I got to do one last exercise:
From the specifications of the function generator calculate the standard uncertainty of the amplitude of a 1 V (peak) sinusoidal signal of 1 kHz.
The specifications say that:
Accuracy at 1kHz = +/- 1% of the specified output
f = 1000 +/- 10 Hz
Amplitude = 1 +/- 0.01 V
How can I compute the uncertainty from this?
And then it continues:
Calculate the standard uncertainty of the oscilloscope when measuring the amplitude and rms value of the previous signal. Take into account the oscilloscope noise.
I have been looking through the entire Oscilloscope's documentation and I can't find said noise. Any ideas?
To compute the standard uncertainty of the amplitude of a 1 V (peak) sinusoidal signal of 1 kHz, based on the given specifications, you can follow these steps:
Step 1: Determine the range of the frequency:
Given: f = 1000 +/- 10 Hz
The range of the frequency is from 990 Hz (1000 Hz - 10 Hz) to 1010 Hz (1000 Hz + 10 Hz).
Step 2: Determine the range of the amplitude:
Given: Amplitude = 1 +/- 0.01 V
The range of the amplitude is from 0.99 V (1 V - 0.01 V) to 1.01 V (1 V + 0.01 V).
Step 3: Determine the maximum and minimum values of the amplitude possible within the range:
The maximum amplitude is 1.01 V, and the minimum amplitude is 0.99 V.
Step 4: Calculate the standard uncertainty:
The standard uncertainty is calculated as half the range of the values. In this case, the range is 1.01 V - 0.99 V = 0.02 V.
Therefore, the standard uncertainty of the amplitude is 0.02 V / 2 = 0.01 V.
So, the standard uncertainty of the amplitude of a 1 V (peak) sinusoidal signal of 1 kHz, based on the given specifications, is 0.01 V.
To compute the standard uncertainty of the amplitude of a 1 V (peak) sinusoidal signal of 1 kHz, using the provided specifications, you can follow these steps:
1. Determine the range of frequency variation:
The specification states that the frequency is 1000 +/- 10 Hz. Therefore, the range of frequency variation is from 990 Hz to 1010 Hz.
2. Determine the range of amplitude variation:
The specification states that the amplitude is 1 +/- 0.01 V. Therefore, the range of amplitude variation is from 0.99 V to 1.01 V.
3. Calculate the standard uncertainty of frequency (delta_f):
The range of frequency variation is 20 Hz (1010 Hz - 990 Hz). Since the frequency range is symmetric, you can take half of the range as the standard uncertainty of frequency. Therefore, delta_f = (20 Hz) / 2 = 10 Hz.
4. Calculate the standard uncertainty of amplitude (delta_A):
The range of amplitude variation is 0.02 V (1.01 V - 0.99 V). Since the amplitude range is symmetric, you can take half of the range as the standard uncertainty of amplitude. Therefore, delta_A = (0.02 V) / 2 = 0.01 V.
5. Calculate the standard uncertainty of the amplitude of the sinusoidal signal:
The standard uncertainty is the square root of the sum of the squares of the individual standard uncertainties. Therefore, you can use the formula:
delta_signal = sqrt(delta_f^2 + delta_A^2)
delta_signal = sqrt((10 Hz)^2 + (0.01 V)^2)
Calculating this will give you the standard uncertainty of the amplitude of the sinusoidal signal at 1 kHz.