[IEEE 2010 10th International Conference on Information Sciences, Signal Processing and their...
Transcript of [IEEE 2010 10th International Conference on Information Sciences, Signal Processing and their...
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 [email protected]
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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