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Low-Voltage Transconductor with Wide Input Range and Large Tuning Capability
TSINGHUA SCIENCE AND TECHNOLOGY ISSNll1007-0214ll17/17llpp106-112 Volume 16, Number 1, February 2011
Low-Voltage Transconductor with Wide Input Range and Large Tuning Capability KONG Yaohui (孔耀晖)**, YANG Hong (杨 宏), JIANG Ming (蒋 明), XU Shuzheng (徐淑正)†, YANG Huazhong (杨华中)† The First Research Institute of the Ministry of Public Security, Beijing 100048, China； † Department of Electronic Engineering, Tsinghua University, Beijing 100084, China Abstract: A CMOS triode transconductor was developed with common mode feedback suitable for operating in low-voltage and low-power applications. The design is based on a body-driven input stage with feedback loops to extend both the signal input range and the tuning capability. The effective transconductance of the body-driven triode stage is increased using a partial positive feedback technique which also partially solves the problem introduced by the small transconductance. This design uses the UMC 0.18 μm CMOS process. Simulations show the transconductor operated with 1 V supply voltage has less than −55 dB total harmonic distortions (THD) in the complete tuning range (0 V - Vcont - 0.43 V) for a 1 MHz 0.8 Vp-p differential input. The power consumption is 70 μW for a 0.43 V control voltage. Key words: low-voltage; CMOS; transconductor; wide input range
Introduction In modern CMOS processes, scaling down of the supply voltage is not followed by a proportional reduction of the transistor threshold voltage, which reduces the headroom of the analog signal and gets a poor linear dynamic range. Thus, a severe challenge for analog circuit designers is to preserve or even increase the circuit performance for low supply voltages. The transconductor is one of the critical building blocks in Gm-C filters[1-9] since in many systems the overall linearity is mainly determined by the transconductor. A large transconductance tuning capability is important for Gm-C filters for both compensating in fabrication tolerances and achieving programmability for relevant parameters. Many kinds of transconductors have been Received: 2010-10-28; revised: 2010-12-10
** To whom correspondence should be addressed. E-mail: [email protected]; Tel: 86-10-88513468
developed[3-7] recently to compensate for the performance loss due to the low supply voltage. Transconductors based on triode-biased MOS transistors are appropriate candidates because of their high linearity and flexible tunability. The traditional way shown in Fig. 1a to implement a triode transconductance is by a compact regulated cascode structure to minimize the variation of the input transistor drain voltage. The transconductance tuning capability of the triode transconductor is limited by the voltage headroom of the input transistor. Recently, Yodprasit[7] proposed the method in Fig. 1b to improve the VDS1 tuning range of triode transconductors using a weak inversion device for the low supply voltage. However, these approaches are still not suitable for very low supply voltages. Firstly, 0 < VDS1 < VDD − VGS4 − VDSsat 2 is not wide enough to obtain a large tuning capability. Secondly, the transconductance of triode based structures is tuned by changing VDS . An NMOS Max Min gate-driven input stage must have VDS1 < VGS1 − VTH to ensure the input transistor works in the triode region.
KONG Yaohui (孔耀晖) et al.：Low-Voltage Transconductor with Wide Input Range …
VDS is constrained by the signal input range. Thus, there is a trade-off: bigger transconductance tuning capability leads to smaller input range and vice versa. This situation gets worse with very low supply voltages due to the relatively high threshold voltage. Thirdly, the linearity of triode transconductors is mainly influenced by the drain to source variation and the mobility deduction. In most designs, rL is only 1 / g m ro g m ( rL is the total small signal resistance looking out of the drain of input transistor, while g m and ro denote the output resistance and transconductance of transistor), which is not small enough to obtain the constant drain to source voltage required by high linearity applications. Moreover, the distortion in gatedriven topologies from mobility reduction will deteriorate in new process. These problems seriously limit the performance of present triode transconductors for low voltage applications.
107
In this paper, a high performance, body-driven transconductor for a 1 V supply voltage is proposed. This triode transconductor overcomes the limitations between transconductance tuning and input range by using feedback loops and body-driven techniques. The triode transconductor supports both a wide input range and a large tuning capability. In addition, the transconductance of the body-driven input stage is enhanced by a partial positive feedback loop. This partially avoids the traditional drawbacks in the bodydriven input stage due to the reduced transconductance. This topology is compact and suitable for low voltage applications.
1
Body-Driven Technology
The body-driven technique was first introduced by Guzinski et al.[10] to overcome threshold limitations in amplifiers. In the body-driven topology, the signal is added to the body instead of the gate and VGS is kept constant. The body-driven structure is similar to a JFET. The channel conductivity is modified by the body to source voltage. Thus, the body-driven MOS transistor can operate with negative, zero, or slightly positive bias voltage, like a depletion type device. The characteristics of gate-driven and body-driven operation of PMOS transistors are shown in Fig. 2 for VDD = 0.8 V by sweeping VSD from 0.1 V to 0.7 V.
Fig. 2
Fig. 1
Triode transconductor core
Simulated transconductance characteristics
If the usual terminology and first order models are adopted[11], the PMOS transistor drain current in the triode region corresponds to the well-known expression W I D = μCox × L
Tsinghua Science and Technology, February 2011, 16(1): 106-112
108
n ⎛ ⎞ ⎜ VSG − | VTH0 | −γ 2 | φF | +VBS + γ 2 | φF | − VSD ⎟ VSD 2 ⎝ ⎠ (1) where φF is the body Fermi potential, VTH0 is the zero bias threshold voltage, and n is the slope factor. When the transistor works as a body-driven device, the linear dependence of transconductance on VSD is given in Eq. (2) by derivation of the v − i characteristics, if the mobility reduction due to the vertical field is neglected. The transconductance of a body-driven PMOS transistor is given by ∂i γ W (2) Gm = g mb = D = μ Cox VSD ∂vBS L 2 (2 | φF | +VBS )
capability is still reachable for very low supply voltage.
2
With the body-driven input stage, the threshold voltage is not limited to the input range. In addition, the trade-off between input range and tuning capability is also improved to produce a wide input range transconductor at very low supply voltage with a large tuning capability.
Transconductor Design
The transconductor core is shown in Fig. 3. M1 is the input transistor. The M2-M3 transistors together with the I1-I2 current mirrors form the feedback loop. This design is based on the N-well process, so only the PMOS transistor is body-driven. This body-driven triode transconductor has many useful features, which are listed in details as follows.
Fig. 3
2.1
Body-driven transconductor core
Large tuning capability
In the triode transconductor, the Gm tuning is realized by changing VSD1 . VSD1 is limited by the drain voltage headroom of the input transistor M1. However, in this circuit the drain voltage headroom of input transistor M1 is extended by the level shifter function of the feedback loop. Thus, this transconductor increases VSD1 to 0 < VSD1 < VDD − 2VDsat , which is wider than many other topologies[7-9]. Thus, a large Gm tuning
2.2
Wide input range
The conventional gate-driven topology has a threshold voltage limitation, which constrains the input signal range. Another problem is that the gate-driven large transconductance tuning capability leads to a small input range and vice versa. Therefore, there is a tradeoff between the input range and the tuning capability. In this body-driven topology, the input transistor gate is connected to ground. The input range is then only limited by the leakage current through the drain body and the source body diode. Max VDD − (VTH0 + γ 2 | φF | +VBSMax − γ 2 | φF |) > VSD (3)
2.3
High linearity
Traditional triode transconductors suffer from two sources of nonlinearities. One is the drain to source voltage variation due to the change of VGS of the input transistor. The other is the mobility reduction owing to an increase of the vertical field in the device. This body-driven transconductor design reduces these two nonlinearities. 2.3.1 Drain to source voltage variation The triode transconductor linearity depends on the stability of the input transistor drain voltage. Different methods have been used to bias the transistor to get a constant VDS in the literature. This variation is primarily determined by the load resistance rL . The rL of proposed transconductor is g m ro times smaller than in previous designs in Refs. [7-9]. A more constant drain node over the variation of the body voltage and drain current can be ensured thanks to the smaller rL . v 1 rL = ds ≅ (4) id g m2 ro2 g m3 ro3 g m4 2.3.2 Mobility reduction The mobility reduction due to the vertical field also affects the triode mode transconductor linearity. The mobility reduction effect can be modeled by the θ -model, which is obtained by replacing the mobility
KONG Yaohui (孔耀晖) et al.：Low-Voltage Transconductor with Wide Input Range …
μ by μeff .
μ μeff = 1 + θV0
(5)
where μeff is the effective mobility, θ is the mobility reduction coefficient, and V0 =VSG − (|VTH0 | +γ 2 |φF | + VBS − γ 2 | φF |). θ increases in the submicron process, which degrades the linearity performance of most gate-driven triode transconductors. The main reason for this effect is due to velocity saturation of carriers in the channel. Significant third-order distortion of the gate-driven is introduced by the mobility reduction effect and can be modeled by 1 θ2 (6) HD3 ≅ Vin2 16 (1 + θV0 )2 The third-order distortion of the body-driven topology can be deduced as 2 1 θ2 γ ⎛ ⎞ 2 HD3 ≅ Vin (7) 16 (1 + θV0 )2 ⎝⎜ 2 (2 | φF | +VBS ) ⎠⎟ V0 in body-driven topologies is commonly larger than that of gate-driven topologies, since VSG is equal to VDD in this body-driven input stage. Furthermore,
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the factor γ / 2 (2 | φF | +VBS ) is less than 1. Thus, the linearity of body-driven triode transconductors is better than that of traditional gate-driven ones due to the mobility reduction effect. Generally speaking, the transconductance of the body-driven input stage is about 1/4 that of a gatedriven input stage, which will bring some problems. First, the input noise is increased due to the reduction of the intrinsic gain in body-driven transistors. Second, the reduction of the input transconductance limits the maximum achievable frequency of circuits based on these devices. A technique to boost the effective transconductance of the body-driven input stage is illustrated in the following section to partially resolve the problem mentioned above.
3 Transconductor Implementation The full schematic of the transconductor is shown in Fig. 4. The transconductor is implemented in pseudodifferential pairs.
Fig. 4 Full transconductor schematic
MA1/MB1 is the input transistor. MA2-MA4/MB2MB4 form the feedback loops, which not only reduce the small signal resistance looking out of the input transistor drain, but also maximize the drain to source voltage tuning range of MA1/MB1. Transconductance tuning is based on changing Vcont to control the drain to source voltage of the input transistor, which can be given by ⎛ 2 I3 ⎞ VSD1 = VDD − ⎜ Vcont + | VT3 | + (8) W3 ⎟⎟ ⎜ C μ ox ⎜ L3 ⎟⎠ ⎝ Here the drain voltage headroom of the input
transistor is no longer the main limitation as in other structures. The practical restriction of the transconductance is that Vcont is constrained to be above zero voltage. Thus, the maximum Gm is limited. The tuning range can be increased by using the twin well process and using an NMOS as the input transistor. The transconductance of the body-driven input stage is improved by the positive feedback loop made by MA22/MB22 in Ref. [12]. The transconductance is given by B∙ g mb1 Gm = (9) 1− k
110
Tsinghua Science and Technology, February 2011, 16(1): 106-112
where B is the transistor size ratio of MA5/MB5 to MA2/MB2, k is the transistor size ratio of MA22/ MB22 to MA2/MB2, and g mb1 is the input transistor MA1/MB1 transconductance. Thus the transconductance is enhanced by B / (1 − k ) . This transconductor can work well by carefully sizing these transistors. In order to stabilize the common mode of outputs to the proper value and achieve a big swing, a novel low voltage low power common mode feedback (CMFB) circuit is implemented as shown in Fig. 5. In the
CMFB, bias current flows directly from the main transconductor circuit and varies with changes of the transconductance. The MD1-MD4 is the input common mode detector which provides the common mode information from the previous stage. Low voltage is ensured by a level shift circuit made of MD11/MD12 and a current mirror is adopted. MB7/MA7 gets the common mode information, Vfb , from the CMFB and stabilizes the output common mode voltage.
(a) CMFB signal flow graph
(b) CMFB schematic Fig. 5 CMFB design
4 Simulation Results The circuit has been simulated using the UMC 0.18 μm 1P6M process. The power supply voltage is 1 V.
The simulation of this transconductor was performed using the HSPICE simulator. Figures 6a and 6b show the output current and transconductance of the proposed circuit for different value of Vcont . It can be seen that this transconductor
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KONG Yaohui (孔耀晖) et al.：Low-Voltage Transconductor with Wide Input Range …
has a large tuning capability, although it works for a very low supply voltage.
(a) Circuit Gm tuning range (a) Circuit output current
(b) Circuit transconductance Fig. 6 Simulated DC circuit characterstics
In Fig. 7a the transconductance vs Vcont curve is plotted in linear scale. It is clear that the transconductance is linearly tunable for more than one decade. In Fig. 7b, the simulated THD for one typical case (Vcont = 0.2 V) and two marginal cases (Vcont = 0 V and Vcont = 0.43 V) are plotted against input amplitudes with a 1 MHz differential input signal. For Vcont = 0.43 V the performance is analyzed for 1 MHz and 100 kHz to test the performance of the lower end of the tuning. THD is less than −60 dB with Vcont = 0 V, 0.2 V, 0.43 V for a differential peak to peak voltage input up to 0.7 V. This transconductor shows that it sustains high linearity in the whole tuning range. The simulated THD for a 1 MHz signal is less than −55 dB in Vcont from 0 V to 0.43 V for a differential input signal up to 0.8 Vp-p. The quiescent power consumption is 70 μW, when 0.43 V control voltage is applied. The parameters and performance of the proposed transconductor are listed in Table 1. The simulated performance is better than those of recently published transconductors[13-15] as shown in Table 2.
(b) Circuit THD Fig. 7 Simulated tuning range and THD of circuit Table 1 Parameters and performance Technology
UMC 0.18 μm CMOS
Supply voltage
1V
Threshold voltage
VTN = 0.49 V, VTP = −0.53 V
Common mode input voltage Transconductance tuning range THD (Vcont=0 V) 1 MHz 0.2 Vp-p 1 MHz 0.4 Vp-p 1 MHz 0.8 Vp-p Power consumption (Vcont=0.43 V)
0.75 V Vcont = 0-0.43 V, Gm = 5.6-66.8 μS −87.8 dB −76 dB −62.5 dB 70 μW
5 Conclusions Simulations have confirmed the performance of the low-voltage triode transconductor. This body-driven triode transconductor is a feasible solution in the area of low voltage and low power applications. The transconductor can work for very low supply voltages and
Tsinghua Science and Technology, February 2011, 16(1): 106-112
112 Table 2 Source Torralba et al.
Comparison with recent transconductor designs
Transconductance range [5]
396-2443 μS
Lujan et al. [13]
50-200 μS
Zhang et al. [14]
8-131 μS
Galan et al. [15]
15-165 μS
This work
5.6-66.8 μS
Technology 0.8 μm CMOS 0.5 μm CMOS 0.18 μm CMOS 0.5 μm CMOS 0.18 μm CMOS
still maintain a wide input range, large tuning capability and highly linearity. With those features, this transconductor will be especially useful for very low supply environment as a critical part of Gm-C filters. References [1] Yang F, Enz C C. A low-distortion BiCMOS seventh-order bessel filter operating at 2.5V supply. IEEE Journal of Solid-State Circuits, 1996, 31(3): 321-330. [2] Python D, Enz C C. A 40 μW 75 dB dynamic range 70 kHz band-width Biquad filter based on complementary MOS transconductors. In: Proceedings of European Solid-State Circuits Conference. Germany, 1999: 38-41. [3] Koziel S, Szczepanski S. Design of highly linear tunable CMOS OTA for continuous-time filters. IEEE Transactions on Circuits and Systems II, 2002, 49(2): 110-122. [4] Pennisi S, Scotti G, Trifiletti A. 150 μA CMOS transconductor with 82 dB SFDR. In: Proceedings of IEEE International Symposium on Circuits and Systems. 2007: 237-240. [5] Torralba A, Martinez J M, Carvajal R G, et al. Low-voltage transconductor with high linearity and large bandwidth. Electronics Letters, 2002, 38(25): 1616-1617. [6] Zhang X, El-Masry E. A 1.8 V CMOS linear transconductor and its application to Continuous-time filters. In: Proceedings of IEEE International Symposium on Circuits and Systems. Canada, 2004: 271-350. [7] Yodprasit U. Low-power and low-voltage baseband and
Power
Supply
4.3 mW
1.5 V
1.25 mW
3.3 V
0.58 mW
1.8 V
0.36 mW
1.8 V
0.07 mW
1.0 V
THD −60 dB @10 MHz −78 dB @1 MHz
Input swing
N/A
0.6 Vp-p
−67 dB @1 MHz −62.5 dB @1 MHz
0.6 Vp-p 1 Vp-p
1 Vp-p 0.8 Vp-p
quadrature frequency synthesizer [Dissertation]. Ecole Polytechinque Federale de Lausanne, Swiss, 2006. [8] Likittanapong P, Worapishet A, Toumazou C. Linear CMOS triode transconductor for low-voltage applications. Electronics Letter, 1998, 34(12): 1224-1225. [9] Zeki A. Low-voltage CMOS triode transconductor with wide-range and linear tunability. Electronics Letters, 1999, 35(20): 1685-1686. [10] Guzinski A, Bialko M, Matheau J C. Body-driven differential amplifier for application in countinous-time active-C filter. In: Proceedings of the European Conferenceon Circuit Theory and Design, 1987: 315-319. [11] Tsividis Y P. Operation and Modeling of the MOS Transistor. NewYork: McGraw-Hill, 1998. [12] Wang R, Harjani R. Partial positive feedback for gain enhancement of low-power CMOS OTAs. Analog Integrated Circuits and Signal Processing, 1995, 8(1): 21-35. [13] Lujan-Martinez C, Carvajal R G, Galan J, et al. A tunable pseudo-differential OTA with -78 dB THD consuming 1.25 mW. IEEE Transactions on Circuits and Systems II, 2008, 55(6): 527-531. [14] Zhang L, Zhang X, El-Masry E. A highly linear bulk-driven CMOS OTA for continuous-time filters. Analog Integrated Circuits and Signal Processing, 2008, 54(3): 229-236. [15] Galan A, Carrasco M, Pennisi M, et al. Low-voltage tunable pseudo-differential transconductor with high linearity. ETRI Journal, 2009, 31(5): 576-584.
Low-Voltage Transconductor with Wide Input Range and Large Tuning Capability KONG Yaohui (孔耀晖)**, YANG Hong (杨 宏), JIANG Ming (蒋 明), XU Shuzheng (徐淑正)†, YANG Huazhong (杨华中)† The First Research Institute of the Ministry of Public Security, Beijing 100048, China； † Department of Electronic Engineering, Tsinghua University, Beijing 100084, China Abstract: A CMOS triode transconductor was developed with common mode feedback suitable for operating in low-voltage and low-power applications. The design is based on a body-driven input stage with feedback loops to extend both the signal input range and the tuning capability. The effective transconductance of the body-driven triode stage is increased using a partial positive feedback technique which also partially solves the problem introduced by the small transconductance. This design uses the UMC 0.18 μm CMOS process. Simulations show the transconductor operated with 1 V supply voltage has less than −55 dB total harmonic distortions (THD) in the complete tuning range (0 V - Vcont - 0.43 V) for a 1 MHz 0.8 Vp-p differential input. The power consumption is 70 μW for a 0.43 V control voltage. Key words: low-voltage; CMOS; transconductor; wide input range
Introduction In modern CMOS processes, scaling down of the supply voltage is not followed by a proportional reduction of the transistor threshold voltage, which reduces the headroom of the analog signal and gets a poor linear dynamic range. Thus, a severe challenge for analog circuit designers is to preserve or even increase the circuit performance for low supply voltages. The transconductor is one of the critical building blocks in Gm-C filters[1-9] since in many systems the overall linearity is mainly determined by the transconductor. A large transconductance tuning capability is important for Gm-C filters for both compensating in fabrication tolerances and achieving programmability for relevant parameters. Many kinds of transconductors have been Received: 2010-10-28; revised: 2010-12-10
** To whom correspondence should be addressed. E-mail: [email protected]; Tel: 86-10-88513468
developed[3-7] recently to compensate for the performance loss due to the low supply voltage. Transconductors based on triode-biased MOS transistors are appropriate candidates because of their high linearity and flexible tunability. The traditional way shown in Fig. 1a to implement a triode transconductance is by a compact regulated cascode structure to minimize the variation of the input transistor drain voltage. The transconductance tuning capability of the triode transconductor is limited by the voltage headroom of the input transistor. Recently, Yodprasit[7] proposed the method in Fig. 1b to improve the VDS1 tuning range of triode transconductors using a weak inversion device for the low supply voltage. However, these approaches are still not suitable for very low supply voltages. Firstly, 0 < VDS1 < VDD − VGS4 − VDSsat 2 is not wide enough to obtain a large tuning capability. Secondly, the transconductance of triode based structures is tuned by changing VDS . An NMOS Max Min gate-driven input stage must have VDS1 < VGS1 − VTH to ensure the input transistor works in the triode region.
KONG Yaohui (孔耀晖) et al.：Low-Voltage Transconductor with Wide Input Range …
VDS is constrained by the signal input range. Thus, there is a trade-off: bigger transconductance tuning capability leads to smaller input range and vice versa. This situation gets worse with very low supply voltages due to the relatively high threshold voltage. Thirdly, the linearity of triode transconductors is mainly influenced by the drain to source variation and the mobility deduction. In most designs, rL is only 1 / g m ro g m ( rL is the total small signal resistance looking out of the drain of input transistor, while g m and ro denote the output resistance and transconductance of transistor), which is not small enough to obtain the constant drain to source voltage required by high linearity applications. Moreover, the distortion in gatedriven topologies from mobility reduction will deteriorate in new process. These problems seriously limit the performance of present triode transconductors for low voltage applications.
107
In this paper, a high performance, body-driven transconductor for a 1 V supply voltage is proposed. This triode transconductor overcomes the limitations between transconductance tuning and input range by using feedback loops and body-driven techniques. The triode transconductor supports both a wide input range and a large tuning capability. In addition, the transconductance of the body-driven input stage is enhanced by a partial positive feedback loop. This partially avoids the traditional drawbacks in the bodydriven input stage due to the reduced transconductance. This topology is compact and suitable for low voltage applications.
1
Body-Driven Technology
The body-driven technique was first introduced by Guzinski et al.[10] to overcome threshold limitations in amplifiers. In the body-driven topology, the signal is added to the body instead of the gate and VGS is kept constant. The body-driven structure is similar to a JFET. The channel conductivity is modified by the body to source voltage. Thus, the body-driven MOS transistor can operate with negative, zero, or slightly positive bias voltage, like a depletion type device. The characteristics of gate-driven and body-driven operation of PMOS transistors are shown in Fig. 2 for VDD = 0.8 V by sweeping VSD from 0.1 V to 0.7 V.
Fig. 2
Fig. 1
Triode transconductor core
Simulated transconductance characteristics
If the usual terminology and first order models are adopted[11], the PMOS transistor drain current in the triode region corresponds to the well-known expression W I D = μCox × L
Tsinghua Science and Technology, February 2011, 16(1): 106-112
108
n ⎛ ⎞ ⎜ VSG − | VTH0 | −γ 2 | φF | +VBS + γ 2 | φF | − VSD ⎟ VSD 2 ⎝ ⎠ (1) where φF is the body Fermi potential, VTH0 is the zero bias threshold voltage, and n is the slope factor. When the transistor works as a body-driven device, the linear dependence of transconductance on VSD is given in Eq. (2) by derivation of the v − i characteristics, if the mobility reduction due to the vertical field is neglected. The transconductance of a body-driven PMOS transistor is given by ∂i γ W (2) Gm = g mb = D = μ Cox VSD ∂vBS L 2 (2 | φF | +VBS )
capability is still reachable for very low supply voltage.
2
With the body-driven input stage, the threshold voltage is not limited to the input range. In addition, the trade-off between input range and tuning capability is also improved to produce a wide input range transconductor at very low supply voltage with a large tuning capability.
Transconductor Design
The transconductor core is shown in Fig. 3. M1 is the input transistor. The M2-M3 transistors together with the I1-I2 current mirrors form the feedback loop. This design is based on the N-well process, so only the PMOS transistor is body-driven. This body-driven triode transconductor has many useful features, which are listed in details as follows.
Fig. 3
2.1
Body-driven transconductor core
Large tuning capability
In the triode transconductor, the Gm tuning is realized by changing VSD1 . VSD1 is limited by the drain voltage headroom of the input transistor M1. However, in this circuit the drain voltage headroom of input transistor M1 is extended by the level shifter function of the feedback loop. Thus, this transconductor increases VSD1 to 0 < VSD1 < VDD − 2VDsat , which is wider than many other topologies[7-9]. Thus, a large Gm tuning
2.2
Wide input range
The conventional gate-driven topology has a threshold voltage limitation, which constrains the input signal range. Another problem is that the gate-driven large transconductance tuning capability leads to a small input range and vice versa. Therefore, there is a tradeoff between the input range and the tuning capability. In this body-driven topology, the input transistor gate is connected to ground. The input range is then only limited by the leakage current through the drain body and the source body diode. Max VDD − (VTH0 + γ 2 | φF | +VBSMax − γ 2 | φF |) > VSD (3)
2.3
High linearity
Traditional triode transconductors suffer from two sources of nonlinearities. One is the drain to source voltage variation due to the change of VGS of the input transistor. The other is the mobility reduction owing to an increase of the vertical field in the device. This body-driven transconductor design reduces these two nonlinearities. 2.3.1 Drain to source voltage variation The triode transconductor linearity depends on the stability of the input transistor drain voltage. Different methods have been used to bias the transistor to get a constant VDS in the literature. This variation is primarily determined by the load resistance rL . The rL of proposed transconductor is g m ro times smaller than in previous designs in Refs. [7-9]. A more constant drain node over the variation of the body voltage and drain current can be ensured thanks to the smaller rL . v 1 rL = ds ≅ (4) id g m2 ro2 g m3 ro3 g m4 2.3.2 Mobility reduction The mobility reduction due to the vertical field also affects the triode mode transconductor linearity. The mobility reduction effect can be modeled by the θ -model, which is obtained by replacing the mobility
KONG Yaohui (孔耀晖) et al.：Low-Voltage Transconductor with Wide Input Range …
μ by μeff .
μ μeff = 1 + θV0
(5)
where μeff is the effective mobility, θ is the mobility reduction coefficient, and V0 =VSG − (|VTH0 | +γ 2 |φF | + VBS − γ 2 | φF |). θ increases in the submicron process, which degrades the linearity performance of most gate-driven triode transconductors. The main reason for this effect is due to velocity saturation of carriers in the channel. Significant third-order distortion of the gate-driven is introduced by the mobility reduction effect and can be modeled by 1 θ2 (6) HD3 ≅ Vin2 16 (1 + θV0 )2 The third-order distortion of the body-driven topology can be deduced as 2 1 θ2 γ ⎛ ⎞ 2 HD3 ≅ Vin (7) 16 (1 + θV0 )2 ⎝⎜ 2 (2 | φF | +VBS ) ⎠⎟ V0 in body-driven topologies is commonly larger than that of gate-driven topologies, since VSG is equal to VDD in this body-driven input stage. Furthermore,
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the factor γ / 2 (2 | φF | +VBS ) is less than 1. Thus, the linearity of body-driven triode transconductors is better than that of traditional gate-driven ones due to the mobility reduction effect. Generally speaking, the transconductance of the body-driven input stage is about 1/4 that of a gatedriven input stage, which will bring some problems. First, the input noise is increased due to the reduction of the intrinsic gain in body-driven transistors. Second, the reduction of the input transconductance limits the maximum achievable frequency of circuits based on these devices. A technique to boost the effective transconductance of the body-driven input stage is illustrated in the following section to partially resolve the problem mentioned above.
3 Transconductor Implementation The full schematic of the transconductor is shown in Fig. 4. The transconductor is implemented in pseudodifferential pairs.
Fig. 4 Full transconductor schematic
MA1/MB1 is the input transistor. MA2-MA4/MB2MB4 form the feedback loops, which not only reduce the small signal resistance looking out of the input transistor drain, but also maximize the drain to source voltage tuning range of MA1/MB1. Transconductance tuning is based on changing Vcont to control the drain to source voltage of the input transistor, which can be given by ⎛ 2 I3 ⎞ VSD1 = VDD − ⎜ Vcont + | VT3 | + (8) W3 ⎟⎟ ⎜ C μ ox ⎜ L3 ⎟⎠ ⎝ Here the drain voltage headroom of the input
transistor is no longer the main limitation as in other structures. The practical restriction of the transconductance is that Vcont is constrained to be above zero voltage. Thus, the maximum Gm is limited. The tuning range can be increased by using the twin well process and using an NMOS as the input transistor. The transconductance of the body-driven input stage is improved by the positive feedback loop made by MA22/MB22 in Ref. [12]. The transconductance is given by B∙ g mb1 Gm = (9) 1− k
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Tsinghua Science and Technology, February 2011, 16(1): 106-112
where B is the transistor size ratio of MA5/MB5 to MA2/MB2, k is the transistor size ratio of MA22/ MB22 to MA2/MB2, and g mb1 is the input transistor MA1/MB1 transconductance. Thus the transconductance is enhanced by B / (1 − k ) . This transconductor can work well by carefully sizing these transistors. In order to stabilize the common mode of outputs to the proper value and achieve a big swing, a novel low voltage low power common mode feedback (CMFB) circuit is implemented as shown in Fig. 5. In the
CMFB, bias current flows directly from the main transconductor circuit and varies with changes of the transconductance. The MD1-MD4 is the input common mode detector which provides the common mode information from the previous stage. Low voltage is ensured by a level shift circuit made of MD11/MD12 and a current mirror is adopted. MB7/MA7 gets the common mode information, Vfb , from the CMFB and stabilizes the output common mode voltage.
(a) CMFB signal flow graph
(b) CMFB schematic Fig. 5 CMFB design
4 Simulation Results The circuit has been simulated using the UMC 0.18 μm 1P6M process. The power supply voltage is 1 V.
The simulation of this transconductor was performed using the HSPICE simulator. Figures 6a and 6b show the output current and transconductance of the proposed circuit for different value of Vcont . It can be seen that this transconductor
111
KONG Yaohui (孔耀晖) et al.：Low-Voltage Transconductor with Wide Input Range …
has a large tuning capability, although it works for a very low supply voltage.
(a) Circuit Gm tuning range (a) Circuit output current
(b) Circuit transconductance Fig. 6 Simulated DC circuit characterstics
In Fig. 7a the transconductance vs Vcont curve is plotted in linear scale. It is clear that the transconductance is linearly tunable for more than one decade. In Fig. 7b, the simulated THD for one typical case (Vcont = 0.2 V) and two marginal cases (Vcont = 0 V and Vcont = 0.43 V) are plotted against input amplitudes with a 1 MHz differential input signal. For Vcont = 0.43 V the performance is analyzed for 1 MHz and 100 kHz to test the performance of the lower end of the tuning. THD is less than −60 dB with Vcont = 0 V, 0.2 V, 0.43 V for a differential peak to peak voltage input up to 0.7 V. This transconductor shows that it sustains high linearity in the whole tuning range. The simulated THD for a 1 MHz signal is less than −55 dB in Vcont from 0 V to 0.43 V for a differential input signal up to 0.8 Vp-p. The quiescent power consumption is 70 μW, when 0.43 V control voltage is applied. The parameters and performance of the proposed transconductor are listed in Table 1. The simulated performance is better than those of recently published transconductors[13-15] as shown in Table 2.
(b) Circuit THD Fig. 7 Simulated tuning range and THD of circuit Table 1 Parameters and performance Technology
UMC 0.18 μm CMOS
Supply voltage
1V
Threshold voltage
VTN = 0.49 V, VTP = −0.53 V
Common mode input voltage Transconductance tuning range THD (Vcont=0 V) 1 MHz 0.2 Vp-p 1 MHz 0.4 Vp-p 1 MHz 0.8 Vp-p Power consumption (Vcont=0.43 V)
0.75 V Vcont = 0-0.43 V, Gm = 5.6-66.8 μS −87.8 dB −76 dB −62.5 dB 70 μW
5 Conclusions Simulations have confirmed the performance of the low-voltage triode transconductor. This body-driven triode transconductor is a feasible solution in the area of low voltage and low power applications. The transconductor can work for very low supply voltages and
Tsinghua Science and Technology, February 2011, 16(1): 106-112
112 Table 2 Source Torralba et al.
Comparison with recent transconductor designs
Transconductance range [5]
396-2443 μS
Lujan et al. [13]
50-200 μS
Zhang et al. [14]
8-131 μS
Galan et al. [15]
15-165 μS
This work
5.6-66.8 μS
Technology 0.8 μm CMOS 0.5 μm CMOS 0.18 μm CMOS 0.5 μm CMOS 0.18 μm CMOS
still maintain a wide input range, large tuning capability and highly linearity. With those features, this transconductor will be especially useful for very low supply environment as a critical part of Gm-C filters. References [1] Yang F, Enz C C. A low-distortion BiCMOS seventh-order bessel filter operating at 2.5V supply. IEEE Journal of Solid-State Circuits, 1996, 31(3): 321-330. [2] Python D, Enz C C. A 40 μW 75 dB dynamic range 70 kHz band-width Biquad filter based on complementary MOS transconductors. In: Proceedings of European Solid-State Circuits Conference. Germany, 1999: 38-41. [3] Koziel S, Szczepanski S. Design of highly linear tunable CMOS OTA for continuous-time filters. IEEE Transactions on Circuits and Systems II, 2002, 49(2): 110-122. [4] Pennisi S, Scotti G, Trifiletti A. 150 μA CMOS transconductor with 82 dB SFDR. In: Proceedings of IEEE International Symposium on Circuits and Systems. 2007: 237-240. [5] Torralba A, Martinez J M, Carvajal R G, et al. Low-voltage transconductor with high linearity and large bandwidth. Electronics Letters, 2002, 38(25): 1616-1617. [6] Zhang X, El-Masry E. A 1.8 V CMOS linear transconductor and its application to Continuous-time filters. In: Proceedings of IEEE International Symposium on Circuits and Systems. Canada, 2004: 271-350. [7] Yodprasit U. Low-power and low-voltage baseband and
Power
Supply
4.3 mW
1.5 V
1.25 mW
3.3 V
0.58 mW
1.8 V
0.36 mW
1.8 V
0.07 mW
1.0 V
THD −60 dB @10 MHz −78 dB @1 MHz
Input swing
N/A
0.6 Vp-p
−67 dB @1 MHz −62.5 dB @1 MHz
0.6 Vp-p 1 Vp-p
1 Vp-p 0.8 Vp-p
quadrature frequency synthesizer [Dissertation]. Ecole Polytechinque Federale de Lausanne, Swiss, 2006. [8] Likittanapong P, Worapishet A, Toumazou C. Linear CMOS triode transconductor for low-voltage applications. Electronics Letter, 1998, 34(12): 1224-1225. [9] Zeki A. Low-voltage CMOS triode transconductor with wide-range and linear tunability. Electronics Letters, 1999, 35(20): 1685-1686. [10] Guzinski A, Bialko M, Matheau J C. Body-driven differential amplifier for application in countinous-time active-C filter. In: Proceedings of the European Conferenceon Circuit Theory and Design, 1987: 315-319. [11] Tsividis Y P. Operation and Modeling of the MOS Transistor. NewYork: McGraw-Hill, 1998. [12] Wang R, Harjani R. Partial positive feedback for gain enhancement of low-power CMOS OTAs. Analog Integrated Circuits and Signal Processing, 1995, 8(1): 21-35. [13] Lujan-Martinez C, Carvajal R G, Galan J, et al. A tunable pseudo-differential OTA with -78 dB THD consuming 1.25 mW. IEEE Transactions on Circuits and Systems II, 2008, 55(6): 527-531. [14] Zhang L, Zhang X, El-Masry E. A highly linear bulk-driven CMOS OTA for continuous-time filters. Analog Integrated Circuits and Signal Processing, 2008, 54(3): 229-236. [15] Galan A, Carrasco M, Pennisi M, et al. Low-voltage tunable pseudo-differential transconductor with high linearity. ETRI Journal, 2009, 31(5): 576-584.