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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 14 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. 16 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 18 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. 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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.