Agilent Spectrum Analysis Basics Application Note 150
Table of Contents Chapter 1 – Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 Frequency domain versus time domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 What is a spectrum? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Why measure spectra? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table of Contents — continued Chapter 5 – Sensitivity and Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 Noise figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 Preamplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 1 Introduction This application note is intended to explain the fundamentals of swept-tuned, superheterodyne spectrum analyzers and discuss the latest advances in spectrum analyzer capabilities. At the most basic level, the spectrum analyzer can be described as a frequency-selective, peak-responding voltmeter calibrated to display the rms value of a sine wave. It is important to understand that the spectrum analyzer is not a power meter, even though it can be used to display power directly.
Some measurements require that we preserve complete information about the signal - frequency, amplitude and phase. This type of signal analysis is called vector signal analysis, which is discussed in Application Note 150-15, Vector Signal Analysis Basics. Modern spectrum analyzers are capable of performing a wide variety of vector signal measurements. However, another large group of measurements can be made without knowing the phase relationships among the sinusoidal components.
Why measure spectra? The frequency domain also has its measurement strengths. We have already seen in Figures 1-1 and 1-2 that the frequency domain is better for determining the harmonic content of a signal. People involved in wireless communications are extremely interested in out-of-band and spurious emissions. For example, cellular radio systems must be checked for harmonics of the carrier signal that might interfere with other systems operating at the same frequencies as the harmonics.
Figure 1-3. Harmonic distortion test of a transmitter Figure 1-4. GSM radio signal and spectral mask showing limits of unwanted emissions Figure 1- 5. Two-tone test on an RF power amplifier Figure 1-6.
Types of measurements Common spectrum analyzer measurements include frequency, power, modulation, distortion, and noise. Understanding the spectral content of a signal is important, especially in systems with limited bandwidth. Transmitted power is another key measurement. Too little power may mean the signal cannot reach its intended destination. Too much power may drain batteries rapidly, create distortion, and cause excessively high operating temperatures.
While we have defined spectrum analysis and vector signal analysis as distinct types, digital technology and digital signal processing are blurring that distinction. The critical factor is where the signal is digitized. Early on, when digitizers were limited to a few tens of kilohertz, only the video (baseband) signal of a spectrum analyzer was digitized. Since the video signal carried no phase information, only magnitude data could be displayed.
Chapter 2 Spectrum Analyzer Fundamentals This chapter will focus on the fundamental theory of how a spectrum analyzer works. While today’s technology makes it possible to replace many analog circuits with modern digital implementations, it is very useful to understand classic spectrum analyzer architecture as a starting point in our discussion. In later chapters, we will look at the capabilities and advantages that digital circuitry brings to spectrum analysis.
Since the output of a spectrum analyzer is an X-Y trace on a display, let’s see what information we get from it. The display is mapped on a grid (graticule) with ten major horizontal divisions and generally ten major vertical divisions. The horizontal axis is linearly calibrated in frequency that increases from left to right. Setting the frequency is a two-step process. First we adjust the frequency at the centerline of the graticule with the center frequency control.
RF attenuator The first part of our analyzer is the RF input attenuator. Its purpose is to ensure the signal enters the mixer at the optimum level to prevent overload, gain compression, and distortion. Because attenuation is a protective circuit for the analyzer, it is usually set automatically, based on the reference level. However, manual selection of attenuation is also available in steps of 10, 5, 2, or even 1 dB.
We need to pick an LO frequency and an IF that will create an analyzer with the desired tuning range. Let’s assume that we want a tuning range from 0 to 3 GHz. We then need to choose the IF frequency. Let’s try a 1 GHz IF. Since this frequency is within our desired tuning range, we could have an input signal at 1 GHz. Since the output of a mixer also includes the original input signals, an input signal at 1 GHz would give us a constant output from the mixer at the IF.
Figure 2-4 illustrates analyzer tuning. In this figure, fLO is not quite high enough to cause the fLO – fsig mixing product to fall in the IF passband, so there is no response on the display. If we adjust the ramp generator to tune the LO higher, however, this mixing product will fall in the IF passband at some point on the ramp (sweep), and we shall see a response on the display.
To separate closely spaced signals (see “Resolving signals” later in this chapter), some spectrum analyzers have IF bandwidths as narrow as 1 kHz; others, 10 Hz; still others, 1 Hz. Such narrow filters are difficult to achieve at a center frequency of 3.9 GHz. So we must add additional mixing stages, typically two to four stages, to down-convert from the first to the final IF. Figure 2-5 shows a possible IF chain based on the architecture of a typical spectrum analyzer.
• IF gain Referring back to Figure 2-1, we see the next component of the block diagram is a variable gain amplifier. It is used to adjust the vertical position of signals on the display without affecting the signal level at the input mixer. When the IF gain is changed, the value of the reference level is changed accordingly to retain the correct indicated value for the displayed signals.
Agilent data sheets describe the ability to resolve signals by listing the 3 dB bandwidths of the available IF filters. This number tells us how close together equal-amplitude sinusoids can be and still be resolved. In this case, there will be about a 3 dB dip between the two peaks traced out by these signals. See Figure 2-7. The signals can be closer together before their traces merge completely, but the 3 dB bandwidth is a good rule of thumb for resolution of equal-amplitude signals3. Figure 2-7.
Another specification is listed for the resolution filters: bandwidth selectivity (or selectivity or shape factor). Bandwidth selectivity helps determine the resolving power for unequal sinusoids. For Agilent analyzers, bandwidth selectivity is generally specified as the ratio of the 60 dB bandwidth to the 3 dB bandwidth, as shown in Figure 2-9. The analog filters in Agilent analyzers are a four-pole, synchronously-tuned design, with a nearly Gaussian shape4.
This allows us to calculate the filter rejection: H(4000) = –10(4) log10[(4000/1149.48)2 + 1] = –44.7 dB Thus, the 1 kHz resolution bandwidth filter does resolve the smaller signal. This is illustrated in Figure 2-10. Figure 2-10. The 3 kHz filter (top trace) does not resolve smaller signal; reducing the resolution bandwidth to 1 kHz (bottom trace) does Digital filters Some spectrum analyzers use digital techniques to realize their resolution bandwidth filters.
Phase noise Even though we may not be able to see the actual frequency jitter of a spectrum analyzer LO system, there is still a manifestation of the LO frequency or phase instability that can be observed. This is known as phase noise (sometimes called sideband noise). No oscillator is perfectly stable. All are frequency or phase modulated by random noise to some extent. As previously noted, any instability in the LO is transferred to any mixing products resulting from the LO and input signals.
Some modern spectrum analyzers allow the user to select different LO stabilization modes to optimize the phase noise for different measurement conditions. For example, the PSA Series spectrum analyzers offer three different modes: • Optimize phase noise for frequency offsets < 50 kHz from the carrier In this mode, the LO phase noise is optimized for the area close in to the carrier at the expense of phase noise beyond 50 kHz offset.
In any case, phase noise becomes the ultimate limitation in an analyzer’s ability to resolve signals of unequal amplitude. As shown in Figure 2-13, we may have determined that we can resolve two signals based on the 3 dB bandwidth and selectivity, only to find that the phase noise covers up the smaller signal.
On the other hand, the rise time of a filter is inversely proportional to its bandwidth, and if we include a constant of proportionality, k, then: Rise time = k RBW If we make the terms equal and solve for sweep time, we have: k (RBW)(ST) = or: RBW Span ST = k (Span) RBW2 The value of k is in the 2 to 3 range for the synchronously-tuned, near-Gaussian filters used in many Agilent analyzers. The important message here is that a change in resolution has a dramatic effect on sweep time.
Envelope detector6 Spectrum analyzers typically convert the IF signal to video7 with an envelope detector. In its simplest form, an envelope detector consists of a diode, resistive load and low-pass filter, as shown in Figure 2-15. The output of the IF chain in this example, an amplitude modulated sine wave, is applied to the detector. The response of the detector follows the changes in the envelope of the IF signal, but not the instantaneous value of the IF sine wave itself. t IF signal Figure 2-15.
The width of the resolution (IF) filter determines the maximum rate at which the envelope of the IF signal can change. This bandwidth determines how far apart two input sinusoids can be so that after the mixing process they will both be within the filter at the same time. Let’s assume a 21.4 MHz final IF and a 100 kHz bandwidth. Two input signals separated by 100 kHz would produce mixing products of 21.35 and 21.45 MHz and would meet the criterion. See Figure 2-16.
Detector types With digital displays, we had to decide what value should be displayed for each display data point. No matter how many data points we use across the display, each point must represent what has occurred over some frequency range and, although we usually do not think in terms of time when dealing with a spectrum analyzer, over some time interval. Figure 2-17.
The “bucket” concept is important, as it will help us differentiate the six detector types: Sample Positive peak (also simply called peak) Negative peak Normal Average Quasi-peak The first 3 detectors, sample, peak, and negative peak are easily understood and visually represented in Figure 2-19. Normal, average, and quasi-peak are more complex and will be discussed later. One bucket Positive peak Sample Negative peak Figure 2-19.
While the sample detection mode does a good job of indicating the randomness of noise, it is not a good mode for analyzing sinusoidal signals. If we were to look at a 100 MHz comb on an Agilent ESA E4407B, we might set it to span from 0 to 26.5 GHz. Even with 1,001 display points, each display point represents a span (bucket) of 26.5 MHz. This is far wider than the maximum 5 MHz resolution bandwidth.
Peak (positive) detection One way to insure that all sinusoids are reported at their true amplitudes is to display the maximum value encountered in each bucket. This is the positive peak detection mode, or peak. This is illustrated in Figure 2-22b. Peak is the default mode offered on many spectrum analyzers because it ensures that no sinusoid is missed, regardless of the ratio between resolution bandwidth and bucket width.
What happens when a sinusoidal signal is encountered? We know that as a mixing product is swept past the IF filter, an analyzer traces out the shape of the filter on the display. If the filter shape is spread over many display points, then we encounter a situation in which the displayed signal only rises as the mixing product approaches the center frequency of the filter and only falls as the mixing product moves away from the filter center frequency.
The normal detection algorithm: If the signal rises and falls within a bucket: Even numbered buckets display the minimum (negative peak) value in the bucket. The maximum is remembered. Odd numbered buckets display the maximum (positive peak) value determined by comparing the current bucket peak with the previous (remembered) bucket peak. If the signal only rises or only falls within a bucket, the peak is displayed. See Figure 2-25.
Average detection Although modern digital modulation schemes have noise-like characteristics, sample detection does not always provide us with the information we need. For instance, when taking a channel power measurement on a W-CDMA signal, integration of the rms values is required. This measurement involves summing power across a range of analyzer frequency buckets. Sample detection does not provide this.
EMI detectors: average and quasi-peak detection An important application of average detection is for characterizing devices for electromagnetic interference (EMI). In this case, voltage averaging, as described in the previous section, is used for measurement of narrowband signals that might be masked by the presence of broadband impulsive noise. The average detection used in EMI instruments takes an envelope-detected signal and passes it through a low-pass filter with a bandwidth much less than the RBW.
Video filtering Discerning signals close to the noise is not just a problem when performing EMC tests. Spectrum analyzers display signals plus their own internal noise, as shown in Figure 2-27. To reduce the effect of noise on the displayed signal amplitude, we often smooth or average the display, as shown in Figure 2-28. Spectrum analyzers include a variable video filter for this purpose.
The effect is most noticeable in measuring noise, particularly when a wide resolution bandwidth is used. As we reduce the video bandwidth, the peakto-peak variations of the noise are reduced. As Figure 2-29 shows, the degree of reduction (degree of averaging or smoothing) is a function of the ratio of the video to resolution bandwidths. At ratios of 0.01 or less, the smoothing is very good. At higher ratios, the smoothing is not so good.
If we set the analyzer to positive peak detection mode, we notice two things: First, if VBW > RBW, then changing the resolution bandwidth does not make much difference in the peak-to-peak fluctuations of the noise. Second, if VBW < RBW, then changing the video bandwidth seems to affect the noise level. The fluctuations do not change much because the analyzer is displaying only the peak values of the noise.
Thus, the display gradually converges to an average over a number of sweeps. As with video filtering, we can select the degree of averaging or smoothing. We do this by setting the number of sweeps over which the averaging occurs. Figure 2-31 shows trace averaging for different numbers of sweeps. While trace averaging has no effect on sweep time, the time to reach a given degree of averaging is about the same as with video filtering because of the number of sweeps required.
Figure 2-32b. Trace averaging Figure 2-32a. Video filtering Figure 2-32. Video filtering and trace averaging yield different results on FM broadcast signal Time gating Time-gated spectrum analysis allows you to obtain spectral information about signals occupying the same part of the frequency spectrum that are separated in the time domain.
In some cases, time-gating capability enables you to perform measurements that would otherwise be very difficult, if not impossible. For example, consider Figure 2-33a, which shows a simplified digital mobile-radio signal in which two radios, #1 and #2, are time-sharing a single frequency channel. Each radio transmits a single 1 ms burst, and then shuts off while the other radio transmits for 1 ms. The challenge is to measure the unique frequency spectrum of each transmitter.
Time gating can be achieved using three different methods that will be discussed below. However, there are certain basic concepts of time gating that apply to any implementation.
Timeslots 0 1 2 3 4 5 6 7 Timeslots Figure 2-35. A TDMA format signal (in this case, GSM) with eight time slots Figure 2-37. The signal in the frequency domain Figure 2-36. A zero span (time domain) view of the two time slots Figure 2-38. Time gating is used to look at the spectrum of time slot 2 Figure 2-39.
There are three common methods used to perform time gating: • Gated FFT • Gated video • Gated sweep Gated FFT Some spectrum analyzers, such as the Agilent PSA Series, have built-in FFT capabilities. In this mode, the data is acquired for an FFT starting at a chosen delay following a trigger. The IF signal is digitized and captured for a time period of 1.83 divided by resolution bandwidth. An FFT is computed based on this data acquisition and the results are displayed as the spectrum.
Gated sweep Gated sweep, sometimes referred to as gated LO, is the final technique. In gated sweep mode, we control the voltage ramp produced by the scan generator to sweep the LO. This is shown in figure 2-41. When the gate is active, the LO ramps up in frequency like any spectrum analyzer. When the gate is blocked, the voltage out of the scan generator is frozen, and the LO stops rising in frequency.
Chapter 3 Digital IF Overview Since the 1980’s, one of the most profound areas of change in spectrum analysis has been the application of digital technology to replace portions of the instrument that had previously been implemented as analog circuits. With the availability of high-performance analog-to-digital converters, the latest spectrum analyzers digitize incoming signals much earlier in the signal path compared to spectrum analyzer designs of just a few years ago.
In Chapter 2, we did a filter skirt selectivity calculation for two signals spaced 4 kHz apart, using a 3 kHz analog filter. Let’s repeat that calculation using digital filters. A good model of the selectivity of digital filters is a near-Gaussian model: ∆f α H(∆f) = –3.01 dB x RBW/2 [ where ] H(∆f) is the filter skirt rejection in dB ∆f is the frequency offset from the center in Hz, and α is a parameter that controls selectivity. α = 2 for an ideal Gaussian filter.
In this case, all 160 resolution bandwidths are digitally implemented. However, there is some analog circuitry prior to the ADC, starting with several stages of down conversion, followed by a pair of single-pole prefilters (one an LC filter, the other crystal-based). A prefilter helps prevent succeeding stages from contributing third-order distortion in the same way a prefilter would in an analog IF. In addition, it enables dynamic range extension via autoranging.
Custom signal processing IC Turning back to the block diagram of the digital IF (Figure 3-2), after the ADC gain has been set with analog gain and corrected with digital gain, a custom IC begins processing the samples. First, it splits the 30 MHz IF samples into I and Q pairs at half the rate (15 Mpairs/s). The I and Q pairs are given a high-frequency boost with a single-stage digital filter that has gain and phase approximately opposite to that of the single pole analog prefilter.
More advantages of the all-digital IF We have already discussed a number of features in the PSA Series: power/ voltage/log video filtering, high-resolution frequency counting, log/linear switching of stored traces, excellent shape factors, an average-across-the display-point detector mode, 160 RBWs, and of course, FFT or swept processing. In spectrum analysis, the filtering action of RBW filters causes errors in frequency and amplitude measurements that are a function of the sweep rate.
Chapter 4 Amplitude and Frequency Accuracy 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.
The general expression used to calculate the maximum mismatch error in dB is: Error (dB) = –20 log[1 ± |(ρanalyzer)(ρsource)|] where ρ is the reflection coefficient Spectrum analyzer data sheets typically specify the input voltage standing wave ratio (VSWR). Knowing the VSWR, we can calculate ρ with the following equation: ρ= (VSWR–1) (VSWR+1) 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.
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.
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.
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.
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.
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.
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.
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.
Chapter 5 Sensitivity and Noise Sensitivity One of the primary uses of a spectrum analyzer is to search out and measure low-level signals. The limitation in these measurements is the noise generated within the spectrum analyzer itself. This noise, generated by the random electron motion in various circuit elements, is amplified by multiple gain stages in the analyzer and appears on the display as a noise signal.
Because the input attenuator has no effect on the actual noise generated in the system, some early spectrum analyzers simply left the displayed noise at the same position on the display regardless of the input attenuator setting. That is, the IF gain remained constant. This being the case, the input attenuator affected the location of a true input signal on the display.
So if we change the resolution bandwidth by a factor of 10, the displayed noise level changes by 10 dB, as shown in Figure 5-2. For continuous wave (CW) signals, we get best signal-to-noise ratio, or best sensitivity, using the minimum resolution bandwidth available in our spectrum analyzer2. Figure 5-2. Displayed noise level changes as 10 log(BW2/BW1) A spectrum analyzer displays signal plus noise, and a low signal-to-noise ratio makes the signal difficult to distinguish.
Noise figure Many receiver manufacturers specify the performance of their receivers in terms of noise figure, rather than sensitivity. As we shall see, the two can be equated. A spectrum analyzer is a receiver, and we shall examine noise figure on the basis of a sinusoidal input. Noise figure can be defined as the degradation of signal-to-noise ratio as a signal passes through a device, a spectrum analyzer in our case.
The 24 dB noise figure in our example tells us that a sinusoidal signal must be 24 dB above kTB to be equal to the displayed average noise level on this particular analyzer. Thus we can use noise figure to determine the DANL for a given bandwidth or to compare DANLs of different analyzers on the same bandwidth.5 Preamplifiers One reason for introducing noise figure is that it helps us determine how much benefit we can derive from the use of a preamplifier.
Using these expressions, we’ll see how a preamplifier affects our sensitivity. Assume that our spectrum analyzer has a noise figure of 24 dB and the preamplifier has a gain of 36 dB and a noise figure of 8 dB. All we need to do is to compare the gain plus noise figure of the preamplifier to the noise figure of the spectrum analyzer.
Finding a preamplifier that will give us better sensitivity without costing us measurement range dictates that we must meet the second of the above criteria; that is, the sum of its gain and noise figure must be at least 10 dB less than the noise figure of the spectrum analyzer.
Let’s first test the two previous extreme cases. As NFPRE + GPRE – NFSA becomes less than –10 dB, we find that system noise figure asymptotically approaches NFSA – GPRE. As the value becomes greater than +15 dB, system noise figure asymptotically approaches NFPRE less 2.5 dB. Next, let’s try two numerical examples. Above, we determined that the noise figure of our analyzer is 24 dB.
We have already seen that both video filtering and video averaging reduce the peak-to-peak fluctuations of a signal and can give us a steady value. We must equate this value to either power or rms voltage. The rms value of a Gaussian distribution equals its standard deviation, σ. Figure 5-6. Random noise has a Gaussian amplitude distribution Let’s start with our analyzer in the linear display mode.
This is the 2.5 dB factor that we accounted for in the previous preamplifier discussion, whenever the noise power out of the preamplifier was approximately equal to or greater than the analyzer’s own noise. Figure 5-7. The envelope of band-limited Gaussian noise has a Rayleigh distribution Another factor that affects noise measurements is the bandwidth in which the measurement is made. We have seen how changing resolution bandwidth affects the displayed level of the analyzer’s internally generated noise.
Let’s consider the various correction factors to calculate the total correction for each averaging mode: Linear (voltage) averaging: Rayleigh distribution (linear mode): 3 dB/noise power bandwidths: Total correction: 1.05 dB –.50 dB 0.55 dB Log averaging: Logged Rayleigh distribution: 3 dB/noise power bandwidths: Total correction: 2.50 dB –.50 dB 2.00 dB Power (rms voltage) averaging: Power distribution: 3 dB/noise power bandwidths: Total correction: 0.00 dB –.50 dB –.
When we add a preamplifier to our analyzer, the system noise figure and sensitivity improve. However, we have accounted for the 2.5 dB factor in our definition of NFSA(N), so the graph of system noise figure becomes that of Figure 5-8. We determine system noise figure for noise the same way that we did previously for a sinusoidal signal.
Chapter 6 Dynamic Range Definition Dynamic range is generally thought of as the ability of an analyzer to measure harmonically related signals and the interaction of two or more signals; for example, to measure second- or third-harmonic distortion or third-order intermodulation. In dealing with such measurements, remember that the input mixer of a spectrum analyzer is a non-linear device, so it always generates distortion of its own. The mixer is non-linear for a reason.
With a constant LO level, the mixer output is linearly related to the input signal level. For all practical purposes, this is true as long as the input signal is more than 15 to 20 dB below the level of the LO. There are also terms involving harmonics of the input signal: (3k3/4)VLOV12 sin(ωLO – 2 ω1)t, (k4 /8)VLOV13 sin(ωLO – 3ω1)t, etc. These terms tell us that dynamic range due to internal distortion is a function of the input signal level at the input mixer.
These represent intermodulation distortion, the interaction of the two input signals with each other. The lower distortion product, 2ω1 – ω2, falls below ω1 by a frequency equal to the difference between the two fundamental tones, ω2 – ω1. The higher distortion product, 2ω2 – ω1, falls above ω2 by the same frequency. See Figure 6-1. Once again, dynamic range is a function of the level at the input mixer.
We can construct a similar line for third-order distortion. For example, a data sheet might say third-order distortion is –85 dBc for a level of –30 dBm at this mixer. Again, this is our starting point, and we would plot the point shown in Figure 6-2. If we now drop the level at the mixer to –40 dBm, what happens? Referring again to Figure 6-1, we see that both third-harmonic distortion and third-order intermodulation distortion fall by 3 dB for every dB that the fundamental tone or tones fall.
Sometimes third-order performance is given as TOI (third-order intercept). This is the mixer level at which the internally generated third-order distortion would be equal to the fundamental(s), or 0 dBc. This situation cannot be realized in practice because the mixer would be well into saturation. However, from a mathematical standpoint, TOI is a perfectly good data point because we know the slope of the line.
Figure 6-2 shows the dynamic range for one resolution bandwidth. We certainly can improve dynamic range by narrowing the resolution bandwidth, but there is not a one-to-one correspondence between the lowered noise floor and the improvement in dynamic range. For second-order distortion, the improvement is one half the change in the noise floor; for third-order distortion, two-thirds the change in the noise floor. See Figure 6-3.
The final factor in dynamic range is the phase noise on our spectrum analyzer LO, and this affects only third-order distortion measurements. For example, suppose we are making a two-tone, third-order distortion measurement on an amplifier, and our test tones are separated by 10 kHz. The third-order distortion components will also be separated from the test tones by 10 kHz. For this measurement we might find ourselves using a 1 kHz resolution bandwidth.
Dynamic range versus measurement uncertainty In our previous discussion of amplitude accuracy, we included only those items listed in Table 4-1, plus mismatch. We did not cover the possibility of an internally generated distortion product (a sinusoid) being at the same frequency as an external signal that we wished to measure. However, internally generated distortion components fall at exactly the same frequencies as the distortion components we wish to measure on external signals.
Next, let’s look at uncertainty due to low signal-to-noise ratio. The distortion components we wish to measure are, we hope, low-level signals, and often they are at or very close to the noise level of our spectrum analyzer. In such cases, we often use the video filter to make these low-level signals more discernable. Figure 6-7 shows the error in displayed signal level as a function of displayed signal-to-noise for a typical spectrum analyzer.
Let’s see what happened to our dynamic range as a result of our concern with measurement error. As Figure 6-6 shows, second-order-distortion dynamic range changes from 72.5 to 61 dB, a change of 11.5 dB. This is one half the total offsets for the two curves (18 dB for distortion; 5 dB for noise). Third-order distortion changes from 81.7 dB to about 72.7 dB for a change of about 9 dB.
Gain compression In our discussion of dynamic range, we did not concern ourselves with how accurately the larger tone is displayed, even on a relative basis. As we raise the level of a sinusoidal input signal, eventually the level at the input mixer becomes so high that the desired output mixing product no longer changes linearly with respect to the input signal. The mixer is in saturation, and the displayed signal amplitude is too low. Saturation is gradual rather than sudden.
The range of the log amplifier can be another limitation for spectrum analyzers with analog IF circuitry. For example, ESA-L Series spectrum analyzers use an 85 dB log amplifier. Thus, only measurements that are within 85 dB below the reference level are calibrated. The question is, can the full display range be used? From the previous discussion of dynamic range, we know that the answer is generally yes. In fact, dynamic range often exceeds display range or log amplifier range.
Adjacent channel power measurements TOI, SOI, 1 dB gain compression, and DANL are all classic measures of spectrum analyzer performance. However, with the tremendous growth of digital communication systems, other measures of dynamic range have become increasingly important. For example, adjacent channel power (ACP) measurements are often done in CDMA-based communication systems to determine how much signal energy leaks or “spills over” into adjacent or alternate channels located above and below a carrier.
Chapter 7 Extending the Frequency Range As more wireless services continue to be introduced and deployed, the available spectrum becomes more and more crowded. Therefore, there has been an ongoing trend toward developing new products and services at higher frequencies. In addition, new microwave technologies continue to evolve, driving the need for more measurement capability in the microwave bands.
In Chapter 2, we used a mathematical approach to conclude that we needed a low-pass filter. As we shall see, things become more complex in the situation here, so we shall use a graphical approach as an easier method to see what is happening. The low band is the simpler case, so we shall start with that. In all of our graphs, we shall plot the LO frequency along the horizontal axis and signal frequency along the vertical axis, as shown in Figure 7-2.
Next let’s see to what extent harmonic mixing complicates the situation. Harmonic mixing comes about because the LO provides a high-level drive signal to the mixer for efficient mixing, and since the mixer is a non-linear device, it generates harmonics of the LO signal. Incoming signals can mix against LO harmonics, just as well as the fundamental, and any mixing product that equals the IF produces a response on the display.
The situation is considerably different for the high band, low IF case. As before, we shall start by plotting the LO fundamental against the signalfrequency axis and then add and subtract the IF, producing the results shown in Figure 7-4. Note that the 1– and 1+ tuning ranges are much closer together, and in fact overlap, because the IF is a much lower frequency, 321.4 MHz in this case. Does the close spacing of the tuning ranges complicate the measurement process? Yes and no.
In examining Figure 7-5, we find some additional complications. The spectrum analyzer is set up to operate in several tuning bands. Depending on the frequency to which the analyzer is tuned, the analyzer display is frequency calibrated for a specific LO harmonic. For example, in the 6.2 to 13.2 GHz input frequency range, the spectrum analyzer is calibrated for the 2– tuning curve. Suppose we have an 11 GHz signal present at the input.
Other situations can create out-of-band multiple responses. For example, suppose we are looking at a 5 GHz signal in band 1 that has a significant third harmonic at 15 GHz (band 3). In addition to the expected multiple pair caused by the 5 GHz signal on the 1+ and 1– tuning curves, we also get responses generated by the 15 GHz signal on the 4+, 4–, 3+,and 3– tuning curves. Since these responses occur when the LO is tuned to 3.675, 3.825, 4.9, and 5.
Can we conclude from this discussion that a harmonic mixing spectrum analyzer is not practical? Not necessarily. In cases where the signal frequency is known, we can tune to the signal directly, knowing that the analyzer will select the appropriate mixing mode for which it is calibrated. In controlled environments with only one or two signals, it is usually easy to distinguish the real signal from the image and multiple responses.
Signal frequency (GHz) 1+ 6 5.3 1– 4.7 4 3 Preselector bandwidth 2 3 4 4.4 5 LO frequency (GHz) 5.6 6 Figure 7-7. Preselection; dashed lines represent bandwidth of tracking preselector The word eliminate may be a little strong. Preselectors do not have infinite rejection. Something in the 70 to 80 dB range is more likely. So if we are looking for very low-level signals in the presence of very high-level signals, we might see low-level images or multiples of the high-level signals.
Amplitude calibration So far, we have looked at how a harmonic mixing spectrum analyzer responds to various input frequencies. What about amplitude? The conversion loss of a mixer is a function of harmonic number, and the loss goes up as the harmonic number goes up. This means that signals of equal amplitude would appear at different levels on the display if they involved different mixing modes. To preserve amplitude calibration, then, something must be done.
For example, suppose that the LO fundamental has a peak-to-peak deviation of 10 Hz. The second harmonic then has a 20 Hz peak-to-peak deviation; the third harmonic, 30 Hz; and so on. Since the phase noise indicates the signal (noise in this case) producing the modulation, the level of the phase noise must be higher to produce greater deviation.
From the graph, we see that a –10 dBm signal at the mixer produces a second-harmonic distortion component of –45 dBc. Now we tune the analyzer to the 6 GHz second harmonic. If the preselector has 70 dB rejection, the fundamental at the mixer has dropped to –80 dBm. Figure 7-11 indicates that for a signal of –80 dBm at the mixer, the internally generated distortion is –115 dBc, meaning 115 dB below the new fundamental level of –80 dBm. This puts the absolute level of the harmonic at –195 dBm.
Looking at these expressions, we see that the amplitude of the lower distortion component (2ω1 – ω2) varies as the square of V1 and linearly with V2. On the other side, the amplitude of the upper distortion component (2ω2 – ω1) varies linearly with V1 and as the square of V2. However, depending on the signal frequencies and separation, the preselector may not attenuate the two fundamental tones equally.
Pluses and minuses of preselection We have seen the pluses of preselection: simpler analyzer operation, uncluttered displays, improved dynamic range, and wide spans. But there are some minuses, relative to an unpreselected analyzer, as well. First of all, the preselector has insertion loss, typically 6 to 8 dB. This loss comes prior to the first stage of gain, so system sensitivity is degraded by the full loss.
External harmonic mixing We have discussed tuning to higher frequencies within the spectrum analyzer. For internal harmonic mixing, the ESA and PSA spectrum analyzers use the second harmonic (N=2–) to tune to 13.2 GHz, and the fourth harmonic (N=4–) to tune to 26.5 GHz.
Table 7-1 shows the harmonic mixing modes used by the ESA and PSA at various millimeter wave bands. You choose the mixer depending on the frequency range you need. Typically, these are standard waveguide bands. There are two kinds of external harmonic mixers; those with preselection and those without. Agilent offers unpreselected mixers in six frequency bands: 18 to 26.5 GHz, 26.5 to 40 GHz, 33 to 50 GHz, 40 to 60 GHz, 50 to 75 GHz, and 75 to 110 GHz.
External harmonic mixer Input signal 3 GHz Atten 321.4 MHz 3.9214 GHz 21.4 MHz Analog or digital IF Input signal 3 - 7 GHz 3.6 GHz Preselector 300 MHz 321.4 MHz Sweep generator Display Figure 7-14. Block diagram of spectrum analyzer and external mixer with built-in preselector Signal identification Even when using an unpreselected mixer in a controlled situation, there are times when we must contend with unknown signals.
Figure 7-15. Which ones are the real signals? 75 16+ 16– 14+ 14– 70 12+ 18+ 18– 10+ 65 Apparent location of image pair 12– 10– 60 Input frequency (GHz) 58.5 57.8572 55 8+ 50 8– 45 40 6+ 35 6– 30 25 3 4 5 LO frequency (GHz) 6 7 Figure 7-16.
Let’s assume that we have some idea of the characteristics of our signal, but we do not know its exact frequency. How do we determine which is the real signal? The image-shift process retunes the LO fundamental frequency by an amount equal to 2fIF/N. This causes the Nth harmonic to shift by 2fIF. If we are tuned to a real signal, its corresponding pair will now appear at the same position on screen that the real signal occupied in the first sweep.
Figure 7-18. The image suppress function displays only real signals Note that both signal identification methods are used for identifying correct frequencies only. You should not attempt to make amplitude measurements while the signal identification function is turned on. Note that in both Figures 7-17 and 7-18, an on-screen message alerts the user to this fact. Once we have identified the real signal of interest, we turn off the signal ID function and zoom in on it by reducing the span.
Chapter 8 Modern Spectrum Analyzers In previous chapters of this application note, we have looked at the fundamental architecture of spectrum analyzers and basic considerations for making frequency-domain measurements. On a practical level, modern spectrum analyzers must also handle many other tasks to help you accomplish your measurement requirements.
Other examples of built-in measurement functions include occupied bandwidth, TOI and harmonic distortion, and spurious emissions measurements. The instrument settings, such as center frequency, span, and resolution bandwidth, for these measurements depend on the specific radio standard to which the device is being tested. Most modern spectrum analyzers have these instrument settings stored in memory so that you can select the desired radio standard (GSM/EDGE, cdma2000, W-CDMA, 802.
RF designers are often concerned with the noise figure of their devices, as this directly affects the sensitivity of receivers and other systems. Some spectrum analyzers, such as the PSA Series and ESA-E Series models, have optional noise figure measurement capabilities available. This option provides control for the noise source needed to drive the input of the device under test (DUT), as well as firmware to automate the measurement process and display the results.
Digital modulation analysis The common wireless communication systems used throughout the world today all have prescribed measurement techniques defined by standardsdevelopment organizations and governmental regulatory bodies. Optional measurement personalities are commonly available on spectrum analyzers to perform the key tests defined for a particular communication format.
Not all digital communication systems are based on well-defined industry standards. Engineers working on non-standard proprietary systems or the early stages of proposed industry-standard formats need more flexibility to analyze vector-modulated signals under varying conditions. This can be accomplished in two ways. First, modulation analysis personalities are available on a number of spectrum analyzers. Alternatively, more extensive analysis can be done with software running on an external computer.
Data transfer and remote instrument control In 1977, Agilent Technologies (part of Hewlett-Packard at that time) introduced the world’s first GPIB-controllable spectrum analyzer, the 8568A. The GPIB interface (also known as HP-IB or IEEE-488) made it possible to control all major functions of the analyzer and transfer trace data to an external computer. This innovation paved the way for a wide variety of automated spectrum analyzer measurements that were faster and more repeatable than manual measurements.
Firmware updates Modern spectrum analyzers have much more software inside them than do instruments from just a few years ago. As new features are added to the software and defects repaired, it becomes highly desirable to update the spectrum analyzer’s firmware to take advantage of the improved performance. The latest revisions of spectrum analyzer firmware can be found on the Agilent Technologies website. This firmware can be downloaded to a file on a local computer.
Summary The objective of this application note is to provide a broad survey of basic spectrum analyzer concepts. However, you may wish to learn more about many other topics related to spectrum analysis. An excellent place to start is to visit the Agilent Technologies Web site at www.Agilent.com and search for “spectrum analyzer.
Glossary of Terms Absolute amplitude accuracy: The uncertainty of an amplitude measurement in absolute terms, either volts or power. Includes relative uncertainties (see Relative amplitude accuracy) plus calibrator uncertainty. For improved accuracy, some spectrum analyzers have frequency response specified relative to the calibrator as well as relative to the mid-point between peak-to-peak extremes.
Delta marker: A mode in which a fixed, reference marker has been established and a second, active marker is available that we can place anywhere on the displayed trace. A read out indicates the relative frequency separation and amplitude difference between the reference marker and the active marker. Digital display: A technique in which digitized trace information, stored in memory, is displayed on the screen. The displayed trace is a series of points designed to present a continuous looking trace.
Dynamic range: The ratio, in dB, between the largest and smallest signals simultaneously present at the spectrum analyzer input that can be measured to a given degree of accuracy. Dynamic range generally refers to measurement of distortion or intermodulation products. Envelope detector: A circuit element whose output follows the envelope, but not the instantaneous variation, of its input signal.
Frequency stability: A general phrase that covers both short- and long-term LO instability. The sweep ramp that tunes the LO also determines where a signal should appear on the display. Any long term variation in LO frequency (drift) with respect to the sweep ramp causes a signal to slowly shift its horizontal position on the display. Shorter term LO instability can appear as random FM or phase noise on an otherwise stable signal.
Image response: A displayed signal that is actually twice the IF away from the frequency indicated by the spectrum analyzer. For each harmonic of the LO, there is an image pair, one below and one above the LO frequency by the IF. Images usually appear only on non-preselected spectrum analyzers. Incidental FM: Unwanted frequency modulation on the output of a device (signal source, amplifier) caused by (incidental to) some other form of modulation, e.g. amplitude modulation.
LO feedthrough: The response on the display when a spectrum analyzer is tuned to 0 Hz, i.e. when the LO is tuned to the IF. The LO feedthrough can be used as a 0-Hz marker, and there is no frequency error. Log display: The display mode in which vertical deflection on the display is a logarithmic function of the voltage of the input signal. We set the display calibration by selecting the value of the top line of the graticule, the reference level, and scale factor in dB/div.
Noise sidebands: Modulation sidebands that indicate the short-term instability of the LO (primarily the first LO) system of a spectrum analyzer. The modulating signal is noise, in the LO circuit itself and/or in the LO stabilizing circuit, and the sidebands comprise a noise spectrum. The mixing process transfers any LO instability to the mixing products, so the noise sidebands appear on any spectral component displayed on the analyzer far enough above the broadband noise floor.
Residual responses: Discrete responses seen on a spectrum analyzer display with no input signal present. Resolution: See Frequency resolution. Resolution bandwidth: The width of the resolution bandwidth (IF) filter of a spectrum analyzer at some level below the minimum insertion loss point (maximum deflection point on the display). For Agilent analyzers, the 3 dB bandwidth is specified; for some others, it is the 6 dB bandwidth.
Spectrum: An array of sine waves of differing frequencies and amplitudes and properly related with respect to phase that, taken as a whole, constitute a particular time-domain signal. Spectrum analyzer: A device that effectively performs a Fourier transform and displays the individual spectral components (sine waves) that constitute a time-domain signal. Phase may or may not be preserved, depending upon the analyzer type and design.
Video: In a spectrum analyzer, a term describing the output of the envelope detector. The frequency range extends from 0 Hz to a frequency typically well beyond the widest resolution bandwidth available in the analyzer. However, the ultimate bandwidth of the video chain is determined by the setting of the video filter. Video amplifier: A post-detection, DC-coupled amplifier that drives the vertical deflection plates of the CRT. See Video bandwidth and Video filter.
Agilent Technologies’ Test and Measurement Support, Services, and Assistance Agilent Technologies aims to maximize the value you receive, while minimizing your risk and problems. We strive to ensure that you get the test and measurement capabilities you paid for and obtain the support you need. Our extensive support resources and services can help you choose the right Agilent products for your applications and apply them successfully. Every instrument and system we sell has a global warranty.
