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Rotational Speed Measurement System Based on Hall-Effect Sensor

Qifang — Wed, 15 Apr 2026 15:27:15 GMT

4.4.3 Mechanical Effects

File:Breadboard implementation of the Hall sensor circuit.jpeg

Qifang — Wed, 15 Apr 2026 14:25:59 GMT

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Rotational Speed Measurement System Based on Hall-Effect Sensor

Qifang — Wed, 15 Apr 2026 14:23:06 GMT

3.3.1 Wiring Connections

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	=== 3.3.1 Wiring Connections ===		=== 3.3.1 Wiring Connections ===

	The breadboard connections were arranged according to the three-pin configuration of the Hall sensor and the requirements of signal measurement. The supply terminal of the sensor was connected to the positive power rail, providing the operating voltage required for the Hall sensor. The ground terminal was connected to the ground rail, thereby establishing the common electrical reference for the circuit. The output terminal of the Hall sensor was then routed to a dedicated signal node on the breadboard. This same node was connected to the oscilloscope input so that the electrical response of the sensor could be observed directly during disk rotation.		The breadboard connections were arranged according to the three-pin configuration of the Hall sensor and the requirements of signal measurement, as shown in '''Fig. 4.''' The supply terminal of the sensor was connected to the positive power rail, providing the operating voltage required for the Hall sensor. The ground terminal was connected to the ground rail, thereby establishing the common electrical reference for the circuit. The output terminal of the Hall sensor was then routed to a dedicated signal node on the breadboard. This same node was connected to the oscilloscope input so that the electrical response of the sensor could be observed directly during disk rotation.

	=== 3.3.2 Role of the Pull-Down Resistor ===		=== 3.3.2 Role of the Pull-Down Resistor ===

Alcohol Sensor Based on Gas-Sensitive Resistive Materials

Jiaxin — Wed, 15 Apr 2026 07:57:43 GMT

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Alcohol Sensor Based on Gas-Sensitive Resistive Materials

Jiaxin — Wed, 15 Apr 2026 07:21:23 GMT

Created page with "== Introduction == The MQ-3 is a low-cost metal-oxide semiconductor (MOS) gas sensor designed for the detection of alcohol (ethanol) vapor in air. It is widely used in breathalyzers, vehicle safety systems, and environmental monitoring due to its high sensitivity to ethanol and relatively low sensitivity to interfering gases such as benzene and smoke. The sensing material is tin dioxide (SnO2), an n-type metal-oxide semiconductor. Structurally, the sensor co..."

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== Introduction ==

The MQ-3 is a low-cost metal-oxide semiconductor (MOS) gas sensor designed for the detection of alcohol (ethanol) vapor in air. It is widely used in breathalyzers, vehicle safety systems, and environmental monitoring due to its high sensitivity to ethanol and relatively low sensitivity to interfering gases such as benzene and smoke.

The sensing material is tin dioxide (SnO2), an n-type metal-oxide semiconductor. Structurally, the sensor consists of a miniature Al2O3 ceramic tube coated with a SnO2 sensitive layer, gold electrodes for signal measurement, platinum lead wires, and a Ni–Cr alloy heater coil. These components are enclosed in a protective housing with a stainless-steel mesh.

The built-in heater maintains the sensing layer at an elevated operating temperature of approximately 250–400 °C, which is required to activate surface reactions. The sensor operates at a supply voltage of 5 V, with a heating power consumption below 750 mW.

In clean air, the SnO2 surface exhibits high resistance due to electron depletion near the surface. When exposed to ethanol vapor, surface reactions release electrons back to the conduction band, leading to a significant decrease in resistance. This resistance change is converted into a measurable voltage signal, which is correlated with ethanol concentration.

== Working Principle ==

The sensing response of SnO2-based gas sensors, including the MQ-3, originates from surface reactions between adsorbed oxygen species and reducing gases such as ethanol. This mechanism governs the relationship between gas concentration and electrical resistance.

In ambient air, oxygen molecules adsorb onto the SnO2 surface and capture electrons from the conduction band, forming negatively charged oxygen species. This electron withdrawal creates an electron depletion layer near the surface, increases the potential barrier at grain boundaries, and results in high sensor resistance.

When ethanol vapor is introduced, it reacts with the pre-adsorbed oxygen species, releasing electrons back into the conduction band. As a result, the depletion layer narrows, the potential barrier decreases, and the overall resistance drops.

This mechanism explains the empirical observation in the MQ-3 datasheet: increasing ethanol concentration leads to a decrease in sensor resistance (Rs). The surface redox reactions therefore establish a direct link between gas concentration and electrical conductivity.

The process can be described in three sequential steps:

=== (1) Oxygen adsorption ===

O2(g) + 2e- ⇄ 2O-(ads)

Oxygen molecules adsorb on the SnO2 surface at elevated temperature (250–400 °C) and capture electrons, forming ionized oxygen species. This creates a depletion layer and increases resistance.

=== (2) Ethanol reaction ===

CH3CH2OH(g) + 6O-(ads) → 2CO2(g) + 3H2O(g) + 6e-

Ethanol reacts with the adsorbed oxygen species, producing CO2 and H2O while releasing electrons back into the conduction band.

=== (3) Resistance change ===

The released electrons increase carrier density and electrical conductivity, leading to a decrease in sensor resistance (Rs). The magnitude of this resistance change depends on ethanol concentration.

In summary:
* electron density ↑
* conductivity ↑
* resistance (Rs) ↓

The resistance variation is converted into a voltage signal through a voltage-divider circuit and measured by an analog-to-digital converter (ADC), enabling real-time ethanol detection. The process is reversible: once ethanol is removed, oxygen re-adsorption restores the initial high-resistance state.

=== Concentration–Response Relationship ===

The MQ-3 alcohol sensor does not exhibit a linear relationship between resistance and ethanol concentration. According to the Rs/R0 curve in the datasheet, the response becomes approximately linear only under logarithmic scaling, indicating a power-law dependence.

This nonlinearity originates from the surface reaction mechanism described above. As ethanol concentration increases, more adsorbed oxygen species participate in redox reactions, releasing electrons and reducing the depletion layer. However, due to limited active sites and reaction equilibrium, this process does not scale linearly with concentration.

This relationship can be described by a power-law model:

<math display="block">
R = aP^{n}
</math>

where the exponent <math>n</math> is determined by surface reaction kinetics and charge transport.

Experimental results for SnO2 ethanol sensors are also commonly expressed as:

<math display="block">
\frac{G_{\text{gas}}}{G_{\text{air}}} = 1 + AC^{Z}
</math>

where <math>Z</math> reflects the dominant surface reaction mechanism. This indicates that the sensor response is inherently non-linear and requires calibration for quantitative use.

=== Sensor Resistance (Rs) and Normalized Response (Rs/R0) ===

The MQ-3 sensor response is characterized by the resistance Rs under gas exposure and a reference resistance R0 measured under standard conditions. In practice, the normalized ratio Rs/R0 is used.

Using Rs alone is not sufficient, as the absolute resistance varies between sensors and is affected by temperature, humidity, and drift. The same ethanol concentration may therefore correspond to different Rs values.

The ratio Rs/R0 normalizes these variations and represents the relative change in resistance caused by surface reactions, making the response comparable and consistent with the datasheet curve.

As ethanol concentration increases, Rs decreases, leading to a lower Rs/R0 value. Therefore, calibration is required to establish the relationship between Rs/R0 and ethanol concentration.

=== Operating Temperature and Preheating ===

In practical applications of the MQ-3 alcohol sensor, operating temperature and preheating directly influence measurement stability and accuracy. The sensor incorporates an internal heater, and the SnO2 sensing layer must operate at elevated temperature to activate surface reactions.

The datasheet specifies a long preheating period (typically over 24 hours) to establish a stable thermal equilibrium and baseline resistance. This indicates that Rs is temperature-dependent and evolves until the thermal field stabilizes.

This behavior originates from temperature-dependent surface reaction kinetics. Temperature controls adsorption–desorption equilibrium and reaction rates, thereby determining the density of adsorbed oxygen species and the depletion layer characteristics.

Metal oxide gas sensors exhibit a characteristic temperature-dependent response: sensitivity increases at low temperature due to enhanced reaction kinetics, reaches a maximum at an optimal temperature, and decreases at higher temperature due to accelerated desorption. For SnO2-based ethanol sensors, the optimal operating range is typically around 250–300 °C.

When the sensor temperature has not fully stabilized, the distribution of adsorbed oxygen species continues to evolve, leading to fluctuations in the depletion layer and carrier concentration. Simultaneously, reaction rates also change over time, resulting in gradual drift of Rs.

This explains experimental observations where the measured concentration slowly decreases over time despite constant conditions, indicating that the system has not yet reached thermal and chemical equilibrium.

=== Sensitivity ===

Sensitivity describes how strongly the MQ-3 sensor responds to changes in ethanol concentration.

For the MQ-3 sensor, sensitivity is typically defined using resistance-based ratios such as:

<math display="block">
S = \frac{R_{\text{air}}}{R_{\text{gas}}}
</math>

or the normalized form Rs/R0.

A higher sensitivity indicates a larger change in signal for a given concentration variation, improving detectability at low concentrations. It is also a key factor affecting calibration accuracy and measurement resolution.

=== Dynamic Response (Rise Time and Recovery Time) ===

The dynamic behavior of the MQ-3 sensor is characterized by its response time and recovery time.

The response time (rise time) is defined as the time required for the sensor signal to reach a specified fraction (typically 90%) of its final value after exposure to ethanol.

The recovery time (decay time) is the time required for the sensor to return to its baseline value after the ethanol source is removed.

These parameters reflect the kinetics of gas diffusion, surface reaction, and desorption processes. Therefore, they depend on both intrinsic material properties and external measurement conditions.

=== Environmental Influence (Humidity and Measurement Conditions) ===

The response of the MQ-3 sensor is influenced by external environmental conditions.

Humidity is a primary factor, as it can modify the baseline resistance and affect the adsorption behavior of oxygen species, leading to deviations under identical ethanol concentrations.

In non-controlled environments, ethanol vapor distribution is often non-uniform. The measured concentration depends on sensor position and airflow conditions, introducing variability.

Therefore, maintaining consistent environmental conditions is necessary to ensure reliable and comparable measurements.

Surface EMG Sensor for Muscle Activity Measurement: AFE Design and Signal Processing

Baoqi — Wed, 15 Apr 2026 03:21:40 GMT

System Architecture

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	==System Architecture==		==System Architecture==
			=== Total Structure Design ===

			For clarity，the proposed physiological signal acquisition system mainly consists of two core parts：the analog front－end （AFE）and the ADC board．The AFE is responsible for the preliminary conditioning of weak bioelectrical signals，including amplification，filtering，interference suppression，and level shifting，so that the analog waveform can be converted into a stable and measurable form．The ADC board then performs high－resolution digitization of the conditioned signal and transfers the sampled data to the host computer for subsequent display，storage，and analysis．Therefore，the overall system forms a complete signal－acquisition chain from weak physiological input to digital output．

			[[File:Figure_2_1.jpg\|thumb\|center\|800px\|Figure 2.1. Overall system architecture of the proposed physiological signal acquisition platform，including the AFE and ADC modules．]]

			=== sEMG AFE Design ===

			To collect the weak bioelectric potential signals of the human body，an analog front－end（AFE）suitable sEMG measurements was designed．The module is powered by an external 5 V supply，and the complete circuit includes a first－ stage instrumentation amplifier based on INA128（Texas Instruments，Dallas，TX，USA），a band－pass filter，a 50 Hz notch filter，a second－order amplification and level shifting stage，a driver electrode circuit，a precise 1.5 V reference source，and a -5 V voltage generation module for powering the operational amplifiers．

			==== First－order Amplifier ====

			The input bioelectric signal is first acquired in differential form and applied to the INA128 instrumentation amplifier，which provides high input impedance，high common－mode rejection，and moderate initial gain for sEMG acquisition．This stage enlarges the weak physiological signal before filtering while reducing the risk of premature saturation caused by electrode offset or motion－induced disturbance，thereby preparing a more stable signal for the subsequent conditioning stages．

			==== Bandpass Filter ====

			After the instrumentation amplifier，the signal passes through a second－order active band－pass filter，as shown in Figure 2．2． This stage suppresses baseline drift and high－frequency noise outside the useful sEMG range，so that the low－frequency envelope information of sEMG can be preserved before further amplification．

			[[File:Figure_2_2.jpg\|thumb\|center\|800px\|Figure 2.2. Schematic diagram of the active band-pass filter used in the sEMG AFE.]]

			This figure shows the band-pass stage used to retain the main physiological signal band while suppressing unwanted lowand high-frequency components.

			==== Notch Filter ====

			To reduce power-line interference, a dedicated 50 Hz notch filter is introduced after the band-pass stage, as shown in Figure 2.3. This filter attenuates the mains-frequency component that commonly contaminates weak bioelectric measurements, thereby improving the signal-to-noise ratio of sEMG signals before the final amplification stage.

			[[File:Figure_2_3.jpg\|thumb\|center\|800px\|Figure 2.3. Schematic diagram of the 50 Hz notch filter used in the sEMG AFE.]]

			This figure shows the circuit used to attenuate 50 Hz mains interference in the analog front end.

			==== Second-order Amplifier & Level Shifter ====

			After filtering, the signal enters the second-stage amplification and level-shifting circuit shown in Figure 2.4. In this stage, the filtered signal is further amplified to improve amplitude utilization and then shifted by a 1.5 V reference so that the output becomes a stable unipolar signal suitable for ADC sampling, while preserving linear operation and providing sufficient output swing margin.

			[[File:Figure_2_4.jpg\|thumb\|center\|800px\|Figure 2.4. Schematic diagram of the second-stage amplifier and level-shifting circuit in the sEMG AFE.]]

			This figure shows how the conditioned signal is further amplified and shifted to a suitable DC level before digitization.

			==== Power Module and Drive-electrode Circuit ====

			The AFE is powered by a 5 V supply and also integrates a 1.5 V precision reference, a -5 V generation circuit, and a driveelectrode circuit. These supporting modules provide the required supply rails and reference level for analog signal conditioning, while the drive-electrode circuit feeds back common-mode voltage to the body to suppress interference at the source. As a result, the complete AFE can support sEMG acquisition with adequate gain, filtering, and noise-reduction performance in a compact hardware structure.

			[[File:Figure_2_5.jpg\|thumb\|center\|800px\|Figure 2.5. Physical picture of the sEMG AFE.]]

			This figure shows the fabricated sEMG analog front-end hardware used in the system.

			Figure 2.5 presents the practical hardware implementation of the proposed sEMG AFE. It integrates amplification, filtering, level shifting, and driven-reference functions in a compact circuit for weak bioelectrical signal acquisition.

			=== ADS1256-based ADC Board ===

			To digitize the conditioned weak physiological signals with sufficient resolution and low noise, this project developed a dedicated ADC board based on the ADS1256 analog-to-digital converter (Texas Instruments, Dallas, TX, USA) and the STM32F103C8T6 microcontroller (STMicroelectronics, Geneva, Switzerland). The overall design objective of this board was not merely to realize analog-to-digital conversion, but to provide a complete hardware interface between the analog front-end and the digital processing unit, including precision reference generation, clocking, input protection and filtering, serial communication, power regulation, and MCU-based acquisition control. The ADS1256 was selected because it is a

			very low-noise 24-bit delta-sigma converter with a programmable gain amplifier (PGA), flexible input multiplexer, programmable digital filter, and SPI-compatible serial interface, which makes it well suited for weak low-frequency physiological signals after analog conditioning. The STM32F103C8T6 was used as the local controller because it provides a 32-bit Cortex-M3 core, up to 72 MHz system clock, SPI, USART, USB, and standard SWD debugging support in a compact and low-cost platform.

			==== ADC Core Architecture and Design Rationale ====

			The ADS1256 was selected as the core ADC because it provides high-resolution, low-noise delta-sigma conversion with an input multiplexer, programmable gain amplifier, and digital filter, which are suitable for weak and low-frequency physiological signals. As shown in Figure 2.6, this architecture emphasizes resolution and noise performance rather than high conversion bandwidth, making it appropriate for sEMG signal digitization after analog conditioning.

			[[File:Figure_2_6.jpg\|thumb\|center\|800px\|Figure 2.6. Internal functional structure of the ADS1256 analog-to-digital converter.]]

			This figure shows the main internal blocks of the ADS1256, including the multiplexer, PGA, modulator, and digital filter.

			==== Analog Front-End Interface, Reference, and Clocking ====

			The ADS1256 analog inputs are connected to the external header through a passive input-conditioning network that helps suppress high-frequency interference and improve input stability. In addition, the board includes a dedicated precision reference and clocking circuits so that the ADC can perform stable and accurate conversion. Together, these circuits provide a reliable analog interface and timing basis for high-resolution digitization of weak physiological signals.

			==== SPI Interface between ADS1256 and STM32F103C8T6 ====

			Communication between the ADS1256 and the STM32F103C8T6 is implemented through an SPI-compatible interface, with dedicated lines for chip select, serial clock, input/output data, data-ready notification, and hardware reset. This connection allows the MCU to configure the ADC, read conversion results in synchrony with DRDY, and maintain efficient and reliable acquisition control for multi-channel physiological measurements.

			==== Power Supply and On-board Regulation ====

			The ADC board uses a USB Type-B connector as the main power input and includes protection, voltage regulation, and local decoupling circuits to provide a stable supply for both the MCU and ADC-related hardware. In addition, analog ground and digital ground are separated in the PCB layout to reduce digital noise coupling into the analog path, which is particularly important for weak physiological signal acquisition.

			==== Basic Peripheral Circuits of the STM32F103C8T6 ====

			The STM32F103C8T6 serves as the local controller of the ADC board and is supported by several basic peripheral circuits, including an external crystal oscillator, reset network, BOOT0 configuration, SWD programming/debugging header, and a CH340N USB-to-UART bridge. These circuits ensure stable MCU operation, convenient firmware downloading and debugging, and reliable data transmission from the board to the host computer for real-time display and storage.

			==== Hardware-level Working Principle of the ADC Board ====

			In operation, the conditioned analog signal from the AFE enters the ADS1256 through the input header, is digitized with high resolution under the control of the local precision reference and clock, and is then read by the STM32 through the SPI interface. The MCU subsequently forwards the sampled data to the host computer through the serial communication link, so that the entire board functions as a compact digital acquisition backend connecting weak physiological analog signals to later software processing, display, and storage.

			[[File:Figure_2_7.jpg\|thumb\|center\|800px\|Figure 2.7. Photograph of the fabricated ADS1256-based ADC board developed in this project and the definitions of some key pins.]]

			Figure 2.7 shows the ADC board fabricated for this project. It integrates the ADS1256 conversion core, STM32 control circuit, power-conditioning circuits, and communication interfaces on a compact PCB for physiological signal digitization.

	== Signal Conditioning and Filtering ==		== Signal Conditioning and Filtering ==

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Surface EMG Sensor for Muscle Activity Measurement: AFE Design and Signal Processing

Baoqi — Wed, 15 Apr 2026 02:42:19 GMT

2.3 ADS1256-based ADC Board

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	==System Architecture==		==System Architecture==

	== Signal Conditioning and Filtering ==		== Signal Conditioning and Filtering ==

Rotational Speed Measurement System Based on Hall-Effect Sensor

Qifang — Tue, 14 Apr 2026 10:24:14 GMT

3.1 Apparatus and Setups

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	\| Mounted on the motor shaft to provide stable rotational motion		\| Mounted on the motor shaft to provide stable rotational motion
	\|-		\|-
	\| ~~Magnets~~ × 2		\| Magnet × 2
	\| Diameter: 5mm		\| Diameter: 5mm
	Thickness: 5mm		Thickness: 5mm

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	The breadboard connections were arranged according to the three-pin configuration of the Hall sensor and the requirements of signal measurement, as shown in '''Fig. 4.''' The supply terminal of the sensor was connected to the positive power rail, providing the operating voltage required for the Hall sensor. The ground terminal was connected to the ground rail, thereby establishing the common electrical reference for the circuit. The output terminal of the Hall sensor was then routed to a dedicated signal node on the breadboard. This same node was connected to the oscilloscope input so that the electrical response of the sensor could be observed directly during disk rotation.		The breadboard connections were arranged according to the three-pin configuration of the Hall sensor and the requirements of signal measurement, as shown in '''Fig. 4.''' The supply terminal of the sensor was connected to the positive power rail, providing the operating voltage required for the Hall sensor. The ground terminal was connected to the ground rail, thereby establishing the common electrical reference for the circuit. The output terminal of the Hall sensor was then routed to a dedicated signal node on the breadboard. This same node was connected to the oscilloscope input so that the electrical response of the sensor could be observed directly during disk rotation.
			[[File: Breadboard_implementation_of_the_Hall_sensor_circuit.jpeg \|thumb\|center\|300px\|'''Fig. 4.''' Breadboard implementation of the Hall sensor circuit.]]

	=== 3.3.2 Role of the Pull-Down Resistor ===		=== 3.3.2 Role of the Pull-Down Resistor ===
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	In addition, a pull-down resistor was connected between the output node and ground to establish a defined low-level state and to prevent the output from floating in the absence of active switching. As illustrated in the figure, without a pull-down path the output node may not return immediately to a well-defined voltage level after switching, which can lead to slow recovery and waveform distortion. By introducing the resistor, the output is driven toward a stable low-level state, thereby improving the sharpness and stability of the digital signal. For this reason, a resistor was incorporated into the present circuit so that a clearer and more reproducible waveform could be obtained on the oscilloscope.		In addition, a pull-down resistor was connected between the output node and ground to establish a defined low-level state and to prevent the output from floating in the absence of active switching. As illustrated in the figure, without a pull-down path the output node may not return immediately to a well-defined voltage level after switching, which can lead to slow recovery and waveform distortion. By introducing the resistor, the output is driven toward a stable low-level state, thereby improving the sharpness and stability of the digital signal. For this reason, a resistor was incorporated into the present circuit so that a clearer and more reproducible waveform could be obtained on the oscilloscope.

	[[File: Effect_of_the_pull-down_resistor_on_the_output_waveform.jpeg\|thumb\|center\|300px\|'''Fig. 4.''' Effect of the pull-down resistor on the output waveform.<ref>Park, Su-Mi, and Hong-Je Ryoo. "Pulsed power modulator with active pull-down using diode reverse recovery time." IEEE Transactions on Power Electronics 35.3 (2019): 2943-2949.</ref>]]		[[File: Effect_of_the_pull-down_resistor_on_the_output_waveform.jpeg\|thumb\|center\|300px\|'''Fig. 5.''' Effect of the pull-down resistor on the output waveform.<ref>Park, Su-Mi, and Hong-Je Ryoo. "Pulsed power modulator with active pull-down using diode reverse recovery time." IEEE Transactions on Power Electronics 35.3 (2019): 2943-2949.</ref>]]


	~~[[File:fig5.jpg]~~

	~~'''Figure 5.''' Breadboard implementation of the Hall sensor circuit~~

	= 4 Experimental Procedures and Results =		= 4 Experimental Procedures and Results =
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	== 4.1 Experimental Process ==		== 4.1 Experimental Process ==

	The ~~apparatus utilized a~~ SS411P Hall effect sensor to detect the rotation of an 8 cm ~~diameter rotor~~. The sensor was ~~powered with~~ a constant ~~input~~ of ~~5V and~~ 0.~~005A~~. ~~A vertical distance of 3 cm was maintained between the magnets and the sensor to ensure a~~ consistent magnetic flux change <math display="inline">\mathrm{\Delta}\Phi</math> during each pass.		The experimental setup employed an SS411P Hall-effect sensor to detect the rotation of a circular disk with a diameter of 8 cm. The sensor was operated at a constant supply voltage of 5 V, corresponding to a current of 0.005 A. To maintain consistent magnetic flux change <math display="inline">\mathrm{\Delta}\Phi</math> during each pass, a vertical separation of 3 cm was kept between the magnets and the Hall sensor.

	=== 4.1.1 Velocity Formula ===		=== 4.1.1 Tangential Velocity Formula ===

	The diameter <math display="inline">D = 8cm</math>, ~~rotor~~ circumference (C) can be calculated as:		The diameter <math display="inline">D = 8cm</math>, circumference (<math display="inline">C</math>) of the disk can be calculated as:

	<math display="block">C = \pi*D \approx 25.13cm</math>		<math display="block">C = \pi*D \approx 25.13cm</math>
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	where <math display="inline">n</math> is the rotational frequency (rev/s).		where <math display="inline">n</math> is the rotational frequency (rev/s).

	Assuming each pulse represents one full rotation, the velocity is:		Assuming each pulse represents one full rotation, the tangential velocity is:

	<math display="block">v = fC = f25.13cm/s</math>		<math display="block">v = fC = f25.13cm/s</math>
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	=== 4.1.2 Stability Metric ===		=== 4.1.2 Stability Metric ===

	The Standard Deviation (StdDev, <math display="inline">\sigma_{f}</math>) recorded by the oscilloscope represents the ~~temporal jitter~~ of the pulse triggers. It is utilized as the primary indicator of measurement uncertainty and system instability.		The Standard Deviation (StdDev, <math display="inline">\sigma_{f}</math>) recorded by the oscilloscope represents the small fluctuation of the pulse triggers. It is utilized as the primary indicator of measurement uncertainty and system instability.

	The velocity uncertainty (<math display="inline">\sigma_{v}</math>):		The velocity uncertainty (<math display="inline">\sigma_{v}</math>):
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	== 4.2 Group I: Asymmetric Magnet Configuration ==		== 4.2 Group I: Asymmetric Magnet Configuration ==

	The ~~rotor~~ was equipped with an asymmetric magnet arrangement comprising four magnets of identical diameter: three with uniform thickness and one with a different thickness.		The disk was equipped with an asymmetric magnet arrangement comprising four magnets of identical diameter: three with uniform thickness and one with a different thickness.

	=== 4.2.1 Constant Voltage Mode ===		=== 4.2.1 Constant Voltage Mode ===
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	'''Figure 9.''' Frequency standard deviation vs. Input voltage		'''Figure 9.''' Frequency standard deviation vs. Input voltage

	In this mode, the data exhibited significant scatter (<math display="inline">R^{2} = 0.90830</math>), with the fluctuation reaching a peak value of 1109.13 mHz at 0.16 A. This suggests that the combination of magnetic field asymmetry and voltage regulation under current-driven operation led to the ~~rotor~~'s instability.		In this mode, the data exhibited significant scatter (<math display="inline">R^{2} = 0.90830</math>), with the fluctuation reaching a peak value of 1109.13 mHz at 0.16 A. This suggests that the combination of magnetic field asymmetry and voltage regulation under current-driven operation led to the disk's instability.

	Also, a higher <math display="inline">R^{2}</math> in constant voltage mode compared to constant current mode indicates that voltage control is more stable for this motor system.		Also, a higher <math display="inline">R^{2}</math> in constant voltage mode compared to constant current mode indicates that voltage control is more stable for this motor system.
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	In the CV mode, the uncertainty <math display="inline">\sigma_{v}</math> remained relatively low (typically < 0.35 cm), indicating that voltage control provides a fundamentally stable rotational environment for this motor.		In the CV mode, the uncertainty <math display="inline">\sigma_{v}</math> remained relatively low (typically < 0.35 cm), indicating that voltage control provides a fundamentally stable rotational environment for this motor.

	In the 1.40 V Anomaly: A localized peak in uncertainty (<math display="inline">\sigma_{v} = 1.7115cm/s</math>) was observed at 1.40 V. Since Magnet Group 1 utilized magnets of varying thickness, this instability likely indicates a mechanical resonance triggered at a specific angular velocity due to the ~~rotor~~'s mass imbalance.		In the 1.40 V Anomaly: A localized peak in uncertainty (<math display="inline">\sigma_{v} = 1.7115cm/s</math>) was observed at 1.40 V. Since Magnet Group 1 utilized magnets of varying thickness, this instability likely indicates a mechanical resonance triggered at a specific angular velocity due to the disk's mass imbalance.

	<ol start="2" style="list-style-type: upper-alpha;">		<ol start="2" style="list-style-type: upper-alpha;">
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	The peak uncertainty reached 27.88 cm/s at 0.16 A. This is a result of the asymmetric magnetic field (one magnet being thicker than the others).		The peak uncertainty reached 27.88 cm/s at 0.16 A. This is a result of the asymmetric magnetic field (one magnet being thicker than the others).

	In CC mode, the power supply must continuously adjust the voltage to maintain a constant current against a varying load. The asymmetry creates a non-uniform torque requirement during each rotation, causing the supply to "hunt" for the correct voltage, which amplifies rotational ~~jitter~~.		In CC mode, the power supply must continuously adjust the voltage to maintain a constant current against a varying load. The asymmetry creates a non-uniform torque requirement during each rotation, causing the supply to "hunt" for the correct voltage, which amplifies rotational fluctuation.

	<ol start="3" style="list-style-type: upper-alpha;">		<ol start="3" style="list-style-type: upper-alpha;">
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	Non-uniform Pulse Timing: Because one magnet had a different thickness, the magnetic field detected by the Hall sensor was non-uniform. This led to variations in the timing of the triggered pulses, directly increasing the StdDev.		Non-uniform Pulse Timing: Because one magnet had a different thickness, the magnetic field detected by the Hall sensor was non-uniform. This led to variations in the timing of the triggered pulses, directly increasing the StdDev.

	Mechanical Imbalance: The mass distribution of the asymmetric magnets caused the ~~rotor~~ to vibrate, especially as speed increased. These vibrations caused the distance between the sensor and magnets to fluctuate slightly, further destabilizing the output signal.		Mechanical Imbalance: The mass distribution of the asymmetric magnets caused the disk to vibrate, especially as speed increased. These vibrations caused the distance between the sensor and magnets to fluctuate slightly, further destabilizing the output signal.

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	=== 4.4.3 Mechanical Effects ===		=== 4.4.3 Mechanical Effects ===

	Mechanical factors such as motor friction, air resistance, vibration, and ~~rotor~~ imbalance could also affect the results. These factors may cause the rotation speed to fluctuate during operation, especially at higher speeds. This can increase the scatter of the measured frequency and make the fitting less ideal.		Mechanical factors such as motor friction, air resistance, vibration, and disk imbalance could also affect the results. These factors may cause the rotation speed to fluctuate during operation, especially at higher speeds. This can increase the scatter of the measured frequency and make the fitting less ideal.

	=== 4.4.4 Why Constant Voltage Gives a Better Fit ===		=== 4.4.4 Why Constant Voltage Gives a Better Fit ===