A Sub-Threshold Di ﬀ erential CMOS Schmitt Trigger with Adjustable Hysteresis Based on Body Bias Technique

: This paper presents a sub-threshold di ﬀ erential CMOS Schmitt trigger with tunable hysteresis, which can be used to enhance the noise immunity of low-power electronic systems. By exploiting the body bias technique to the positive feedback transistors, the hysteresis of the proposed Schmitt trigger is generated, and it can be adjusted by the applied bias voltage to the bulk terminal of the utilized PMOS transistors. The principle of operation and the main formulas of the proposed circuit are discussed. The circuit is designed in a 0.18- µ m standard CMOS process with a 0.6 V power supply. Post-layout simulation results show that the hysteresis width of the Schmitt trigger can be adjusted from 45.5 mV to 162 mV where the ratio of the hysteresis width variation to supply voltage is 19.4%. This circuit consumes 10.52 × 7.91 µ m 2 of silicon area, and its power consumption is only 1.38 µ W, which makes it a suitable candidate for low-power applications such as portable electronic, biomedical, and bio-implantable systems.


Introduction
As the electronics world is heading toward the future, electronic devices require longer lifetime batteries. Hence, the IC designers are obliged to make use of some design techniques to provide a prolonged battery life. One of the common techniques is reducing the supply voltage to decrease the power consumption of the circuits by operating transistors in the weak inversion region. At low voltage, one of the main constraints faced is the device noise level. The weak inversion region is also known as the sub-threshold region because it occurs under the threshold voltage of transistors where very small currents can be provided. The current-voltage equation in this region is an exponential relationship, and although for a given power budget, the g m /I D ratio is at its maximum level; since the values of currents are so small, the circuit may become sensitive to noise [1,2]. Moreover, circuits which operate in the sub-threshold region face some limitations such as poor frequency response and poor linearity [2]. Thus, in general, these circuits are meant for low-frequency and low-current applications such as biomedical and biotelemetry devices and are not suitable for medium power applications [3,4].
A valuable solution to improve the robustness of the circuits to noise is using Schmitt triggers. Schmitt triggers can improve the sensitivity of electronic systems to electromagnetic interferences, i.e., they increase the static noise margin of the circuits but at the cost of more power consumption Due to the tail current, when the DC voltage of the positive input, V + in , increases from 0 to positive voltages while V − in is fixed at a mid-point (reference voltage), I 1a will be increased, and inversely, I 1b will be decreased, which are the drain currents of transistors M 1a and M 1b , respectively. Thus, based on the differential behavior of the circuit, the drain voltage of M 1a decreases and the drain voltage of M 1b increases, and V d−1a switches from high to low in V 2 . The DC transfer characteristics of V d−1a are shown in Figure 2 (gray curve).
It should be noted that because of M 3a , which is a voltage-controlled current source and provides a fixed current, an increase in I 1a will increase the drain current of M 2a , i.e., I 2a . On the other hand, when I 1b decreases, I 2b reduces as well under the same circumstance. However, the reduction of V d−1a will force I 2b to increase and retain its former situation. Therefore, I 1b and accordingly V d−1b will not change either. Hence, I 2a will also retain its former situation, and I 1a and V d−1a will remain unchanged as well. This situation will continue until the difference between V + in and V − in becomes so large that I 1a overcomes I 2a and the state changes. At this point, V d−1a will change; its position is denoted as V 3 in Figure 2. In contrast, when V + in becomes significantly smaller than V − in , the output current will change its state at the voltage of V 1 , which is shown in the figure. This voltage shift from V 2 is caused by the positive feedback transistors; M 2a and M 2b . In the absence of these transistors, the circuit will operate as a comparator. It is perceivable that the proposed Schmitt trigger operates at a current mode, and its operation analysis is described in the following.
Electronics 2020, 9, x FOR PEER REVIEW 3 of 13 is a controlled current source that provides the tail current of the differential pair by a bias voltage of V B1 . M 2a and M 2b implement positive feedback to create the hysteresis of the proposed Schmitt trigger.
Due to the tail current, when the DC voltage of the positive input, V in + , increases from 0 to positive voltages while V in is fixed at a mid-point (reference voltage), I 1a will be increased, and inversely, I 1b will be decreased, which are the drain currents of transistors M 1a and M 1b , respectively. Thus, based on the differential behavior of the circuit, the drain voltage of M 1a decreases and the drain voltage of M 1b increases, and V d-1a switches from high to low in V 2 . The DC transfer characteristics of V d-1a are shown in Figure 2 (gray curve). It should be noted that because of M 3a , which is a voltage-controlled current source and provides a fixed current, an increase in I 1a will increase the drain current of M 2a , i.e., I 2a . On the other hand, when I 1b decreases, I 2b reduces as well under the same circumstance. However, the reduction of V d-1a will force I 2b to increase and retain its former situation. Therefore, I 1b and accordingly V d-1b will not change either. Hence, I 2a will also retain its former situation, and I 1a and V d-1a will remain unchanged as well. This situation will continue until the difference between V in + and V in becomes so large that I 1a overcomes I 2a and the state changes. At this point, V d-1a will change; its position is denoted as V 3 in Figure 2. In contrast, when V in + becomes significantly smaller than V in -, the output current will change its state at the voltage of V 1 , which is shown in the figure.
This voltage shift from V 2 is caused by the positive feedback transistors; M 2a and M 2b . In the absence of these transistors, the circuit will operate as a comparator. It is perceivable that the proposed Schmitt trigger operates at a current mode, and its operation analysis is described in the following. According to Figure 1, using KCL at the drain node of the positive input transistor M 1a results in: Electronics 2020, 9, x FOR PEER REVIEW 3 of 13 is a controlled current source that provides the tail current of the differential pair by a bias voltage of V B1 . M 2a and M 2b implement positive feedback to create the hysteresis of the proposed Schmitt trigger.
Due to the tail current, when the DC voltage of the positive input, V in + , increases from 0 to positive voltages while V in is fixed at a mid-point (reference voltage), I 1a will be increased, and inversely, I 1b will be decreased, which are the drain currents of transistors M 1a and M 1b , respectively. Thus, based on the differential behavior of the circuit, the drain voltage of M 1a decreases and the drain voltage of M 1b increases, and V d-1a switches from high to low in V 2 . The DC transfer characteristics of V d-1a are shown in Figure 2 (gray curve).
It should be noted that because of M 3a , which is a voltage-controlled current source and provides a fixed current, an increase in I 1a will increase the drain current of M 2a , i.e., I 2a . On the other hand, when I 1b decreases, I 2b reduces as well under the same circumstance. However, the reduction of V d-1a will force I 2b to increase and retain its former situation. Therefore, I 1b and accordingly V d-1b will not change either. Hence, I 2a will also retain its former situation, and I 1a and V d-1a will remain unchanged as well. This situation will continue until the difference between V in + and V in becomes so large that I 1a overcomes I 2a and the state changes. At this point, V d-1a will change; its position is denoted as V 3 in Figure 2. In contrast, when V in + becomes significantly smaller than V in -, the output current will change its state at the voltage of V 1 , which is shown in the figure.
This voltage shift from V 2 is caused by the positive feedback transistors; M 2a and M 2b . In the absence of these transistors, the circuit will operate as a comparator. It is perceivable that the proposed Schmitt trigger operates at a current mode, and its operation analysis is described in the following. According to Figure 1, using KCL at the drain node of the positive input transistor M 1a results in: According to Figure 1, using KCL at the drain node of the positive input transistor M 1a results in: The drain current equation in the sub-threshold region has an exponential relationship and for a where n and V t are sub-threshold coefficient and thermal voltage, respectively. Consequently, Equation (1) can be written as: If we repeat the same path for the drain node of the negative input transistor M 1b and subtract V gs,1b from V gs,1a , the voltage difference of input terminals becomes:

Two-Stage Schmitt Trigger Circuit
In Figure 2, voltage levels of V 1 and V 3 are LTP and UTP of the Schmitt trigger, respectively. As can be seen, the hysteresis curve will not reach to logical zero or one, which is because of the low gain of the circuit. To solve this problem, an output stage is added to the structure illustrated in Figure 3. After amplifying the signal by the second stage, the hysteresis characteristic will be consistent with Figure 4. In other words, immediately after V d−1a 's decrease, the drain current of M 4a will also reduce. Then, because of the current mirror of M 5a,b and higher current of M 4b , I out will approach zero and a sharper transition will occur, as depicted in Figure 4. where n and are sub-threshold coefficient and thermal voltage, respectively. Consequently, Equation (1) can be written as: If we repeat the same path for the drain node of the negative input transistor M 1b and subtract V gs,1b from V gs,1a , the voltage difference of input terminals becomes:

Two-Stage Schmitt Trigger Circuit
In Figure 2, voltage levels of V 1 and V 3 are LTP and UTP of the Schmitt trigger, respectively. As can be seen, the hysteresis curve will not reach to logical zero or one, which is because of the low gain of the circuit. To solve this problem, an output stage is added to the structure illustrated in Figure  3. After amplifying the signal by the second stage, the hysteresis characteristic will be consistent with Figure 4. In other words, immediately after V d-1a 's decrease, the drain current of M 4a will also reduce. Then, because of the current mirror of M 5a,b and higher current of M 4b , I out will approach zero and a sharper transition will occur, as depicted in Figure 4.   where n and are sub-threshold coefficient and thermal voltage, respectively. Consequently, Equation (1) can be written as: If we repeat the same path for the drain node of the negative input transistor M 1b and subtract V gs,1b from V gs,1a , the voltage difference of input terminals becomes:

Two-Stage Schmitt Trigger Circuit
In Figure 2, voltage levels of V 1 and V 3 are LTP and UTP of the Schmitt trigger, respectively. As can be seen, the hysteresis curve will not reach to logical zero or one, which is because of the low gain of the circuit. To solve this problem, an output stage is added to the structure illustrated in Figure  3. After amplifying the signal by the second stage, the hysteresis characteristic will be consistent with Figure 4. In other words, immediately after V d-1a 's decrease, the drain current of M 4a will also reduce. Then, because of the current mirror of M 5a,b and higher current of M 4b , I out will approach zero and a sharper transition will occur, as depicted in Figure 4.   A KVL from V dd to the source terminal of M 4b will result in V gs,2a = −V dd +V gs,4b . Afterward, we can write: Electronics 2020, 9, 806 In the following, because of a reduction in the drain voltage of M 1a , the current of M 4a and subsequently the currents of M 5a,b will decrease. On the other hand, increasing the drain voltage of M 1b will increase I 4b .
It is clear that the output current is the difference between I 5b and I 4b . Now, by considering w 5a = w 5b , we will have I out = I 4a − I 4b . After utilizing the sub-threshold drain current equation for transistors M 4a,b , the following equation will be obtained: Substituting Equation (5) in Equation (4) and then in Equation (3) will yield: According to the former explanations, when the DC voltage of the positive input increases, the output current decreases, and the output voltage level approaches zero. In contrast, when V + in goes from positive voltages to negative voltages, I out increases, and V out changes to the logic one.

Proposed Structure of the Two-Stage Schmitt Trigger with Adjustable Hysteresis
The proposed low-voltage, low-power differential Schmitt trigger with tunable hysteresis is illustrated in Figure 5. Hysteresis characteristic of this circuit can be controlled by the bulk terminal of the positive feedback transistors M 2a,b . Despite similar works reported in [15,25], no additional transistors are needed to equip the Schmitt trigger with controllable hysteresis. According to Equation (6), when the threshold voltages of M 2a,b change, the hysteresis width of the circuit will also change. Hence, by applying the body bias technique to the positive feedback transistors, an adjustable hysteresis will result.
By exploiting the body bias technique and using the V th equation, which is (6) will be changed to: where γ and 2ϕ F are the body-effect coefficient and surface potential, respectively. Equation (7) declares that by variation of V c1 and V c2 (bulk terminals of M 2a,b ), hysteresis width can be tuned. It should be noted that V c must be smaller than |2ϕ F |+V dd . Since the proposed circuit has a 0.6 V supply voltage, the value of V c cannot exceed |2ϕ F |+0.6 mathematically. To avoid leakage current, it is important to consider that V c cannot be smaller than the supply voltage, and the corresponding voltage levels must be chosen optimally.
Electronics 2020, 9, x FOR PEER REVIEW 5 of 13 A KVL from V dd to the source terminal of M 4b will result in V gs,2a =-V dd +V gs,4b . Afterward, we can write: In the following, because of a reduction in the drain voltage of M 1a , the current of M 4a and subsequently the currents of M 5a,b will decrease. On the other hand, increasing the drain voltage of M 1b will increase I 4b .
It is clear that the output current is the difference between I 5b and I 4b . Now, by considering w 5a = w 5b , we will have I out = I 4a -I 4b . After utilizing the sub-threshold drain current equation for transistors M 4a,b , the following equation will be obtained: V gs,4a -V gs,4b = nV t ln I out , Substituting Equation (5) in Equation (4) and then in Equation (3) will yield: According to the former explanations, when the DC voltage of the positive input increases, the output current decreases, and the output voltage level approaches zero. In contrast, when V in + goes from positive voltages to negative voltages, I out increases, and V out changes to the logic one.

Proposed Structure of the Two-Stage Schmitt Trigger with Adjustable Hysteresis
The proposed low-voltage, low-power differential Schmitt trigger with tunable hysteresis is illustrated in Figure 5. Hysteresis characteristic of this circuit can be controlled by the bulk terminal of the positive feedback transistors M 2a,b . Despite similar works reported in [15,25], no additional transistors are needed to equip the Schmitt trigger with controllable hysteresis. According to Equation (6), when the threshold voltages of M 2a,b change, the hysteresis width of the circuit will also change. Hence, by applying the body bias technique to the positive feedback transistors, an adjustable hysteresis will result.
By exploiting the body bias technique and using the V equation, which is V th = V th0 + γ 2φ F +V sb -2φ F , Equation (6) will be changed to: where γ and 2φ F are the body-effect coefficient and surface potential, respectively. Equation (7) declares that by variation of V c1 and V c2 (bulk terminals of M 2a,b ), hysteresis width can be tuned. It should be noted that V c must be smaller than 2φ F +V dd . Since the proposed circuit has a 0.6 V supply voltage, the value of V c cannot exceed 2φ F +0.6 mathematically. To avoid leakage current, it is important to consider that V c cannot be smaller than the supply voltage, and the corresponding voltage levels must be chosen optimally.

Post-Layout Simulation Results
The proposed sub-threshold differential Schmitt trigger with tunable hysteresis is designed and post-layout simulated in a standard 0.18 µm CMOS technology. The utilized technology allows bulk and body contacts to be different in the wafer fabrication process. Power consumption of the circuit is 1.38 µW, which makes it suitable for biomedical applications. The layout of the proposed Schmitt trigger is shown in Figure 6, which occupies the chip area of 10.52 × 7.91 µm 2 . The aspect ratios of transistors are set according to Table 1. The DC voltage transfer characteristic of the proposed Schmitt trigger is shown in Figure 7 where V + in is initially swept from 0 to 0.6 V and then from 0.6 V to 0 to observe the hysteresis curve, while V − in is fixed at 0.3 V. The UTP and LTP of the circuit are 380.1 mV and 254.1 mV, respectively, so the hysteresis width is 126 mV. A triangular waveform with the amplitude of 0.6 V and 500 kHz frequency is applied to V + in , and its corresponding transient output is illustrated in Figure 8. Figure 9 shows the hysteresis characteristic of the proposed Schmitt trigger while V c1 is swept from 0.3 V to 0.6 V. It is clear that the hysteresis width can be varied in proportion to the bias voltage applied to the bulk terminal of the positive feedback transistors M 2a and M 2b . Moreover, the variation of the transient response of the circuit according to the changes of the body bias voltage, i.e., V c1 , is depicted in Figure 10. The voltage transfer characteristic of the proposed Schmitt trigger over different process corners at 27 • C is shown in Figure 11. Variations of the hysteresis width and the center of the circuit in three process corners over temperatures from −20 • C to 60 • C is simulated, and the result is illustrated in Figure 12a,b, respectively. Electronics 2020, 9, x FOR PEER REVIEW 6 of 13

Post-Layout Simulation Results
The proposed sub-threshold differential Schmitt trigger with tunable hysteresis is designed and post-layout simulated in a standard 0.18 μm CMOS technology. The utilized technology allows bulk and body contacts to be different in the wafer fabrication process. Power consumption of the circuit is 1.38 μW, which makes it suitable for biomedical applications. The layout of the proposed Schmitt trigger is shown in Figure 6, which occupies the chip area of 10.52 × 7.91 μm 2 . The aspect ratios of transistors are set according to Table 1.  Figure 7 where V in + is initially swept from 0 to 0.6 V and then from 0.6 V to 0 to observe the hysteresis curve, while V in is fixed at 0.3 V. The UTP and LTP of the circuit are 380.1 mV and 254.1 mV, respectively, so the hysteresis width is 126 mV. A triangular waveform with the amplitude of 0.6 V and 500 kHz frequency is applied to V in + , and its corresponding transient output is illustrated in Figure 8. Figure 9 shows the hysteresis characteristic of the proposed Schmitt trigger while V c1 is swept from 0.3 V to 0.6 V. It is clear that the hysteresis width can be varied in proportion to the bias voltage applied to the bulk terminal of the positive feedback transistors M 2a and M 2b . Moreover, the variation of the transient response of the circuit according to the changes of the body bias voltage, i.e., V c1 , is depicted in Figure 10. The voltage transfer characteristic of the proposed Schmitt trigger over different process corners at 27 °C is shown in Figure 11. Variations of the hysteresis width and the center of the circuit in three process corners over temperatures from −20 °C to 60 °C is simulated, and the result is illustrated in Figure 12a,b, respectively.              Figure 13 shows the variation of the hysteresis width and its center versus the reference voltage for a constant value of control voltage. In addition to the hysteresis width variation of the circuit by changing Vc1, the width and the center of its hysteresis vary through sweeping Vin − from 250 mV to 450 mV. Figure 14 provides a more comprehensive review of the dependency of the hysteresis width on the control voltage and the reference voltage. It shows that by sweeping Vc1 from 400 mV to 600 mV and simultaneously changing Vin − from 250 mV to 350 mV, hysteresis width changes in a range of 116 mV.
To examine the effect of process variations and component mismatches on the transient response of the proposed Schmitt trigger, 100 runs of Monte Carlo analysis are performed for all employed transistors. Figure 15 shows the transient responses of input and output voltages for post-layout simulation of Monte Carlo analysis. Finally, in Figure 16a,b, post-layout simulated histograms for 100 runs of Monte Carlo for LTP and UTP of the circuit are presented. As can be seen, the majority of the iterations for LTP and UTP fit in about 254 mV ± 11% and 380 mV ± 15%, respectively. Moreover, the proposed circuit was simulated with ±10% variation in power supply, for which proper operation was observed (Figure 17). Table 2 illustrates the comparison of the proposed and the recent CMOS Schmitt triggers which have almost common properties. The comparison is mainly considered in terms of supply voltage, single or differential input, voltage or current mode, static power consumption, occupied chip area,   Figure 13 shows the variation of the hysteresis width and its center versus the reference voltage for a constant value of control voltage. In addition to the hysteresis width variation of the circuit by changing Vc1, the width and the center of its hysteresis vary through sweeping Vin − from 250 mV to 450 mV. Figure 14 provides a more comprehensive review of the dependency of the hysteresis width on the control voltage and the reference voltage. It shows that by sweeping Vc1 from 400 mV to 600 mV and simultaneously changing Vin − from 250 mV to 350 mV, hysteresis width changes in a range of 116 mV.
To examine the effect of process variations and component mismatches on the transient response of the proposed Schmitt trigger, 100 runs of Monte Carlo analysis are performed for all employed transistors. Figure 15 shows the transient responses of input and output voltages for post-layout simulation of Monte Carlo analysis. Finally, in Figure 16a,b, post-layout simulated histograms for 100 runs of Monte Carlo for LTP and UTP of the circuit are presented. As can be seen, the majority of the iterations for LTP and UTP fit in about 254 mV ± 11% and 380 mV ± 15%, respectively. Moreover, the proposed circuit was simulated with ±10% variation in power supply, for which proper operation was observed ( Figure 17). Table 2 illustrates the comparison of the proposed and the recent CMOS Schmitt triggers which have almost common properties. The comparison is mainly considered in terms of supply voltage, single or differential input, voltage or current mode, static power consumption, occupied chip area, Figure 11. Variation of the hysteresis width in different process corners at 27 degrees Celsius. Figure 13 shows the variation of the hysteresis width and its center versus the reference voltage for a constant value of control voltage. In addition to the hysteresis width variation of the circuit by changing Vc 1, the width and the center of its hysteresis vary through sweeping V in − from 250 mV to 450 mV. Figure 14 Figure 15 shows the transient responses of input and output voltages for post-layout simulation of Monte Carlo analysis. Finally, in Figure 16a,b, post-layout simulated histograms for 100 runs of Monte Carlo for LTP and UTP of the circuit are presented. As can be seen, the majority of the iterations for LTP and UTP fit in about 254 mV ± 11% and 380 mV ± 15%, respectively. Moreover, the proposed circuit was simulated with ±10% variation in power supply, for which proper operation was observed ( Figure 17). Table 2 illustrates the comparison of the proposed and the recent CMOS Schmitt triggers which have almost common properties. The comparison is mainly considered in terms of supply voltage, single or differential input, voltage or current mode, static power consumption, occupied chip area, and hysteresis width. The proposed current mode CMOS Schmitt trigger operates at a voltage supply of 0.6 V and its transistors are biased in the sub-threshold region. Therefore, this circuit has significantly lower power consumption and a smaller occupied chip area, which make it suitable for low-voltage and low-power applications. and hysteresis width. The proposed current mode CMOS Schmitt trigger operates at a voltage supply of 0.6 V and its transistors are biased in the sub-threshold region. Therefore, this circuit has significantly lower power consumption and a smaller occupied chip area, which make it suitable for low-voltage and low-power applications.

Conclusions
A low-voltage, low-power differential Schmitt trigger for biomedical applications, which operates at 0.6 V supply voltage and current mode, has been presented in this paper. By applying bias voltages in the range of 0.3 V to 0.6 V to the positive feedback transistors, the hysteresis width of the proposed circuit can be varied from 126 mV to 132 mV, which means that its hysteresis width is adjusted by the body bias technique. Moreover, by changing the control voltage and reference voltage simultaneously, a bigger range of hysteresis width variation from 45.5 mV to 162 mV is achievable. This Schmitt trigger consumes 1.38 μW of static power and occupies 10.52 × 7.91 μm 2 of the chip area. Properties of this circuit make it a good candidate for low-voltage and low-power applications such as electronic healthcare devices and implantable microsystems.

Conclusions
A low-voltage, low-power differential Schmitt trigger for biomedical applications, which operates at 0.6 V supply voltage and current mode, has been presented in this paper. By applying bias voltages in the range of 0.3 V to 0.6 V to the positive feedback transistors, the hysteresis width of the proposed circuit can be varied from 126 mV to 132 mV, which means that its hysteresis width is adjusted by the body bias technique. Moreover, by changing the control voltage and reference voltage simultaneously, a bigger range of hysteresis width variation from 45.5 mV to 162 mV is achievable. This Schmitt trigger consumes 1.38 µW of static power and occupies 10.52 × 7.91 µm 2 of the chip area. Properties of this circuit make it a good candidate for low-voltage and low-power applications such as electronic healthcare devices and implantable microsystems.