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迷你演示實驗「電磁學小盒子」之開發與「生生有實驗」教學成效研究;Development of the Mini Demonstration Experiment Kit "Electromagnetic Learning Box" and a Study of the Teaching Effectiveness of "Classroom Experiments for Every Student"

Tue, 20 Oct 2026 07:41:19 GMT

title: 迷你演示實驗「電磁學小盒子」之開發與「生生有實驗」教學成效研究;Development of the Mini Demonstration Experiment Kit "Electromagnetic Learning Box" and a Study of the Teaching Effectiveness of "Classroom Experiments for Every Student" abstract: 本研究旨在開發可應用於國中電磁學課堂之迷你演示實驗教具「電磁學小盒子」，並探討以每位學生皆能親自操作教具為核心之「生生有實驗」教學方式。教具包含伏打電池、看見磁力線、電流的磁效應、電動馬達、電流與磁場的交互作用及電磁感應六項，目的在將抽象電磁學概念轉化為可於一般教室操作與觀察的實驗現象。本研究採準實驗研究設計並結合量化與質性資料分析。第一階段以北部一所私立完全中學 294 位國三學生為原始樣本，比較實作教學與影片教學，並訪談 48 位學生；第二階段以北部一所公立學校 193 位國三學生為原始樣本，比較實作教學、平板影片教學與教師示範教學三種教學方法，並蒐集概念測驗、理化學習動機問卷、學習風格問卷及 42 位學生訪談資料。結果顯示，第一階段實作教學與影片教學皆能提升學生概念表現；其中「電流與磁場的交互作用」在控制後測後，實作組延後測顯著高於影片組。第二階段三種教學法皆能提升四項實驗整體概念表現；分別以前測與後測作為共變數進行分析後，三種教學法未呈現顯著差異。兩階段結果皆顯示不同學業成就學生均能獲得學習支持，未發現教學法與學業成就分群的穩定交互作用。學習風格分析呈現部分教學法與學習風格交互作用，但不同測驗時間的結果不一致，未形成固定配對關係。理化學習動機方面，第二階段研究期間實作組與教師示範組顯著上升，平板影片組則顯著下降。訪談顯示，不同教學法皆可形成於後續課程與作答時重新喚起的實驗經驗；回想有時能協助理解題意或概念判斷，但操作或觀看實驗並不等於立即理解，仍需將實驗現象與物理概念建立連結。綜合而言，「電磁學小盒子」教具與「生生有實驗」的方式能增加學生接觸與操作電磁學實驗現象的機會；其中，在涉及方向與空間關係的較複雜主題中，親自操作可能有助於學生經過一段時間與後續學習後的概念表現。;This study developed the Electromagnetic Learning Box， a set of mini demonstration experiment kits for junior high school electromagnetism instruction， and investigated Classroom Experiments for Every Student， an instructional approach in which each student operates an individual set of apparatus. The six experiments cover the Voltaic pile， visualization of magnetic field lines， the magnetic effect of electric current， the electric motor， the interaction between electric current and a magnetic field， and electromagnetic induction. The kits were designed to transform abstract electromagnetism concepts into experimental phenomena that can be produced and observed in a regular classroom. A quasi-experimental research design combining quantitative and qualitative data analyses was adopted. In Phase 1， the initial sample consisted of 294 ninth-grade students from a private secondary school in northern Taiwan. Hands-on instruction was compared with video instruction， and 48 students were interviewed. In Phase 2， the initial sample consisted of 193 ninth-grade students from a public school in northern Taiwan. Three instructional approaches—hands-on instruction， tablet-based video instruction， and teacher-demonstration instruction—were compared. Data were collected through concept tests， a questionnaire on motivation toward learning physics and chemistry， a learning-style questionnaire， and interviews with 42 students. The results showed that both hands-on and video instruction improved students’ conceptual performance in Phase 1. For the topic of the interaction between electric current and a magnetic field， the hands-on group significantly outperformed the video group on the delayed test after posttest performance was controlled. In Phase 2， all three instructional approaches improved students’ overall conceptual performance across the four experiments. When pretest and posttest scores were used as covariates in the respective analyses， no significant differences were found among the three instructional approaches. Across both phases， students at different achievement levels benefited from the instructional activities， and no stable interaction was found between instructional approach and achievement group. Learning-style analyses revealed some interactions between instructional approach and learning style; however， the patterns differed across testing occasions and did not form a fixed matching relationship. During Phase 2， motivation toward learning physics and chemistry increased significantly in the hands-on and teacher-demonstration groups but decreased significantly in the tablet-based video group. The interviews showed that all instructional approaches could provide experimental experiences that students later recalled during subsequent lessons and problem solving. Such recall sometimes helped students understand problem contexts or make conceptual judgments. However， operating or observing an experiment did not necessarily lead to immediate understanding; the observed phenomena still needed to be connected with the relevant physics concepts. Overall， the Electromagnetic Learning Box and Classroom Experiments for Every Student increased students’ opportunities to engage with and operate electromagnetism experiments. For more complex topics involving directional and spatial relationships， direct manipulation may support students’ conceptual performance after a period of time and subsequent learning.

尖晶石錳釩氧化物Mn₃V₃O₈的結構與磁性研究;尖晶石錳釩氧化物Mn₃V₃O₈的結構與磁性研究

Tue, 20 Oct 2026 07:41:16 GMT

title: 尖晶石錳釩氧化物Mn₃V₃O₈的結構與磁性研究;尖晶石錳釩氧化物Mn₃V₃O₈的結構與磁性研究 abstract: 本研究以Mn₂.₉₀V₃.₁₀O₈為研究對象，探討其結構、價態與磁性之間的關聯。微觀結構分析顯示，EDS mapping 中Mn、V與 O元素在顆粒中的分布相對均勻，TEM與HRTEM則顯示樣品具有良好的局部結晶性。FFT圖樣大致可沿I4₁/amd結構之 [001] zone axis進行索引，此結果表示前述結構與價態特徵應可視為樣品本身的性質，而非局部成分分離所造成。結構分析以變溫中子繞射顯示材料在本研究量測溫區內始終維持四方扭曲的尖晶石相關結構，並未出現明確的 cubic-to-tetragonal 結構相變；其四方扭曲程度隨溫度升高而逐漸減弱。局部配位分析顯示，鍵長與鍵角於磁有序溫度附近呈現明顯變化，其中 B-site planar 方向的結構改變較為顯著，顯示該溫區的局部結構調整可能與八面體平面方向晶格扭曲及 Jahn–Teller 作用有關。　　本研究分別利用磁化量測所得的有效磁矩，在電荷中性與不同價態離子自旋貢獻的限制下進行自洽計算，並與中子粉末繞射的佔位率精算結果比較。磁性分析顯示，A 位點的 Mn 與 V 佔位比例分別為 0.89(2) 與 0.11(2)，B 位點則分別為 0.28(1) 與 0.72(1)，對應的化學組成為 [Mn1.78(4)V0.22(4)]A[Mn1.12(4)V2.88(4)]BO，總組成為 Mn2.90(6)V3.10(6)O8。中子繞射精算得到 A 位點的 Mn 與 V 佔位比例分別為 0.822(30) 與 0.178(30)，B 位點則為 0.269(34) 與 0.731(34)，對應組成為 [Mn1.64(6)V0.36(6)]A[Mn1.12(4)V2.88(4)]BO8，總組成為 Mn2.72(15)V3.28(15)O8。兩種方法在定量結果上存在一定差異，但均顯示 Mn 離子主要佔據 A 位點，而 V 離子主要分布於 B 位點。考量有效磁矩分析同時受到電荷中性、離子價態及自旋貢獻的限制，本研究以 Mn₂.₉₀V₃.₁₀O₈ 作為後續平均磁性與總磁矩討論的主要組成。　　價態分析方面，Mn 與V K-edge XANES結果皆落在不同價態標準樣品之間，顯示兩者皆具有混合價態特徵。BVS結果則指出A-site 平均價數接近 +2、B-site平均價數接近 +3。然而，若結合中子繞射精算所得之佔位比例進一步分析，可發現樣品並非理想正尖晶石中的完全有序價態分布，而是同時具有A、B site混合佔據與混合價數的特性；其中A site仍以Mn佔據為主，B site則除V外亦存在反位Mn，並呈現較高價態的特徵。這些結果顯示Mn₂.₉₀V₃.₁₀O₈的局部電子態與鍵結環境已偏離理想尖晶石圖像。　　磁性量測結果顯示，Mn₂.₉₀V₃.₁₀O₈於低溫下具有明顯磁化訊號與磁滯行為，ZFC與FC曲線在低溫區出現分岔，隨溫度升高，磁化強度快速下降，磁化率隨溫度之一階微分訊號在約58 K左右具有最大值，顯示巨觀磁化量測之磁有序溫度。Curie–Weiss 擬合得到有效磁矩約 10.02(1) μB / f.u.、Curie–Weiss 溫度 θCW = 138(1) K，系統中主要交換作用傾向反平行排列；若以58 K估算，其挫折參數約為 2.38。另一方面，M–H 曲線顯示樣品在4 K具有有限淨磁矩與磁滯，飽和磁矩由4 K的1.96(4) μB/f.u.隨溫度升高而系統性下降，至75 K數據已明顯衰減，顯示其低溫磁有序較適合描述為具有淨磁矩的亞鐵磁或傾斜亞鐵磁磁有序。變溫中子繞射結果進一步顯示，3.5 K的繞射圖譜可由四方晶系核結構 I4₁/amd 搭配磁結構模型 I4₁/am′d′良好描述；相較之下，300 K時低角度區的額外磁散射已不再明顯，對應高溫下無長程磁有序的狀態。磁結構精算結果指出，A-site與B-site子晶格磁矩分量在升溫過程中存在重新分配，A位磁矩大小主要沿著c軸方向縮小，而B位磁矩的大小變化相對較弱，並伴隨著磁有序溫度以下y和z分量的調整。將中子繞射精算所得總磁矩以臨界指數冪定律擬合，可得其磁有序溫度為56(2) K，低溫極限有序磁矩約 1.40(2) μB，且與 VSM 所得 4 K 飽和磁矩 1.96(4) μB/f.u.接近。考量巨觀磁性量測可反映整體樣品的平均磁性響應，本研究以磁化率量測所得的TN=58 K作為主要的有序溫度。在A、B site 的有序磁矩隨溫度變化呈現不同的臨界行為，其臨界指數分別為 βA = 0.29(1) 與 βB = 0.20(2)，其中，A site 的臨界行為較接近三維 Ising 模型，B site 則較偏向二維 Ising 模型，顯示兩個磁性子晶格可能具有不同的有效交換維度。　　A、B site 的 BVS 於TN附近呈現同步變化，並伴隨鍵長、鍵角與有序磁矩的調整，顯示磁性轉變涉及局部價態、鍵結環境與晶格扭曲的重新配置。綜合結構、價態與磁性分析結果，Mn₂.₉₀V₃.₁₀O₈ 的亞鐵磁有序與具方向性的交換路徑密切相關，並於TN附近呈現自旋—軌道耦合行為。;This study investigates the relationships among the crystal structure， valence states， and magnetic properties of Mn₂.₉₀V₃.₁₀O₈. Microscopic characterization showed that Mn， V， and O were distributed relatively uniformly within the particles， as revealed by energy-dispersive X-ray spectroscopy (EDS) mapping. Transmission electron microscopy (TEM) and high-resolution TEM (HRTEM) further demonstrated good local crystallinity. The fast Fourier transform (FFT) pattern could be approximately indexed along the [001] zone axis of the I4₁/amd structure， suggesting that the observed structural and valence characteristics are intrinsic to the sample rather than arising from local compositional segregation. Variable-temperature neutron diffraction showed that the material retained a tetragonally distorted spinel-related structure throughout the measured temperature range， without a distinct cubic-to-tetragonal structural transition. The degree of tetragonal distortion gradually decreased with increasing temperature. Local coordination analysis revealed pronounced changes in the bond lengths and bond angles near the magnetic ordering temperature. These changes were more evident within the B-site octahedral plane， suggesting that the local structural response in this temperature region may be associated with in-plane lattice distortion of the octahedra and the Jahn–Teller effect. 　　Self-consistent calculations were performed using the effective magnetic moment obtained from magnetic susceptibility measurements under the constraints of charge neutrality and the spin contributions of ions with different valence states. The results were compared with the site occupancies refined from neutron powder diffraction. The magnetic analysis yielded Mn and V occupancies of 0.89(2) and 0.11(2)， respectively， at the A site， and 0.28(1) and 0.72(1)， respectively， at the B site. These values correspond to [Mn₁.₇₈₍₄₎V₀.₂₂₍₄₎]A[Mn₁.₁₂₍₄₎V₂.₈₈₍₄₎]BO₈， with an overall composition of Mn₂.₉₀V₃.₁₀O₈. Neutron diffraction refinement yielded Mn and V occupancies of 0.822(30) and 0.178(30)， respectively， at the A site， and 0.269(34) and 0.731(34)， respectively， at the B site. The corresponding composition was [Mn1.64(6)V0.36(6)]A[Mn1.12(4)V2.88(4)]BO8， with an overall composition of Mn2.72(15)V3.28(15)O8. Although the two methods yielded some quantitative differences， both indicated that Mn preferentially occupies the A site， whereas V is primarily distributed over the B site. Because the effective-moment analysis is simultaneously constrained by charge neutrality， ionic valence states， and spin contributions， Mn₂.₉₀V₃.₁₀O₈ was adopted as the representative composition for the subsequent discussion of the average magnetic properties and total magnetic moment. 　　Regarding the valence states， the Mn and V K-edge X-ray absorption near-edge structure (XANES) spectra were located between those of reference compounds with different oxidation states， indicating mixed-valence characteristics for both elements. Bond-valence-sum (BVS) analysis showed that the average valence was close to +2 at the A site and +3 at the B site. Combined with the site occupancies obtained from neutron diffraction refinement， these results indicate that the sample deviates from the fully ordered valence distribution expected for an ideal normal spinel and instead exhibits mixed A/B-site occupancy and mixed valence. The A site remains predominantly occupied by Mn， whereas the B site contains antisite Mn in addition to V and exhibits characteristics associated with higher oxidation states. These findings demonstrate that the local electronic states and bonding environments of Mn₂.₉₀V₃.₁₀O₈ deviate from the idealized spinel picture. 　　Magnetic measurements revealed pronounced magnetization and hysteresis at low temperatures. The zero-field-cooled and field-cooled curves exhibited a low-temperature bifurcation， while the magnetization decreased rapidly with increasing temperature. The first derivative of the magnetic susceptibility showed a maximum near 58 K， indicating the magnetic ordering temperature observed by macroscopic magnetic measurements. Curie–Weiss fitting yielded an effective magnetic moment of approximately 10.02(1) μB/f.u. and a Curie–Weiss temperature of θCW = 138(1) K， suggesting that the dominant exchange interactions favor antiparallel spin alignment. Using 58 K as the ordering temperature， the frustration parameter was estimated to be approximately 2.38. The M–H curves showed a finite net magnetic moment and magnetic hysteresis at 4 K. The saturation magnetization decreased systematically from 1.96(4) μB/f.u. at 4 K and was substantially reduced by 75 K， indicating that the low-temperature magnetic state can be described as ferrimagnetic or canted ferrimagnetic order with a finite net moment. Variable-temperature neutron diffraction further showed that the diffraction pattern at 3.5 K could be well described by the tetragonal nuclear structure I4₁/amd combined with the magnetic structure model I4₁/am′d′. At 300 K， the additional low-angle magnetic scattering was no longer evident， consistent with the absence of long-range magnetic order at high temperature. Magnetic structure refinement revealed a redistribution of the magnetic-moment components of the A- and B-site sublattices upon warming. The decrease in the A-site magnetic moment occurred primarily along the c axis， whereas the magnitude of the B-site moment varied less substantially and was accompanied by changes in its y and z components below the magnetic ordering temperature. Fitting the total ordered moment obtained from neutron diffraction refinement using a critical power law yielded a magnetic ordering temperature of 56(2) K and a low-temperature limiting ordered moment of approximately 1.40(2) μB. This value is close to the saturation magnetization of 1.96(4) μB/f.u. measured by VSM at 4 K. Because macroscopic magnetic measurements reflect the average magnetic response of the entire sample， TN = 58 K， determined from the magnetic susceptibility measurements， was adopted as the primary ordering temperature. The temperature-dependent ordered moments of the A and B sites exhibited distinct critical behaviors， with critical exponents of βA = 0.29(1) and βB = 0.20(2)， respectively. The critical behavior of the A site is closer to that of the three-dimensional Ising model， whereas that of the B site tends toward the two-dimensional Ising model， suggesting that the two magnetic sublattices may possess different effective exchange dimensionalities. 　　The BVS values of the A and B sites exhibited correlated changes near TN， accompanied by variations in the bond lengths， bond angles， and ordered magnetic moments. These observations indicate that the magnetic transition involves a reconfiguration of the local valence states， bonding environments， and lattice distortions. The combined structural， valence-state， and magnetic analyses suggest that the ferrimagnetic order in Mn₂.₉₀V₃.₁₀O₈ is closely associated with directional exchange pathways and exhibits spin–orbit coupling near TN.

Measurement of charged hadron multiplicity in Au+Au collisions at √sNN = 200 GeV with the sPHENIX detector;Measurement of charged hadron multiplicity in Au+Au collisions at √sNN = 200 GeV with the sPHENIX detector

Tue, 20 Oct 2026 07:41:13 GMT

title: Measurement of charged hadron multiplicity in Au+Au collisions at √sNN = 200 GeV with the sPHENIX detector;Measurement of charged hadron multiplicity in Au+Au collisions at √sNN = 200 GeV with the sPHENIX detector abstract: 本論⽂使⽤ sPHENIX 粒⼦探測器，量測質⼼系統能量為 √sNN = 200 GeV 的 Au+Au 碰撞事件，中快度區域 (mid-rapidity， η) 的帶電強⼦贗快度密度 dNch/dη。 dNch/dη 是研究相對論性重離⼦碰撞整體性質 (bulk properties) 的⼀項關鍵全域觀測量。此觀測量反映碰撞中的整體粒⼦產⽣情形，並可對碰撞幾何、初始條件，以及所產⽣之量⼦⾊動⼒學（QCD）介質的後續演化提供重要的constraints。 sPHENIX 的dNch /dη量測主要使⽤中間層矽軌跡探測器（Intermediate Silicon Tracker，INTT）所收集的資料。INTT 是⼀座由兩層矽微條偵測器構成的桶狀軌跡偵測器。由於 INTT 是新建成的偵測器，因此在將其應⽤於物理量測之前，必須先對其效能進⾏評估。本論⽂透過在⽇本 RARiS 進⾏的束流測試實驗(test beam experiment) 完成此項評估。束流測試分析結果顯⽰，INTT 的偵測效 (hit detection efficiency) 率⾼於 99%，為 sPHENIX的 dNch /dη 量測奠定了重要基礎。在 Au+Au 碰撞事件的 dNch /dη 分析中，我們⾸先利⽤ INTT 獲取的數據來重建對撞點在橫斷⾯上的平均位置 (beam spot)，並逐事件重建碰撞點的 z 軸位置 (per-event z-vertex)。帶電強⼦數量則是透過配對 INTT 桶狀偵測器兩層中的叢集 (clusters)，形成短徑跡（tracklets）後加以擷取。此分析中針對偵測器接受度、重建效率，以及輕⼦和次級衰變所造成的粒⼦數貢獻進⾏修正。本研究建⽴了兩種相互獨⽴的分析⽅法，本論⽂負責其中⼀個分析⽅法。兩種⽅法所得的結果具有良好的⼀致性。本論⽂報告了|η| < 1.1範圍內、中⼼度 (centrality) 介於 0-70% 的各中⼼度區間 (centrality classes) 之dNch /dη分布。對於中心度最高的 0-3% 之碰撞事件，中快度區域 (mid-rapidity) 的帶電強子贗快度密度 dNch /dη(|η|<0.3) 測得為723.45±45.3。此外，本研究進一步探討以參與碰撞核子對數目 (number of participating nucleon paris) 歸一化後的中快度帶電強子多重度，如何隨參與碰撞核子數目 (Npart) 而變化。本論文使用 sPHENIX 數據所量測的結果與過去的 RHIC 量測結果一致，並在中等中心度區域 (mid-centrality region) 提供了更小的不確定度 (uncertainty)。除了其物理上的重要性之外，此項量測亦作為一項以 sPHENIX tracking system 為基礎的標準燭光量測 (standard candle measurement)，用以驗證偵測器效能、重建演算法及分析框架，進而為更廣泛的 sPHENIX 物理研究計畫奠定了重要基礎。;This thesis presents the measurement of the charged-hadron pseudorapidity density， $\dndeta$， at midrapidity in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200~\mathrm{GeV}$ with the sPHENIX detector. The charged-hadron pseudorapidity density is a critical global observable for studying the bulk properties of relativistic heavy-ion collisions， as it reflects the overall particle production and provides constraints on the collision geometry， initial conditions， and subsequent evolution of the produced QCD medium. The \dndeta measurement in sPHENIX is performed primarily using data collected by the Intermediate Silicon Tracker (INTT)， a two-layer barrel silicon strip tracker. As a newly constructed detector， the performance of the INTT must be evaluated before its application to physics measurements. This evaluation is conducted through a test beam experiment at RARiS in Japan. The beam test analysis demonstrates that the INTT achieves a hit-detection efficiency above 99\%， providing an essential foundation for the sPHENIX \dndeta measurement. In the \dndeta analysis with Au+Au collisions， INTT data are used to determine the beam spot and reconstruct the per-event z-vertex. Charged-hadron yields are extracted from tracklets formed by pairing clusters in the two layers of INTT barrel， with corrections applied for detector acceptance， reconstruction efficiency， and contributions from leptons and secondary decays. Two independent analysis methods are developed， and their results are found to be in good agreement. The measured $\dndeta$ distributions are reported within $|\eta|<1.1$ for centrality classes ranging from 0-70\%. For the 3\% most central collisions， the mid-rapidity charged-hadron pseudorapidity density， $\left.dN_{\mathrm{ch}}/d\eta\right|_{|\eta|<0.3}$， is measured to be $723.45 \pm 45.3$ (syst.). The mid-rapidity charged-hadron multiplicity， normalized by the number of participating nucleon pairs， is further studied as a function of the number of participating nucleons. The results are consistent with all previous RHIC measurements and provide improved uncertainties in the mid-centrality region. In addition to its physics importance， this measurement serves as a tracking-based standard candle for validating detector performance， reconstruction algorithms， and the analysis framework， thereby supporting the broader sPHENIX physics program.

傳遞885奈米光鐘穩定度至儀器用10-MHz頻率;Transferring the stability of an 885-nm optical clock into that of the 10-MHz instrument time base

Tue, 20 Oct 2026 07:41:11 GMT

title: 傳遞885奈米光鐘穩定度至儀器用10-MHz頻率;Transferring the stability of an 885-nm optical clock into that of the 10-MHz instrument time base abstract: 本研究以實驗室的 885 nm 光鐘作為光頻穩定度參考，利用光頻梳連接光頻與射頻訊號，將其頻率穩定度傳遞至一般電子儀器所使用的 10 MHz 外部時基。經過在 Red Pitaya 開發板上建立以數位帶通濾波器(DBPF)為基礎的偏移頻率鎖定系統[1][2]，將拍頻鎖定於 DBPF 的中心頻率，並完成光頻梳載波包絡偏移頻率 $f_{ceo}$ 的鎖相。在系統優化方面，本研究透過調整 DBPF 帶寬改善拍頻鎖定效果，並利用帶阻濾波器抑制 PZT 所產生的 1.6 kHz 共振，以提高迴路增益及低頻雜訊抑制能力。藉由比較拍頻鎖定、Red Pitaya 內部時脈、$f_{rep}$ 與 885 nm 光鐘的頻率穩定度，結果推測$f_{rep}$ 與 885 nm 光鐘的頻率穩定度差距在短期(0.1$\sim$ 1 s)穩定度主要來自頻率計數器自身的不穩定度限制，而長期穩定度(100 s以上)推測是受限於 885 nm 光鐘限制，說明本次DBPF鎖頻方法具備足夠的性能可以將光頻穩定度傳遞到$f_{rep}$。最終輸出的10 MHz 訊號，其 Allan deviation 在平均時間2048 秒時達到 $6.04\times10^{-13}$。後續透過降低誤差訊號的零交越頻率對拍頻功率的靈敏度，並導入雙頻寬數位帶通濾波器(Dual Bandwidth Digital Bandpass Filter， DBW-DBPF)[2]的鎖頻方法，進一步改善了拍頻鎖定的短期與長期穩定度，讓鎖定後的拍頻在平均時間 205 s時，達到 10.5 Hz 的頻率不穩定度。;This study demonstrates the transfer of optical frequency stability from a home-built 885 nm optical clock to a standard 10 MHz instrumental timebase， utilizing an optical frequency comb (OFC) to bridge the optical and radio frequency domains. By implementing a digital band-pass filter (DBPF)-based frequency offset locking system on a Red Pitaya FPGA board， the beat note ($f_{beat}$) was successfully locked to the center frequency of the DBPF， achieving phase-locking of the carrier-envelope offset frequency ($f_{ceo}$). In terms of system optimization， the locking performance of the beat note was enhanced by adjusting the DBPF bandwidth. Furthermore， an IIR notch filter was employed to suppress a 1.6 kHz PZT resonance peak， enabling a higher loop gain and thereby strengthening low-frequency noise suppression. Stability analysis reveals that the frequency stability gap between $f_{rep}$ and the 885 nm optical clock in the short term (0.1–1 s) is primarily limited by the instability of the frequency counter itself， whereas the long-term stability (beyond 100 s) is bounded by the 885 nm optical clock. This demonstrates that the proposed DBPF locking method possesses sufficient performance to transfer the optical frequency stability to $f_{rep}$. Ultimately， the Allan deviation of the output 10 MHz signal reaches $6.04 \times 10^{-13}$ at an averaging time of 2048 s. In addition， by reducing the sensitivity of the error signal′s zero-crossing frequency to beat note power and introducing a Dual-Bandwidth DBPF (DBW-DBPF) locking scheme， both the short-term and long-term locking stabilities of the beat note were further improved， reaching a frequency instability of 10.5 Hz at an averaging time of 205 s.