Self-Biased and Supply-Voltage Scalable Inverter-Based Operational Transconductance Ampliﬁer with Improved Composite Transistors

: This paper deals with a single-stage single-ended inverter-based Operational Transconductance Ampliﬁers (OTA) with improved composite transistors for ultra-low-voltage supplies, while maintaining a small-area, high power-efﬁciency and low output signal distortion. The improved composite transistor is a combination of the conventional composite transistor and forward-body-biasing to further increase voltage gain. The impact of the proposed technique on performance is demonstrated through post-layout simulations referring to the TSMC 180 nm technology process. The proposed OTA achieves 54 dB differential voltage gain, 210 Hz gain–bandwidth product for a 10 pF capacitive load, with a power consumption of 273 pW with a 0.3 V power supply, and occupies an area of 1026 µm². For a 0.6 V voltage supply, the proposed OTA improves its voltage gain to 73 dB, and achieves a 15 kHz gain–bandwidth product with a power consumption of 41 nW.


Introduction
The development of electronic devices that are increasingly less dependent on battery charging requires Integrated Circuits (ICs) able to operate with Ultra-Low-Voltage (ULV) supply with an Ultra-Low-Power (ULP) consumption. A recent approach to address this request relies on digital-based and supply-voltage scalable ICs [1][2][3][4][5][6][7][8][9]. In this framework, the design of ULV Operational Transconductance Amplifiers (OTA) with appreciable performance (i.e., rail-to-rail input/output voltage swing and high transconductance-gain independent of process, supply voltage, and temperature variations [10]) becomes more and more challenging.
Inverter-based OTA topologies [11,12] and their respective ULV variations [13,14] have been proposed, as well as push-pull-based, bulk-driven OTAs [15][16][17][18]. An improved single-ended OTA has been proposed in [19], exploiting the properties of improved composite transistors [20] into a variation of the bulk Nauta inverter-based OTA [21]. This approach improves the voltage gain for a single-stage amplifier but shows a limited input voltage swing.
This work further exploits the improved composite transistors of inverters [19] into a single-ended version of the fully differential OTA in [14]. This results in an enhanced voltage gain, a higher linearity and a lower power consumption at the minimum supply voltages.
In Section 2, the improved composite transistor technique is briefly reviewed. Then, in Section 3, the employed self-biased inverter with the forward body bias is described.
Based on this, in Section 4, the proposed inverter-based OTA is described. In Section 5, the characteristics of the proposed OTA are then verified and compared through postlayout simulations with similar circuits designed in the 180 nm technology process. Finally, in Section 6, conclusions are drawn. Figure 1 represents an N-type improved composite transistor. It consists of a series connection of two independently forward-body-biased N-type Metal-Oxide Semiconductor (MOS) transistors M N1 and M N2 , as first proposed in [20] and described in detail in [19], by using the Unified Current Control Model (UICM) all-region transistor model [22]. Considering that I D = I DN1 = I DN2 , M N1 operates in the linear region, M N2 operates in the saturation region, and both transistors operate in weak inversion, the improved composite transistor drain current I D can be calculated as follows:

Composite Transistor Forward-Body-Biasing Analysis
where is the sheet normalization current, V G and V B1 are, respectively, the transistor M N1 gate and bulk terminal voltages referenced to the ground, V T is the threshold voltage, n is the slope factor, φ t is the thermal voltage, µ is the charge mobility, and C ox is the gate oxide capacitance per area. The improved composite transistor equivalent aspect ratio S eq is defined as: where represents a correction factor for the current drain I D definition due to the difference between the body-bias of the series transistors M N2 and M N1 ∆V B = V B2 − V B1 , assuming the transistors are operating in weak inversion, and is the ratio between transistors M N1 and M N2 physical aspect ratios S N1 and S N2 . Figure 2a shows how the drain current increases with V B2 for equally sized transistors with 1.26 um width and 0.42 length, in the TSMC 180 nm Complementary Metal-Oxide Semiconductor (CMOS) technology process, operating at 27 • C, for V G = V D = 300 mV, and ∆V B ranging from 0 to 600 mV. Figure 2b shows how the parasitic substrate current I B2 increases with V B2 . When V B2 is approximately 170 mV, I B2 is almost zero, as V B2 is almost equal to the transistor M N2 source terminal voltage. For voltages higher than 170 mV, M N2 is forward-body-biased and increases exponentially for voltages higher than 400 mV.
Referring to the same specification, Figure 3a shows the improved composite transistor transconductance G m = (dI D /dV G ) and output conductance G o = (dI D /dV D ), and Figure 3b shows its intrinsic voltage gain A V , which is the ratio between G m and G o . Figure 3b shows how A V increases exponentially with ∆V B till ∆V B ≈ 300 mV. Then, A V increases with a reduced slope until it reaches its peak at ∆V B = 500 mV. In particular, A V is increased by an order of magnitude (20 dB) for ∆V B = 250 mV and almost two orders of magnitude (38 dB) for ∆V B = 500 mV .  Figure 3. Improved composite transistor simulation results for Figure 4a,b shows, respectively, N-type and P-type rectangular transistor arrays [23,24] M NxA and M PxA . The PMOS devices are 2:1 parallel arrays (two single P-MOS transistors of size W P /L P in parallel), whereas the NMOS devices are 1:2 series arrays (two single N-MOS transistors of size W N /L N in series). Both NMOS and PMOS single transistors that build each N-type and P-type transistor array have identical width and lengths and aspect ratios, but the PMOS equivalent transistors have an aspect ratio four times larger than the NMOS equivalent transistors in order to balance the PMOS pull-up and NMOS pull-down networks. The same ratio between pull-up and pull-down networks could be achieved by using a single PMOS transistor with channel widths four times larger than the single NMOS transistors channel width while keeping the transistor length identical, but this would increase the inverter total active area by 25%.

Proposed Inverter Made of Composite Transistors with Forward-Body-Bias
The improved composite transistor can be represented as single transistors with an equivalent aspect ratio S eq as in (3). Two N-type and 2 P-type transistor arrays, respectively, M P1A , M N2A and M P1A , M P2A , are placed in series as in Figure 4c to build an inverter.
The inverter small-signal voltage gain A V is equal to the ratio between an equivalent inverter transconductance G m and output conductance G o .
These G m and G o are, respectively, functions of the PMOS and NMOS equivalent transistors gate-drain small-signal transconductance g mg and drain conductance g md , as derived from Equations (7) and (8), accordingly to the UICM model approximation to the transistor weak inversion operation [22]. These small-signal parameters are a function of the quiescent current I Q [21] (also known as short-circuit current), slope factor n, the thermal voltage φ t and the early voltage V A .
Therefore, the inverter small-signal voltage gain A V can be rewritten as: This schematic in Figure 4c can be equivalently translated into a pull-up and pull-down network (respectively, PUN and PDN) of an inverter biased by two additional voltages V BP and V BN . This represents an equivalent inverter made of composite transistors with a forward-body-bias. Such an inverter is the building block of the proposed inverter-based OTA described in this paper.

Proposed Operational Transconductance Amplifier
Differential inverter-based OTAs can use positive feedback and active load [11,13], or forward common-mode cancellation [12,14], to attenuate common-mode signals , as shown in Figure 5.  Figure 5. Fully-differential inverter-based Operational Transconductance Amplifier (OTA) with forward common-mode cancellation [12]. Figure 6a shows the single-ended version based on the fully-differential OTA shown in Figure 5. The small-signal circuit of this OTA is shown in Figure 6b, where the corresponding transconductance and output conductance are represented as G m and G o , and its unloaded low frequency voltage gain A V can be modeled as G m /G o , as described in Equation (8).
The small-signal differential output voltage v OUT at very low frequencies can be expressed as Considering that v I NP = −v I N M , the small-signal differential voltage gain A VDIFF can be derived as and, considering that v I NP = v I N M , the common-mode voltage gain A VCM can be derived as Figure 7 shows the proposed inverter-based OTA, which is equivalent to the OTA shown in Figure 6a, but the former has two inverters in parallel for each one represented in the latter. All inverters are identical and made of improved composite transistors. By doubling each inverter, the common-centroid technique can be used to design this OTA layout. Furthermore, by using N inverters in parallel, the OTA transconductance is multiplied by N, and both mismatch and noise are reduced by √ N. Obviously, power consumption and area also multiplied by N. Since the OTA output conductance is also multiplied, the OTA voltage gain remains the same.  Figure 8 shows the transistor-level proposed OTA schematic. As shown in Figure 3b, the intrinsic voltage gain A V can be increased by means of the two bulk terminals of the composite transistor. The higher their voltage difference ∆V B , the higher the intrinsic voltage gain A V . Therefore, in order to maximize A V with no additional supply voltages, the transistors pull-down networks are connected to the ground or to the supply voltage V DD . In particular, bulk terminals of the transistors M N1A-D are connected to the ground, whereas those of the transistors M N2A-D are tied to the node BN, which is connected indirectly to the supply voltage V DD . In fact, BN is connected to the drain of transistor M P2E and both transistors M P1E and M P2E are pseudo-resistors with very large resistances. Thus, if the substrate parasitic current increases, the pseudo-resistor voltage drop increases and limits it to relatively insignificant levels [21,25]. Notice that for FD-SOI process technologies [26], those transistors would not be necessary because there is no parasitic substrate current. Symmetrically, the same body-bias is applied to the pull-up network referring to the BP node.  Figure 9 shows the proposed OTA layout. The width W of each unit transistor is set on the basis of the minimum sizing requirement of the isolated n-well and p-well.
Based on this, all the unit transistors, both PMOS and NMOS have an identical aspect ratio equal to All inverters are doubled in order to use the common-centroid layout technique. The transistors located at the edge of the layouts are the pseudo-resistors used to limit the substrate current and also function as dummies.

Simulation Results
The performance of the proposed OTA, designed in TSMC 180 nm CMOS technology, operating at 27 • C, at 0.3 and 0.6 V supply voltages, has been validated by using an openloop and non-inverting buffer OTA test-bench circuits with a 10 pF capacitive load C L , as shown in Figure 10a,b.  Figure 11 shows how voltage gain and power consumption are affected by the supply voltage variation. In particular, Figure 11a shows that, at the lowest supply voltages, the voltage gain increases exponentially until the supply voltage reaches approximately 400 mV. At higher supply voltages, the improved composite transistor voltage gain technique progressively loses its effectiveness, as expected from the results shown in Figure 3b. Figure 11b shows how the current consumption and the gain-bandwidth product (GBW) are affected by the supply voltage variation. The OTA power consumption increases exponentially with the supply voltage, and its gain-bandwidth product GBW increases proportionately, as the inverter transconductance G m for the weak inversion operation is also proportional to its current consumption [21,22].  Figure 11. Voltage supply dependence: (a) voltage gain; (b) total current consumption I T and gain-bandwidth product (GBW). Figure 12a,b shows how voltage gain and power consumption are affected by temperature variation for a 0.3 V voltage supply. As temperature increases, the voltage gain decreases, as a direct result from G m and β reduction, as can be directly inferred from (6) and (4). Furthermore, as the temperature increases, the total current increases as a consequence of the threshold voltage reduction, and GBW increases accordingly.   Figures 13b and 14b, the output voltage affects the OTA voltage gain as a consequence of the reverse transistor current and channel length modulation [22]; therefore, the output conductance G o varies accordingly. For these reasons, considering a gain A V > 30 dB, output voltage swings between 100 and 500 mV can be obtained for the proposed OTA while supplied with V DD = 0.6 V. The output range limitation is imposed by either PMOS or NMOS transistors entering the linear region outside these limits. For V DD = 0.3 V, the reverse transistor current dominates the output conductance G o behavior and voltage gain reaches its peak while the input is about half V DD . This is a very important aspect, as small-signal voltage gain can be misleading because it shows only the maximum voltage gain, and voltage gain should be large for a large output voltage range to ensure good signal linearity for any OTA applications with feedback circuits.

Unity-Gain Buffer Analysis
As with the output voltage swing limitations observed in open-loop DC simulations (as in Figure 10a), the non-inverting buffer simulations (as in Figure 10) also reveal the limits of input voltage swing, which are shown in Figures 17 and 18. In particular, Figure 18a shows how the output voltage saturation is a consequence of the voltage gain from the input INP to node X (see Figure 7). The X node voltage potential V X can be expressed as approximately V I NP − V Q ≈ −(V X − V Q ), where V Q is the inverter quiescent voltage [21]. As expected, V X is approximately the inverted positive input voltage signal V I NP . However, V X is clipped at approximately 100 and 500 mV for the proposed OTA for V DD = 0.6 V, as the inverting voltage buffer does not work properly as the transistors enter the linear operation region. Figures 17a,b and 18a,b show the main difference between the proposed OTA operation at different voltage supplies for the non-inverting buffer configuration. For V DD = 0.6 V, the OTA has a more linear output due to its higher open-loop voltage gain and larger output voltage excursion, as expected. The OTAs proposed in [19] use a similar topology with half the number of inverters, but the V X voltage excursion is also limited by the transistor slope factor n, which further limits those OTAs input range compared to the OTAs proposed in this work.
The same limitations, from the point of view of time-domain, are shown in Figures 19a,b and 20a,b for a rail-to-rail input sine-wave for V DD = 0.3 V and V DD = 0.6 V, respectively. The corresponding total harmonic distortion (THD) is displayed in Figures 17b and 18b for a 10 pF capacitive load C L and no load except from the input impedance resulted from connecting the OTA output to the inverting input. A total harmonic distortion of 1% is achieved for input peak-to-peak amplitudes ranges of 300 and 375 mV for V DD = 0.3 V and V DD = 0.6 V, respectively. For lower input voltage amplitudes and no output load, the proposed OTA shows an even better linearity, achieving 80 dB THD for a 200 mV input amplitude for V DD = 0.6 V. This is a direct consequence of the DC characteristic curves shown in Figure 18a,b, due to its higher open-loop voltage gain and that GBW is many times higher for lower capacitive loads. By analyzing Figure 18b Table 1 summarizes the corner simulation results. As expected, the greatest deviations from typical corner results are GBW and power for SS (Slow-Slow) and FF (Fast-Fast) corners. The worst corners for intrinsic input offset are SF (Slow-Fast) and FS (Fast-Slow), as the inverter transistor dimensions were optimized for the typical corner TT. As explained before, the OTA linearity is a function of the internal node voltage V X , and input signal frequency and GBW. For better performance stability, PVT variability could be reduced by extra biasing circuits [21] or calibration [27]. Table 2 summarizes the mean µ and the standard variation σ from 1000 Monte Carlo simulation runs. Process and mismatch variations are analyzed individually and combined. The OTA results show that gain-bandwidth product GBW, total current I DD , and power consumption are greatly affected by the process variability, as suggested by corner results. The power efficiency Figure of Merit, FoM, defined as 100 × (GBW · C L )/I T , shows a negligible variation, since GBW is somehow proportional to I T , as shown in Figure 11b. It is the same for the open-loop voltage gain. As a main drawback, the mismatch variations strongly affect the offset voltage V OS of both OTAs. The simulations show 8.7 and 8.9 mV input offset voltage for 3σ mismatch variation for V DD = 0.3 V and V DD = 0.6 V, respectively.  Table 3 summarizes the proposed OTA results and compares them to the state-of-art counterparts. The state-of-art OTAs can be categorized by the input terminal of their first stage amplifier block, and can be gate-driven [19,21,24,[27][28][29][30][31] and bulk-driven [18,28,[32][33][34]. Gate-driven OTAs are usually more power-efficient, as the bulk-drain transconductance is a fraction of the gate-drain transconductance, while bulk-driven OTAs have an extended voltage input range, which leads to less signal distortion for larger voltage signal amplitudes.

Performance Comparison
Additionally, the OTAs reported in Table 3 are classified as single-ended and fully differential. The fully differential circuits use more area and power, but their signals are more insensitive to power and common-mode fluctuations, and they have increased voltage range and output less distortion.
The proposed OTAs main feature is its voltage gain per number of stages, while still maintaining a relatively small area, a high power-efficiency figure of merit, and a high linearity for an extremely low voltage supply. A higher voltage gain could be achieved by using more amplifier stages; however, it would come at the cost of more area and the need for a stability compensation circuit.
The best power-efficient design for a 0.3 V supply voltage was proposed in [27], with a 1020 FoM. The proposed design has a 229 FoM, which is 4.45× smaller. However, it has a 1% THD for a 120 mV peak-to-peak amplitude signal, while the former has a 3% THD for a 100 mV peak-to-peak amplitude signal. As compared to the other state-of-art designs with supply voltage under 0.3 V, despite having a single gain stage, it still has the second best voltage gain. The best voltage gain under 0.3 V supply voltage [32] is 60 dB; however, as it is a multiple-stage OTA design, it has an area 25× larger, whereas the proposed OTA would have a 40 dB voltage gain for the same supply voltage at 0.25 V. The best voltage gain among all OTAs [18] has an 81 dB voltage gain at a 0.4 V supply voltage. The proposed OTA can achieve a 66 dB voltage gain with a single gain stage alone at 0.4 V supply voltage and has a total area about 5× smaller.  Technology  180  130  130  180  130  180  180  180  130  65  65  180  180  180  nm  Input  GD  GD  GD  GD  GD  GD  GD  BD  BD  BD  BD  BD  GD  GD  -Output  FD  FD  FD  SE  SE  FD  FD  FD  SE  FD  SE  FD L   20  2  30  80  150  10  10  20  15  3  5  5  10  10  10  pF  FoM  133  303  143  1020  468  229  370  22  29  22  20  187  443  229  The best comparison can be made with the inverter-based OTA proposed in [21], as it was designed for the same process using the same transistor dimensions and voltage supply. For V DD = 0.3 V, it has 1.4× more area and about half of its power-efficiency FoM; however, it has a 3.4× larger input voltage excursion for the same THD. It also has a slightly larger voltage gain.

Conclusions
This paper shows how to maximize the gain of an inverter-based OTA topology with independently forward-body-biased composite transistors without reducing its input voltage swing. Compared with other state-of-art OTAs in similar operation conditions, the proposed OTAs have the largest voltage gain by the number of amplifier gain stages (54 dB at 0.3 V V DD and 73 dB at 0.6 V V DD ), while still keeping a relatively small die area (1026 µm 2 ). Notice that the same technique could also be exploited in fully differential inverter-based OTA topologies.