Calculate Reaction Time using Quartus on DE2-115

Accurate measurement and analysis for digital design and testing.

Reaction Time Calculator for DE2-115

This calculator helps determine your reaction time based on measurements taken using a Quartus-developed system on a DE2-115 FPGA board. It takes into account the system clock frequency and the number of clock cycles recorded between stimulus presentation and user response.

What is Reaction Time Measurement using Quartus on DE2-115?

Reaction time measurement using Quartus on a DE2-115 FPGA board is a precise method to quantify the duration between a stimulus being presented and an individual’s response. This technique leverages the high-speed, deterministic nature of Field-Programmable Gate Arrays (FPGAs) to achieve measurements with millisecond or even microsecond accuracy, far exceeding typical software-based reaction time tests. Quartus, Altera’s (now Intel FPGA) integrated development environment, is used to design, synthesize, and program the FPGA logic that handles stimulus presentation and response capture.

Who should use this method? This advanced technique is valuable for researchers in psychology, neuroscience, and human-computer interaction studying cognitive processes, motor control, and user interface responsiveness. It’s also essential for engineers developing high-performance embedded systems, control systems, or testing hardware interfaces where precise timing is critical. For educators, it serves as an excellent practical project to demonstrate digital logic design, timing analysis, and FPGA capabilities.

Common misconceptions: A common misunderstanding is that reaction time is a fixed personal attribute. In reality, it varies significantly based on factors like attention, fatigue, stimulus modality, and complexity. Another misconception is that software-based timers are sufficient for high-accuracy measurements; however, operating system scheduling and hardware variations introduce significant jitter, making them unsuitable for research-grade precision. Using an FPGA like the DE2-115 with Quartus provides a hardware-level timing solution, bypassing these software limitations.

Reaction Time Calculation Formula and Mathematical Explanation

The core principle behind calculating reaction time on the DE2-115 using Quartus involves measuring the elapsed time in terms of clock cycles and then converting this to a standard time unit like milliseconds. The DE2-115 board typically operates with a system clock frequency, often sourced from an oscillator on the board. Quartus is used to design a Verilog or VHDL module that:

1. Detects the onset of a stimulus (e.g., an LED turning on, a button press event).
2. Starts a counter driven by the FPGA’s system clock.
3. Detects the user’s response (e.g., a button press).
4. Stops the counter upon detecting the response.
5. Outputs the final counter value (representing clock cycles) and the system clock frequency.

The calculation then proceeds as follows:

1. Convert Clock Frequency to Hz:

The system clock frequency is usually given in Megahertz (MHz). To work with standard time units, we convert it to Hertz (Hz):

Frequency (Hz) = Frequency (MHz) × 1,000,000

2. Calculate Time per Clock Cycle:

The period of one clock cycle (the time it takes for one oscillation) is the inverse of the frequency:

Time per Cycle (seconds) = 1 / Frequency (Hz)

To get this in nanoseconds (ns), we multiply by 1 billion (10⁹):

Time per Cycle (ns) = (1 / (Frequency (MHz) × 1,000,000)) × 1,000,000,000

Time per Cycle (ns) = 1,000,000,000 / (Frequency (MHz) × 1,000,000)

Time per Cycle (ns) = 1000 / Frequency (MHz)

3. Calculate Total Elapsed Time:

The total elapsed time is the number of clock cycles recorded multiplied by the time per cycle:

Total Time (seconds) = Recorded Clock Cycles × Time per Cycle (seconds)

Substituting the expression for Time per Cycle (seconds):

Total Time (seconds) = Recorded Clock Cycles × (1 / Frequency (Hz))

Total Time (seconds) = Recorded Clock Cycles / (Frequency (MHz) × 1,000,000)

4. Convert Total Elapsed Time to Milliseconds:

Since reaction times are commonly expressed in milliseconds (ms), we convert the total time from seconds to milliseconds by multiplying by 1000:

Reaction Time (ms) = Total Time (seconds) × 1000

Reaction Time (ms) = (Recorded Clock Cycles / (Frequency (MHz) × 1,000,000)) × 1000

Simplifying this gives the formula used in the calculator:

Reaction Time (ms) = (Recorded Clock Cycles / Frequency (MHz)) * 1

Wait, the simplification above is incorrect. Let’s re-derive carefully:

Reaction Time (ms) = (Recorded Clock Cycles / Frequency (Hz)) * 1000

Reaction Time (ms) = (Recorded Clock Cycles / (Frequency (MHz) * 10^6)) * 10^3

Reaction Time (ms) = Recorded Clock Cycles * (10^3 / 10^6) / Frequency (MHz)

Reaction Time (ms) = Recorded Clock Cycles * 10^-3 / Frequency (MHz)

This still doesn’t match the simpler form. Let’s rethink the units. If Clock Frequency is in MHz (10^6 cycles/sec), then Frequency/10^6 is Cycles/sec. The reciprocal is Seconds/Cycle. If we multiply cycles by Seconds/Cycle, we get Seconds. Then multiply by 1000 for ms.

Time per Cycle (seconds) = 1 / (Clock Frequency (MHz) * 10^6)

Total Time (seconds) = Recorded Clock Cycles * Time per Cycle (seconds)

Total Time (seconds) = Recorded Clock Cycles / (Clock Frequency (MHz) * 10^6)

Reaction Time (ms) = Total Time (seconds) * 1000

Reaction Time (ms) = (Recorded Clock Cycles * 1000) / (Clock Frequency (MHz) * 10^6)

Reaction Time (ms) = Recorded Clock Cycles / (Clock Frequency (MHz) * 1000)

Ah, the calculator’s displayed formula was missing a factor of 1000 in the denominator. Let’s correct the explanation and calculator logic.

Corrected Formula: Reaction Time (ms) = (Recorded Clock Cycles * 1000) / (System Clock Frequency (MHz) * 10^6)

Simplified Corrected Formula: Reaction Time (ms) = Recorded Clock Cycles / (System Clock Frequency (MHz) * 1000)

Let’s re-check the example calculation: 50 MHz, 150,000 cycles. Time per cycle = 1 / (50 * 10^6) sec = 20 ns. Total time = 150,000 cycles * 20 ns/cycle = 3,000,000 ns = 3 ms. Using the simplified formula: 150,000 / (50 * 1000) = 150,000 / 50,000 = 3 ms. This seems correct. The calculator’s *displayed* formula needs updating.

Variables Table

Variable	Meaning	Unit	Typical Range (DE2-115 Context)
Clock Frequency	The frequency of the master clock oscillator provided to the FPGA.	MHz (Megahertz)	50 MHz (common for DE2-115 onboard oscillator)
Recorded Clock Cycles	The count of clock ticks between the stimulus event and the response event.	Integer (cycles)	0 to system clock limit (e.g., millions)
Reaction Time	The calculated duration from stimulus onset to response.	ms (milliseconds)	10 ms to 500 ms (typical human range)
Time per Clock Cycle	The duration of a single clock cycle.	ns (nanoseconds)	20 ns (for 50 MHz clock)
Frequency in Hz	System clock frequency expressed in cycles per second.	Hz (Hertz)	50,000,000 Hz
Cycles per ms	Number of clock cycles occurring within one millisecond.	Cycles/ms	50,000 cycles/ms (for 50 MHz clock)

Practical Examples

Example 1: Simple Stimulus-Response Test

A researcher is using the DE2-115 to measure reaction time to a visual stimulus (an LED lighting up). The FPGA system is programmed using Quartus. The system clock is the standard 50 MHz oscillator. The stimulus is presented, and the counter starts. The user presses a button as soon as they see the LED light up. The counter stops, recording 250,000 clock cycles.

Inputs:

• System Clock Frequency: 50 MHz
• Recorded Clock Cycles: 250,000

Calculation using the tool:

• Time per Clock Cycle = 1000 / 50 = 20 ns
• Frequency in Hz = 50 * 1,000,000 = 50,000,000 Hz
• Cycles per ms = 50 * 1000 = 50,000 cycles/ms
• Reaction Time = 250,000 / (50 * 1000) = 250,000 / 50,000 = 5.0 ms

Interpretation: The user’s reaction time in this trial was 5.0 milliseconds. This is an exceptionally fast reaction time, likely indicating a well-trained participant or potential issues with stimulus presentation/response capture accuracy. It highlights the precision achievable with an FPGA-based system.

Example 2: Auditory Stimulus Latency Test

An engineer is testing the latency of an audio alert system controlled by the DE2-115. An audio chip receives a trigger signal from the FPGA. The FPGA system uses a 50 MHz clock. The trigger signal is sent at time t=0. The system measures the time until a specific audio output threshold is detected by another input pin on the FPGA. The counter records 1,250,000 clock cycles.

Inputs:

• System Clock Frequency: 50 MHz
• Recorded Clock Cycles: 1,250,000

Calculation using the tool:

• Time per Clock Cycle = 1000 / 50 = 20 ns
• Frequency in Hz = 50,000,000 Hz
• Cycles per ms = 50,000 cycles/ms
• Reaction Time = 1,250,000 / (50 * 1000) = 1,250,000 / 50,000 = 25.0 ms

Interpretation: The total latency from triggering the audio system to achieving the output threshold is 25.0 milliseconds. This value is crucial for assessing the performance of the audio system and ensuring it meets the required specifications for real-time applications.

How to Use This Reaction Time Calculator

Using the DE2-115 Reaction Time Calculator is straightforward. Follow these steps to get accurate results:

1. Input System Clock Frequency: Enter the frequency of the system clock configured for your DE2-115 board in Megahertz (MHz). The default is 50 MHz, which is common for the onboard oscillator, but verify this setting in your Quartus project.
2. Input Recorded Clock Cycles: Enter the total number of clock cycles that were counted by your FPGA design between the presentation of the stimulus and the detection of the user’s response. Ensure this value is a non-negative integer.
3. Validate Inputs: As you type, the calculator performs inline validation. Error messages will appear below the input fields if you enter invalid data (e.g., text, negative numbers, decimals where integers are expected for cycles).
4. Calculate: Click the “Calculate Reaction Time” button. The results will update dynamically.
5. Read Results:
   • Reaction Time: This is the primary result, displayed prominently in milliseconds (ms).
   • Time per Clock Cycle: Shows how long each individual clock cycle lasts in nanoseconds (ns).
   • Frequency in Hz: The system clock frequency converted to Hertz.
   • Cycles per Millisecond: Indicates how many clock cycles occur within a 1ms timeframe, useful for quick estimations.
6. Interpret: Use the calculated reaction time to analyze participant performance, system latency, or other time-critical processes. Remember that human reaction times typically fall within a range (e.g., 100-300 ms for simple visual stimuli), while hardware latencies can be much shorter.
7. Reset: Click the “Reset” button to clear all input fields and results, returning them to their default values.
8. Copy Results: Click the “Copy Results” button to copy the calculated values (Reaction Time, Time per Cycle, Frequency in Hz, Cycles per ms) and key assumptions (input values) to your clipboard for easy pasting into reports or other documents.

Decision-Making Guidance: Consistently fast or slow reaction times compared to expected norms might indicate issues with the experimental setup, the participant’s condition, or the performance of the system being tested. Use these precise measurements to make informed decisions about system optimization or experimental validity.

Key Factors That Affect Reaction Time Results

While the calculation itself is straightforward, several factors influence the *measured* reaction time when using an FPGA system, and also the *interpretation* of the results:

1. System Clock Stability and Accuracy: The accuracy of the reaction time measurement is directly tied to the stability and known frequency of the system clock. If the oscillator is not accurate or drifts, the calculated time will be skewed. Using a calibrated crystal oscillator is crucial.
2. Stimulus Modality and Intensity: Different senses (vision, hearing, touch) have different biological reaction times. A brighter light or louder sound might elicit faster responses. The *perceived* onset time by the user matters.
3. Stimulus Complexity and Predictability: Simple, predictable stimuli (e.g., a single red light appearing) yield faster reaction times than complex stimuli requiring decisions (e.g., identify the color of a flashing shape). Choice reaction time tests are significantly slower.
4. User’s Physiological and Psychological State: Factors like alertness, fatigue, caffeine intake, practice, age, and motivation dramatically affect an individual’s reaction time. Measurements should ideally control for these variables or account for them in analysis.
5. Response Mechanism Latency: The time it takes for the physical response to be registered is critical. If using a button, the button’s own mechanical delay (debounce time in software/hardware) adds to the measured time. For FPGA implementations, ensure the response capture logic is optimized.
6. FPGA Design and Implementation: The design of the Quartus project itself introduces latency. The propagation delay through combinatorial logic, the setup and hold time requirements of flip-flops, and the clock-to-output delay of the FPGA fabric all contribute. Ensure your design accurately captures the *exact* moment of stimulus onset and response. Debouncing logic for button inputs is essential to avoid multiple false triggers.
7. Quantization Error: Since time is measured in discrete clock cycles, there’s an inherent quantization error. The smallest time resolution is one clock cycle. If a response occurs very close to the end of a cycle, the counter might increment by one extra cycle, slightly overestimating the reaction time. This is usually negligible with fast clocks but worth noting.
8. Setup and Environmental Factors: Ambient noise, lighting conditions, and distractions can influence focus and reaction speed. Ensuring a controlled environment minimizes external variability.

Frequently Asked Questions (FAQ)

What is the standard clock frequency for the DE2-115 board?

The DE2-115 board typically comes with a 50 MHz crystal oscillator, which is the most common system clock frequency used. However, it’s essential to verify this setting within your Quartus project configuration.

Can I measure reaction times in microseconds using this method?

Yes, with a faster clock frequency. If you use a 500 MHz clock, for instance, each cycle is 2 ns. For microsecond resolution, you’d need a clock frequency of at least 1 MHz (1,000,000 Hz), giving a time resolution of 1 microsecond per cycle. The DE2-115 supports clock speeds achievable with its FPGA chip, though higher frequencies might require careful board layout and design considerations.

What is considered a “good” reaction time?

For simple visual stimuli, average human reaction times typically range from 180 to 250 milliseconds. For simple auditory stimuli, it’s slightly faster, around 140 to 180 milliseconds. Extremely fast times (like those calculated in Example 1) might indicate an issue with the measurement setup or learning effect rather than genuine biological speed.

How do I handle button debouncing in my Quartus design?

Button presses generate noisy signals. In your Verilog or VHDL code within Quartus, you need to implement debouncing logic, typically using a counter or a shift register synchronized to the system clock, to ensure only one valid press is registered per actual button push.

Is this method more accurate than using a web-based reaction time test?

Yes, significantly. Web-based tests rely on the operating system and browser, introducing variable delays (jitter) in stimulus presentation and response capture. FPGA-based measurement provides hardware-level timing, bypassing these software uncertainties for much higher accuracy and reliability.

What if my recorded clock cycles are very high?

High clock cycle counts simply mean the reaction time was longer, or the clock frequency was lower. As long as the counter in your Quartus design has enough bits to hold the maximum expected count, the calculation remains valid. A higher count divided by the frequency will result in a longer reaction time.

Can I use this calculator for different FPGA boards?

The calculation logic is universal. You can use this calculator for any FPGA project where you measure elapsed clock cycles. Just ensure you input the correct system clock frequency (in MHz) specific to that board and FPGA design.

Does the calculator account for the stimulus presentation time itself?

No, this calculator only converts the measured clock cycles into a time duration. It assumes your Quartus design accurately captures the *start* time of the stimulus and the *end* time of the response. The actual time taken for a stimulus (like an LED turning on) to physically become visible is a separate biological/physical factor not included in this calculation.