Matlab Thd N Calculation

What is THD+N?

THD+N is a combined measurement of Total Harmonic Distortion (THD) and background noise in a signal. It represents the total distortion and noise relative to the fundamental frequency component.

The formula for THD+N is:

Where:

• THD is the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency
• Noise is the ratio of the noise power to the fundamental frequency power

THD+N is typically expressed as a percentage. Lower values indicate better signal quality.

MATLAB Calculation Method

In MATLAB, you can calculate THD+N using the following approach:

1. Acquire your signal data
2. Identify the fundamental frequency component
3. Calculate the power of each harmonic component
4. Calculate the noise power
5. Compute THD and Noise ratios
6. Combine them using the THD+N formula

MATLAB Code Example

% Sample MATLAB code for THD+N calculation
fs = 1000; % Sampling frequency
t = 0:1/fs:1; % Time vector
f0 = 50; % Fundamental frequency
signal = sin(2*pi*f0*t); % Pure sine wave

% Add harmonics and noise
signal = signal + 0.1*sin(2*pi*2*f0*t) + 0.05*sin(2*pi*3*f0*t);
noise = 0.02*randn(size(t));
signal = signal + noise;

% Calculate FFT
N = length(signal);
X = fft(signal);
X_mag = abs(X)/N;
f = fs*(0:(N/2))/N;

% Find fundamental component
[~, idx] = max(X_mag(1:N/2+1));
fundamental_power = X_mag(idx)^2;

% Calculate harmonic power
harmonic_power = 0;
for k = 2:5 % Check up to 5th harmonic
    [~, idx_h] = min(abs(f - k*f0));
    harmonic_power = harmonic_power + X_mag(idx_h)^2;
end

% Calculate noise power
noise_power = sum(X_mag.^2) - fundamental_power - harmonic_power;

% Calculate THD and Noise
THD = sqrt(harmonic_power)/sqrt(fundamental_power);
Noise = sqrt(noise_power)/sqrt(fundamental_power);

% Calculate THD+N
THD_N = sqrt(THD^2 + Noise^2);

Example Calculation

Consider a 50Hz signal with:

• 2nd harmonic at 10% of fundamental amplitude
• 3rd harmonic at 5% of fundamental amplitude
• Noise level of 2% of fundamental amplitude

Using the MATLAB code above, we calculate:

Calculations:

• THD = √(0.0125)/√(1.00) = 0.1118 or 11.18%
• Noise = √(0.0004)/√(1.00) = 0.02 or 2.00%
• THD+N = √(0.1118² + 0.02²) = 0.1136 or 11.36%

Interpreting Results

THD+N values are typically interpreted as follows:

• Below 1% - Excellent signal quality
• 1-3% - Good signal quality
• 3-5% - Acceptable for most applications
• Above 5% - May require filtering or redesign

In power electronics, THD+N values below 5% are generally acceptable for most applications. Higher values may indicate the need for better filtering or component selection.