Calculate Reaction Time Using Quartus on DE2-115

Reaction Time Calculator for DE2-115 (Quartus)

Use this calculator to determine human reaction time based on counter values from your DE2-115 FPGA project implemented with Quartus. Account for clock frequency, counter bit width, and system latency for accurate results.

Formula Used

The calculator uses the following formulas to determine reaction time:

• Clock Period (ns) = 1000 / FPGA Clock Frequency (MHz)
• Raw Reaction Time (ms) = (Measured Counter Ticks * Clock Period (ns)) / 1,000,000
• Adjusted Reaction Time (ms) = Raw Reaction Time (ms) - System Latency (ms)
• Maximum Measurable Time (ms) = ( (2^Counter Bit Width) * Clock Period (ns) ) / 1,000,000
• Perceived Reaction Time (ms) = Adjusted Reaction Time (ms) + Human Perception Adjustment (ms)

These calculations convert the raw counter ticks from your DE2-115 FPGA into a human-readable time, with adjustments for system-level delays and optional human perception factors.

Detailed Reaction Time Analysis

Measured Counter Ticks	Raw Reaction Time (ms)	Adjusted Reaction Time (ms)

This table provides a breakdown of reaction times for various counter tick values, demonstrating the impact of your settings.

What is Reaction Time Using Quartus on DE2-115?

Calculating reaction time using Quartus on a DE2-115 FPGA involves designing a digital circuit to precisely measure the elapsed time between a visual or auditory stimulus and a user’s physical response, typically a button press. The DE2-115, a popular Altera (now Intel) FPGA development board, provides the necessary hardware (LEDs, buttons, high-speed clock) to implement such experiments. Quartus Prime software is used to design, synthesize, and program the digital logic onto the FPGA.

This method offers extremely high precision compared to software-based measurements on general-purpose computers, as the timing is controlled by the FPGA’s dedicated hardware clock, eliminating operating system latencies and software overhead. It’s a fundamental experiment in digital logic design, embedded systems, and human-computer interaction studies.

Who Should Use This Method?

• Electrical Engineering Students: For hands-on experience with FPGA programming, digital counter design, and real-time measurement.
• Computer Science Students: To understand hardware-software interaction and the precision benefits of dedicated hardware.
• Researchers in Human Factors: To conduct precise psychological experiments on human reaction times without software timing inaccuracies.
• Hobbyists and Educators: To explore FPGA capabilities and create interactive projects.

Common Misconceptions

• “Software is accurate enough”: While software can measure time, operating system scheduling, display refresh rates, and input polling introduce significant variability and latency, making it less precise for sub-millisecond reaction time measurements.
• “It’s just a simple counter”: While the core is a counter, designing a robust system involves debouncing inputs, synchronizing asynchronous events, and correctly converting clock cycles to real-world time, which requires careful digital design.
• “All delays are human”: System latency (LED turn-on time, button debounce, display refresh) can significantly contribute to the measured time and must be accounted for to isolate the true human reaction time.

Reaction Time Using Quartus on DE2-115 Formula and Mathematical Explanation

The core principle behind calculating reaction time using Quartus on a DE2-115 is to count the number of clock cycles that occur between a stimulus and a response. This raw count is then converted into a time duration using the FPGA’s known clock frequency.

Step-by-Step Derivation

1. Determine Clock Period: The FPGA operates at a specific clock frequency (e.g., 50 MHz). The period of this clock (the time for one cycle) is the inverse of its frequency.
   Clock Period (ns) = 1000 / FPGA Clock Frequency (MHz)
   (Since 1 MHz = 1000 ns/µs, and 1 µs = 1000 ns, 1 MHz = 10^6 Hz, so Period = 1 / (Freq * 10^6) seconds. To get ns, multiply by 10^9. So, (1 / Freq) * 10^3 ns. If Freq is in MHz, then 1/Freq is in µs, so 1000/Freq is in ns.)
2. Calculate Raw Reaction Time: The FPGA counter records a certain number of clock ticks. Multiplying this count by the clock period gives the total time in nanoseconds. To convert to milliseconds, divide by 1,000,000.
   Raw Reaction Time (ms) = (Measured Counter Ticks * Clock Period (ns)) / 1,000,000
3. Adjust for System Latency: Real-world systems have inherent delays. The LED might take a few milliseconds to fully illuminate, or the button debounce circuit might introduce a small delay. Subtracting this known system latency provides a more accurate human reaction time.
   Adjusted Reaction Time (ms) = Raw Reaction Time (ms) - System Latency (ms)
4. Calculate Maximum Measurable Time: The counter’s bit width determines its maximum count value (2^N – 1 for an N-bit counter). This limits the longest reaction time that can be measured before the counter overflows.
   Maximum Measurable Time (ms) = ( (2^Counter Bit Width) * Clock Period (ns) ) / 1,000,000
5. Perceived Reaction Time (Optional): For psychological studies, one might add an estimated human perception delay (e.g., time for visual processing) to the adjusted time to get a “total perceived” time.
   Perceived Reaction Time (ms) = Adjusted Reaction Time (ms) + Human Perception Adjustment (ms)

Variable Explanations

Variable	Meaning	Unit	Typical Range
FPGA Clock Frequency	The main clock speed of the DE2-115 board.	MHz	50 – 100
Counter Bit Width	The number of bits used in the digital counter.	Bits	16 – 32
Measured Counter Ticks	The raw count value from the FPGA counter.	Ticks	1,000,000 – 50,000,000
System Latency	Combined delays from stimulus display and response registration.	ms	5 – 20
Human Perception Adjustment	Estimated inherent human processing delay.	ms	30 – 70
Clock Period	Time duration of one clock cycle.	ns	10 – 20
Raw Reaction Time	Calculated time directly from counter ticks.	ms	100 – 1000
Adjusted Reaction Time	Raw time minus system latency.	ms	50 – 900
Maximum Measurable Time	Longest time measurable before counter overflow.	ms	Hundreds to thousands

Practical Examples: Real-World Use Cases for Reaction Time Using Quartus on DE2-115

Example 1: Standard Reaction Time Test

A student is conducting a basic reaction time experiment using a DE2-115 board. An LED turns on, and the user presses a button. The FPGA measures the time.

• FPGA Clock Frequency: 50 MHz
• Counter Bit Width: 24 bits
• Measured Counter Ticks: 12,500,000 ticks
• System Latency: 8 ms (estimated for LED turn-on and button debounce)
• Human Perception Adjustment: 50 ms

Calculation:

• Clock Period = 1000 / 50 = 20 ns
• Raw Reaction Time = (12,500,000 * 20) / 1,000,000 = 250 ms
• Adjusted Reaction Time = 250 ms – 8 ms = 242 ms
• Maximum Measurable Time = ((2^24) * 20) / 1,000,000 = (16,777,216 * 20) / 1,000,000 = 335.54 ms
• Perceived Reaction Time = 242 ms + 50 ms = 292 ms

Interpretation: The user’s actual reaction time, after accounting for system delays, is 242 ms. The system can measure up to 335.54 ms before the counter overflows, which is sufficient for typical human reaction times.

Example 2: High-Precision Measurement with Higher Clock and Lower Latency

A researcher wants to measure reaction time with higher precision, using a PLL to generate a faster clock and a system with minimal latency.

• FPGA Clock Frequency: 100 MHz (using a PLL)
• Counter Bit Width: 30 bits
• Measured Counter Ticks: 28,000,000 ticks
• System Latency: 3 ms (optimized display and input)
• Human Perception Adjustment: 45 ms

Calculation:

• Clock Period = 1000 / 100 = 10 ns
• Raw Reaction Time = (28,000,000 * 10) / 1,000,000 = 280 ms
• Adjusted Reaction Time = 280 ms – 3 ms = 277 ms
• Maximum Measurable Time = ((2^30) * 10) / 1,000,000 = (1,073,741,824 * 10) / 1,000,000 = 10737.42 ms (approx 10.7 seconds)
• Perceived Reaction Time = 277 ms + 45 ms = 322 ms

Interpretation: With a faster clock and lower system latency, the adjusted reaction time is 277 ms. The 30-bit counter provides a very long maximum measurable time, ensuring no overflow for even very slow responses.

How to Use This Reaction Time Using Quartus on DE2-115 Calculator

This calculator is designed to simplify the post-processing of raw data obtained from your DE2-115 FPGA reaction time experiment. Follow these steps to get accurate results:

Step-by-Step Instructions

1. Input FPGA Clock Frequency (MHz): Enter the exact clock frequency your DE2-115 is running at. For most standard projects, this is 50 MHz. If you’re using a Phase-Locked Loop (PLL) to generate a different clock, enter that frequency.
2. Input Counter Bit Width: Specify the number of bits you’ve used for your reaction time counter in your Quartus design. Common values are 16, 24, or 32 bits. This affects the maximum measurable time.
3. Input Measured Counter Ticks: This is the crucial value. After running your reaction time experiment on the DE2-115, your FPGA design will output a raw count value (e.g., to 7-segment displays or a UART). Enter that exact number here.
4. Input System Latency (ms): Estimate or measure any inherent delays in your system. This includes the time it takes for an LED to fully illuminate, the debounce time for a button press, or any display refresh delays. A typical value might be 5-15 ms.
5. Input Human Perception Adjustment (ms): This is an optional, theoretical value. If you want to account for the inherent delay in human visual processing and motor response (e.g., 30-70 ms), enter it here. This is often used in psychological studies.
6. View Results: As you adjust the inputs, the calculator will automatically update the “Adjusted Reaction Time” as the primary result, along with intermediate values and a dynamic chart and table.
7. Reset or Copy: Use the “Reset” button to restore default values. Use “Copy Results” to quickly grab all calculated values and assumptions for your reports or documentation.

How to Read Results

• Adjusted Reaction Time (Primary Result): This is the most practical measure of human reaction time, as it subtracts known system delays from the raw measurement. It represents the time taken by the human subject to perceive and respond.
• Raw Reaction Time: The direct time calculated from the FPGA counter ticks. Useful for verifying the basic hardware measurement.
• Clock Period: The duration of a single clock cycle. A smaller clock period means higher precision in time measurement.
• Maximum Measurable Time: Indicates the longest reaction time your current FPGA counter configuration can measure before it overflows. Ensure this is greater than expected human reaction times.
• Perceived Reaction Time (Adjusted + Human): This value includes an additional theoretical human perception delay, useful for specific psychological analyses.

Decision-Making Guidance

Understanding these values helps in:

• Validating Hardware Design: If your raw reaction time is unexpectedly high or low, it might indicate issues with your counter logic or clocking.
• Optimizing System Latency: By understanding the impact of system latency, you can design better stimulus and response mechanisms to minimize these delays.
• Interpreting Human Performance: The adjusted reaction time provides a clearer picture of human cognitive and motor speed, free from hardware artifacts.
• Choosing Counter Bit Width: The maximum measurable time helps you select an appropriate counter size to avoid overflow for your specific experiment.

Key Factors That Affect Reaction Time Using Quartus on DE2-115 Results

Several critical factors influence the accuracy and interpretation of reaction time measurements performed using a DE2-115 FPGA and Quartus. Understanding these helps in designing robust experiments and drawing valid conclusions.

• FPGA Clock Frequency:

  The clock frequency directly determines the resolution of your time measurement. A 50 MHz clock provides a 20 ns resolution (1/50MHz). A 100 MHz clock provides 10 ns resolution. Higher frequencies allow for more precise measurements, but also require faster logic and can consume more power. Ensure your counter is synchronized to this clock.

• Counter Bit Width:

  The number of bits in your counter dictates the maximum duration it can measure before overflowing. For example, a 24-bit counter at 50 MHz can measure up to ~335 ms. If human reaction times exceed this, the counter will wrap around, leading to incorrect results. Choose a bit width that comfortably exceeds the expected maximum reaction time.

• System Latency (Stimulus & Response):

  This is a crucial factor often overlooked. It includes the time for an LED to fully illuminate, the propagation delay through display drivers, the debounce time for mechanical buttons, and the time for the button signal to propagate through the FPGA logic. These delays are inherent to the hardware and add to the measured time, so they must be subtracted for an accurate human reaction time. Techniques for measuring system latency are vital.

• Input Debouncing:

  Mechanical buttons “bounce” when pressed, generating multiple rapid transitions. A debouncing circuit (implemented in Quartus) is essential to ensure only a single, stable press is registered. Improper debouncing can lead to inaccurate start/stop signals for the counter, affecting the reaction time calculation.

• Synchronization of Asynchronous Inputs:

  Button presses are asynchronous to the FPGA’s clock. Directly using an asynchronous signal to stop a counter can lead to metastability and incorrect readings. Proper synchronization (e.g., using a two-flip-flop synchronizer) is necessary to safely bring the button signal into the clock domain of the counter. This introduces a small, predictable delay.

• Display Refresh Rate (if using external display):

  If your stimulus is displayed on an external monitor connected to the DE2-115, the monitor’s refresh rate introduces latency. A 60 Hz monitor has a frame latency of up to 16.67 ms. This must be considered as part of the system latency, especially for visual stimuli. FPGA display interface design can minimize this.

• Human Perception and Motor Delay:

  While not a hardware factor, the inherent biological delays in human perception (e.g., visual processing) and motor response (e.g., nerve conduction, muscle activation) contribute to the total measured time. These are typically around 30-70 ms and are often considered when analyzing the “true” cognitive reaction time.

• Quartus Design Optimization:

  The efficiency of your VHDL/Verilog code and Quartus’s synthesis and place-and-route results can impact signal propagation delays within the FPGA. While usually negligible for reaction time experiments, complex designs might introduce unexpected delays.

Frequently Asked Questions (FAQ) about Reaction Time Using Quartus on DE2-115

Q: Why use an FPGA like the DE2-115 for reaction time measurement instead of a computer?

A: FPGAs offer superior timing precision because they operate on a dedicated hardware clock, free from operating system overhead, software scheduling delays, and variable input/output latencies common in general-purpose computers. This allows for sub-millisecond accuracy, crucial for scientific studies of human reaction time.

Q: What is “system latency” and why is it important for reaction time calculation?

A: System latency refers to any delays introduced by the hardware itself, such as the time it takes for an LED to fully illuminate, the debounce time of a mechanical button, or display refresh delays. It’s crucial because these delays are part of the total measured time but are not part of the human’s reaction. Subtracting system latency isolates the true human response time.

Q: How do I determine the “Measured Counter Ticks” from my DE2-115?

A: In your Quartus design, you’ll typically have a counter that starts on stimulus and stops on response. The final value of this counter is the “Measured Counter Ticks.” You can display this value on the DE2-115’s 7-segment displays, send it via UART to a computer, or store it in memory for retrieval.

Q: What happens if my “Measured Counter Ticks” exceed the “Maximum Measurable Time”?

A: If the measured ticks exceed the maximum count capacity of your counter (determined by its bit width), the counter will “overflow” or “wrap around.” This means it will reset to zero and continue counting, leading to an incorrect, much lower measured time. You must ensure your counter bit width is large enough for the longest expected reaction times.

Q: Can I use a different clock frequency than 50 MHz on the DE2-115?

A: Yes, the DE2-115 has a 50 MHz oscillator, but you can use a Phase-Locked Loop (PLL) IP core in Quartus to generate higher or lower clock frequencies. Just ensure your entire design is stable at the new frequency and update the “FPGA Clock Frequency” in the calculator accordingly.

Q: How can I minimize system latency in my DE2-115 reaction time project?

A: To minimize system latency, use fast-response LEDs, implement efficient button debouncing, and ensure your display mechanism (if any) has low latency. For visual stimuli, consider direct LED control rather than complex display interfaces. Careful digital logic design best practices are key.

Q: Is the “Human Perception Adjustment” a fixed value?

A: No, the “Human Perception Adjustment” is an estimated, theoretical value. It varies significantly between individuals and depends on the type of stimulus and response. It’s included for analytical purposes, especially in psychological research, but it’s not a direct measurement from the FPGA. It’s an average value often derived from other studies.

Q: Where can I find example Quartus projects for reaction time on DE2-115?

A: Many university courses and online FPGA communities provide example projects. Searching for “DE2-115 reaction time Quartus VHDL” or “DE2-115 human reaction time Verilog” will yield numerous resources and tutorials. These often include the necessary DE2-115 tutorials for setup.

Related Tools and Internal Resources

• FPGA Clock Frequency Calculator: Determine optimal clock settings for your FPGA projects. This tool helps you understand the relationship between clock frequency and timing constraints.
• Digital Logic Design Basics: A comprehensive guide to fundamental concepts in digital electronics, essential for anyone working with FPGAs and Quartus.
• DE2-115 Tutorials: Step-by-step guides and example projects specifically for the Altera DE2-115 development board, covering various peripherals and applications.
• Human Factors Engineering: Explore the principles of designing systems that optimize human well-being and overall system performance, including aspects of human reaction time.
• Embedded System Design: Learn about the process of designing and implementing embedded systems, where real-time performance and precise timing, like in reaction time measurements, are critical.
• System Latency Measurement Techniques: Discover methods and tools to accurately quantify delays in your hardware and software systems, crucial for precise reaction time experiments.