Signal Analysis & Testing

The Three S’s of Sensor Performance

1. Stability (Zero Uncertainty)

The ability of the sensor to maintain a constant output in clean air.

• Zero drift — slow baseline shift over time or temperature
• Noise — high-frequency random fluctuations

Firmware implementation: StabilityMonitor — 30-sample circular buffer at 1 Hz. Stability criterion: rate-of-change (newest − oldest sample) ≤ 0.1 mV over the 30-second window.

2. Sensitivity (Slope)

$$S = \frac{V_{span} - V_{zero}}{C_{span}}$$

where $C_{span}$ is the reference concentration (ppm) and voltages are in mV.

Typical H₂S sensitivity with this circuit: ~10 mV/ppm.

3. Selectivity (Cross-Sensitivity)

Common interferents for electrochemical H₂S sensors:

The SHT45 sensor provides temperature and humidity data for future compensation.

Noise Floor Analysis

With 8× hardware oversampling on a 12-bit ADC (170 MHz clock, 6.5 cycle sample time):

Practical noise floor will be dominated by TIA Johnson noise and PCB layout, not ADC quantisation.

Experimental Protocols

Experiment A: Stability & Noise (Zero Air)

Objective: Quantify baseline noise and drift.

1. Power on, warm up 30–60 minutes
2. Log STABILITY and GAS at 1 Hz for 1 hour
3. Analyse:
   • Noise (Vpp): max − min over 1-minute windows
   • RMS noise (σ): standard deviation of samples
   • Drift: linear regression slope over the full hour
   • Pass criterion: noise < ½ × expected signal for 1 ppm

Experiment B: Sensitivity & Linearity

Objective: Determine slope, verify linearity.

1. Zero air for 5 minutes → record average RAW value
2. Span gas (e.g. 50 ppm) for 5 minutes → record average RAW value
3. Calculate slope: $S = (ADC_{span} - ADC_{zero}) / 50$
4. Optionally test mid-point (25 ppm) to check linearity

Experiment C: Response Time (T₉₀)

Objective: Measure the time to 90% of final stable reading.

1. Establish stable baseline with zero air
2. Instantly switch to span gas (3-way valve)
3. Record timestamps from log until signal reaches 90% of final value
4. $T_{90} = t_{90%} - t_{switch}$

Expected T₉₀ for City Technology / equivalent H₂S sensors: ≤ 30–35 seconds.

MATLAB Analysis Script

%% Gas Sensor — Stability Analysis
filename = 'sensor_data.log';
v_ref = 3.3; adc_res = 4096;

% Parse "RAW:2048" lines
fileID = fopen(filename, 'r');
raw_data = []; t = [];
i = 0;
while ~feof(fileID)
    line = fgetl(fileID);
    if contains(line, 'RAW:')
        tok = regexp(line, 'RAW:(\d+)', 'tokens');
        if ~isempty(tok)
            raw_data(end+1) = str2double(tok{1}{1});
            t(end+1) = i;
            i = i + 1;
        end
    end
end
fclose(fileID);

voltage = (raw_data / adc_res) * v_ref * 1000;  % mV

% Statistics
fprintf('Mean:    %.2f mV\n', mean(voltage));
fprintf('Std Dev: %.3f mV\n', std(voltage));
fprintf('Vpp:     %.2f mV\n', max(voltage) - min(voltage));
p = polyfit(t, voltage, 1);
fprintf('Drift:   %.5f mV/sample\n', p(1));

% Plot
figure; plot(t, voltage); hold on;
plot(t, polyval(p, t), 'r--', 'LineWidth', 1.5);
title('Sensor Signal (mV)'); xlabel('Sample'); ylabel('mV');
legend('Signal', 'Drift trend'); grid on;