Vol. 34, No. 7
Journal of Semiconductors
July 2013
A CMOS G m –C complex filter with a reconfigurable center and cutoff frequencies
in low-IF WiMAX receivers
Cheng Xin(程心)1; 2 , Yang Haigang(杨海钢)1; Ž , Gao Tongqiang(高同强)1 , and Yin Tao(尹韬)1
1 Institute
of Electronics, Chinese Academy of Sciences, Beijing 100190, China
of Chinese Academy of Sciences, Beijing 100049, China
2 University
Abstract: This paper presents a reconfigurable fifth-order complex Gm –C filter for different data rates in low-IF
WiMAX applications. The design procedure and linearized measures to realize the complex filter are described. In
order to achieve the reconfigurability of bandwidth window, the center frequency and the cutoff frequency filter are
adjusted simultaneously by changing capacitor values while keeping transconductors unchanged. Also, the filter
integrates an on-chip automatic frequency tuning circuit based on a PLL. Experimental results show that it has an
IRR of 32 dB, a THD of –43 dB, and an input-referred noise of 21 Vrms. The chip is fabricated in 0.13 m CMOS
process, occupies 0.7 1 mm2 , and consumes 4.8 mA current from a 1.2 V power supply.
Key words: complex filter; low-IF receiver; WiMAX; frequency tuning
DOI: 10.1088/1674-4926/34/7/075004
EEACC: 1270E; 2570D
1. Introduction
As one of the emerging wireless communication standards,
worldwide interoperability for microwave access (WiMAX)
adopts the multiple-input, multiple-output (MIMO) technique
and an orthogonal frequency division multiplexing (OFDM)
modulation scheme to offer high data ratesŒ1; 2 . According to
the communication protocol, the channel bandwidth should be
adjustable from 1.25 to 20 MHz separatelyŒ1 . Thus developing
a multimode configurable RF receiver that can receive signals
from all of the WiMAX system is the direction of the present research. Accordingly, a reconfigurable and widely tunable baseband filter in configurable radio receivers is necessary, and is
described in this work.
Usually, integrated RF CMOS receivers use either a lowIF or zero-IF conversion technique to extract the baseband signal. Among the two familiar methods, zero-IF receivers suffer from flicker noise and DC offset, which cause significant
degradation in the signal-to-noise ratio, while low-IF receivers
are immune to these effects. For this reason, a lot of modern
wireless receivers are implemented with low-IF architectureŒ3 .
Nevertheless, the low-IF scheme is very sensitive to the image
problem. Since both the information and image signal are located symmetrically around the carrier frequency, the image
signal can be considered as an interferer that needs to be eliminated. Thus the complex filter becomes an indispensable component in low-IF receivers for image rejection. Conventionally,
passive, active-RC or Gm –C topologies are applied for implementing the complex filters. Since Gm –C configurations have
better frequency response and consume lower power, they are
becoming the most popular selectionsŒ4 . As a result, a reconfigurable channel selection complex filter is required in order
to satisfy the different channel bandwidths in WiMAX radios.
Recently, adjustable filters have gained increasing popularity. Several reconfigurable filters were reported in Refs. [5–
7]. These designs show reconfigurable filter types (Butterworth, Bessel etc.), selectable orders, tunable cutoff frequency,
and even adjustable frequency response (real low pass or complex band pass). But most of them are real filters which are
unsuitable in low-IF receivers. As for complex filters, there
are two variable frequencies, center frequency and cutoff frequency, which increase the difficulty of reconfigurable design.
In this paper, a CMOS complex Gm –C filter with reconfigurable center and cutoff frequencies is proposed for lowIF WiMAX applications. Also an automatic frequency tuning
scheme based on a PLL is integrated to compensate for variations of process, voltage, and temperature (PVT). The block
diagram of the low-IF receiver is shown in Fig. 1. The filter is tuned by the PLL periodically, which is controlled by
a micro-control unit (MCU) or biased with a voltage sampled
from the PLL and held by the MCU. The proposed architecture can be utilized to depress interference and reduce power
consumptions.
2. Architecture of the reconfigurable complex
filter
2.1. Basics of the complex filter
The complex filter can be considered as an asymmetrical
single-band band-pass filter, which can be flatly shifted to a
certain frequency wo from the low-pass prototype. To realize
frequency transformation s ! s jwo , additional components
are needed in circuit implementation. Figure 2 shows real and
complex Gm –C integrators which are the basic components of
real and complex Gm –C filters, respectively. The transfer characteristic of a real integrator is described by
* Project supported by the National High Technology Research and Development Program of China (No. 2012AA012301) and the National
Natural Science Foundation of China (No. 61106025).
† Corresponding author. Email: yanghg@mail.ie.ac.cn
Received 29 November 2012, revised manuscript received 15 January 2013
© 2013 Chinese Institute of Electronics
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Cheng Xin et al.
Fig. 1. Block diagram of a low-IF receiver.
filter, the complex one needs another series of transconductor (Gm0 / to form the feedback loop. Since the output common mode level needs to be fixed only once for any OTAs
which share the same output, the transconductors in the main
path (Gm / need a common mode feedback (CMFB) circuit
while the transconductors for feedback (Gm0 / and cross coupling (˙Gmi .i D 1; ; 5// do not.
2.3. Realization of the reconfigurable filter
Fig. 2. (a) Real Gm –C integrator. (b) Complex Gm –C integrator.
H.s/ D
vo .s/
G
D
:
vi .s/
sC
(1)
The complex integrator, as shown in Fig. 2(b), consists of a
pair of real integrators which are cross-coupled by the transconductors Go and Go , whose transfer characteristic is described
by
vo .s/
G
H.s/ D
D
;
(2)
vi .s/
.s jwo /C
As for real filters, the reconfigurability can be realized normally by changing transconductors or by tuning passive devices (resistors or capacitors) to adjust the cutoff frequency
(namely, bandwidth). However, for complex filters, there are
two frequency variables, center frequency and cutoff frequency, which increase the difficulty of reconfigurable design. In this paper a new method to realize the reconfigurability is utilized. Based on this method, the center frequency
and the cutoff frequency of a complex filter can be adjusted simultaneously just by changing capacitor values while keeping
transconductors unchanged.
With the selected center frequency fo and cutoff frequency
fc , the capacitances are expressed as
Ci D
Go
:
C
This demonstrates that the transformation s ! s
being performed as required.
Gmi D 2fo Ci ;
(3)
jwo is
2.2. Filter topology
Based on the demands of the WiMAX protocol, which
gives 11 dB rejection at the adjacent channel and 30 dB rejection at the alternate channelŒ1 , a fifth-order Butterworth Gm –
C complex filter is designed to meet the requirements with
some margins. In this design, a filter with a leapfrog structure
is utilized because of its lowest sensitivity and best DR performanceŒ8 . Based on the description in last section, the complex
filter prototype is obtained, as shown in Fig. 3, which comprises a pair of real filters and a series of cross-branch transconductors (˙Gmi .i D 1; ; 5//. Compared with a single-ended
i D 1; ; 5;
(4)
and the cross coupled transconductors
where wo is the frequency shift given by
wo D
i Gm
;
2fc
i D 1; ; 5;
(5)
where i (i D 1; ; 5/ are constant depending on the adopted
filter. It can be seen that cutoff frequency fc varies with Ci
and Gm , while cutoff frequency fo varies with Ci and Gmi .
This make it possible to adjust fc and fo simultaneously by
changing Ci only.
Considering the trade-off between the value of Ci and Gmi ,
a transconductor with Gm D 30 S is chosen. To relax the
image rejection requirement and reduce the level of foldedback interference, three kinds of center frequency 1.75, 2.5,
and 5 MHz are set, which are half of the bandwidth 3.5, 5,
and 10 MHz defined in IEEE 802.16d standard, respectivelyŒ1 .
Considering the spacing between channels, a cutoff frequency
of 1.5 MHz is chosen with the center frequency of 1.75 MHz.
As shown in Table 1, the other two cutoff frequencies are designed to meet
fo2
fo3
fo1
D
D
;
(6)
fc1
fc2
fc3
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Cheng Xin et al.
Fig. 3. Architecture of the complex filter.
which means cutoff frequencies are proportional to not only
center frequencies but also channel bandwidths, because center
frequencies are set as half of the channel bandwidths. In this
way, the filter can maintain a fixed attenuation degree even if
there are various channel bandwidths. That is to say, an 11 dB
rejection at an adjacent channel and a 30 dB rejection at an
alternate channel.
As for operation mode 1, Equations (4) and (5) become
C1i D
i Gm
;
2fc1
Gm1i D 2fo1 C1i ;
i D 1; ; 5;
i D 1; ; 5:
Table 1. Center frequencies and cutoff frequencies in three modes.
Mode
1
2
3
fo (MHz)
1.75
2.5
5
fc (MHz)
1.5
2.14
4.28
Node capacitor Ca C Cb C Cc
Ca C Cb
Ca
(7)
(8)
For mode 2,
C2i D
i G m
;
2fc2
Gm2i D 2fo2 C2i D
i D 1; ; 5;
fo2 i Gm
;
fc2
i D 1; ; 5:
(9)
Fig. 4. Capacitor array for mode selection.
(10)
every node are selected with two control switches S1 , S2 , and
thus the operation modes. For example, when S1 turns on and
S2 turns off, the value of capacitor is set as Ca C Cb and mode
2 is selected.
According to Eq. (6), it can be derived that
Gm2i D
fo2 i Gm
fo1 i Gm
D
fc2
fc1
D 2fo1 C1i D Gm1i ;
i D 1; ; 5;
3. Design of the linearized OTA with configurable CMFB and CMFF
(11)
which means reconfigurability can be achieved by setting
different capacitor values while keeping transconductors unchanged. Sharing all the transconductors for the three operation modes simplifies the design greatly. As shown in Fig. 4,
three different values of capacitor Ca , Ca C Cb , Ca C Cb C Cc at
In Fig. 3, among all the transconductors which constitute
the complex filter, some (Gm / need a CMFB circuit while others (Gm0 , ˙Gmi .i D 1; ; 5// do not. Thus a differential
transconductor with configurable CMFB loopŒ8 is adopted in
Fig. 5. Figure 5(a) shows the transconductor including a CMFB
loop which is outlined with a dashed line, while the transcon-
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Cheng Xin et al.
Fig. 5. OTA structure (a) with CMFB or (b) without CMFB.
ductor without a CMFB loop is shown in Fig. 5(b). Both structures include a common mode feed-forward (CMFF) circuit
which is outlined with dashed line in Fig. 5(b).
Although CMFF improves the rejection to the common
mode signal components at the output, it is incapable of properly fixing the dc common mode output voltage which is done
by a CMFB circuit. In Fig. 5(a), CMFB can be obtained by judiciously connecting two of the OTAs. The connection at the
output stage is taken from Vx of the next stage, which is now
sensing the common mode level of the output (input of the next
stage). It should be noted that this structure not only suppresses
the common mode signal generated by this stage, but also detects the common mode signal of the former stage and forms
a CMFB loop to the former stage, which makes it suitable in
cascade design and to improve the stability of a high order complex filter. Also, there is no need to add an extra circuit to implement the CMFB loop.
In order to improve the linearity of transconductors,
the source degeneration technique is adopted (N19, N20 in
Fig. 5(a)). It can be derived that for the proposed OTA
Gm D
gmN1
:
1 C ˇN1 =.4ˇN19 /
(12)
Then the third-order harmonic distortion is
HD3 D
1
Vin
;
32n2 VgsN1 VthN1
(13)
ˇN1
i
where ˇi D n Cox W
, n D 1 C 4ˇ
. That is, the larger n
Li
N19
is, the better linearity is. On the other hand, increasing n also
consumes more power for a given Gm . Figure 6 shows the variation of HD3 and gmN1 with n for a given Vin D VgsN1 VthN1
and a given Gm D 30 S. It can be seen that to achieve better linearity with an acceptable power budget, n should vary
around 3, namely ˇN1 =ˇN19 varies around 8. In this work the
value of ˇN1 =ˇN19 is set as 6.7. It should be also noted that
the transconductance of the OTA can be controlled efficiently
by the floating voltage source Vb , and thus the function of frequency tuning can be realized.
Fig. 6. Variation of HD3 and gmN1 with n.
4. Automatic frequency tuning
In order to achieve accurate filtering characteristics, an automatic tuning scheme is required to compensate for the drifts
of the transconductors derived from process, voltage, and temperature (PVT)Œ9; 10 . Therefore an automatic frequency tuning
system based on a PLL is used as shown in Fig. 7. The output
of the VCO, which is combined by the same transconductor as
the complex filter, is reshaped by a hysteresis comparator, and
then compared with a reference pulse by a PFD. The PFD generates a pulse to drive the charge pump, whose output filtering
by a loop filter is the frequency control signal both for the VCO
and the complex filter. In this design, the tuning system works
when the control signal is connected with the bias voltage Vb
in Fig. 5. So we can compensate the frequency characteristics
of the filter with the tuning circuit at intervals.
The VCO used here is shown in Fig. 8, where the transconductor Gm is the same as in the complex filter. For better matching between the VCO and the complex filter, the active positive
resistor 1=GmC and negative resistor 1=Gm are used to limit
the oscillation amplitude in the linear range of the OTA. A different capacitor is chosen for different mode selection in Fig. 4.
The oscillation frequency can be expressed as Gm =C , while the
center frequency of the filter is given by Gmi =Ci . Thus when
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Cheng Xin et al.
Fig. 7. Frequency tuning system based on a PLL.
Fig. 10. The transfer function of a complex filter with different input
phase sequences.
Fig. 8. The VCO structure used in Fig. 7.
Fig. 9. Chip photograph of the whole complex filter.
the output of the VCO is locked to the reference frequency,
which is set to the desired center frequency, the actual center
frequency in the complex filter will be tuned to the design value
by the control signal.
5. Measurement results
The filter has been fabricated in a Global Foundry 0.13 m
CMOS process. The microphotograph of the chip is shown in
Fig. 9. The whole area including pads is 0.7 1 mm2 .
Normally, the transfer function of the complex filter should
be measured not only in the positive frequency domain but also
in the negative frequency domain by an S-parameter analyzer
because of its asymmetric response. Thanks to the characteristics of a complex filter, as shown in Fig. 10, where the solid
Fig. 11. The output with different input phase sequences at 2.5 MHz.
line and dashed line represent the transfer function with a phase
sequence (0ı , 180ı , 90ı , 270ı ) and (0, 180ı , 90ı , 270ı )
of input Vip , Vin , Vqp , Vqn , respectively, the filter response at
negative frequency (point B0 for example) can be measured alternatively at the corresponding positive frequency (point B).
The only modification is to change the phase sequence of input
signal from (0ı , 180ı , 90ı , 270ı ) to (0, 180ı , 90ı , 270ı ).
Figure 11 compares the output with different phase sequence
of input at 2.5 MHz, where Figures 11(a) and 11(b) represent
points A and B in Fig. 10 respectively. It can be seen that the
amplitude ratio Vout =Vin differs greatly, whose difference is de-
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J. Semicond. 2013, 34(7)
Parameter
Topology
Process (m)
VDD (V)
Power (mW)
Function
fC (MHz)
Bandwidth (MHz)
IRR (dB)
Linearity
Noise (Vrms)
Cheng Xin et al.
Table 2. Comparison with other works.
Ref. [4]
Ref. [7]
Ref. [8]
Real
Real
Complex
0.35
0.13
0.35
2.85
1.2
3.3
4/8
3.4/14.2
6.0
Reconfigurable/Tunable Reconfigurable/Tunable Tunable
0
0
1
5/10
2.11/11
0.65
—
—
28
THD D 1%
THD D 40 dB
IIP3 D 9 dBm
100
36
18.5
This work
Complex
0.13
1.2
5.8
Reconfigurable/Tunable
1.75/2.5/5
1.5/2.14/4.28
32
THD D 43 dB
21
Fig. 12. The comparison of frequency characteristic between simulation and measurement.
Fig. 14. The tuning function of the proposed PLL.
Fig. 13. The frequency characteristics under three operation modes.
fined as image rejection ratio (IRR).
Based on the above method, the frequency characteristic
of the proposed complex filter is obtained. The frequency characteristic of simulation and measurement for mode 3 is illustrated in Fig. 12. The existing difference of bandwidth is resulted from parasitics mainly. The frequency characteristics
under different operation modes are shown in Fig. 13. For all
of the modes, the measured IRR is about 32 dB and the filter
attenuates the first- and second-adjacent channels by more than
25 dB and more than 40 dB, respectively.
Taking mode 2 as an example, Figure 14(a) compares the
frequency response of the tuned filter with the untuned one,
and Figure 14(b) shows the frequency responses with different
power supply. The untuned filter is centered at 1.8 MHz with
bandwidth of 1.9 MHz. After tuning, the filter is centered at
2.4 MHz with a bandwidth of 2.1 MHz, which meets the design
goals in Table 1 well.
The measured harmonic distortion is shown in Fig. 15. The
THD is about 0.9% for 0.23-Vpp input signal. Figure 16 gives
the plot of THD versus input amplitude. Figure 17 shows the
output spectrum of the filter without an input signal. Figure 18
gives the measured IIP3 by applying two tones of 1 MHz and
1.1 MHz. The whole filter including the tuning circuit operates from a 1.2 V power supply and draws 4.8 mA. Table 2
compares the performance of the filter with that of some other
works.
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J. Semicond. 2013, 34(7)
Cheng Xin et al.
Fig. 18. The measured IIP3.
Fig. 15. The measured harmonic distortion.
urable bandwidth, including an on-chip automatic tuning circuit based on a PLL. Experimental results show that the complex filter achieves an IRR of 32 dB, an adjacent channel rejection of more than 25 dB, a nonadjacent channel rejection of
more than 40 dB, a THD of 0.9%, and an input-referred noise
of 21 Vrms with 5.8 mW of power consumption, making the
filter suitable for WiMAX applications. Also, the accurate tuning function is verified for this filter.
References
Fig. 16. THD versus input amplitude.
Fig. 17. The measured output noise.
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In this paper, a feasible method to change the bandwidth
window of a filter is proposed and a Gm –C complex filter
based on this technique for a low-IF WiMAX receiver has been
discussed. It is a fifth-order Butterworth filter with reconfig-
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