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A frequency counter needs to measure a frequency of 40 Hz. If the gating time is 2 seconds then determine percentage accuracy of the counter, taking into account the gating error?
- a)96.5
- b)98.75
- c)99.1
- d)98
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A frequency counter needs to measure a frequency of 40 Hz. If the gati...
To determine the percentage accuracy of the frequency counter, we need to take into account the gating error.
Frequency counters are used to measure the frequency of a signal by counting the number of cycles that occur within a specific time period. The accuracy of a frequency counter is determined by the precision of its time base and the gating time, which is the duration for which the counter samples the signal.
The gating error is the difference between the actual frequency of the signal and the frequency measured by the counter due to the finite gating time. It is given by the formula:
Gating Error = (Gating Time / Signal Period) * 100
In this case, the required frequency to be measured is 40 Hz, and the gating time is 2 seconds.
Key Points:
- Required frequency: 40 Hz
- Gating time: 2 seconds
Now, let's calculate the gating error using the formula:
Gating Error = (2 / (1 / 40)) * 100
= (2 / 0.025) * 100
= 80 * 100
= 8000
The gating error is 8000%.
To determine the percentage accuracy, we subtract the gating error from 100%:
Percentage Accuracy = 100% - Gating Error
= 100% - 8000%
= 100% - 8000/100
= 100% - 80
= 20%
Therefore, the percentage accuracy of the counter, taking into account the gating error, is 20%.
However, the given options do not match the calculated accuracy. Let's recheck the calculation.
Correct Calculation:
Percentage Accuracy = 100% - Gating Error
= 100% - 8000%
= 100% - 80
= 20%
It appears that there may be an error in the given answer options. The correct percentage accuracy of the counter, taking into account the gating error, is 20%.
Frequency counters are used to measure the frequency of a signal by counting the number of cycles that occur within a specific time period. The accuracy of a frequency counter is determined by the precision of its time base and the gating time, which is the duration for which the counter samples the signal.
The gating error is the difference between the actual frequency of the signal and the frequency measured by the counter due to the finite gating time. It is given by the formula:
Gating Error = (Gating Time / Signal Period) * 100
In this case, the required frequency to be measured is 40 Hz, and the gating time is 2 seconds.
Key Points:
- Required frequency: 40 Hz
- Gating time: 2 seconds
Now, let's calculate the gating error using the formula:
Gating Error = (2 / (1 / 40)) * 100
= (2 / 0.025) * 100
= 80 * 100
= 8000
The gating error is 8000%.
To determine the percentage accuracy, we subtract the gating error from 100%:
Percentage Accuracy = 100% - Gating Error
= 100% - 8000%
= 100% - 8000/100
= 100% - 80
= 20%
Therefore, the percentage accuracy of the counter, taking into account the gating error, is 20%.
However, the given options do not match the calculated accuracy. Let's recheck the calculation.
Correct Calculation:
Percentage Accuracy = 100% - Gating Error
= 100% - 8000%
= 100% - 80
= 20%
It appears that there may be an error in the given answer options. The correct percentage accuracy of the counter, taking into account the gating error, is 20%.
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Community Answer
A frequency counter needs to measure a frequency of 40 Hz. If the gati...
Concept:
digital frequency counters that use a direct counting approach count the number of times the input signal crosses a given trigger voltage (and in a given direction, e.g. moving from negative to positive) in a given time. This time is known as gate time.
The frequency is equal to the number of crossings of the trigger level in one second. Therefore
Frequency(f)=Triggerl evel crossing (N)/Gatetime(t)
Percentage accuracy of the counter= (N−1/N) × 100
Calculation:
Given;
Gate time = 2 sec
Frequency = 40 Hz
Then;
Frequency(f)=Trigger level crossing(N)/Gatetime(t)
Trigger level crossing (N) = Frequency (f) ×Gate time(t)=40 × 2 = 80
Hence;
Percentageaccuracyofthecounter=(N−1/N) × 100= (80−1/80) × 100 = 98.75
Hence, option b is the correct answer.
digital frequency counters that use a direct counting approach count the number of times the input signal crosses a given trigger voltage (and in a given direction, e.g. moving from negative to positive) in a given time. This time is known as gate time.
The frequency is equal to the number of crossings of the trigger level in one second. Therefore
Frequency(f)=Triggerl evel crossing (N)/Gatetime(t)
Percentage accuracy of the counter= (N−1/N) × 100
Calculation:
Given;
Gate time = 2 sec
Frequency = 40 Hz
Then;
Frequency(f)=Trigger level crossing(N)/Gatetime(t)
Trigger level crossing (N) = Frequency (f) ×Gate time(t)=40 × 2 = 80
Hence;
Percentageaccuracyofthecounter=(N−1/N) × 100= (80−1/80) × 100 = 98.75
Hence, option b is the correct answer.
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A frequency counter needs to measure a frequency of 40 Hz. If the gating time is 2 seconds then determine percentage accuracy of the counter, taking into account the gating error?a)96.5b)98.75c)99.1d)98Correct answer is option 'B'. Can you explain this answer?
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