Comparative Study of Voltage Divider Circuits

Study Case Comparative Study of Voltage Divider Circuits and Validation of Simulation Michael Kurniawan (2018123456) University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States kurniaml@mail.uc.edu Abstract This study provides an in-depth description of voltage divider circuits with the aim of improving understanding of the working principles of voltage dividers using simulation tools. The research approach was conducted through simulation using eleven popular types of offline simulators, namely Proteus (Pr), Circuit Wizard (CW – circuit and virtual modes), Electronics Workbench (EWB), Multisim (Mu), PSpice (PS), Yenka (Ye), TINA-TI (TS), QUCS, LTSpice (LTS), Siemens Simcenter (SI), and PhET. Two main scenarios. The simulations were then compared with the theoretical analysis results. All simulators have an intuitive graphical user interface (GUI) and are capable of simulating DC voltage measurements with high accuracy (100%), except for Circuit Wizard, which has an accuracy of 98%. Most simulators allow the use of free resistor values, except for Yenka and PhET, which have limitations. The results of this study provide an in-depth understanding for early-level electrical engineering students and novice engineers, especially regarding the topology, basic theory, and working principles of a simple two-resistor voltage divider. In addition, this study is expected to assist users in selecting the most suitable offline simulator for analyzing DC voltage parameters. Thus, students can apply this concept in various practical electronic designs. Keywords: Voltage Divider Circuit, Offline Simulation Software, Electrical Engineering Education MICHAEL KURNIAWAN 1 Study Case INTRODUCTION A voltage divider circuit is a basic configuration in electrical engineering consisting of two or more resistors connected in series with a direct current (DC) voltage source as the input (Vin) [1][2][3][4]. The midpoint between the resistors is connected to ground to produce an output voltage (Vout). Figure 1. Simple Voltage Divider Circuit [1] The main function of a voltage divider circuit is to reduce the DC voltage value from the Vin source to a smaller voltage, which can then be used in various electronic applications [1][5][3]. In general, batteries act as a stable power source to supply energy to the circuit, and are still considered the best DC voltage source in simple systems [6]. The Vout value can be measured using a digital voltmeter or multimeter by connecting the probes to the output point and ground. This measuring device is used to verify whether the output voltage is in accordance with the design target [7]. For this reason, the concept of voltage dividers is often used as basic material in fundamental electronics courses at engineering universities. For engineers in the field of electronics, voltage divider circuits are known as one of the most fundamental configurations and are widely applied in various systems, including: 1. Electronic sensor and instrumentation systems [8][9][10]. 2. Transistor biasing circuits [11][12][13]. 3. Stable DC voltage sources for electronic modules that require specific voltages (e.g., 1.5V, 3V, 9V, 12V, etc.) [14][15]. 4. Sensor input configurations for analog comparators [16][17][18][19]. 5. Wireless optical communication systems [20][21][22][23]. MICHAEL KURNIAWAN 2 Study Case Although the working principle of this circuit is relatively simple, exploration for educational purposes is still very important, especially for beginner students in the field of electrical engineering. Understanding the concept of Vout calculation, as well as how to determine the combination of R1 and R2 to produce the required output voltage, is a basic skill that must be mastered [2]. Although there are many online articles discussing this concept, most of the information is scattered. Students often have to search for more comprehensive sources covering both theoretical analysis and practical resistor design. Based on a literature search, specific research related to voltage dividers is still rare because it is considered a “mature” topic in the world of electronic engineering. Previously, similar research has been conducted using online simulators, which provided a new perspective on the importance of re-exploring basic circuits for educational purposes [24]. This study then expanded on that research by utilizing offline simulators that are more commonly used by the community of engineers, researchers, and engineering students, such as Proteus, Circuit Wizard, Electronics Workbench, Multisim, Yenka, and TINA. Previously, similar research has been conducted using online simulators, which provided new insights into the importance of re-exploring basic circuits for educational purposes [24]. This study then expanded on that research by utilizing offline simulators that are more commonly used by the community of engineers, researchers, and engineering students, such as Proteus, Circuit Wizard, Electronics Workbench, Multisim, Yenka, TINA-TI, QUCS, LTSpice, Siemens Simcenter, and PhET [24]. The results of this study provide a comprehensive overview of the relationship between the mathematical calculation of Vout and the actual simulation results, as well as comparing the features of each simulator in terms of completeness, GUI display, and accuracy. Through this study, it is hoped that teachers and tutors can recommend the most appropriate DC simulator to support electrical engineering learning objectives [25]. METHODOLOGY This study employs a theoretical approach combined with simulation-based validation using several offline circuit simulators. Two experimental scenarios were designed: MICHAEL KURNIAWAN 3 Study Case 1. Scenario I: Comparison between theoretical calculations of output voltage (Vout) from a voltage divider and simulation results. The resistor configurations were varied as follows: (a)R_1>R_2, (b) R_1=R_2, and (c) R_1< R_2. 2. Scenario II: Determining resistor values R₁ and R₂ through four different calculation methods given known values of input voltage (Vin) and desired output voltage (Vout). The computed resistor values were then inserted into the simulation circuit to compare theoretical and simulated results. A total of eleven offline simulation platforms were used for circuit verification: Proteus (Pr), Circuit Wizard (CW), Electronics Workbench (EWB), Multisim (Mu), PSpice (PS), Yenka (Ye), TINA-TI (TS), QUCS, LTSpice (LTS), Siemens Simcenter (SI), and PhET. These simulators were selected due to their broad availability and educational relevance, although most are commercial software with trial versions limited to one month. Trial versions often restrict certain features such as component libraries, dragand-drop flexibility, and access to virtual instruments. However, since the simulated circuits were simple (two resistors, a DC source, and a voltmeter), these limitations did not affect the experiments. Scenario I Scenario I aimed to determine Vout theoretically and verify it via simulation using all eleven simulators. The primary equation used for the voltage divider is shown in Equation (1) [1][5][3]: 𝑉𝑜𝑢𝑡 = 𝑅2 × 𝑉𝑖𝑛 (1) 𝑅1 + 𝑅2 Each simulator’s behavior and characteristics are summarized below. 1. Proteus (Pr): Developed by Labcenter Electronics (UK), this software supports analog and digital circuit simulation with PCB layout features. It is widely used for both academic and industrial applications [26][27][28]. 2. Circuit Wizard (CW): Produced by New Wave Concepts (UK), CW combines circuit simulation, schematic capture, and PCB layout. It includes two modes: schematic and virtual mode, where components and instruments (oscilloscope, DMM, power supply) appear as real-world devices [29][30][31]. 3. Electronics Workbench (EWB): An offline SPICE-based tool designed for analog and mixed-signal circuits [32][33]. It includes various virtual MICHAEL KURNIAWAN 4 Study Case instruments for measurement and is commonly used in electrical and physics education [34]. 4. Multisim (Mu): Developed by National Instruments, Multisim is an advanced version of EWB with extensive component libraries and educational tools [35][36][37]. It supports both analog and digital simulation and integrates seamlessly with NI ELVIS and LabVIEW systems. 5. PSpice (PS): A SPICE-based simulator primarily used in power electronics [38][39], offering high accuracy (up to 100%) for manual computation validation [40]. 6. Yenka (Ye): An educational software suite by Sumdog (Edinburgh, UK) integrating science, math, computing, and electronics into 3D interactive simulations [41][42]. 7. TINA-TI (TS): A free SPICE-based simulator by Texas Instruments, supporting DC, AC, transient, noise, and frequency response analyses [43][44]. 8. QUCS: An open-source SPICE-based simulator supporting DC, AC, Sparameter, noise, and harmonic balance analyses. The latest version (0.0.19) runs offline across multiple operating systems [45][46]. 9. LTSpice (LTS): A free SPICE variant by Analog Devices, widely used for educational and professional circuit analysis [47][48]. Though powerful, it requires user familiarity with SPICE syntax and analysis parameters. 10. PhET Interactive Simulations: Developed by University of Colorado Boulder, founded by Nobel Laureate Carl Wieman, this platform provides free, interactive science simulations used globally for STEM education [49][50]. 11. SimulIDE (SI): A lightweight, open-source, real-time circuit simulator capable of analog, logic, and microcontroller simulation (Arduino, AVR, PIC) [51]. For Scenario I, input voltages were varied at 3V, 6V, and 12V. Three test groups were created based on resistor ratios: Table 1. Resistor values used for Scenario I. MICHAEL KURNIAWAN 5 Study Case Each configuration was simulated using all eleven platforms. The DC source was connected to the voltage divider circuit, and the voltmeter measured Vout (Figure 2). The results were compared with theoretical calculations to verify accuracy. Figure 2. Flowchart for determining V_out. Scenario II In Scenario II, both V_in and V_out are predetermined, and the task is to calculate R_1 and R_2 using four mathematical methods, labeled as Methods I–IV [2][5]. MICHAEL KURNIAWAN 6 Study Case Figure 3. Flowchart for determining R₁ and R₂. RESULTS AND DISCUSSION Scenario I Table 2 shows the mathematical calculation results in scenario I with Vin variations of 3V, 6V, and 12V. Vout calculations use equation (1). These calculation results are then compared with the output from eleven offline simulators. Table 3 displays the simulation results for test groups 1, 2, and 3 with Vin = 3V. The data in Table 3 is used to create a graph of the simulation results (Figure 4). The Circuit Wizard (CW) simulator provides two interfaces: virtual mode (CWV) and schematic mode (CW). The graphs of the results for scenario I are summarized in Figures 5, 6, and 7. All simulators offer a user interface (GUI) that is beginner-friendly. MICHAEL KURNIAWAN 7 Study Case Table 2. Vout Calculation Results from the Voltage Divider Circuit Table 3. Vout measurement results from the voltage divider circuit simulation for Test Groups i, ii, and iii (Vin = 3V) Figure 4. Display of the voltage divider circuit in different simulations for Vin = 3V in test group i MICHAEL KURNIAWAN 8 Study Case Figure 5. Test I data graph (R1 = 330 Ω, R2 = 390 Ω) with Vin variations Figure 6. Test II data graph (R1 = 390 Ω, R2 = 100 Ω) with Vin variations Figure 7. Test III data graph (R1 = 120 Ω, R2 = 120 Ω) with Vin variations The experiment shows that all simulators are able to calculate Vout with nearly 100% accuracy, in accordance with theoretical calculations. Some simulators produce values with long decimals, for example Pr = 0.61V, EWB = 612 mV, PS = 0.61224V, Ye = 612 mV, TS = 612.24 mV, QUCS = 1.62V, LTS = 612 mV, SI = 1.625V, and PhET = 1.62V (Figure 6). After rounding, the values of all simulators became approximately 0.61V. Figures 5, 6, and 7 represent the comparison between theoretical calculations and simulation results for scenario I in each test group. Therefore, simulations for Vin = 6V and 12V were not performed because the results would be the same, differing only in the number of digits after the decimal point. Scenario II Table 4 shows the values of R1 and R2 obtained from four calculation methods for Vout = 1.7V. Figure 8 visualizes the graph from Table 4. In method IV, the voltage value is multiplied by 1000 so that the resistors obtained are easier to find on the market. For example, R1 = 1.3 Ω is more practical when MICHAEL KURNIAWAN 9 Study Case multiplied by 1000 to become 1300 Ω (1.3 kΩ), which can be obtained from a series resistor combination such as 1.2 kΩ + 100 Ω. The Vin value is then changed to 12V, so that R1 and R2 also change, with the calculation results presented in Figure 9. Next, Vout is lowered to 0.7V with variations of Vin = 3V and 12V, the results are shown in Figure 10 and Figure 11. Experiments show that different combinations of R1 and R2 from the four methods produce different Vout variations. Method IV is the most effective because it produces resistors that are easy to find on the market compared to the other three methods, which produce difficult decimal numbers. Table 4. Theoretical calculation results for R1 and R2 values with Vout = 1.7V and Vin = 3V Figure 8. Visualization of R1 and R2 values for Vout = 1.7V and Vin = 3V Figure 9. R1 and R2 values for Vout = 1.7V and Vin = 12V MICHAEL KURNIAWAN 10 Study Case Figure 10. Values of R1 and R2 for Vout = 0.7V and Vin = 3V Figure 11. Values of R1 and R2 for Vout = 0.7V and Vin = 12V In the next experiment, R1 and R2 were incorporated into a voltage divider circuit to verify whether Vout matched the initial value. Figure 12 shows the Vout measurement results with Vin = 3V, following the calculation methods in Figure 8: • Method I: R1 = 764.7 Ω, R2 = 1000 Ω • Method II: R1 = 1000 Ω, R2 = 1307 Ω • Method III: R1 = 433.3 Ω, R2 = 566.7 Ω • Method IV: R1 = 1700 Ω, R2 = 1300 Ω MICHAEL KURNIAWAN 11 Study Case Figure 13 shows the Vout measurement results with Vin = 3V based on the R1 and R2 values from Figure 10: • Method I: R1 = 3285.7 Ω, R2 = 1000 Ω • Method II: R1 = 1000 Ω, R2 = 304.3 Ω • Method III: R1 = 766.7 Ω, R2 = 233.3 Ω • Method IV: R1 = 2300 Ω, R2 = 700 Ω The zero on the graph indicates an error in the simulation. Figure 12. Verification of Vout values for R1 and R2 from Methods I–IV in various software (Vin = 3V) Figure 13. Verification of Vout values for R1 and R2 from Methods I–IV in various software (Vin = 3V) The results show that Vout is as expected (1.7V and 0.7V) for all methods. The voltage divider circuit is capable of reducing Vin to one or more smaller Vout points (Boylestad, 2016). Almost all simulators can accept random resistor values, but some, such as Ye, show errors if the resistor exceeds a certain limit. In general, the eleven simulators show results that are very close to theoretical calculations, supporting the findings of Utomo et al. [1]. Each software has different input precision: some accept direct input, while others require unit settings first. This causes slight differences in output values. All software is beginner-friendly because it includes standard component symbols, for example, Mu with more than 1,700 modifiable elements (Guan & Zhou, 2017), and EWB with a Windows-like GUI. Although most simulators are accurate to 100%, CWV has an accuracy of approximately 98% for DC analysis, with a difference of 0.01–0.12V depending on the combination of R1, R2, and Vin. The LTC simulator displays Vout in a DC Transient graph that needs to be enlarged on the y-axis to see the values with high precision. QUCS automatically increases the resistor units if the value exceeds 3 digits. PhET limits resistor values between 0–1000 Ω, with 10x increments for values above 120 Ω. MICHAEL KURNIAWAN 12 Study Case All simulators are effective for education (Wahyuni, 2020), helping with pre-lab learning, reducing the risk of equipment damage, supporting remote practice, and reinforcing conceptual understanding. Further research could compare theoretical results, offline and online simulations, and real experiments. Actual Vout usually differs because resistors are not ideal, especially the difference between metal film and carbon film [1]. CONCLUSION The voltage divider circuit has been comprehensively analyzed based on two main scenarios: (1) measuring the output voltage (Vout) and (2) determining the combination of resistor values (R1 and R2) through a theoretical approach and simulation. Four calculation methods were tested, and all of them were able to produce the target Vout value. However, only one method provided the most realistic combination of R1–R2 values, due to its compatibility with the standard resistor values available in the US electronics market. Eleven offline simulators — Proteus (Pr), Circuit Wizard (CW), Electronics Workbench (EWB), Multisim (Mu), PSpice (PS), Yenka (Ye), TINA-TI (TS), QUCS, LTSpice (LTS), SimulIDE (SI), and PhET — were used to validate the voltage divider theory. The results from both scenarios show that all simulators are capable of verifying the basic voltage divider equation with an accuracy of nearly 100%, where the simulation results are almost identical to the analytical calculations. Each simulator offers an intuitive graphical user interface (GUI) and easy-tooperate virtual measurement instruments. Based on the results of DC analysis parameter testing, particularly for electrical voltage measurements, all simulators can be recommended as learning and basic research tools. Although there are minor differences in the computational results between software programs, the deviations are minimal and do not affect the main conclusions. From an educational perspective, the results of this study can be used as a practical reference for beginner electrical and electronic engineering students in understanding the working principles of voltage dividers, while also introducing various offline simulators that can be used for virtual experiments without the need for physical laboratory equipment. For further research, it is recommended to use more open-source or license-free simulation software to expand learning access. MICHAEL KURNIAWAN 13 Study Case REFERENCE MICHAEL KURNIAWAN 14