Download 10.7-MHz Fully Balanced, High-Q, Wide-Dynamic-Range Current-Tunable Gm-C Bandpass Filter Worawat Sa-Ngiamvibool

10.7-MHz Fully Balanced, High-Q, Wide-Dynamic-Range Current-Tunable Gm-C Bandpass Filter
13
10.7-MHz Fully Balanced, High-Q,
Wide-Dynamic-Range Current-Tunable Gm-C
Bandpass Filter
Worawat Sa-Ngiamvibool1 and Banlue Srisuchinwong2 , Non-members
ABSTRACT
A 10.7-MHz fully balanced, high-Q, wide-dynamicrange current-tunable Gm-C bandpass filter is presented. The technique is relatively simple based on
two fully balanced components, i.e. an adder and a
low-Q-based bandpass filter. The Q factor is approximately equal to a typically high and constant value of
a common-emitter current gain (β) and is, for the first
time, independent of variables such as a center frequency. Sensitivities of either the Q factor or the center frequency are constant between -1 to 1 and are no
longer strongly affected by the Q factor or variables.
As a simple example at 10.7 MHz, the paper demonstrates the high-Q factor of 121, the low total output
noise of 5.303 µVrms , the 3rd -order intermodulationfree dynamic range (IMFDR3 )of 74.45 dB and the
wide dynamic range of 87.45 dB at 1% IM3 . The
center frequency is current tunable over 3 orders of
magnitude. Comparisons to other 10.7-MHz Gm-C
approaches are also included.
Keywords: 10.7 MHz, fully balanced, high-Q, wide
dynamic range, Gm-C bandpass filter, sensitivities
1. INTRODUCTION
Bandpass filters are employed in many applications such as in a radio-frequency (RF) filter for image rejection or an intermediate-frequency (IF) filter
for channel selection of a wireless receiver. Typically,
FM radio receivers require an IF filter set at a center frequency (f0 ) of 10.7 MHz based on off-chip devices such as discrete ceramic or surface acoustic wave
(SAW) components [1,2]. As off-chip filters are bulky
and consume more power to drive external devices,
the need for possible on-chip filters for fully viable
integrated receivers has increasingly been motivated.
Recently, attempts at possible on-chip filters have
particularly been demonstrated for 10.7-MHz IF filters based on, for example, switched capacitors (SC)
[3-8], and Gm-C [9-13] techniques. Such techniques
have, however, repeatedly suffered from low quality
Manuscript received on August 1, 2006 ; revised on November
3, 2006.
1,2 The authors are with the Sirindhorn International Institute of Technology,Thammasat University, Bangkadi Campus,
131 Moo 5, Tiwanont Road,Bangkadi, Maung, Pathum Thani
12000, Thailand Tel.+66(0) 25013505- 20, Fax:+66(0) 2501
3524, Email: [email protected].
(Q) factors from 10 to 55, high total noise from 226 to
707 µVrms and limited dynamic ranges from 58 to 68
dB. In addition, most Q factors have generally been
a function of variables such as a center frequency [14,
15]. For example, the quality factors of some existing Gm-C approaches [16, 17] have particularly been
inversely proportional to the center frequency. Such
variable quality factors have been difficult to tune
as the variables may vary rapidly and drastically resulting in the need for additional or complicated Qtunable circuits. In addition, sensitivities of neither
the Q factor nor the center frequency at 10.7 MHz
have been clearly reported, although sensitivities of
the Q factor at other center frequencies have been
undesirably a function of the Q factors [14, 15].
In this paper, a high-Q, wide-dynamic-range
current-tunable Gm-C bandpass filter is introduced
using two fully balanced devices, i.e. an adder and
a low-Q-based bandpass filter. The high-Q factor is
equal to a common-emitter current gain β. For the
first time, the high-Q factor is typically constant as
it is no longer a function of variables such as a center
frequency. This results in not only a great reduction
in the need for additional Q-tunable circuits but also
a much better sensitivity of the Q factor. The sensitivities of either the Q factor or the center frequency
are constant values and are not affected by the Q factor or variables. Possible solutions for good stability
of the Q factor with temperature are also suggested.
The technique is demonstrated through an example
at 10.7 MHz. Temperature compensations for both
the center frequency and the Q factor are summarized. Other 10.7-MHz Gm-C approaches are also
compared.
2. THE PROPOSED 10.7-MHZ HIGH-Q
WIDE-DYNAMIC-RANGE BANDPASS
FILTER
2. 1 System Realization
Figure 1 shows the proposed system realization of
a high-Q bandpass filter where the system is relatively
simple based on three fully balanced components, i.e.
a two-input adder AD , an amplifier AG and a low-Qbased bandpass filter ALQ (s).
The transfer function of the low-Q-based bandpass
filter ALQ (s) can be written as
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ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.2 August 2007
Fig.1: Proposed system realization of a high-Q bandpass filter.
ALQ (s) =
o
)s
a1 ( QωLQ
o
)s + ωo2
s2 + ( QωLQ
(1)
where a1 is a pass band gain, i.e. a1 = ALQ (s) at s
= jωo and QLQ is a relatively low-Q factor of ALQ (s).
Consequently, a closed-loop gain AHQ (s) = vo /vin is
given by
AHQ (s) =
AD ALQ (s)
1 − AD AG ALQ (s)
(2)
Fig.2: A 10.7-MHz fully balanced, high-Q, widedynamic-range current-tunable Gm-C bandpass filter.
Substituting ALQ (s) in (2) with (1) yields
AHQ (s) =
o
AD a1 ( QωLQ
)s
o
)s + ωo2
s2 + ( QωHQ
(3)
where the quality factor QHQ is given by
QHQ =
QLQ
1 − AD AG a1
(4)
It can be seen from (4) that QHQ may ideally approach infinite if the denominator (1 - AD AG a1 ) approaches zero. In other words,
AG −→
1
a1 AD
(5)
In practice, the denominator of (4) may be made
relatively small, i.e. AG is in the proximity of
1/(a1 AD ), resulting in a relatively high quality factor
QHQ .
2. 2 Circuit Realization
Figure 2 shows the proposed circuit realization for
Fig 1 through an example of a fully balanced high-Q
current-tunable Gm-C bandpass filter (AHQ ). The
circuit consists of two fully balanced components, i.e.
a two-input adder (AD ) and a low-Q-based bandpass
filter (ALQ ) whilst AG = 1 (i.e. a direct connection),
using matched transistors T1 to T10. In this case,
equation (5) suggests that the gain of the adder AD ∼
=
1 and a1 ∼
= 1. Firstly, the adder AD is a modified
version of an existing adder [18] and consists of a
differential pair (T1, T2), a common-collector pair
(T3, T4) and two current sinks I1 . The 1st smallsignal input voltage of AD is vAB between the bases
of T1 and T2 (or nodes A and B). The 2nd smallsignal input voltage of AD is vCD between the bases
of T3 and T4 (or nodes C and D). A small-signal
output voltage of AD is vEF between the emitters of
T3 and T4 (or nodes E and F).
Secondly, the low-Q-based bandpass filter ALQ is a
modified version of an existing low-Q bandpass filter
[19] and consists of a differential pair (T5, T6), two
capacitors C1 and 2C1 , two current sinks I2 and four
loading diode-connected transistors T7 to T10. A
small-signal input voltage of ALQ is vEF between the
bases of T5 and T6 (or nodes E and F) and is obtained
from the output vEF of AD . A small-signal output
voltage of ALQ is vCD between the emitters of T7 and
T8 (or nodes C and D). Finally, the transfer function
of the high-Q bandpass filter is AHQ = vO / vin where
vin = vAB and vO = vCD . It can be seen from Fig.
2 that the circuit is fully balanced.
2. 3 A Current Tunable Gm-C Bandpass Filter
Parameters re1 , re2 ,...,re9 and re10 are the smallsignal emitter resistance of transistors T1, T2,..., T9
and T10, respectively, where (re1 = re2 ) = VT /I1 , (re3
= re4 ) ∼
= VT /(αI1 ) ∼
= re1 /α, (re5 = re6 ) = VT /I2 ,
(re7 = re8 = re9 = re10 ) ∼
= VT /(αI2 ) ∼
= re5 /α for
α = β/(β + 1) and β is the common-emitter current
gain of a BJT. The usual thermal voltage VT is approximately 25 mV associated with an pn junction at
room temperature
Firstly, the two-input adder AD is considered. The
output vEF of AD is obtained through superposition,
i.e. vEF = vO1 + vO2 . The voltage vO1 is the output
vEF of AD when the 1st -input vAB of AD is activated,
i.e. vAB = vin , but the 2nd -input vCD of AD is tem-
10.7-MHz Fully Balanced, High-Q, Wide-Dynamic-Range Current-Tunable Gm-C Bandpass Filter
porary deactivated or separately connected to an ac
ground, i.e. vCD = 0. In contrast, the voltage vO2 is
the output vEF of AD when the 2nd -input vCD of AD
is activated, i.e. vCD = vO , but the 1st -input vAB of
AD is temporary deactivated or connected to an ac
ground, i.e. vAB = vin = 0.
On the one hand, vO1 can be found at vCD = 0.
Therefore, vin of AD enables a small-signal emitter
current ie1 = vin /(2re1 ) passing through the emitters
of T1 and T2. The resulting small-signal collector
current of T1 and T2 is ic1 = αie1 . Most of ic1 passes
through a loading impedance Z1 = 2re3 formed by
T3 and T4. As vO1 ∼
= ic1 Z1 , therefore vO1 /vin ∼
= 1.
∼
Consequently, vO1 = vin .
On the other hand, vO2 can be found at vin = 0.
Therefore, the gain of the common-collector pair (T3,
T4) is vO2 /vCD ∼
= 1, or vO2 ∼
= vCD . Consequently,
vEF = vO1 + vO2 ∼
= vin + vCD , i.e. the gain of the
adder AD ∼
= 1. As vCD = vO , therefore
vEF ∼
= vin + vo
(6)
Secondly, the low-Q-based bandpass filter ALQ is
considered. The input vEF of ALQ enables a smallsignal emitter current ie2 = vEF (2sC1 )/(1 + sτ1 )
passing through the emitters of T5 and T6, where
τ1 = 4re5 C1 . The resulting small-signal collector current of T5 and T6 is ic2 = αie2 . Most of ic2 passes
through a loading impedance Z2 = 4re7 /(1 + sτ2 )
formed by T7 to T10 where τ2 = 4re7 C1 and therefore τ2 ∼
= τ1 /α. The resulting output of ALQ is
vCD ∼
= ic2 Z2 , therefore ALQ = vCD /vEF = vO /vEF
represents a low-Q-based bandpass filter ALQ of the
form
ALQ =
vO
2sα/τ1
= 2
vEF
s + (1 + α) τs1 +
α
τ12
(7)
The center frequency of (7) is ωLQ = (α1/2 )/τ1 .
The quality factor of (7) is QLQ = (α1/2 )/(1 + α) ∼
=
0.5 which is a relatively low value. It can be seen from
(1) and (7) that a1 = 2α/(1+α) ∼
= 1. In other words,
at s = jωLQ , the passband gain of (7) is ALQ = a1 =
2α/(1 + α) ∼
= 1.
Finally, the high-Q bandpass filter AHQ can be
considered by substituting vEF in (7) with (6), therefore AHQ = vO /vin ∼
= ALQ /(1 − ALQ ), i.e.
AHQ =
2αs/τ1
vo
= 2
vin
s + (1 − α) τs1 +
α
τ12
(8)
The center frequency of (8) is ωHQ = (α1/2 )/τ1 =
gm5 /[(α1/2 )4C1 ] where the transconductance gm5 =
α/re5 . At s = jωHQ , the passband gain of (8) is ideally (i.e. without loading effect) AHQ (s) = 2α/(1 −
α) ∼
= 2β which is much greater than the passband
gain of (7) where ALQ = a1 = 2α/(1 + α) ∼
= 1 at s =
jωLQ . The center frequency ωHQ is current tunable
by I2 of the form
15
s
ωHQ
I2
=
4C1 VT
β
β+1
(9)
2. 4 A High Quality Factor
The quality factor of (8) is QHQ = (α1/2 )/(1 − α)
and therefore
QHQ ∼
=β
(10)
The quality factor QHQ of the proposed technique
is approximately equal to a typically high (> 100)
and constant value of the current gain β and is, for
the first time, no longer a function of variables such
as a center frequency. The typically constant quality
factor QHQ results in not only a great reduction in the
need for additional or complicated tunable circuits,
but also a much better sensitivity of the Q factor.
Variations of QHQ with temperature may be expected, as β may depart from its typically constant
value due to temperature. Such variations, however,
are relatively much smaller and slower than the variations of most reported Q factors which have generally been a function of variables such as a center
frequency [14, 15] or have particularly been inversely
proportional to the center frequency [16, 17].
In addition, possible solutions for good stability of the quality factor QHQ with temperature
could be suggested through the use of, for example, InGaP/GaAs Heterojunction Bipolar Transistors (HBTs) where a relatively constant current
gain β has been reported as a function of temperature up to 300 ◦ C [20], or through the use of
AlX Ga0.52−X In0.48P /GaAs HBTs where good stability of β with collector current and temperature has
been demonstrated for X = 0.18 − 0.30 [21].
2. 5 Sensitivities
Generally, a sensitivity of y to a variation of x is
given by Sxy = [δy/δx][x/y] where y is a parameter
of interest and x is a parameter of variation. Table
1 shows the sensitivity Sxy where (x, y) = (β, QHQ ),
(C1 , ωHQ ), (VT , ωHQ ), (I2 , ωHQ ) or (β, ωHQ ). The
thermal voltage VT also represents effects of temperature on the centre frequency ωHQ whilst the current
gain β also represents effects of temperature on the
quality factor QHQ . For a relatively large value of β,
ω
the last sensitivity Sβ HQ is not only relatively small
ωHQ
(e.g. Sβ = 0.0041 at β = 120) but also relatively
constant if the variation of β is comparatively smaller
ω
than its value (e.g.Sβ HQ = 0.0035 at β = 140). Consequently, it can be seen from Table 1 that the sensitivities of both QHQ and ωHQ are relatively constant
between -1 to 1. Such sensitivities are, unlike existing
approaches [14, 15], no longer strongly affected by the
Q factor or variables.
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ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.2 August 2007
Table 1: Sensitivity Sxy where (x, y) = (β, QHQ ), (C1 , ωHQ ), (VT , ωHQ ),(I2 , ωHQ ) or (β, ωHQ ).
Q
sβ HQ
1.0
ω
sCHQ
1
-1.0
ω
sVTHQ
-1.0
ω
sI2HQ
1.0
ω
sβ HQ
1/[2(β + 1)]
Table 2: Summaries of dynamic ranges (DRs) using second-order Gm-C techniques.
Capacitors
vmax
This paper (fully balanced)
Ca = C and Cb = 2C
2vM 1
1
DR1 = 2.67 (kTMξQ)
1
[24] (single ended)
Ca = C and Cb = C
vM 2
2
DR2 = 0.50 (kTMξQ)
2
[22] (single ended)
Ca = C/2 and Cb = C/2
vM 3
DR =
2
vmax
(kT ξQ)( C1a + C1 )
Ref s
v2
C
v2
C
b
2
vM
3C
DR2 = 0.25 (kT ξQ)3
2. 6 Dynamic Ranges
Dynamic ranges (DRs) of either a specific biquad
or an optimized high-Q biquad in a general way have
been presented [22]. An expression for the dynamic
range of a second-order Gm-C biquad in a general
way is given by [22]:
DR =
2
vmax
2
vnoise
=
2
vmax
kT ξQ( C1a +
1
Cb )
(11)
where vmax is the maximal signal level (at the in2
put or output of a system), vnoise
is the mean squared
noise voltage at the same point, Ca and Cb are two
capacitors in the filter, k is the Boltzmann’s constant,
T is the absolute temperature, ξ is the noise factor of
the transconductor (Gm) and Q is the quality factor.
The dynamic range of the proposed technique can be
2
improved by not only increasing vmax
, but also re2
ducing vnoise of (11) as follows.
On the one hand, it is known that, the maximal
signal level vmax of a fully balance circuit is typically
twice the maximal signal level vM of a single-ended
circuit [22], i.e. vmax ∼
= 2vM . In other words, the
magnitude vmax of (11) may be double through the
use of a fully balanced circuit. On the other hand, the
mean squared noise voltage can be reduced through
the use of a shunt positive feedback configuration providing enhanced current gain and thereby improving the overall noise [23]. Table 2 summarizes values of Ca , Cb , and dynamic ranges (DRs) of the proposed Gm-C techniques and other existing Gm-C approaches [22, 24].
It can be seen from Table 2 that if vM 1 = vM 2 =
vM 3 and (KT ξQ)1 = (KT ξQ)2 = (KT ξQ)3 , then
DR1 > DR2 > DR3 . The proposed Gm-C fullybalanced technique can therefore enable a higher dy2
namic range DR1 , especially when vnoise
is also additionally reduced. In particular, as the quality factor
Q in (11) becomes QHQ which is no longer a function
of variables such as a center frequency, the dynamic
range DR1 is therefore, unlike existing approaches
[22, 24], no longer strongly affected by those variables
Fig.3: A measured frequency response at the centre
frequency f0 = ωHQ /(2π) = 10.7 MHz and the quality
factor QHQ = 121.
previously associated in the Q factor. As an example,
it can be expected from Table 2 that DR1 = 88.28
dB if vmax = 2vM 1 = 127mV (i.e. -5 dBm through a
50 − Ω load), vM 1 = 63.5 mV, kT ξ = 2 × 10−23 [24],
Q = 120 and C = 150 pF.
3. EXPERIMENTAL RESULTS
3. 1 A 10.7-MHz High-Q Current-Tunable
Gm-C Bandpass Filter
As a simple example, all transistors in Fig. 2 are
modeled by a simple transistor 2N2222 where the average transition frequency (fT ) is 120 MHz and β is
approximately 120 [25]. All current sinks are LM334
[26]. The bias current I1 = 1 mA and C1 = 150 pF.
Figure 3 illustrates the measured frequency response
of Fig. 2 at the center frequencies f0 = ωHQ /(2π)
= 10.7 MHz. It can be seen from Fig. 3 that the
bandwidth (BW) is 2 × 44 = 88 kHz and therefore
the measured quality factor QHQ (= f0 /BW ) is relatively high at approximately 121 which is consistent
with the value of β =120.
10.7-MHz Fully Balanced, High-Q, Wide-Dynamic-Range Current-Tunable Gm-C Bandpass Filter
17
Table 3: Summaries of related noise parameters obtained from Fig.5 .
Noise Parameters
(1) Resolution bandwidth (RBW)
(2) Noise Density
PN 1 = 10log(PN 2 /1mW )
PN 2
VN2 = PN 2 ×p(50Ω)
VN 1 = (VN2 )
(3) Total Noise
VN 2 = VN2 × (RBW
√ )
VN 3 = VN 2
2
VN
3
PN 3 = 10log (50Ω)(1mW
)
Fig.4: Plots of the center frequency f0 = ωHQ /(2π)
and the quality factor QHQ versus the bias current
I2 .
Figure 4 shows plots of the center frequencies
f0 = ωHQ /(2π) and the corresponding quality factor QHQ of Fig. 2 versus the bias current I2 for three
cases, i.e. the analysis, the SPICE simulations, and
the experimental results. It can be seen from Fig.
4 that f0 is current tunable over 3 orders of magnitude. As expected, QHQ essentially remains almost
constant at approximately 121 and is, unlike existing
approaches, independent of variables such as a center
frequency. When I2 > 1 mA, f0 drops with further
increase of the bias current due to effects of parasitic
capacitances at higher frequencies. Although the upper value of I2 can be expected to be higher than
10 mA, the upper limit of the circuit prototypes has
been set to 5 mA, for save operation of the current
sources.
3. 2 Low Noise Performance
Figure 5 shows the measured output noise spectrum shaped by the transfer function of the filter,
where the power noise density PN 1 is relatively low at
-142.5 dBm/Hz and the resolution bandwidth (RBW)
Values
100
Units
kHz
-142.5
5.62 × 10−18
2.81 × 10−16
1.68 × 10−8
dBm/Hz
W/Hz
V 2 /Hz
√
Vrms / Hz
2.81 × 10−11
5.303 × 10−6
−92.45
V2
Vrms
dBm
Fig.5: Measured output noise spectrum.
is at 100 kHz. Table 3 summarizes resulting noise
parameters in terms of (1) the resolution bandwidth,
(2) the noise density and (3) the total noise. Table 3 concludes √that the output noise density VN 1
= 0.016 µVrms / Hz, the total output noise VN 3 =
5.303 µVrms and the total noise power PN 3 = -92.45
dBm.
3. 3 Wide Dynamic Range
The circuit is excited with two sinusoids at frequencies f1 = f0 − 7.5kHz = 10.6925M Hz, and
f2 = f0 + 7.5kHz = 10.7075M Hz. The 3rd -order intermodulation (IM3 ) products |2f1 −f2 | and |2f2 −f1 |
are 10.6775 and 10.7225 MHz, respectively. Figure 6
shows the measured output spectrums at QHQ = 121
using the two-frequency excitation of -20 dBm at f1
and f2 . It can be seen that the IM3 products are approximately 40 dB down from the fundamentals and
correspond to 1%(or1%IM3 ).
Through a 50 − Ω load of the spectrum analyzer
without the output buffer, Figure 7 depicts the measured output levels (dBm) of the fundamental at f1
and the IM3 at |2f1 − f2 | versus the input levels
(dBm). It can be seen from Fig. 7 that the noise
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ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.2 August 2007
Fig.6:
Measured output spectrums at the twofrequency excitation of -20 dBm.
Fig.8: Normalized centre frequencies versus ambient
temperature for the uncompensated and compensated
cases.
compensated. The second case is a “compensated”
case where the effects of temperature on f0 have been
compensated.
Fig.7: Measured output levels of the fundamental at
f1 and the IM3 at |2f1 − f2 | versus input levels.
power PN 3 = -92.45 dBm. At the input level of -35
dBm, the output level of f1 is -18 dBm whilst the output level of the IM3 is adjacent to PN 3 (or intermodulation free). Therefore the 3rd -order intermodulationfree dynamic range (IM F DR3 ) = (-18 dBm) - (92.45 dBm) = 74.45 dB. In addition, at the input
level of -20 dBm, the output level of f1 is -5 dBm,
whilst the output level of the IM3 is 40 dB down from
f1 (or 1%IM3 ). Therefore, the wide dynamic range
(at 1%IM3 ) = (-5 dBm) - (-92.45 dBm) = 87.45 dB
which is consistent with the expected value DR1 =
88.28 dB predicted in Section 2.6 .
3. 4 Effects of Temperature on the Center Frequency
For the high-Q bandpass filter AHQ , Figure 8
shows two cases of the measured variations of the
normalized center frequency f0 / (10.7 MHz) versus
the ambient temperature (Celsius). The first case is
an “uncompensated” case where the effects of temperature on the center frequency f0 have not been
The uncompensated case can be demonstrated by
taking Fig. 2 into an oven except that the connected
two current sinks I2 are located outside the oven (i.e.
the two current sinks I2 will be independent of the
ambient temperature in the oven). It can be seen
from Fig. 8 that the normalized frequency of the
“uncompensated” case decreases inversely with the
ambient temperature (in the oven) as can be expected
from (9) where effects of temperature caused by the
thermal dependent voltage VT is in the denominator
of (9).
The compensated case can be demonstrated by
taking Fig.2 into an oven including the connected two
current sinks I2 (i.e. the two current sinks I2 will also
be affected by the ambient temperature in the oven).
It can be seen from Fig. 8 that the normalized frequency of the “compensated” case remains relatively
constant, as can be expected from (9) where effects
of temperature caused by VT in the denominator of
(9) can be compensated by the relatively similar effects caused by VT of I2 in the numerator of (9), i.e.
I2 ∝ vBE where vBE = VT ln (IC /Is ), IC and Is
are the collector and saturation currents of a BJT in
LM334.
In the compensated case, the temperature coefficients of the normalized center frequencies decrease
drastically. The measured temperature coefficients
for ambient temperature ranging from T1 = 30 ◦ C
to T2 = 75 ◦ C are approximately -30 ppm/◦ C, i.e.
∼
= [f (T2 )−f (T1 )]×106 /[f (T1 )×(T2 −T1 )] = (0.9986−
1) × 106 /[(1)(75 − 30)]. The measurements have been
obtained by putting the two frequency-determining
capacitors outside the oven, and the measured temperature coefficients are therefore due to the intrinsic
circuit parameters only.
10.7-MHz Fully Balanced, High-Q, Wide-Dynamic-Range Current-Tunable Gm-C Bandpass Filter
Fig.9:
The quality factor QHQ versus ambient
temperature for the uncompensated and compensated
cases.
19
Fig.10:
Preliminary interpolation of the power
consumption (PC ) and the dynamic range (DR at
1%IM3 ) versus C1 at f0 = 10.7 MHz and QHQ =
121.
3. 5 Effects of Temperature on the Quality
Factor
Effects of temperature on the quality factor have
never clearly been reported. In a similar manner to
Section 3.4, Fig. 9 shows two cases of the measured
variations of the quality factor QHQ versus the ambient temperature (Celsius), i.e. the uncompensated
and the compensated cases. It can be seen from Fig.
9 that QHQ in the “uncompensated” case increases
versus the ambient temperature as can be expected
from (10) where β is proportional to temperature
[20], [25]. In addition, the variation of QHQ in the
“compensated” case is reduced. Such variations of
QHQ are not only gradually but also relatively much
smaller and slower than the variations of most reported Q factors which have generally been a function of variables such as a center frequency [14, 15] or
have particularly been inversely proportional to the
center frequency [16, 17].
The measured temperature coefficients, ranging
from T1 = 30 ◦ C to T2 = 75 ◦ C, are reduced approximately from 1,010 ppm/◦ C in the “uncompensated”
case to 367 ppm/◦ C in the “compensated” case. As
mentioned earlier, alternative solutions for good stability of the quality factor QHQ with temperature
should be suggested through the use of special HBTs
where good stability of β with temperature has been
reported [20, 21].
4. COMPARISONS TO OTHER 10.7-MHZ
GM-C TECHNIQUES
As mentioned earlier, 10.7-MHz bandpass filters
are typically based on switched capacitors (SC) or
Gm-C techniques. Table 4 particularly compares various results of the proposed Gm-C technique to those
of existing Gm-C approaches. In an attempt to enable fair comparisons, all center frequencies are fully
homogenous at 10.7 MHz. For purposes of informa-
Fig.11: An example of the center frequencies f0 and
the quality factor QHQ versus capacitance C1 with
fixed bias currents I1 = I2 = 1 mA.
tion, irrelevant results of SC techniques as well as relevant results of Gm-C techniques that are not fully
homogenous are also included in Table 4, although
some comparisons may be somewhat unfair. It can
be observed from Table 4 that the proposed 10.7MHz technique offers not only the high-Q factor of
121 compared to others between 10 to 55, but also
the wide dynamic range of 87.45 dB at 1%IM3 compared to others between 61 to 68 dB. In addition, the
total output noise is 5.303 µVrms compared to others
between 226 to 707 µVrms .
5. POSSIBLE ON-CHIP HIGH-Q WIDEDYNAMIC-RANGE BANDPASS FILTER
Preferable requirements for an on-chip integrated
bandpass filter include low power consumption, low
silicon areas of capacitors, high dynamic ranges and
high center frequencies whilst maintaining high quality factors. On the one hand, equation (9) suggests
20
ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.2 August 2007
Table 4: Comparisons of the proposed Gm-C bandpass filter and existing Gm-C approaches SwitchedCapacitor (SC) techniques are also included for information.
Performances
Design
techniques
Technologies
Orders
Simulation
results
Experimental
results
IC Fabrication
Center freq.
:fO (MHz)
Bandwidth
(kHz)
Q factors
Sampling freq.
(MHz)
Sensitivity of
ωO
Sensitivity of
Q
Output noise
√ rms )
density( µV
Hz
Total Output
noise (µVrms )
Dynamic range
@ 1%IM3 (dB)
@ 3%IM3 (dB)
Power
consumption
PC (mW)
This
Tajalli Chung Munoz Steven- Steyert GarDesign 2003
Yu
2001
son
1992
duno
2001
1998
2005
Gm-C Gm-C Gm-C Gm-C Gm-C Gm-C SC
BJTs
2
√
√
Ham- Quinn Nagari Nagari
mouda 2000
1998
1997
2002
SC
SC
SC
SC
BiCMOS CMOS CMOS CMOS CMOS CMOS CMOS CMOS CMOS CMOS CMOS
2
2
2
2
4
2
6
6
2
2
√
√
√
√
√
√
×
×
×
×
×
×
×
×
×
10.7
×
10.7
×
10.7
×
10.7
88
-
500
121
-
-
√
√
√
Matinez
2003
SC
√
√
√
√
10.7
10.7
×
10.7
×
√
√
√
√
√
√
10.7
10.7
10.7
10.7
10.7
267.5
535
300
1070
464
305.7
-
1070
368.9
21.4
-
40
-
20
-
-
10
65
-
35
-
55
-
10
107
29
22.8
-1 to 1 -
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
0.016
-
-
-
-
-
-
-
-
-
1
0.38
5.303
-
-
-
-
-
-
295
-
226
707
240
87.45
60
16
6
-
108
68
220
-
58
9
-
61
16
58.4
23
68
17
that not only the power consumption (PC ) due to I2
but also the silicon areas due to C1 , can be simultaneously reduced for the same ratio of (9). On the other
hand, equation (11) suggests that the smaller values
of the capacitance in the circuit, the smaller value
of the dynamic range (DR). As a result, higher dynamic ranges on chip require higher power consumptions and more silicon areas of capacitors.
As an example at the center frequency f0 = 10.7
MHz whilst maintaining the high quality factor QHQ
= 121, Fig. 10 predicts preliminary interpolation of a
power consumption PC and a corresponding dynamic
range (DR at 1 %IM3 ) versus the capacitance C1 . It
can be seen from Fig. 10 that a higher dynamic range
DR = 87.45 dB requires a higher power consumption
PC = 60 mW at C1 = 150 pF, whilst a lower DR =
65.7 dB requires a lower PC = 0.4 mW at C1 = 1 pF.
High-frequency performance of the circuit will be
limited by the transition frequency (fT ) of the tran-
sistor. Equation (9) suggests that a higher, more useful, center frequency can be expected using a smaller
value of capacitor C1 (e.g. using stray capacitances),
a higher value of I2 and a higher fT (e.g. in the region
of several GHz) of better transistors. As a particular
example, all transistors in Fig. 2 are modeled by a
better transistor BFR90A with higher fT at 5 GHz
[27], β = 120 and the bias currents I1 = I2 = 1 mA.
Figure 11 shows high-frequency performance of Fig.
2 through the analysis and the SPICE simulations in
terms of the center frequency and the quality factor
QHQ . In this particular example, QHQ is maintained
relatively high and the upper frequency is limited at
approximately 600 MHz at C1 = 1 pF.
6. CONCLUSION
A fully-balanced high-Q, wide-dynamic-range
current-tunable Gm-C bandpass filter has been proposed based on two simple components, i.e. the adder
10.7-MHz Fully Balanced, High-Q, Wide-Dynamic-Range Current-Tunable Gm-C Bandpass Filter
and the low-Q-based bandpass filter. The Q factor is
as high as the relatively constant value of a commonemitter current gain (β). For the first time, a high-Q
factor is no longer a function of variables such as a
center frequency resulting in not only a great reduction in additional Q-tunable circuits but also a much
better sensitivity of the Q factor. Sensitivities of either the Q factor or the center frequency have been
constant between -1 to 1 independent of the Q factor or variables. An example has been demonstrated
at 10.7 MHz for a high-Q factor of 121, the low noise
power of -92.45 dBm, the wide dynamic range of 87.45
dB at 1 %IM3 and the 3rd -order intermodulation-free
dynamic range (IM F DR3 ) of 74.45 dB. The center
frequency has been current tunable over 3 orders of
magnitude. The proposed technique has been compared with other 10.7-MHz Gm-C approaches and has
offered a potential alternative to a 10.7-MHz high-Q
wide-dynamic-range bandpass filter.
[7]
[8]
[9]
[10]
[11]
7. ACKNOWLEDGMENT
The authors are grateful to The Thailand Research Fund (TRF) for the research grant No.
PHD/0214/2543 of the Royal Golden Jubilee Program, to Mr. M. Watchakittikorn for his introduction
to the adder in [18], and to Prof. Dr. W. Surakampontorn for his useful suggestions.
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Worawat Sa-ngiamvibool received
the BEng degree in electrical Engineering, and MEng degree in electrical
engineering from Khonkaen University
(KKU), Khonkaen, Thailand, in 1996
and 1999, respectively. He is currently a
PhD candidate in the School of Communications, Instrumentation and Control
Systems, Sirindhorn International Institute of Technology (SIIT), Bangkadi,
Thammasat University, Thailand. His
research interests include analog circuits and power systems.
Banlue Srisuchinwong was born in
Bangkok, Thailand in 1963. He received
the BEng (Hons) degree in Electrical
Engineering from King Mongkut’s Institute of Technology Ladkrabang, Thailand, in 1985, the Diploma of the Philips
International Institute of Technological
Studies (electronics), the Netherlands,
in 1987, the MSc and the PhD degrees
from University of Manchester Institute
of Science and Technology (UMIST),
UK, in 1990 and 1992, respectively. Since 1993, he has been
with Sirindhorn International Institute of Technology (SIIT),
Thammasat University, Thailand, where he is currently an Associate Professor of Electrical Engineering and an Executive
Assistant Director.
At SIIT, he was an Institute Secretary (2000 to 2002), an
Acting Deputy Director (1997 to 1998) and a Chairperson of
the Department of Electrical Engineering (1993 to 1996). From
1992 to 1993, he was an employee of UMIST where he worked
on integrated sensors of electron detectors. From 1987 to 1988,
he involved in the design of integrated quadrature oscillators at
the Data Transmission System Group, Philips Research Laboratories, Eindhoven, the Netherlands. His research interests
include microelectronics and nonlinear dynamics. He has coedited the volume Circuits for Wireless Communications : Selected Readings, published by IEEE Press.