Now that we can view our signal on the display screen, let's look at amplitude accuracy, or perhaps better, amplitude uncertainty. Most spectrum analyzers are specified in terms of both absolute and relative accuracy. However, relative performance affects both, so let's look at those factors affecting relative measurement uncertainty first.
Before we discuss these uncertainties, let's look again at the block diagram of an analog swept-tuned spectrum analyzer, shown in Figure 4-1, and see which components contribute to the uncertainties. Later in this chapter, we will see how a digital IF and various correction and calibration techniques can substantially reduce measurement uncertainty.
Figure 4-1. Spectrum analyzer block diagram
Components which contribute to uncertainty are:
Input connector (mismatch)
RF Input attenuator
Mixer and input filter (flatness)
IF gain/attenuation (reference level )
RBW filters
Display scale fidelity
Calibrator (not shown)
An important factor in measurement uncertainty that is often overlooked is impedance mismatch. Analyzers do not have perfect input impedances, and signal sources do not have ideal output impedances. When a mismatch exists, the incident and reflected signal vectors may add constructively or destructively. Thus the signal received by the analyzer can be larger or smaller than the original signal. In most cases, uncertainty due to mismatch
is relatively small. However, it should be noted that as spectrum analyzer amplitude accuracy has improved dramatically in recent years, mismatch uncertainty now constitutes a more significant part of the total measurement uncertainty. In any case, improving the match of either the source or analyzer reduces uncertainty 1.
1. For more information, see the Agilent PSA Performance Spectrum Analyzer Series Amplitude Accuracy Product Note, literature number 5980-3080EN.
The general expression used to calculate the maximum mismatch error in dB is:
As an example, consider a spectrum analyzer with an input VSWR of 1.2 and a device under test (DUT) with a VSWR of 1.4 at its output port. The resulting mismatch error would be ± 0.13 dB.
Since the analyzer's worst-case match occurs when its input attenuator is set to 0 dB, we should avoid the 0 dB setting if we can. Alternatively, we can attach a well-matched pad (attenuator) to the analyzer input and greatly reduce mismatch as a factor. Adding attenuation is a technique that works well to reduce measurement uncertainty when the signal we wish to measure is well above the noise. However, in cases where the signal-to-noise ratio is small (typically 7 dB), adding attenuation will increase measurement error
because the noise power adds to the signal power, resulting in an erroneously high reading.
Let's turn our attention to the input attenuator. Some relative measurements are made with different attenuator settings. In these cases, we must consider the input attenuation switching uncertainty. Because an RF input attenuator must operate over the entire frequency range of the analyzer, its step accuracy varies with frequency. The attenuator also contributes to the overall frequency response. At 1 GHz, we expect the attenuator performance to be quit good; at 26 GHz, not as good.
The next component in the signal path is the input filter. Spectrum analyzers use a fixed low-pass filter in the low band and a tunable band pass filter called a preselector (we will discuss the preselector in more detail in Chapter 7) in the higher frequency bands. The low-pass filter has a better frequency response than the preselector and adds a small amount of
uncertainty to the frequency response error. A preselector, usually a YIG-tuned filter, has a larger frequency response variation, ranging from 1.5 dB to 3 dB at millimeter-wave frequencies.
Following the input filter are the mixer and the local oscillator, both of which add to the frequency response uncertainty. Figure 4-2 illustrates what the frequency response might look like in one frequency band. Frequency response is usually specified as ± x dB relative to the midpoint between the extremes. The frequency response of a spectrum analyzer represents the overall system performance resulting from the flatness characteristics and interactions of individual components in the signal path up to and including
the first mixer. Microwave spectrum analyzers use more than one frequency band to go above 3 GHz. This is done by using a higher harmonic of the local oscillator, which will be discussed in detail in Chapter 7. When making relative measurements between signals in different frequency bands, you must add the frequency response of each band to determine the overall frequency response uncertainty. In addition, some spectrum analyzers have a band switching uncertainty which must be added to the overall measurement uncertainty.
Figure 4-2. Relative frequency response in a single band
After the input signal is converted to an IF, it passes through the IF gain amplifier and IF attenuator which are adjusted to compensate for changes in the RF attenuator setting and mixer conversion loss. Input signal amplitudes are thus referenced to the top line of the graticule on the display, known as the reference level. The IF amplifier and attenuator only work at one frequency and, therefore, do not contribute to frequency response. However, there is always some amplitude uncertainty introduced by how accurately they can be
set to a desired value. This uncertainty is known as reference level accuracy.
Another parameter that we might change during the course of a measurement is resolution bandwidth. Different filters have different insertion losses. Generally, we see the greatest difference when switching between LC filters (typically used for the wider resolution bandwidths) and crystal filters (used for narrow bandwidths). This results in resolution bandwidth switching uncertainty.
The most common way to display signals on a spectrum analyzer is to use a logarithmic amplitude scale, such as 10 dB per div or 1 dB per div. Therefore, the IF signal usually passes through a log amplifier. The gain characteristic of the log amplifier approximates a logarithmic curve. So any deviation from a perfect logarithmic response adds to the amplitude uncertainty. Similarly, when the spectrum analyzer is in linear mode, the linear amplifiers do not have a perfect linear response. This type of uncertainty is called display
scale fidelity.
Relative uncertainty
When we make relative measurements on an incoming signal, we use either some part of the same signal or a different signal as a reference. For example, when we make second harmonic distortion measurements, we use the fundamental of the signal as our reference. Absolute values do not come into play; we are interested
only in how the second harmonic differs in amplitude from the fundamental.
In a worst-case relative measurement scenario, the fundamental of the signal may occur at a point where the frequency response is highest, while the harmonic we wish to measure occurs at the point where the frequency response is the lowest. The opposit scenario is equally likely. Therefore, if our relative frequency response specification is ± 0.5 dB as shown in Figure 4-2, then the total uncertainty would be twice that value, or ± 1.0 dB.
Perhaps the two signals under test might be in different frequency bands of the spectrum analyzer. In that case, a rigorous analysis of the overall uncertainty must include the sum of the flatness uncertainties of the two frequency bands.
Other uncertainties might be irrelevant in a relative measurement, like the RBW switching uncertainty or reference level accuracy, which apply to both signals at the same time.
Absolute amplitude accuracy
Nearly all spectrum analyzers have a built-in calibration source which provides a known reference signal of specified amplitude and frequency.
We then rely on the relative accuracy of the analyzer to translate the absolute calibration of the reference to other frequencies and amplitudes. Spectrum analyzers often have an absolute frequency response specification, where the zero point on the flatness curve is referenced to this calibration signal. Many Agilent spectrum analyzers use a 50 MHz reference signal. At this frequency, the specified absolute amplitude accuracy is extremely good: ± 0.34 dB for the ESA-E Series and ± 0.24 dB for the PSA Series analyzers.
It is best to consider all known uncertainties and then determine which ones can be ignored when doing a certain type of measurement. The range of values shown in Table 4-1 represents the specifications of a variety of different spectrum analyzers.
Some of the specifications, such as frequency response, are frequency-range dependent. A 3 GHz RF analyzer might have a frequency response of ± 0.38 dB, while a microwave spectrum analyzer tuning in the 26 GHz range could have a frequency response of ± 2.5 dB or higher. On the other hand, other sources
of uncertainty, such as changing resolution bandwidths, apply equally to all frequencies.
Table 4-1. Representative values of amplitude uncertainty for common spectrum analyzers Amplitude uncertainties (± dB)
Improving overall uncertainty
When we look at total measurement uncertainty for the first time, we may well be concerned as we add up the uncertainty figures. The worst case view assumes that each source of uncertainty for your spectrum analyzer is at the maximum specified value, and that all are biased in the same direction at the same time. Since the sources of uncertainty can be considered independent variables, it is likely that some errors will be positive while others will be negative. Therefore, a common practice is to calculate the root sum of squares (RSS) error.
Regardless of whether we calculate the worst-case or RSS error, there are some things that we can do to improve the situation. First of all, we should know the specifications for our particular spectrum analyzer. These specifications may be good enough over the range in which we are making our measurement. If not, Table 4-1 suggests some opportunities to improve accuracy.
Before taking any data, we can step through a measurement to see if any controls can be left unchanged. We might find that the measurement can be made without changing the RF attenuator setting, resolution bandwidth, or reference level. If so, all uncertainties associated with changing these controls drop out. We may be able to trade off reference level accuracy against display fidelity, using whichever is more accurate and eliminating the other as an uncertainty factor. We can even get around frequency response if we are
willing to go to the trouble of characterizing our particular analyzer 2. This can be accomplished by using a power meter and comparing the reading of the spectrum analyzer at the desired frequencies with the reading of the power meter.
The same applies to the calibrator. If we have a more accurate calibrator, or one closer to the frequency of interest, we may wish to use that in lieu of the built-in calibrator. Finally, many analyzers available today have self-calibration routines. These routines generate error coefficients (for example, amplitude changes versus resolution bandwidth), that the analyzer later uses to correct measured data. As a result, these self-calibration routines allow us to make good amplitude measurements with a spectrum analyzer and give us more freedom to change controls during the course of a measurement.
Specifications, typical performance, and nominal values
When valuating spectrum analyzer accuracy, it is very important to have a clear understanding of the many different values found on an analyzer data sheet. Agilent Technologies defines three classes of instrument performance data:
Specifications describe the performance of parameters covered by the prod-uct warranty over a temperature range of 0 to 55° C (unless otherwise noted). Each instrument is tested to verify that it meets the specification, and takes into account the measurement uncertainty of the equipment used to test the
instrument. 100% of the units tested will meet the specification.
Some test equipment manufacturers use a 2 sigma or 95% confidence value for certain instrument specifications. When valuating data sheet specifications for instruments from different manufacturers, it is important to make sure you are comparing like numbers in order to make an accurate comparison.
2. Should we do so, then mismatch may become a more significant error.
Typical performance describes additional product performance information that is not covered by the product warranty. It is performance beyond specification that 80% of the units exhibit with a 95% confidence level over the temperature range 20 to 30° C. Typical performance does not include
measurement uncertainty. During manufacture, all instruments are tested for typical performance parameters.
Nominal values indicate expected performance, or describe product performance that is useful in the application of the product, but is not covered by the product warranty. Nominal parameters generally are not
tested during the manufacturing process.
The digital IF section
As described in the previous chapter, a digital IF architecture eliminates or minimizes many of the uncertainties experienced in analog spectrum analyzers. These include:
Reference level accuracy (IF gain uncertainty)
Spectrum analyzers with an all digital IF, such as the Agilent PSA Series, do not have IF gain that changes with reference level. Therefore, there is no IF gain uncertainty.
Display scale fidelity
A digital IF architecture does not include a log amplifier. Instead, the log function is performed mathematically, and traditional log fidelity uncertainty does not exist. However, other factors, such as RF compression (especially for input signals above 20 dBm) , ADC range gain alignment accuracy, and ADC
linearity (or quantization error) contribute to display scale uncertainty. The quantization error can be improved by the addition of noise which smoothes the average of the ADC transfer function. This added noise is called dither.
While the dither improves linearity, it does slightly degrade the displayed average noise level. In the PSA Series, it is generally recommended that dither be used when the measured signal has a signal-to-noise ratio of greater than or equal to 10 dB. When the signal-to-noise ratio is under 10 dB, the degradations to accuracy of any single measurement (in other words, without averaging) that come from a higher noise floor are worse than the linearity problems solved by adding dither, so dither is best turned off.
RBW switching uncertainty
The digital IF in the PSA Series includes an analog prefilter set to 2.5 times the desired resolution bandwidth. This prefilter has some uncertainty in bandwidth, gain, and center frequency as a function of the RBW setting. The rest of the RBW filtering is done digitally in an ASIC in the digital IF section.
Though the digital filters are not perfect, they are very repeatable, and some compensation is applied to minimize the error. This results in a tremendous overall improvement to the RBW switching uncertainty compared to analog
implementations.
Examples
Let's look at some amplitude uncertainty examples for various measurements. Suppose we wish to measure a 1 GHz RF signal with an amplitude of 20 dBm. If we use an Agilent E4402B ESA-E Series spectrum analyzer with Atten = 10 dB, RBW = 1 kHz, VBW = 1 kHz, Span = 20 kHz, Ref level = 20 dBm, log
scale, and coupled sweep time, and an ambient temperature of 20 to 30° C, the specifications tell us that the absolute uncertainty equals ± 0.54 dB plus the absolute frequency response. An E4440A PSA Series spectrum analyzer measuring the same signal using the same settings would have a specified uncertainty of ± 0.24 dB plus the absolute frequency response. These values are summarized in Table 4-2.
Table 4-2. Amplitude uncertainties when measuring a 1 GHz signal
At higher frequencies, the uncertainties get larger. In this example, we wish to measure a 10 GHz signal with an amplitude of 10 dBm. In addition, we also want to measure its second harmonic at 20 GHz. Assume the following measurement conditions: 0 to 55° C, RBW = 300 kHz, Atten = 10 dB, Ref level = 10 dBm. In Table 4-3, we compare the absolute and relative amplitude uncertainty of two different Agilent spectrum analyzers, an 8563EC (analog IF) and an E4440A PSA ( digital IF).
Table 4-3. Absolute and relative amplitude accuracy comparison (8563EC and E4440A PSA)
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Frequency accuracy
So far, we have focused almost exclusively on amplitude measurements. What about frequency measurements? Again, we can classify two broad categories, absolute and relative frequency measurements. Absolute measurements are used to measure the frequencies of specific signals. For example, we might want to measure a radio broadcast signal to verify that it is operating at its assigned frequency. Absolute measurements are also used to analyze undesired signals, such as when doing a spur search. Relative
measurements, on the other hand, are useful to know how far apart spectral components are, or what the modulation frequency is.
Up until the late 1970s, absolute frequency uncertainty was measured in megahertz because the first LO was a high-frequency oscillator operating above the RF range of the analyzer, and there was no attempt to tie the LO to a more accurate reference oscillator. Today's LOs are synthesized to provide better accuracy. Absolute frequency uncertainty is often described under the frequency readout accuracy specification and refers to center frequency, start, stop, and marker frequencies.
With the introduction of the Agilent 8568A in 1977, counter-like frequency accuracy became available in a general-purpose spectrum analyzer and ovenized oscillators were used to reduce drift. Over the years, crystal reference oscillators with various forms of indirect synthesis hav been added to analyzers in all cost ranges. The broadest definition of indirect synthesis is that the frequency of the oscillator in question is in some way determined by a reference oscillator. This includes techniques such as phase lock, frequency discrimination, and counter lock.
What we really care about is the effect these changes have had on frequency accuracy (and drift) . A typical readout accuracy might be stated as follows:
± [ (freq readout x freq ref error) + A% of span + B% of RBW + C Hz ]
Note that we cannot determine an exact frequency error unless we know something about the frequency reference. In most cases we are given an annual aging rate, such as ± 1 x 10 -7 per year, though sometimes aging is given over a shorter period (for example, ± 5 x 10 -10 per day). In addition, we need to know when the oscillator was last adjusted and how close it was set to its nominal frequency (usually 10 MHz) . Other factors that we often overlook when we think about frequency accuracy include how long the
reference oscillator has been operating. Many oscillators take 24 to 72 hours to reach their specified drift rate. To minimize this effect, some spectrum analyzers continue to provide power to the reference oscillator as long as the instrument is plugged into the AC power line. In this case, the instrument is not really turned off, but more properly is on standby. We also need to consider the temperature stability, as it can be worse than the drift rate. In short, there are a number of factors to consider before we can determine
frequency uncertainty.In a factory setting, there is often an in-house frequency standard available that is traceable to a national standard. Most analyzers with internal reference oscillators allow you to use an external reference. The frequency reference error in the foregoing expression then becomes the error of the
in-house standard.
When making relative measurements, span accuracy comes into play. For Agilent analyzers, span accuracy generally means the uncertainty in the indicated separation of any two spectral components on the display.
For example, suppose span accuracy is 0. 5% of span and w have two signals separated by two divisions in a 1 MHz span ( 100 kHz per division) . The uncertainty of the signal separation would be 5 kHz. The uncertainty would be the same if w used delta markers and the delta reading would be 200 kHz.
So w would measure 200 kHz ± 5 kHz.
When making measurements in the field, we typically want to turn our analyzer on, complete our task, and mov on as quickly as possible. It is helpful to know how the reference in our analyzer behaves under short warm up conditions. For example, the Agilent ESA-E Series of portable spectrum analyzers will meet published specifications aft r a fiv -minute warm up time.
Most analyzers include mark rs that can be put on a signal to giv us absolute frequency, as w ll as amplitude. How ver, the indicated frequency of the marker is a function of the frequency calibration of the display, the
location of the mark r on the display, and the number of display points selected. Also, to get the best frequency accuracy w must be careful to place the marker exactly at the peak of the response to a spectral component. If w place the mark r at some other point on the response, we will get a different frequency reading. For the best accuracy, w may narrow the span and resolution bandwidth to minimize their effects and to make it easier to place the marker at the peak of the response.
Many analyzers hav marker modes that include int rnal counter schemes to liminate the effects of span and resolution bandwidth on frequency accuracy. The counter does not count the input signal directly, but instead
counts the IF signal and perhaps one or more of the LOs, and the processor computes the frequency of the input signal. A minimum signal-to-noise ratio is required to liminate noise as a factor in the count. Counting the signal in the IF also eliminates the need to place the marker at the exact peak of the signal response on the display. If you are using this mark r counter function, placement anywhere sufficiently out of the noise will do. Mark r count accuracy might be stated as:
± [ ( marker freq x freq ref error) + counter resolution ]
W must still deal with the frequency ref rence error as previously discussed.
Counter resolution ref rs to the least significant digit in the counter readout, a factor here just as with any simple digital counter. Some analyzers allow the counter mode to be used with delta markers. In that case, the effects of counter resolution and the fixed frequency would be doubled.
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