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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Adaptive Voltage Scaling System Based on Indirect Timing Mon- itoring 1</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Hao Wang</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Sheng Liu</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Yulong Qiao</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>School of Computer Science, National University of Defense Technology</institution>
          ,
          <addr-line>Changsha</addr-line>
          ,
          <country country="CN">China</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>School of Information and Communication Engineering, Harbin Engineering University</institution>
          ,
          <addr-line>Harbin</addr-line>
          ,
          <country country="CN">China</country>
        </aff>
      </contrib-group>
      <fpage>174</fpage>
      <lpage>181</lpage>
      <abstract>
        <p>With the rapid development of semiconductor manufacturing technology, the number of transistors integrated in the same area has increased by an order of magnitude. This has led to higher power consumption per unit area of the chip, which in turn imposes additional requirements for low-power design technology. In order to reduce the power consumption of the chip, this paper constructs an adjustable delay chain that indirectly monitors the timing information of the chip's critical path and regulates the scaling of the power supply voltage, thereby reducing the chip's power consumption. In addition, the AXI-based adaptive voltage scaling bus (AVSBus) is implemented to achieve real-time communication between the chip system and the power system. Experimental simulation shows that the chip's operating frequency changes from 1.3GHz to 800MHz at 12nm and 125℃, saving power consumption by 10.6~53.4% compared with fixed voltage.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Adaptive voltage scaling</kwd>
        <kwd>Low-power design</kwd>
        <kwd>Timing monitoring</kwd>
        <kwd>AVSBus</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Background and current situation of AVS research</title>
      <p>After the integrated circuit entered the system on chip era, semiconductor manufacturing
technology has developed rapidly in a manner that has not only improved chip integration, but also led to a
sharp increase in chip power consumption. The latter has gradually become a limiting factor in the
development of semiconductor devices. At the same time, power consumption has become an
important indicator for use in measuring the performance of a chip. Therefore, researchers who focus on
integrated circuits have conducted extensive research into methods that reduce power consumption
under the premise of ensuring the chip’s basic performance. Among them, adaptive voltage scaling
(AVS) technology, a low-power method that can monitor the timing of the chip system and regulate
the power supply voltage in real time, has become a research hotspot due to its remarkable ability to
reduce chip power consumption.</p>
      <p>
        In 2003, ARM and the National Semiconductor (NS) corporation of the United States jointly
proposed AVS technology in [1]. Under AVS, the timing information of the chip system is detected in
real time through the hardware performance monitor and, transmitted to the power control unit for
judgment; the voltage regulation information is then output, after which the energy management unit
is used to regulate the chip power supply voltage. In the same year, the classical Razor structure was
proposed in [2]. This structure adds a shadow latch on the basis of the main trigger at the end of the
critical path, and obtains the timing alarm information (via XOR) of the output results of the two.
Several works [
        <xref ref-type="bibr" rid="ref3">3−5</xref>
        ] have conducted structural optimization on the basis of Razor; however, these
works are still based on the principle of obtaining critical path timing information by means of the
double sampling method. In [6], timing information is obtained by inserting timing monitoring units
in the middle of the critical path, which effectively reduces the number of monitoring units. The
method of indirectly monitoring timing information by copying the critical path is introduced in
[7−10].
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. AVS principle</title>
      <p>Power consumption in the chip can be broadly divided into dynamic power consumption and static
power consumption. In turn, the former can be subdivided into switching power consumption and
short-circuit power consumption. Here, switching power consumption is the power consumed by
charging and discharging the load capacitor when the circuit signal is overturned, while short-circuit
power consumption is generated by the short-circuit current due to the intermediate level of the input
signal during the rising or falling period, which makes the NMOS tube and PMOS tube in the logic
gate circuit conduct at the same time. The switching power consumption can be obtained by
integrating the instantaneous power consumption in the corresponding period with equation (1) in [11].</p>
      <p>T
Pswitch = f ⋅ Nsw ⋅ 0 p(t)dt =
1
2</p>
      <p>C ⋅VD2D ⋅ f ⋅ Nsw
(1)</p>
      <p>Here, Nsw is the number of transistors flipped in a single clock cycle, f is the working clock
frequency of the system, C is the load capacitance, and VDD is the supply voltage. The static power
consumption occurs primarily due to current leakage in the transistor, which is mainly related to the chip
manufacturing process and cannot be effectively reduced in the chip design stage. The main
component of dynamic power consumption is switching power consumption, which is proportional to the
square of the supply voltage and the operating frequency according to formula (1); thus, the chip
power consumption can be effectively reduced by reducing the voltage.</p>
      <p>There is a correlation between chip power supply voltage and path timing. A higher power supply
voltage can improve the charging and discharging speed of the load capacitor, thus reducing the delay
of the logic gate circuit. Equation (2) in [12] reflects the relationship between CMOS logic gate delay
and power supply voltage.</p>
      <p>tgate ∝</p>
      <p>VDD
β (VDD −VT )α
(2)</p>
      <p>Here, VDD is the supply voltage, VT is the effective threshold voltage, and α and β are the fitting
parameters of the actual delay of the logic gate. In the design phase, the chip reserves a certain amount
of voltage slack after considering the impact of process, voltage, and temperature (PVT) along with
the actual working situation, which result in a certain degree of power wastage when the chip is
operating. AVS technology can adjust the power supply voltage to the lowest possible level to ensure the
normal operation of the chip by monitoring the chip’s timing information in real time, which resolves
whether to scale or maintain the voltage. This approach effectively compresses the voltage slack
reserved at the design stage and reduces the power consumption of the chip.</p>
    </sec>
    <sec id="sec-3">
      <title>3. AVS system structure design</title>
    </sec>
    <sec id="sec-4">
      <title>3.1. Overall structure of AVS</title>
      <p>As shown in Figure 1, the AVS system designed in this paper is mainly composed of a delay chain,
timing monitoring unit, AVS control unit, and AVSBus. Among them, the delay chain tracks the
timing change of the critical path in the chip system through concatenate adjustable-number inverters.
The timing monitoring unit obtains the timing information by using multiple triggers to sample the
status of signal flipping in the delay chain. The AVS control unit converts the sampling results into a
signal to increase, decrease, or maintain voltage. The voltage regulation signal is then transmitted to
the Point of Load (POL) power supply control unit through the AVSBus to regulate the supply
voltage of the digital load.</p>
    </sec>
    <sec id="sec-5">
      <title>3.2. Construction of delay chain</title>
      <p>The most important element of the AVS system is obtaining the timing information of the chip's
critical path in real time. The length of the critical path in the chip system is often affected by the PVT
and other conditions. This requires that the delay chain constructed in the indirect monitoring method
should have a good ability to track the timing changes of the critical path, to ensure that the timing
information obtained by monitoring the delay chain can accurately reflect the timing changes of the
critical path.</p>
      <p>In this paper, the 64-bit multiplication and accumulation operation unit (MAC) in a DSP chip is
used as the digital load, and the delay chain is constructed through concatenate inverters to indirectly
monitor the timing change of the critical path in the digital load. First, we conduct static timing
analysis on the digital load and delay chain respectively on the basis of layout generation. After
determining the length of the critical path in the digital load, the delay chain (L) length (number of inverters)
of the copied critical path in Figure 2 is determined under the constraints of the following two
conditions:</p>
      <p>(1) The delay of the inverter delay chain shall not be less than the delay of the critical path in the
digital load;
(2) The number of inverters in the delay chain shall be even.</p>
      <p>In more detail, the first condition is that when the delay of the inverter delay chain is less than the
critical path delay, the timing monitoring unit detects that the delay chain has a larger timing slack
than the critical path, this causes the AVS control unit to generate an incorrect voltage reduction
signal, making the supply voltage lower than that required for normal operation of the digital load, which
can in turn cause serious errors such as chip timing violations. The second condition is implemented
to ensure that the signal flipping direction of the trigger sampling position in the timing monitoring
unit is consistent with that of the delay chain input.</p>
      <p>In Figure 2, in order to monitor the timing slack of the digital load critical path in real time, some
adjustment chains (ΔL) are added on the basis of the delay chain (L) for copying the critical path. In
this paper, the scaling step value of the voltage is 50mv. However, because the digital load has
different timing changes in the critical path (caused by increasing or decreasing a voltage step value under
different voltage levels), a dynamic simulation is carried out for the digital load to obtain the
maximum value of the timing change in the critical path caused by scaling a voltage step value under
different voltage levels. Moreover, the maximum value of the timing change is mapped to the delay
chain (ΔL) reflected by the step voltage value in Figure 2, which also needs to meet the condition that
the number of inverters shall be even.</p>
    </sec>
    <sec id="sec-6">
      <title>3.3. Timing monitoring unit</title>
      <p>The timing monitoring unit developed in this paper consists of multiple triggers, which monitor the
timing information of the inverter delay chain in real time. As shown in Figure 2, one of the triggers
divides the system clock (sclk) frequency by two to generate a monitoring pulse signal, and the
inverse phase output of the divider is used as the monitoring clock (dclk) for the timing monitoring unit.
Other triggers sample the signal overturning at a specific position in the delay chain, then output the
sampling results to the AVS control unit, which outputs a signal to adjust the voltage according to the
sampling results. The number of sampling triggers depends on the regulation range of the power
supply voltage. In this paper, the digital load operates between 0.7V and 1.2V, and the voltage scaling
step value is 50mv. Therefore, there are a total of 10 delay regulation chains (ΔL). In addition, there is
a delay chain (L) for replicating the critical path derived from the static timing simulation. The output
signal flipping status for all of these 11 inverter delay chains needs to be sampled. Therefore, the
timing monitoring unit is composed of 12 triggers, 11 of which are used to sample the signal flipping
status in the delay path.</p>
      <p>The output timing relationship of the trigger in the timing monitoring unit is illustrated in Figure 3.
When the rising edge of the monitoring clock arrives, the output signal of the K-segment adjustment
chain did not flip, while the output of the K+1 and all subsequent adjustment chains has flipped,
indicating that there is timing slack in the critical path of the digital load. Moreover, this timing slack is
the delay from the first to the K-th segment adjustment chain. The value of the K indicates the timing
slack of the critical path in the digital load: the larger the K value, the greater the timing slack of the
critical path in the digital load.</p>
      <p>The timing monitoring unit implemented in this paper maps the K value to the number of 1 in
an11-bit binary number through trigger sampling. The AVS control unit will then output a signal to
scale or maintain voltage according to the number of 1. First, the highest bit in this 11-bit binary
number must be 1, because it is the sampling output of the delay chain that replicates the critical path;
otherwise, timing violations will occur. Then, the number of 1 in this 11-bit binary number (we use N
to represent this number) can be divided into three cases. The first is when N is less than 2, which
indicates that the critical path of the digital load is time-tight and the power supply voltage needs to be
increased. The second is when N is greater than 2, which means the timing of the critical path of the
digital load is loose, and the AVS control unit will output the lower voltage signal. Moreover, when N
is equal to 2, the AVS control unit will output a voltage hold signal.</p>
    </sec>
    <sec id="sec-7">
      <title>3.4. AVSBus and its implementation</title>
      <p>As an interface bus protocol, AVSBus is used to implement point-to-point communication
between ASIC, FPGA or other logical storage, processor devices and POL power control devices on the
system to achieve adaptive voltage scaling of the circuit system. In March 2014, AVSBus was
released as the third part of the Power Management Bus (PMBus) version 1.3, an extension of the
System Management Bus (SMBus), which was developed and maintained by the System Management
Interface Forum (SMIF) in 2005.</p>
      <p>The AVSBus implemented in this paper is a three-wire communication link. As Figure 4 shows,
the three links are AVS_Clock, AVS_MData and AVS_SData. Here, AVS_MData is driven by the
master device and sends data to the slave device, AVS_SData is driven by the slave device and sends
data (response) to the master device, and AVS_ Clock is driven by the master device and provides
AVS_MData and AVS_SData with the clock.</p>
      <p>As shown in Figure 5, the AVSBus communication protocol consists of two frames, namely a
write frame and read frame; the bit width of each frame is 64 bits. Each frame is in turn composed of
two subframes: the main subframe is sent by AVS_MData, and the slave subframe is sent by
AVS_SData. All subframes also support 3-bit CRC verification. The sender uses the CRC generation
polynomial of formula (3) for the first 29 bits of the subframe, and the receiver obtains the entire
subframe including the 3-bit CRC, using the same polynomial to verify the CRC to confirm the
completeness of the data.</p>
      <p>CRC(x) = x3 + x2 + x</p>
      <p>(3)
(a) The structure of write frame
(b) The structure of read frame</p>
      <p>The meaning of each field in the read/write frame is shown in Table 1. When the AVS control unit
outputs a signal to decrease, increase, or maintain the voltage, the &lt;CmdDataType&gt; is 0110, 0111,
and 1000 respectively in the AVSBus main subframe of the write frame.
&lt;CmdGroup&gt;
&lt;CmdDataType&gt;</p>
      <p>&lt;Select&gt;
&lt;CmdData&gt;</p>
      <p>&lt;CRC&gt;
&lt;Reserved_N&gt;
&lt;SlaveACK&gt;
&lt;StatusResp&gt;
2
1
4
4</p>
      <p>The AVSBus slave device will respond to the &lt;SlaveAck&gt; in the slave subframe to indicate that
the specific operation requested by the AVSBus master device has not been executed due to a CRC
check error, and that the AVSBus master device command that exceeds the voltage write execution
range has also not been executed. In addition, when the AVS_MData maintains a high level, AVSBus
will resynchronize its communication interface after the slave device receives 34 clock pulses
continuously, after which it waits for the next &lt;StartCode&gt; to start another communication. This
resynchronization mechanism enables AVSBus to avoid error states caused by line noise and other human
factors.</p>
    </sec>
    <sec id="sec-8">
      <title>4. Simulation and analysis of AVS system performance</title>
    </sec>
    <sec id="sec-9">
      <title>4.1. Simulation of AVS system performance</title>
      <p>Using the C language Application Program Interface (API) of the HSIM simulation software
proposed in [13] to simulate and model the off-chip voltage regulation module, this paper achieves the
simulation and evaluation of the voltage scaling function of the AVS system. On this basis, a hybrid
simulation platform based on VCS-HSIM is built to simulate the performance of the AVS system in
the 64-bit MAC unit of a DSP under 12 nm process, SS process angle and 125℃ temperature
conditions. As shown in Figure 6, compared with a fixed voltage of 1.2V, the AVS system adjusts the
power supply voltage to the lowest voltage, which guarantees that the digital circuit system will work
properly at different operating frequencies, resulting in a voltage drop of 4.2~41.7% and a power loss
of 10.6~53.4%.</p>
    </sec>
    <sec id="sec-10">
      <title>4.2. Analysis of simulation results</title>
      <p>The AVS system built in this paper can obtain the timing slack of the critical path in the digital
load in real time, quantify it as the number of inverters in the delay chain, and adaptively scale the
power supply voltage according to the actual timing status of the digital load, thereby achieving the
effect of reducing power consumption. Because the static power consumption produced by leakage
current in a lower process (12nm in this paper) is larger than that in a higher process (55nm in [14]), it
can be seen from Table 2 that the AVS system designed in this paper produces a somewhat smaller
reduction in chip power consumption (primarily dynamic power consumption), 53.4% in this paper vs
64.7% in [14]. However, compared with the fixed power supply voltage, this is still a significant chip
power consumption reduction effect over a wide range of voltages and high frequencies. In addition,
the AVS system designed in this paper has less area cost and reaches competitive performance.
Table 2 Performance of the AVS system designed in this paper compared with published literature</p>
      <p>This Paper Reference 7 Reference 9 Reference 14</p>
      <p>Process/nm 12 0.18μm 22 55
Frequency/MHz 800~1300 3~123 250~800 300~700</p>
      <p>Voltage/V 0.7~1.2 0.9~1.6 0.4~0.7 1.0~1.5
Energy Saving 53.4% 40% 33% 64.7%</p>
      <p>Area/mm2 0.013 not report (core an3d.3m8onitor) 0.016
Architecture 64 bits MAC 6a4MMbPUDRwAitMh a gratpiohniccsoerxeecu- FIR</p>
    </sec>
    <sec id="sec-11">
      <title>5. Conclusion</title>
      <p>The AVS system designed in this paper simulates the timing changes of the critical path in digital
circuit systems by constructing an adjustable-length delay chain with inverters, using triggers to build
the timing monitoring unit in order to detect the signal flipping of the inverter delay chain. This
indirectly allows for the timing slack information of the actual critical path to be obtained. The AVS
system will adjust the power supply voltage to the minimum required to support the normal operation of
the digital circuit system, according to the timing slack. When the working frequency of the MAC
unit decreases from 1.3GHz to 800MHz under 12 nm process, SS process corner, and 125℃
conditions, the AVS system achieves energy savings of 10.6~53.4% compared to the fixed 1.2V supply
voltage. In addition, the AVS system proposed in this paper has completed point-to-point
communication with the power system using AVSBus, which can be applied to the digital power management of
digital circuit systems. In the future, the AVS technology can be integrated in Chiplet technology to
reduce chip power consumption more flexibly.</p>
    </sec>
    <sec id="sec-12">
      <title>6. Acknowledgement</title>
      <p>7. References</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          <source>agreement number 2009ZYHJ0007. [1</source>
          ]
          <string-name>
            <surname>Maksimovic</surname>
            <given-names>D</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Dhar</surname>
            <given-names>S</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Ambatipudi</surname>
            <given-names>R</given-names>
          </string-name>
          , et al.
          <article-title>Adaptive voltage scaling power supply for use in a</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          <article-title>digital processing component and method of operating the same:</article-title>
          <source>U.S. Patent</source>
          <volume>6</volume>
          ,
          <issue>548</issue>
          ,991[P].
          <year>2003</year>
          -
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          4-
          <fpage>15</fpage>
          . [2]
          <string-name>
            <surname>Ernst</surname>
            <given-names>D</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kim</surname>
            <given-names>N S</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Das</surname>
            <given-names>S</given-names>
          </string-name>
          , et al.
          <article-title>Razor: A low-power pipeline based on circuit-level timing specu-</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          <string-name>
            <surname>lation</surname>
          </string-name>
          [C]//Proceedings. 36th
          <string-name>
            <surname>Annual</surname>
            <given-names>IEEE</given-names>
          </string-name>
          /ACM International Symposium on Microarchitecture,
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          2003. MICRO-36. IEEE Computer Society,
          <year>2003</year>
          :
          <fpage>7</fpage>
          -
          <lpage>7</lpage>
          . [3]
          <string-name>
            <surname>Calhoun</surname>
            <given-names>B H</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Chandrakasan A P.</surname>
          </string-name>
          <article-title>Standby power reduction using dynamic voltage scaling and</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          <article-title>canary flip-flop structures[J]</article-title>
          .
          <source>IEEE Journal of Solid-State Circuits</source>
          ,
          <year>2004</year>
          ,
          <volume>39</volume>
          (
          <issue>9</issue>
          ):
          <fpage>1504</fpage>
          -
          <lpage>1511</lpage>
          . [4]
          <string-name>
            <surname>Fojtik</surname>
            <given-names>M</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Fick</surname>
            <given-names>D</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kim</surname>
            <given-names>Y</given-names>
          </string-name>
          , et al.
          <article-title>Bubble razor: Eliminating timing margins in an ARM cortex-M3</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          <article-title>processor in 45 nm CMOS using architecturally independent error detection and correction</article-title>
          [J].
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          <source>IEEE Journal of Solid-State Circuits</source>
          ,
          <year>2012</year>
          ,
          <volume>48</volume>
          (
          <issue>1</issue>
          ):
          <fpage>66</fpage>
          -
          <lpage>81</lpage>
          . [5]
          <string-name>
            <surname>Reyserhove</surname>
            <given-names>H</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Dehaene</surname>
            <given-names>W.</given-names>
          </string-name>
          <article-title>Margin elimination through timing error detection in a near-</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          <article-title>threshold enabled 32-bit</article-title>
          microcontroller in 40-
          <string-name>
            <surname>nm</surname>
            <given-names>CMOS</given-names>
          </string-name>
          [J].
          <source>IEEE Journal of Solid-State Cir-</source>
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          <string-name>
            <surname>cuits</surname>
          </string-name>
          ,
          <year>2018</year>
          ,
          <volume>53</volume>
          (
          <issue>7</issue>
          ):
          <fpage>2101</fpage>
          -
          <lpage>2113</lpage>
          . [6]
          <string-name>
            <surname>Lai</surname>
            <given-names>L</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Chandra</surname>
            <given-names>V</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Aitken</surname>
            <given-names>R</given-names>
          </string-name>
          , et al.
          <article-title>Slackprobe: A low overhead in situ on-line timing slack moni-</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          <string-name>
            <surname>toring methodology</surname>
          </string-name>
          [C]//2013 Design, Automation &amp; Test in Europe Conference &amp; Exhibition
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          <string-name>
            <surname>(DATE). IEEE</surname>
          </string-name>
          ,
          <year>2013</year>
          :
          <fpage>282</fpage>
          -
          <lpage>287</lpage>
          . [7]
          <string-name>
            <surname>Nakai</surname>
            <given-names>M</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Akui</surname>
            <given-names>S</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Seno</surname>
            <given-names>K</given-names>
          </string-name>
          , et al.
          <article-title>Dynamic voltage and frequency management for a low-power</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          <article-title>embedded microprocessor[J]</article-title>
          .
          <source>IEEE journal of solid-state Circuits</source>
          ,
          <year>2005</year>
          ,
          <volume>40</volume>
          (
          <issue>1</issue>
          ):
          <fpage>28</fpage>
          -
          <lpage>35</lpage>
          . [8]
          <string-name>
            <surname>Wilson</surname>
            <given-names>R</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Beigne</surname>
            <given-names>E</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Flatresse</surname>
            <given-names>P</given-names>
          </string-name>
          , et al.
          <source>A 460mhz at 397mv, 2.6 ghz at 1</source>
          .
          <article-title>3 v, 32b vliw dsp</article-title>
          , em-
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>bedding f max tracking[C]//2014 IEEE International Solid-State Circuits Conference Digest of</mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          <string-name>
            <given-names>Technical</given-names>
            <surname>Papers (ISSCC). IEEE</surname>
          </string-name>
          ,
          <year>2014</year>
          :
          <fpage>452</fpage>
          -
          <lpage>453</lpage>
          . [9]
          <string-name>
            <surname>Cho</surname>
            <given-names>M</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kim S</surname>
            <given-names>T</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Tokunaga</surname>
            <given-names>C</given-names>
          </string-name>
          , et al.
          <article-title>Postsilicon voltage guard-band reduction in a 22 nm</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          <string-name>
            <surname>nal of</surname>
          </string-name>
          Solid-State
          <string-name>
            <surname>Circuits</surname>
          </string-name>
          ,
          <year>2016</year>
          ,
          <volume>52</volume>
          (
          <issue>1</issue>
          ):
          <fpage>50</fpage>
          -
          <lpage>63</lpage>
          . [10]
          <string-name>
            <surname>Gomez</surname>
            <given-names>R G</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Bano</surname>
            <given-names>E</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Cathelin</surname>
            <given-names>A</given-names>
          </string-name>
          , et al. A
          <string-name>
            <surname>Performance-Flexible Energy-Optimized</surname>
          </string-name>
          Automotive-
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          <string-name>
            <given-names>Grade</given-names>
            <surname>Cortex-R4F SoC through Combined</surname>
          </string-name>
          <string-name>
            <surname>AVS</surname>
          </string-name>
          /ABB/
          <article-title>Bias-in-</article-title>
          <string-name>
            <surname>Memory-Array</surname>
          </string-name>
          Closed-Loop
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          <article-title>Regulation in 28nm FD-</article-title>
          <string-name>
            <surname>SOI</surname>
          </string-name>
          [C]//2020 IEEE Symposium on VLSI Circuits. IEEE,
          <year>2020</year>
          :
          <fpage>1</fpage>
          -
          <lpage>2</lpage>
          . [11]
          <string-name>
            <surname>Wei</surname>
            <given-names>Guo</given-names>
          </string-name>
          ,
          <article-title>SoC design method</article-title>
          and implementation [M]. Electronic Industry Press,
          <year>2017</year>
          . [12]
          <string-name>
            <surname>Sakurai</surname>
            <given-names>T</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Newton</surname>
            <given-names>A</given-names>
          </string-name>
          R.
          <article-title>Alpha-power law MOSFET model and its applications to CMOS invert-</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation>
          <article-title>er delay and other formulas[J]</article-title>
          .
          <source>IEEE Journal of solid-state circuits</source>
          ,
          <year>1990</year>
          ,
          <volume>25</volume>
          (
          <issue>2</issue>
          ):
          <fpage>584</fpage>
          -
          <lpage>594</lpage>
          . [13]
          <string-name>
            <given-names>Zhaoxuan</given-names>
            <surname>Tian</surname>
          </string-name>
          .
          <article-title>Design and implementation of low power consumption SOC chip based on adap-</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation>
          <article-title>tive voltage regulation[D]</article-title>
          . Southeast University,
          <year>2014</year>
          . [14]
          <string-name>
            <surname>Shengnan</surname>
            <given-names>Lin</given-names>
          </string-name>
          ,
          <string-name>
            <given-names>Liping</given-names>
            <surname>Liang</surname>
          </string-name>
          .
          <article-title>Adaptive voltage regulating system based on performance matching</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation>
          <source>for SoC [J]. Electronic Design Engineering</source>
          ,
          <year>2022</year>
          ,
          <volume>30</volume>
          (
          <issue>6</issue>
          ):
          <fpage>6</fpage>
          .
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>