**1.2 Key points for an in-situ measurement**

Three key points need to be considered in order to measure the power supply noise at multiple points on a chip: area overhead, transmission method, and dynamic range.


**Local VSS Power Supply**

frequency is modulated by the voltage fluctuation.

with Millivolt Accuracy and Nanosecond-Order Time Resolution

**2.1 Time resolution and tracking of LSD**

τf1

τr1

Fig. 6. Sampling of a ring oscillator

τf1

Voltage

τf2

converted delay *τ* is a unique value based on the LSD,

τr2

τf3

τr3

τf4

corresponding delay information. In the ring oscillator, since only one inverter in the ring is activated, each inverter converts the LSD voltages into delays one after another. This

τr4

τr2 τf3 τr4 τf5 τr1 τf2 τr3 τf4 τr5

τf5

τr5

*τ*fi = *f*f(*V*LSDi), *τ*ri = *f*r(*V*LSDi), (1)

**VMON: Ring Oscillator**

**Local VDD Power Supply** **VDD noise waveform**

Fig. 5. Concept of the voltage-controlled oscillation. VMON is a ring oscillator whose

simple monotonic increasing function of the supply voltage(Chen, et al., 1996).

Period:

fluctuation, which is based on the fact that the oscillation frequency of a ring oscillator is a

<sup>103</sup> In-Situ Supply-Noise Measurement in LSIs

The ring oscillator's oscillation period consists of each inverter's delay, which depends on its LSD (Chen, et al., 1996). The voltage-measurement mechanism of the ring oscillator and the definition of our measured voltage are depicted in Fig. 6 in the simple case of a five-stage ring oscillator. The inverter circuit of each stage of the ring oscillator converts the LSD to

TOSC

VLSD

**Local supply difference (LSD) (VDD – VSS) noise**

**f ( VDD – VSS )**

t

TOSC

VLSDm

**VSS noise waveform VMON frequency is a function of LSD:**

**VMON output**

there is no flat (global) reference voltage in an LSI. Dual-ended signal transmission is a promising technique to get around this problem; however, this method gives rise to another issue: the difficulty of routing by using a ready-made EDA tool. Noise immunity of the transmission is another concern, because analog signal transmission is still needed.

3. The third point is the dynamic range of the voltage measurement. To measure supply-voltage fluctuation, a dedicated supply voltage for the probes needs to have a greater range than that of the measured local supply voltage difference.

#### **2. In-situ supply-noise map measurement**

An in-situ power-supply-noise map measurement scheme was developed by considering the above key points. Figure 4 shows the overall configuration of our proposed measurement scheme. The key feature of this scheme is the minimal size of the on-chip measurement circuits and the support of off-chip high resolution digital signal processing with frequent calibration (Kanno, et al., 2006),(Kanno, et al., 2007). The on-chip measurement circuit therefore does not need to have a sample-and-hold circuit.

Fig. 4. In-situ supply-noise-map measurement scheme

The on-chip circuits consist of several voltage monitors (VMONs) and their controller (VMONC). The VMON is a ring oscillator that acts as a supply-voltage-controlled oscillator, so that the local supply difference (LSD) between *V*DD1 and *V*SS1 can be translated to a frequency-modulated signal (see Fig. 5). The VMONC activates only one of the VMONs and outputs the selected frequency-modulated signal to the external part of the chip. Every VMON can be turned off when measurement is not necessary.

The output signal is then demodulated in conjunction with time-domain analysis by an oscilloscope and calibrations by a PC. The frequency-modulated signal between the VMONs and VMONC is transmitted only via metal wires, so dozens of power-domain partitions can be easily implemented in an LSI (Kanno, et al., 2006). The frequency-modulated signal has high noise immunity for long-distance, wired signal transmission. Although the measurement results are averaged out in the nanoseconds of the VMON's sampling period, this method can analyze voltage fluctuation easily as the voltage fluctuation map in LSIs by using multi-point measurement.

The dynamic range of the measuring voltage is not limited despite requiring no additional dedicated supply voltage. This is because we measure a frequency fluctuation as a voltage 4 Will-be-set-by-IN-TECH

3. The third point is the dynamic range of the voltage measurement.

**2. In-situ supply-noise map measurement**

need to have a sample-and-hold circuit.

VDD1

VSS1

VDDn

VSSn

measurement.

there is no flat (global) reference voltage in an LSI. Dual-ended signal transmission is a promising technique to get around this problem; however, this method gives rise to another issue: the difficulty of routing by using a ready-made EDA tool. Noise immunity of the transmission is another concern, because analog signal transmission is still needed.

To measure supply-voltage fluctuation, a dedicated supply voltage for the probes needs to

An in-situ power-supply-noise map measurement scheme was developed by considering the above key points. Figure 4 shows the overall configuration of our proposed measurement scheme. The key feature of this scheme is the minimal size of the on-chip measurement circuits and the support of off-chip high resolution digital signal processing with frequent calibration (Kanno, et al., 2006),(Kanno, et al., 2007). The on-chip measurement circuit therefore does not

PC

off-chip

calibration

**+**

AVDD

time-domain analyzer

have a greater range than that of the measured local supply voltage difference.

VMON1 VMONC

The on-chip circuits consist of several voltage monitors (VMONs) and their controller (VMONC). The VMON is a ring oscillator that acts as a supply-voltage-controlled oscillator, so that the local supply difference (LSD) between *V*DD1 and *V*SS1 can be translated to a frequency-modulated signal (see Fig. 5). The VMONC activates only one of the VMONs and outputs the selected frequency-modulated signal to the external part of the chip. Every

The output signal is then demodulated in conjunction with time-domain analysis by an oscilloscope and calibrations by a PC. The frequency-modulated signal between the VMONs and VMONC is transmitted only via metal wires, so dozens of power-domain partitions can be easily implemented in an LSI (Kanno, et al., 2006). The frequency-modulated signal has high noise immunity for long-distance, wired signal transmission. Although the measurement results are averaged out in the nanoseconds of the VMON's sampling period, this method can analyze voltage fluctuation easily as the voltage fluctuation map in LSIs by using multi-point

The dynamic range of the measuring voltage is not limited despite requiring no additional dedicated supply voltage. This is because we measure a frequency fluctuation as a voltage

VDD2

VSS2

VMON2

VMONn

Fig. 4. In-situ supply-noise-map measurement scheme

VMON can be turned off when measurement is not necessary.

Fig. 5. Concept of the voltage-controlled oscillation. VMON is a ring oscillator whose frequency is modulated by the voltage fluctuation.

fluctuation, which is based on the fact that the oscillation frequency of a ring oscillator is a simple monotonic increasing function of the supply voltage(Chen, et al., 1996).

#### **2.1 Time resolution and tracking of LSD**

The ring oscillator's oscillation period consists of each inverter's delay, which depends on its LSD (Chen, et al., 1996). The voltage-measurement mechanism of the ring oscillator and the definition of our measured voltage are depicted in Fig. 6 in the simple case of a five-stage ring oscillator. The inverter circuit of each stage of the ring oscillator converts the LSD to

Fig. 6. Sampling of a ring oscillator

corresponding delay information. In the ring oscillator, since only one inverter in the ring is activated, each inverter converts the LSD voltages into delays one after another. This converted delay *τ* is a unique value based on the LSD,

$$
\tau\_{\rm fi} = f\_{\rm f}(V\_{\rm LSDi}) , \tau\_{\rm ri} = f\_{\rm r}(V\_{\rm LSDi}) , \tag{1}
$$

(>GHz). Especially, the low-frequency domain is important in the case such as the operational mode switching and the power gating by on-chip power switches. Thus, in these cases, the accuracy of this method is sufficient to the tracking with high accuracy and the time resolution. Recently measurement of the influence of the on-chip power gating is reported (Fukuoka, 2007). Although the measured voltage is averaged out in the period of the VMON, however, the measurement of the voltage fluctuations at the actual operational mode in the product

<sup>105</sup> In-Situ Supply-Noise Measurement in LSIs

with Millivolt Accuracy and Nanosecond-Order Time Resolution

The higher the frequency of the ring oscillator, the higher the time resolution and improving the tracking accuracy; however, signal transmission at a higher frequency limits the length of the transmission line between the VMONs and VMONC due to the bandwidth limitation of the transmission line. There is therefore a trade-off between time resolution and transmission length. Although bandwidth can be widened by adding a repeater circuit, isolation cells, *µ*I/O s (Kanno, et al., 2002), are needed when applying many power domains, and, thus, the design

Accurate measurement of the VMON output frequency is also important in the in-situ measurement scheme. The accuracy also depends on the resolution of the oscilloscope

φ = 0

φ = π/4

φ = π/2

φ = 3π/4

φ = π

φ = 5π/4

φ = 3π/2

φ = 7π/4

multiple

φ = 0

φ = π/4

φ = π/2

φ = 3π/4

φ = π

φ = 5π/4

φ = 3π/2

φ = 7π/4

multiple

Fig. 7. Simulated results of voltage calculated by ring oscillator frequency: voltage fluctuation was (a) 150 MHz and (b) 300MHz. *φ* is the initial phase difference between voltage fluctuation and VMON output. The solid lines are voltage fluctuations and the dots

are the calculated voltage from the VMON output.

**(a) (b)**

level LSI is innovative.

will be complicated.

**2.2 Accuracy of waveform analysis**

where *τ*ri is the rise delay of the i-th stage, *τ*fi is the fall delay of the i-th stage, and *V*LSDi is the LSD supplying the i-th stage.

The output signal of the ring oscillator used to measure the external part of the chip has a period of *T*osc, which is the sampling period of the ring oscillator. The *T*osc is the total summation of all of the rise and fall delays of all the stages; that is,

$$T\_{\rm osc} = \sum\_{i=1}^{5} \tau\_{\rm ri} + \sum\_{i=1}^{5} \tau\_{\rm fi} \tag{2}$$

$$=\sum\_{i=1}^{5} f\_{\mathbf{f}}(V\_{\text{LSDi}}) + \sum\_{i=1}^{5} f\_{\mathbf{f}}(V\_{\text{LSDi}}).\tag{3}$$

Since we can only measure the period of the ring oscillator *T*osc and its inverse frequency(*f*osc), we must calculate the voltage from (3) in order to determine the LSD. However, it is impossible to solve (3) because there are many combinations of *V*LSDi that satisfy (3). Therefore, the measured LSD, *V*LSDm, is defined as the constant voltage which provides the same period *T*osc,

$$T\_{\rm osc} = f(V\_{\rm LSDm}).\tag{4}$$

The period *T*osc is thus the time resolution of the *V*LSDm.

In this scheme, the LSD is calculated from a measured period *T*osc or a measured frequency *f*osc. The measured LSD denoted as *V*LSDm is therefore an average value. Since the voltage fluctuation is integrated through the period *T*osc, the time resolution is determined by the period *T*osc.

Next the tracking of the LSD is discussed. There is a limitation in the tracking because the measurement of the voltage fluctuation is done by a ring oscillator as mentioned above, and the local voltage fluctuation is averaged out at the period of the ring oscillator. When the voltage fluctuation has a high-frequency element, the reproduction is difficult. In addition, a single measurement is too rough to track the target voltage fluctuation. However, although the voltage fluctuation is synchronized to the system clock, in general, since the ring oscillator oscillates asynchronously to the system frequency, the sampling points are staggered with each measurement. It is well known that averaging multiple low-resolution samples yields a higher resolution measurement if the samples have an appropriate dither signal added to them (Gray,et al., 1993).

For example, Fig. 7 (a) illustrates the case where the supply voltage fluctuation frequency is 150 MHz, which is about half the frequency of the ring oscillator. In this case, a single measurement cannot track the original fluctuation, but a composite of all measured voltages follows the power supply fluctuation. Another example is shown in Fig. 7 (b). In this case, since the frequency of the power supply fluctuation is similar to the frequency of the ring oscillator, the measured voltage *V*LSDm is almost constant. These examples show that this scheme tracks the LSD as an averaged value during the period of *T*osc. Therefore, as shown in these examples, a rounding error occurs even when the frequency of the LSD is the half that of the VMON frequency. Thus, for precise tracking, the frequency of the ring oscillator should be designed to be more than 10 times higher than that of the LSD. In general, the frequency of the power-supply voltage fluctuation can be classified into three domains; a low-frequency domain (∼MHz), a middle-frequency domain (∼100 MHz), and a high-frequency domain (>GHz). Especially, the low-frequency domain is important in the case such as the operational mode switching and the power gating by on-chip power switches. Thus, in these cases, the accuracy of this method is sufficient to the tracking with high accuracy and the time resolution. Recently measurement of the influence of the on-chip power gating is reported (Fukuoka, 2007). Although the measured voltage is averaged out in the period of the VMON, however, the measurement of the voltage fluctuations at the actual operational mode in the product level LSI is innovative.

The higher the frequency of the ring oscillator, the higher the time resolution and improving the tracking accuracy; however, signal transmission at a higher frequency limits the length of the transmission line between the VMONs and VMONC due to the bandwidth limitation of the transmission line. There is therefore a trade-off between time resolution and transmission length. Although bandwidth can be widened by adding a repeater circuit, isolation cells, *µ*I/O s (Kanno, et al., 2002), are needed when applying many power domains, and, thus, the design will be complicated.

#### **2.2 Accuracy of waveform analysis**

6 Will-be-set-by-IN-TECH

where *τ*ri is the rise delay of the i-th stage, *τ*fi is the fall delay of the i-th stage, and *V*LSDi is the

The output signal of the ring oscillator used to measure the external part of the chip has a period of *T*osc, which is the sampling period of the ring oscillator. The *T*osc is the total

> 5 ∑ *i*=1

*f*f(*V*LSDi) +

Since we can only measure the period of the ring oscillator *T*osc and its inverse frequency(*f*osc), we must calculate the voltage from (3) in order to determine the LSD. However, it is impossible to solve (3) because there are many combinations of *V*LSDi that satisfy (3). Therefore, the measured LSD, *V*LSDm, is defined as the constant voltage which provides the same period

In this scheme, the LSD is calculated from a measured period *T*osc or a measured frequency *f*osc. The measured LSD denoted as *V*LSDm is therefore an average value. Since the voltage fluctuation is integrated through the period *T*osc, the time resolution is determined by the

Next the tracking of the LSD is discussed. There is a limitation in the tracking because the measurement of the voltage fluctuation is done by a ring oscillator as mentioned above, and the local voltage fluctuation is averaged out at the period of the ring oscillator. When the voltage fluctuation has a high-frequency element, the reproduction is difficult. In addition, a single measurement is too rough to track the target voltage fluctuation. However, although the voltage fluctuation is synchronized to the system clock, in general, since the ring oscillator oscillates asynchronously to the system frequency, the sampling points are staggered with each measurement. It is well known that averaging multiple low-resolution samples yields a higher resolution measurement if the samples have an appropriate dither signal added to

For example, Fig. 7 (a) illustrates the case where the supply voltage fluctuation frequency is 150 MHz, which is about half the frequency of the ring oscillator. In this case, a single measurement cannot track the original fluctuation, but a composite of all measured voltages follows the power supply fluctuation. Another example is shown in Fig. 7 (b). In this case, since the frequency of the power supply fluctuation is similar to the frequency of the ring oscillator, the measured voltage *V*LSDm is almost constant. These examples show that this scheme tracks the LSD as an averaged value during the period of *T*osc. Therefore, as shown in these examples, a rounding error occurs even when the frequency of the LSD is the half that of the VMON frequency. Thus, for precise tracking, the frequency of the ring oscillator should be designed to be more than 10 times higher than that of the LSD. In general, the frequency of the power-supply voltage fluctuation can be classified into three domains; a low-frequency domain (∼MHz), a middle-frequency domain (∼100 MHz), and a high-frequency domain

5 ∑ *i*=1

*τ*fi, (2)

*T*osc = *f*(*V*LSDm). (4)

*f*r(*V*LSDi). (3)

summation of all of the rise and fall delays of all the stages; that is,

5 ∑ *i*=1

*τ*ri +

*T*osc =

The period *T*osc is thus the time resolution of the *V*LSDm.

= 5 ∑ *i*=1

LSD supplying the i-th stage.

*T*osc,

period *T*osc.

them (Gray,et al., 1993).

Accurate measurement of the VMON output frequency is also important in the in-situ measurement scheme. The accuracy also depends on the resolution of the oscilloscope

Fig. 7. Simulated results of voltage calculated by ring oscillator frequency: voltage fluctuation was (a) 150 MHz and (b) 300MHz. *φ* is the initial phase difference between voltage fluctuation and VMON output. The solid lines are voltage fluctuations and the dots are the calculated voltage from the VMON output.

Preheating

with Millivolt Accuracy and Nanosecond-Order Time Resolution

Supply Voltage: fix as VDD1 Clock frequency: fix as F1 Temperature of atmosphere: Ta1

Execution Program: Program A

Calibration

In-situ measurement

• Replacement of execution program • Replacement of Measurement Die • Change of measurement clock frequency • Change of measurement supply voltage

Supply Voltage: fix as VDD1 Clock frequency: fix as F1 Temperature of atmosphere: Ta1

Execution Program: Program A

• Re-selection of VMONs

as described in section2.1, since the ring oscillator oscillates asynchronously with the chip operating frequency, high resolution can be achieved by averaging multiple low-resolution measurements using an oscilloscope (Abramzon, et al., 2004). This method is also effective for eliminating noise from measurements. If the wire length between VMON and VMONC is longer, the amplitude of the signal becomes small. This small amplitude suffers from the effect of noise. However, by using this averaging method, the influence of noise can be reduced, and

<sup>107</sup> In-Situ Supply-Noise Measurement in LSIs

The in-situ measurement scheme was implemented in a 3G cellular phone processor (Hattori et al., 2006) as an example. Supply-noise maps for the processor were obtained while several actual applications were running. Figure 9 shows a chip photomicrograph. Three CPU cores and several IPs, such as an MPEG-4 accelerator, are implemented in the chip. A general-purpose OS runs on the AP-SYS CPU, and a real-time OS runs on the APL-RT CPU. The chip was fabricated using 90-nm, 8-Metal (7Cu+1Al), dual-Vth low-power CMOS process

This chip has 20 power domains, and seven VMONs are implemented in several of the power domains (Kanno, et al., 2006). Five VMONs are implemented in the application part (AP-Part), and two VMONs are implemented in the baseband part (BB-Part). VMONs 1, 3, 4, and 5 are in the same power domain, whereas the others are in separate power domains. The reason these four VMONs were implemented in the same power domain is that this domain is the

Execution Program: standby

Temperature of atmosphere: Ta1

Fig. 8. Procedure for in-situ measurement

largest one, and many IPs are integrated in it.

signals can be measured clearly.

**3. Measurement results**

technology.

Supply Voltage: varied Clock frequency: gating

used. Generally, frequency measurement is carried out by using a fast-Fourier-transform (FFT) based digital sampling oscilloscope. Sampling frequency and memory capacity of the oscilloscope are key for the FFT analysis.

First, the sampling frequency of the oscilloscope must be set in compliance with Shannon's sampling theorem. To satisfy this requirement, the sampling frequency must be set to at least double that of the VMONs. Second, the frequency resolution of the oscilloscope must be determined in order to obtain the necessary voltage resolution. Basically, the frequency resolution ∆*f* of an FFT is equal to the inverse of the measurement period *T*meas. If a 100-M word memory and a sampling speed of 40 GS/s are used, continuous measurement during a maximum measurement period of 25 ms can be carried out. If the frequency of the VMON output is several hundred megahertz and the coefficient of voltage-to-frequency conversion is about several millivolts per megahertz, highly accurate voltage measurement of the low-frequency LSD with an accuracy of about 1 mV can be achieved.

#### **2.3 Support of off-chip digital signal processing**

The proposed scheme has several drawbacks due to the simplicity of the ring-oscillator probe. One of the drawbacks is that the voltage-to-frequency dependence of the ring oscillator suffers from process and temperature variation. However, we can calibrate it by measuring the frequency-to-voltage dependence of each VMON before the in-situ measurement by setting the chip in standby mode. We can also compensate for temperature variation by doing this calibration frequently.

Figure 8 shows the measurement procedure of the proposed in-situ measurement scheme. First, the chip must be preheated in order to set the same condition for in-situ measurement, because the temperature is one of the key parameters for the measurement. This preheating is carried out by running a measuring program in the same condition as for the in-situ measurement. A test program is coded in order to execute an infinite loop because multiple measurements are necessary for improving the measurement accuracy. Because the measuring program is executed continuously, the temperature of the chip eventually reaches a state of thermal equilibrium. After the chip has reached this state, the calibration for the target VMON is executed just before the in-situ measurement. In the calibration, the frequency of the VMON output of a selected VMON is measured by varying the supply voltage while the chip is set in standby mode. Note that the calibration method can compensate for macroscopic temperature fluctuations, but not for microscopic fluctuations that occur in a short period of time that are much less than the calibration period. After the calibration, the in-situ measurement is executed by resetting the supply voltage being measured. In measuring the other VMONs continuously, the calibration step is repeated for each measurement. If other measurement conditions such as supply voltage, clock frequency, and the program being measured are changed, the chip must be preheated again.

Each VMON consumes a current of about 200 *µ*A under the worst condition, and this current flows to and from the measurement points. This current itself also causes an IR drop; however, this current is almost constant, so the influence of this IR drop is also constant. In addition, the effect of the IR drop is assumed to obey a superposition principle, so the IR drop caused by the VMON can be separated from the IR drop caused by the chip operating current. Therefore, the IR drop caused by the VMON can be compensated for by the calibration.

Another drawback of our measurement scheme is that the simple ring-oscillator probe does not have any sample-and-hold circuits. This results in degradation of resolution. However,

8 Will-be-set-by-IN-TECH

used. Generally, frequency measurement is carried out by using a fast-Fourier-transform (FFT) based digital sampling oscilloscope. Sampling frequency and memory capacity of the

First, the sampling frequency of the oscilloscope must be set in compliance with Shannon's sampling theorem. To satisfy this requirement, the sampling frequency must be set to at least double that of the VMONs. Second, the frequency resolution of the oscilloscope must be determined in order to obtain the necessary voltage resolution. Basically, the frequency resolution ∆*f* of an FFT is equal to the inverse of the measurement period *T*meas. If a 100-M word memory and a sampling speed of 40 GS/s are used, continuous measurement during a maximum measurement period of 25 ms can be carried out. If the frequency of the VMON output is several hundred megahertz and the coefficient of voltage-to-frequency conversion is about several millivolts per megahertz, highly accurate voltage measurement of

The proposed scheme has several drawbacks due to the simplicity of the ring-oscillator probe. One of the drawbacks is that the voltage-to-frequency dependence of the ring oscillator suffers from process and temperature variation. However, we can calibrate it by measuring the frequency-to-voltage dependence of each VMON before the in-situ measurement by setting the chip in standby mode. We can also compensate for temperature variation by doing this

Figure 8 shows the measurement procedure of the proposed in-situ measurement scheme. First, the chip must be preheated in order to set the same condition for in-situ measurement, because the temperature is one of the key parameters for the measurement. This preheating is carried out by running a measuring program in the same condition as for the in-situ measurement. A test program is coded in order to execute an infinite loop because multiple measurements are necessary for improving the measurement accuracy. Because the measuring program is executed continuously, the temperature of the chip eventually reaches a state of thermal equilibrium. After the chip has reached this state, the calibration for the target VMON is executed just before the in-situ measurement. In the calibration, the frequency of the VMON output of a selected VMON is measured by varying the supply voltage while the chip is set in standby mode. Note that the calibration method can compensate for macroscopic temperature fluctuations, but not for microscopic fluctuations that occur in a short period of time that are much less than the calibration period. After the calibration, the in-situ measurement is executed by resetting the supply voltage being measured. In measuring the other VMONs continuously, the calibration step is repeated for each measurement. If other measurement conditions such as supply voltage, clock frequency, and the program being

Each VMON consumes a current of about 200 *µ*A under the worst condition, and this current flows to and from the measurement points. This current itself also causes an IR drop; however, this current is almost constant, so the influence of this IR drop is also constant. In addition, the effect of the IR drop is assumed to obey a superposition principle, so the IR drop caused by the VMON can be separated from the IR drop caused by the chip operating current. Therefore,

Another drawback of our measurement scheme is that the simple ring-oscillator probe does not have any sample-and-hold circuits. This results in degradation of resolution. However,

the IR drop caused by the VMON can be compensated for by the calibration.

the low-frequency LSD with an accuracy of about 1 mV can be achieved.

oscilloscope are key for the FFT analysis.

**2.3 Support of off-chip digital signal processing**

measured are changed, the chip must be preheated again.

calibration frequently.

Fig. 8. Procedure for in-situ measurement

as described in section2.1, since the ring oscillator oscillates asynchronously with the chip operating frequency, high resolution can be achieved by averaging multiple low-resolution measurements using an oscilloscope (Abramzon, et al., 2004). This method is also effective for eliminating noise from measurements. If the wire length between VMON and VMONC is longer, the amplitude of the signal becomes small. This small amplitude suffers from the effect of noise. However, by using this averaging method, the influence of noise can be reduced, and signals can be measured clearly.
