuation

as compared as the NRZ DAC pulse wave.

4. CONCLUSION

A new fourth order RF subsampling CT bandpass I:�

modulator based on sine-shape feedback DAC is presented

in this paper. The proposed modulator have less sensitiv­

ity to timing jitter with the presented approach. However,

the main drawback of using subsampling technique is the

poor SNDR (44 dB) as compared with conventional mod­

ulator architecture. In the future , it is possible to increase

the SNDR of the subsampling modulator by using multi­

bit structured combined with Dynamic Element matching

(DEM) technique.

184

50 1�--��--�--r=:::::::!:=��C:::;=====il .--- NRZ feedback pulse 45 .-e- Sine shaped feedback pulse

40 35

iii � 30 z <J) 25

10 '----�--��,_,__�____,��,___�___:_�-:-'c:,-----::-' 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 rms jitter (% of samplig period T)

Fig. 8. Comparaison of jitter limited SNR for the pro­

posed modulator with sine shaped and NRZ feedback

DAC.

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