LOW-POWER FLIP FLOP CIRCUIT
20230048735 · 2023-02-16
Inventors
- Po-Chia Lai (Fremont, CA, US)
- Meng-Hung Shen (Zhubei City, TW)
- Chi-Lin Liu (New Taipei City, TW)
- Stefan Rusu (Sunnyvale, CA)
- Yan-Hao Chen (Hsin-Chu, TW)
- Jerry Chang-Jui Kao (Taipei, TW)
Cpc classification
H03K3/012
ELECTRICITY
International classification
H03K3/012
ELECTRICITY
Abstract
A flip-flop circuit configured to latch an input signal to an output signal is disclosed. The circuit includes a first latch circuit; and a second latch circuit coupled to the first latch circuit. In some embodiments, in response to a clock signal, the first and second latch circuits are complementarily activated so as to latch the input signal to the output signal, and the first and second latch circuits each comprises at most two transistors configured to receive the clock signal.
Claims
1. A method to operate a flip-flop circuit, comprising: receiving a scan-in signal and a data signal; selectively coupling either the scan-in signal or the data signal to coupled master and slave latches; and based on a clock signal, selectively activating either the master latch or the slave latch so as to latch either the scan-in signal or the data signal as an output signal of the flip-flop circuit.
2. The method of claim 1, wherein the master latch circuit comprises a pair of cross-coupled OR-AND-Inverter (OAI) logic gates, and the slave latch circuit comprises a pair of cross-coupled AND-OR-Inverter (AOI) logic gates, and wherein the master and slave latch circuits each comprises at most two transistors configured to receive the clock signal.
3. The method of claim 2, wherein the at most two transistors of the first and second latch circuits, respectively, each receives the clock signal at a respective gate.
4. The method of claim 2, further comprising: selecting either a data signal or a scan-in signal as the input signal in response to an enable signal.
5. The method claim 4, further comprising: providing a logically inverted clock signal to the at most two transistors of the first latch circuit and the at most two transistors of the second latch circuit, respectively.
6. The method of claim 1, wherein the at most two transistors of the first and second latch circuits, respectively, comprise a p-type metal-oxide-semiconductor transistor and an n-type metal-oxide-semiconductor transistor.
7. The method of claim 1, further comprising: delaying the clock signal to the master latch circuit but not delaying the clock signal to the slave latch circuit.
8. A method of operating a flip-flop circuit, comprising: in response to a clock signal, complementarily activating first and second latch circuits so as to latch a first input signal to an output signal via the first latch circuit, or latch a second input signal to the output signal via the second latch circuit; and delaying the clock signal to the first latch circuit, but not delaying the clock signal to the second latch circuit.
9. The method of claim 8, wherein the first and second latch circuits each comprises at most two transistors configured to receive the clock signal, wherein the first latch circuit includes a pair of cross-coupled OR-AND-Inverter (OAI) logic gates, and the second latch circuit includes a pair of cross-coupled AND-OR-Inverter (AOI) logic gates.
10. The method of claim 9, wherein the at most two transistors of the first and second latch circuits, respectively, each receives the clock signal at a respective gate.
11. The method of claim 9, wherein the at most two transistors of the first and second latch circuits, respectively, comprise a p-type metal-oxide-semiconductor transistor and an n-type metal-oxide-semiconductor transistor.
12. The method of claim 9, wherein the first input signal comprises a scan-in signal; and the second input signals comprises a data signal.
13. The method of claim 9, further comprising: providing a logically inverted clock signal to the at most two transistors of the first latch circuit and the at most two transistors of the second latch circuit, respectively.
14. A method of operating a flip-flop circuit, the method, comprising: receiving a clock signal by a first circuit; receiving the clock signal by a second circuit coupled to the first circuit; activating the first circuit in response to the clock signal to couple a first input signal to an output of the flip-flop circuit; subsequently deactivating the first circuit and activating the second circuit in response to the clock signal to couple a second input signal to the output of the flip-flop circuit; and delaying the clock signal to the first circuit, but not delaying the clock signal to the second circuit.
15. The method of claim 14, wherein the first circuit comprises a first latch circuit and the second circuit comprises a second latch circuit.
16. The method of a claim 15, wherein the second latch circuit is coupled to the first latch circuit, and wherein in response to a clock signal, the first and second latch circuits are complementarily activated so as to latch the first and second input signals, respectively to the output signal.
17. The method of claim 16, wherein the first and second latch circuits each comprises at most two transistors configured to receive the clock signal, wherein the first latch circuit includes a pair of cross-coupled OR-AND-Inverter (OAI) logic gates, and the second latch circuit includes a pair of cross-coupled AND-OR-Inverter (AOI) logic gates.
18. The method of claim 17, wherein the at most two transistors of the first and second latch circuits, respectively, each receives the clock signal at a respective gate.
19. The method of claim 17, wherein the at most two transistors of the first and second latch circuits, respectively, comprise a p-type metal-oxide-semiconductor transistor and an n-type metal-oxide-semiconductor transistor.
20. The method of claim 14, further comprising: selecting either the first signal or the second signal to couple to the output in response to an enable signal.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0004] Aspects of the present disclosure are best understood from the following detailed description when read with the accompanying figures. It is noted that various features are not necessarily drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion.
[0005]
[0006]
[0007]
[0008]
[0009]
[0010]
[0011]
[0012]
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
[0013] The following disclosure describes various exemplary embodiments for implementing different features of the subject matter. Specific examples of components and arrangements are described below to simplify the present disclosure. These are, of course, merely examples and are not intended to be limiting. For example, it will be understood that when an element is referred to as being “connected to” or “coupled to” another element, it may be directly connected to or coupled to the other element, or one or more intervening elements may be present.
[0014] The present disclosure provides various embodiments of a scan flip-flop circuit that can be used to perform a scan test (e.g., a scan chain testing) without using a complementary clock signal. More specifically, the disclosed scan flip-flop circuit utilizes one or more complex logic gates, e.g., an OR-AND-Inverter (OAI), an AND-OR-Inverter (AOI), etc., to circumvent the use of transmission gates that are conventionally used to generate a complementary clock signal, which advantageously reduces power consumption of the disclosed scan flip-flop circuit. Also, by using the complex logic gates, one or more performance characteristics of the scan flop-flop circuit may be improved, for example, a more robust hold time (i.e., less susceptible to manufacturing variations), a shorter hold time, etc.
[0015]
[0016]
[0017] The scan flip-flop circuit 200 is configured to receive input signals 201, 203, and 205, and provide an output signal 231 based on a synchronization signal 209. In some embodiments, the input signal 201 may be a data signal provided from the respective subset of logic gates of the to-be tested circuit 102, e.g., 109 of
[0018] As shown, the scan flip-flop circuit 200 includes a first inverter 202, a multiplexer 204, a second inverter 202′, a master latch circuit 206, a slave latch circuit 208, and a third inverter 210. In some embodiments, the multiplexer 204 is configured to selectively couple either the data signal 201 or the scan-in signal 203 to the master and slave latch circuits (206 and 208) based on the scan enable signal 205. For example, when the scan enable signal 205 is asserted to a logical low state (e.g., a logical “0”), the multiplexer 204 may couple the data signal 201 to the latch circuits 206 and 208; when the scan enable signal 205 is asserted to a logical high state (e.g., a logical “1”), the multiplexer 204 may couple the scan-in signal 203 to the latch circuits 206 and 208. It is understood that the signals coupled by the multiplexer 204 in response to the logical state of the scan enable signal 205 may be reversed from the above while remaining within the scope of the present disclosure. When the data signal 201 is selected (i.e., the data signal 201 is coupled to the master and slave latch circuits 206 and 208), in some embodiments, the master and slave latch circuits 206 and 208 are configured to cause the output signal 231 to follow the data signal 201 based on the clock signal 209, which will be discussed in further detail below.
[0019] Referring still to
[0020] In some embodiments, the output signal 217 and 227 are provided to the cross-coupled AOI's 218 and 228 of the slave latch circuit 208. More specifically, the AOI 218 is configured to receive the signal 217 and a signal 229 provided by the AOI 228, then perform an “AOI” logic function on the signals 217 and 229 based on the clock signal 209, and output signal 219 to the third inverter 210; the AOI 228 is configured to receive the signal 227 and the signal 219 provided by the AOI 218, then perform an “AOI” logic function on the signals 227 and 219 based on the clock signal 209, and output the signal 229. Accordingly, in some embodiments, the third inverter 210 may provide the output signal 231 based on a logical inversion of the signal 219.
[0021] In some embodiments, the OAI's (216 and 226) of the master latch circuit 206 and the AOI's (218 and 228) of the slave latch circuit 208 may be activated complementarily in accordance with the clock signal 209. More specifically, when the clock signal 209 transitions from a low logical state to a high logical state (i.e., the clock signal 209 at the high logical state), the master latch circuit 206 is activated and the slave latch circuit 208 is deactivated. As such, the master latch circuit 206 may latch either the signal 201 or 203 to the third inverter 210 while the slave latch circuit 208 may serve as a “transparent” circuit. When the clock signal 209 transitions from the high logical state to the low logical state (i.e., the clock signal 209 at the low logical state), the master latch circuit 206 is deactivated and, on the other hand, the slave latch circuit 208 is activated. As such, the slave latch circuit 208 may directly latch either the signal 201 or 203 to the third inverter 210 while the master latch circuit 206 may serve as a “transparent” circuit.
[0022] Referring to
[0023] By using the OAI (e.g., 216, 226, etc.) and AOI (e.g., 218, 228, etc.) in a scan flip-flop circuit (e.g., 200), in some embodiments, the clock signal 209 of the scan flip-flop circuit 200 may be commonly used by the OAI's (216 and 226) and AOI's (218 and 228), respectively. As such, a logically inverted clock signal and corresponding components (e.g., one or more inverters) used to generate such a logically inverted clock signal may not be needed, which may advantageously reduce power consumption and design complexity of the scan flip-flop circuit 200. Further, as shown in
[0024]
[0025] In some embodiments, the first inverter 202 is implemented by transistors M.sub.11 and M.sub.12 that are connected in series between a first supply voltage 200-1 (e.g., Vdd) and a second supply voltage 200-2 (e.g., ground). For brevity, the first and second supply voltages 200-1 and 200-2 are hereinafter referred to as Vdd and ground, respectively. In some embodiments, the transistor M.sub.11 includes a p-type metal-oxide-semiconductor (PMOS) transistor (hereinafter “PMOS”), and the transistor M.sub.12 includes an n-type metal-oxide-semiconductor (NMOS) transistor (hereinafter “NMOS”). Further, gates of the transistors M.sub.11 and M.sub.12 are commonly coupled to the scan enable signal 205, and a common node, coupled to respective drains of the transistors M.sub.11 and M.sub.12, is configured to provide signal 205′ that is logically inverted to the scan enable signal 205.
[0026] In some embodiments, the multiplexer 204 is implemented by transistors M.sub.13, M.sub.14, M.sub.15, M.sub.16, M.sub.17, M.sub.18, M.sub.19, and M.sub.20. More specifically, transistors M.sub.13 and M.sub.14 are connected in series between Vdd and a common node “X;” transistors M.sub.15 and M.sub.16 are connected in series between Vdd and the node X; transistors M.sub.17 and M.sub.18 are connected in series between the node X and ground; transistors M.sub.19 and M.sub.20 are connected in series between the node X and ground. In some embodiments, gates of the serially connected transistors M.sub.13 and M.sub.14 are configured to receive signals 203 and 205′, respectively; gates of the serially connected transistors M.sub.15 and M.sub.16 are configured to receive signals 205 and 201, respectively; gates of the serially connected transistors M.sub.17 and M.sub.18 are configured to receive signals 205 and 203, respectively; gates of the serially connected transistors M.sub.19 and M.sub.20 are configured to receive signals 201 and 205′, respectively. In some embodiments, transistors M.sub.13, M.sub.14, M.sub.15, and M.sub.16 each includes a PMOS; and transistors M.sub.17, M.sub.18, M.sub.19, and M.sub.20 each includes an NMOS. By implementing the multiplexer 204 in accordance with such a circuit design, the multiplexer 204 may selectively couple either the signal 201 or the signal 203 to the node X as the signal 213 based on the logical state of the scan enable signal 205, as described above.
[0027] Similar to the first inverter 202, the second inverter 202′ is also implemented as a pair of serially coupled transistors M.sub.21 and M.sub.22. In some embodiments, the transistors M.sub.21 and M.sub.22 are coupled between Vdd and ground. The transistor M.sub.21 includes a PMOS, and the transistor M.sub.22 includes an NMOS. Gates of the transistors M.sub.21 and M.sub.22 are commonly coupled to the node X so as to receive the single 213, and drains of the transistors M.sub.21 and M.sub.22 are coupled to a common node so as to provide the signal 215 that is logically inverted to the signal 213.
[0028] In accordance with various embodiments of the present disclosure, the master latch circuit 206 includes transistors M.sub.23, M.sub.24, M.sub.25, M.sub.26, M.sub.27, M.sub.28, M.sub.29, M.sub.30, M.sub.31, and M.sub.32. More specifically, the OAI 226 of the master latch circuit 206 may be formed by the transistors M.sub.23, M.sub.24, M.sub.25, M.sub.26, M.sub.27, and M.sub.28; and the OAI 216 of the master latch circuit 206 may be formed by the transistors M.sub.27, M.sub.28, M.sub.29, M.sub.30, M.sub.31, and M.sub.32. It is noted that the transistors M.sub.27 and M.sub.28 that are configured to receive the clock signal 209 are shared by the cross-coupled OAI's 216 and 226. Such a sharing of transistors M.sub.27 and M.sub.28 may be due to the symmetric circuit design of the cross-coupled OAI's 216 and 226 (
[0029] Referring still to the master latch circuit 206, in some embodiments, transistors M.sub.24, M.sub.25, M.sub.28, M.sub.31, and M.sub.32 each includes an NMOS, and transistors M.sub.23, M.sub.26, M.sub.27, M.sub.29, and M.sub.30 each includes a PMOS. More specifically, the clock-coupled transistors M.sub.27 and M.sub.28 are each configured to receive the clock signal 209 at their respective gates. The transistor M.sub.27 is coupled between Vdd and sources of the transistors M.sub.26 and M.sub.29. The transistor M.sub.28 is coupled between node Y at the transistor M.sub.28's drain that is also coupled to a source of the transistor M.sub.31 and a drain of the transistor M.sub.32, and node Z at the transistor M.sub.28's source that is coupled to a source of the transistor M.sub.24 and a drain of the transistor M.sub.25. The signal 213 is received by the transistors M.sub.29 and M.sub.32 at their respective gates, and the signal 215 is received by the transistors M.sub.25 and M.sub.26 at their respective gates. In some embodiments, the signal 217, provided based on logical states of the signals 213, 209, and 227, is generated from a common node Y′ that is coupled to a drain of the transistor M.sub.29, a drain of the transistor M.sub.30, and a drain of the transistor M.sub.31, and fed into gates of the transistors M.sub.23 and M.sub.24. The signal 227, provided based on logical states of the signals 215, 209, and 217, is generated from a common node Z′ that is coupled to a drain of the transistor M.sub.23, a drain of the transistor M.sub.24, and a drain of the transistor M.sub.26, and fed into gates of the transistors M.sub.30 and M.sub.31. By implementing the master latch circuit 206 in accordance with such a circuit design, the master latch circuit 206 may, based on the logical state of the clock signal 209, latch either the signal 201 or the signal 203 as the signals 217 and 227 to the third inverter 210, as described above.
[0030] Similarly, in some embodiments, the slave latch circuit 208 includes transistors M.sub.33, M.sub.34, M.sub.35, M.sub.36, M.sub.37, M.sub.38, M.sub.39, M.sub.40, M.sub.41, and M.sub.42. More specifically, the AOI 228 of the slave latch circuit 208 may be formed by the transistors M.sub.33, M.sub.34, M.sub.35, M.sub.36, M.sub.37, and M.sub.38; and the AOI 218 of the slave latch circuit 208 may be formed by the transistors M.sub.37, M.sub.38, M.sub.39, M.sub.40, M.sub.41, and M.sub.42. Similar to the master latch circuit 206, the transistors M.sub.37 and M.sub.38 that are configured to receive the clock signal 209 are shared by the cross-coupled AOI's 218 and 228. As described above, such a sharing of the clock-coupled transistors, i.e., M.sub.37 and M.sub.38, by the cross-coupled AOI's 218 and 228 may in turn reduce the power consumption and design complexity of the scan flip-flop circuit 200.
[0031] In some embodiments, transistors M.sub.35, M.sub.36, M.sub.38, M.sub.39, and M.sub.42 of the slave latch circuit 208 each includes an NMOS, and transistors M.sub.33, M.sub.34, M.sub.37, M.sub.40, and M.sub.41 of the slave latch circuit 208 each includes a PMOS. More specifically, the clock-coupled transistors M.sub.37 and M.sub.38 are each configured to receive the clock signal 209 at their respective gates. The transistor M.sub.38 is coupled between ground and sources of the transistors M.sub.36 and M.sub.39. The transistor M.sub.37 is coupled between node A at the transistor M.sub.37's drain that is also coupled to a source of the transistor M.sub.34 and a drain of the transistor M.sub.33, and node B at the transistor M.sub.37's source that is coupled to a source of the transistor M.sub.41 and a drain of the transistor M.sub.40. The signal 217 is received by the transistors M.sub.39 and M.sub.40 at their respective gates, and the signal 227 is received by the transistors M.sub.33 and M.sub.36 at their respective gates. In some embodiments, the signal 219, provided based on logical states of the signals 217, 209, and 229, is generated from a common node B′ that is coupled to a drain of the transistor M.sub.41, a drain of the transistor M.sub.42, and a drain of the transistor M.sub.39, and fed into gates of the transistors M.sub.34 and M.sub.35. The signal 229, provided based on logical states of the signals 227, 209, and 219, is generated from a common node A′ that is coupled to a drain of the transistor M.sub.34, a drain of the transistor M.sub.35, and a drain of the transistor M.sub.36, and fed into gates of the transistors M.sub.41 and M.sub.42. By implementing the slave latch circuit 208 in accordance with such a circuit design, the slave latch circuit 208 may, based on the logical state of the clock signal 209, latch either the signal 201 or the signal 203 to the third inverter 210, as described above.
[0032] In some embodiments, the third inverter 210 is also implemented as a pair of serially coupled transistors M.sub.43 and M.sub.44. In some embodiments, the transistors M.sub.43 and M.sub.44 are coupled between Vdd and ground. The transistor M.sub.43 includes a PMOS, and the transistor M.sub.44 includes an NMOS. Transistors M.sub.43 and M.sub.44 are commonly coupled to the slave latch circuit 208 so as to receive the single 219 at their respective gates, and drains of the transistors M.sub.43 and M.sub.44 are coupled to a common node so as to provide the signal 231 that is logically inverted to the signal 219.
[0033] In accordance with various embodiments of the present disclosure, the disclosed scan flip-flop circuit 200 uses the cross-coupled AOI's and OAI's, and their symmetric characteristic, as described above. As such, the number of “clock-coupled” transistors of the disclosed scan flip-flop circuit 200 may be substantially reduced to 4, which is much lower than a number of clock-coupled transistors (e.g., at least 12) of the conventional scan flip-flop circuit that use a transmission gate. The substantially reduced number of the clock-coupled transistors may advantageously reduce the power consumption of the disclosed scan flip-flop circuit, for example, by about 33%. Moreover, since each of the AOI's/OAI's has a higher number of stacks than conventional transmission gate flip flop (each AND gate corresponds to a stack), the disclosed scan flip-flop circuit may have a lower leakage current.
[0034]
[0035] In some embodiments, the time-borrowing circuit 302 includes one or more inverters 302-1, 302-2, 302-3, and 302-4 that are serially coupled to one another. Although the illustrated embodiment of
[0036] In some embodiments, each inverter (e.g., 302-1, 302-2, 302-3, 302-4, etc.) of the time-borrowing circuit 302 is substantially similar to the inverters 202, 202′, and 210. Thus, for clarity, the inverter(s) of the time-borrowing circuit 302 will be briefly discussed. For example, the inverter 302-1 includes a pair of serially coupled transistors M.sub.51 (a PMOS) and M.sub.52 (an NMOS), and the pair of the serially coupled transistors M.sub.51 and M.sub.52 are coupled between Vdd and ground. Gates of the transistors M.sub.51 and M.sub.52 are coupled to a common node that is configured to receive the clock signal 209 at the respective gates of transistors M.sub.51 and M.sub.52. Drains of the transistors M.sub.51 and M.sub.52 are coupled to a common node that is configured to provide a signal that is logically inverted to and has a gate delay behind the clock signal 209. In some embodiments, transistors M.sub.53 and M.sub.54 of the inverter 302-2, transistors M.sub.55 and M.sub.56 of the inverter 302-3, and transistors M.sub.57 and M.sub.58 of the inverter 302-4 have similar functionalities to the transistors M.sub.51 and M.sub.52, respectively. As such, clock signal 209′ received by the master latch circuit 206 may have about four gate delays behind the clock signal 209.
[0037]
[0038] In order to implement the master latch circuit 404 by the AOI's and the slave latch circuit 406 the OAI's, the scan flip-flop circuit 400 further includes an inverter 402 that is configured to receive the clock signal 209 and provide a logically inverted signal 209″ to the master and slave latch circuits 404 and 406, respectively. In some embodiments, the inverter 402, including a pair of serially coupled PMOS M.sub.61 and NMOS M.sub.62, is substantially similar to the above-described inverters (e.g., 302-1, 302-2, 302-3. 302-4, etc.) so the discussion of the inverter 402 is omitted.
[0039]
[0040]
[0041] The method 600 starts with operation 602 in which a scan-in signal (e.g., 203) and a data signal (e.g., 201) is received by a scan flip-flop circuit (e.g., 200), in accordance with various embodiments. As mentioned above, in some embodiments, the scan-in signal 203 may include one or more test patterns that are used to detect a fault of a scan flip-flop circuit, and the data signal 201 may include data generated based on logic operations of the respective subset of logic gates.
[0042] The method 600 continues to operation 604 in which the scan-in signal and the input signal are selectively coupled to coupled OAI master latch (e.g., 206) and AOI slave latch (e.g., 208), in accordance with various embodiments. As mentioned above, the scan flip-flop circuit 200 further receives the scan enable signal 205 to determine whether the data signal 201 or the scan-in signal 203 is to be provided to following stages (e.g., the OAI master and AOI slave latches 206 and 208) of the scan flip-flop circuit 200. In some embodiments, when the scan enable signal 205 is at the high logical state, the multiplexer 204 provides the scan-in signal 203 to the OAI master and AOI slave latches 206 and 208; and when the scan enable signal 205 is at the low logical state, the multiplexer 204 provides the data signal 201 to the master and slave latches 206 and 208.
[0043] The method 600 continues to operation 606 in which the OAI master latch and the AOI slave latch are selectively activated based on a clock signal (e.g., 209) so as to latch either the scan-in signal or the data signal as an output signal, in accordance with various embodiments. As described above, when the clock signal 209 is at the high logical state, the OAI master latch 206 is activated and the AOI slave latch 208 is deactivated; and when the clock signal 209 is at the low logical state, the OAI master latch 206 is deactivated and the AOI slave latch 208 is activated. More specifically, in some embodiments, the OAI master latch 206 and the AOI slave latch 208 each includes at most two transistors configured to receive the clock signal 209.
[0044] In an embodiment, a flip-flop circuit configured to latch an input signal to an output signal is disclosed. The circuit includes a first latch circuit; and a second latch circuit coupled to the first latch circuit. In some embodiments, in response to a clock signal, the first and second latch circuits are complementarily activated so as to latch the input signal to the output signal, and the first and second latch circuits each comprises at most two transistors configured to receive the clock signal.
[0045] In another embodiment, a flip-flop circuit configured to latch an input signal to an output signal is disclosed. The circuit includes a multiplexer configured to select from at least two signals as the input signal; a first latch circuit serially coupled to the multiplexer; and a second latch circuit serially coupled to the first latch circuit, wherein in response to a clock signal, the first and second latch circuits are complementarily activated so as to latch the input signal to the output signal, and wherein the first and second latch circuits each comprises at most two transistors configured to receive the clock signal.
[0046] Yet in another embodiment, a method to operate a flip-flop circuit is disclosed. The method includes receiving a scan-in signal and a data signal; selectively coupling either the scan-in signal or the data signal to coupled master and slave latches; and based on a clock signal, selectively activating either the master latch or the slave latch so as to latch either the scan-in signal or the data signal as an output signal of the flip-flop circuit.
[0047] The foregoing outlines features of several embodiments so that those ordinary skilled in the art may better understand the aspects of the present disclosure. Those skilled in the art should appreciate that they may readily use the present disclosure as a basis for designing or modifying other processes and structures for carrying out the same purposes and/or achieving the same advantages of the embodiments introduced herein. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the present disclosure, and that they may make various changes, substitutions, and alterations herein without departing from the spirit and scope of the present disclosure.