Accuracy vs. Precision: What It Means for Your Measurements
Written by Tit Bin Teo, Technical Engineering Manager
In manufacturing, how confident are you that the RF receiver that passed your test meets all specifications? Are you wasting money by over rejecting perfectly good units? Do you know you can easily improve yield by improving accuracy? Good accuracy allows you to reduce manufacturing costs while maintaining high product quality.
Accuracy is often confused with precision but they are not the same. Accuracy is defined as how close a result is to the actual value. In the case of a signal generator, the accuracy is how close the output value is to the desired value. Precision, on the other hand, is defined as the standard deviation of the output values. In the case of a signal generator, a high precision generator has a stable output with little variation. A high precision generator has a very stable output, but not necessarily close to the desired value. For example, in Figure 1, the diagram to the left shows high accuracy results, while the diagram on the right shows high precision results. The bullseye is the desired value, and the red crosses are the output values.
Figure 1: High accuracy results vs. high precision results
What Types of Output Accuracy Matter?
There are two key accuracy specifications – amplitude accuracy and frequency accuracy. Does accuracy matter? It all depends on your application. If you want to make filters with 3 dB roll-off frequency that are better than your competitors’, you want to be able to measure the roll-off frequency accurately. You are only able to spec your 1 GHz filter’s roll-off frequency up to +/- 1 kHz accuracy if your source’s frequency accuracy is 1 ppm.
Amplitude accuracy of a signal generator is the degree to which the signal generator’s output amplitude conforms to its set amplitude. Amplitude accuracy is often specified within a frequency and temperature range. The temperature range is specified because a signal generator is often calibrated within a temperature-controlled environment. The farther the operating temperature is from the temperature at which the signal generator was calibrated, the worse the amplitude accuracy becomes. Figure 2 shows the amplitude accuracy specification of the N5182B MXG signal generator. Amplitude accuracy can be improved with the use of automatic leveling control (ALC).
Table 1: Amplitude accuracy specifications of the N5182B MXG Signal Generators
Signal Generator Flatness Over Frequency
Amplitude accuracy affects the frequency sweeping capability of a signal generator. Frequency sweeps are used in testing filters and power amplifiers. The less the amplitude changes from one frequency to another, the flatter the output is. The change in amplitude while moving from one frequency to another is called flatness. While closely related to amplitude accuracy, flatness is not the same as amplitude accuracy. Flatness limits can be tighter than the amplitude accuracy specifications because flatness limits are often specified within a limited frequency range and with reference to the amplitude at the starting frequency. Figure 2 illustrates this difference.
Figure 2: Output amplitude accuracy specification vs. flatness limit
When does Amplitude Accuracy Matter?
One application where amplitude accuracy matters is receiver sensitivity testing. Receiver sensitivity test determines if a receiver is able to detect weak signals at or below a specified power level. For example, a 4G mobile phone receiver has a specified sensitivity level of -110 dBm. The receiver sensitivity test will only accept receivers that are sensitive enough to detect transmissions with a signal strength of -110 dBm or less.
For example, we will use a signal generator with an amplitude accuracy of +/-5 dB from 5MHz to 3 GHz to illustrate the effects of amplitude accuracy on yield. The signal generator is set up to output -115 dBm because the actual output power could vary from -110 dBm to -120 dBm and we do not want a false positive. Unfortunately, this also means that we will inadvertently reject perfectly good receivers with borderline performance. Figure 3 illustrates this situation.
Figure 3: Receiver sensitivity testing results comparison between an ideal signal generator and a signal generator with +/-5 dB amplitude accuracy
To improve this situation, we can go for a more accurate signal generator with an amplitude accuracy of +/-1 dB. The signal generator is now set up to output -111 dBm. Figure 4 shows that four of the six receivers tested now pass the sensitivity test. By using a more accurate signal generator, we managed to double our test yield from 33% to 66%.
Figure 4: Test results comparison between signal generators with different levels of amplitude accuracy
The frequency accuracy of a signal generator is the degree to which the signal generator’s output frequency conforms to its set frequency. The frequency accuracy of a signal generator is affected by two factors – the stability of the reference oscillator, and the amount of time that has passed since the source was last calibrated. For example, a typical reference oscillator has an aging rate of 0.152 ppm (parts-per-million) per year. The aging rate indicates how fast the reference will drift from its specified value. A 1 GHz source with an aging rate of 0.152 ppm per year that has not been calibrated for one year will have an accuracy of +/- 152 Hz. The equation for calculating the frequency accuracy appears below.
Frequency Accuracy (Hz) = Output Frequency (Hz)*Aging Rate (ppm/year)*Time Since Last Calibration (Year)
= 1 GHz*0.152ppm/year*1 year = 152 Hz
Table 2: Frequency accuracy of an MXG signal generator
Frequency accuracy is also affected to a lesser extent by temperature, line voltage, and calibration accuracy. However, the largest effect on frequency accuracy, by far, is the aging rate of the oscillator and time since the last calibration.
When is Frequency Accuracy Important?
Frequency accuracy is increasingly important in crowded frequency spectrums. The adjacent channel selectivity test measures a receiver's ability to process a signal while rejecting a strong signal from an adjacent channel. This test is important for communication receivers where frequency spectrum spacings are narrow and signal density is high in a crowded area. The block diagram of an adjacent channel selectivity test setup appears in Figure 5.
Figure 5: Adjacent or alternate channel selectivity test setup
This test uses two signal generators. One signal generator inputs a test signal at the desired channel frequency at a level above the sensitivity of the receiver. The second signal generator outputs the adjacent channel signal. The output of the out-of-channel signal increases until the sensitivity of the receiver degrades to a specified level.
In this test, frequency accuracy and the spectral characteristics of the test and interfering signal are important. Poor frequency accuracy will cause the signals to be either too close or too far from each other and from the filter skirts. This can have the effect of appearing to improve or degrade receiver performance.
For example, assume you are trying to set a 1-kHz separation between two signals centered at 200 MHz, and your sources have an aging rate of ±1 x 10-6/year. Your sources’ frequency error, in this case, is 200 MHz x 1 x 10-6, or ±200 Hz. As shown in Figure 6, the separation could be anywhere from 600 Hz to 1400 Hz.
Figure 6: The shaded area shows the range of the relative-frequency error
If the signals are far apart, this frequency error will incorrectly show improvements in adjacent channel selectivity performance. The reverse will happen if the signals are near each other.
Accuracy is only one of several important considerations when selecting the right signal generator for the job. Understand your test requirements to select the signal generator with enough accuracy to save money. Better accuracy does not mean better. There are several other specifications to consider such as spectral purity, modulation quality, speed, and much more.
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