SPECTRUM ANALYZER; Tuning the analyzer

Tuning the analyzer
We need to know how to tune our spectrum analyzer to the desired frequency range. Tuning is a function of the center frequency of the IF filter, the frequency range of the LO, and the range of frequencies allowed to reach the mixer from the outside world ( allowed to pass through the low-pass filter) . Of all the mixing products emerging from the mix r, the two with the greatest amplitudes, and therefore the most desirable, are those created from the sum
of the LO and input signal and from the difference between the LO and input signal. If w can arrange things so that the signal we wish to examine is either above or below the LO frequency by the IF, then one of the desired mixing products will fall within the pass-band of the IF filter and be detected to create an amplitude response on the display.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. The 1 GHz signal would thus pass through the system and give us a constant amplitude response on the display regardless of the tuning of the LO. The result would be a hole in the frequency range at which we could not properly examine signals because the amplitude response would be independent of the LO frequency. Therefore, a 1 GHz IF will not work.
So we shall choose, instead, an IF that is above the highest frequency to which we wish to tune. In Agilent spectrum analyzers that can tune to 3 GHz, the IF chosen is about 3.9 GHz. Remember that we want to tune from 0 Hz to 3 GHz. (Actually from some low frequency because we cannot view a 0 Hz signal with this architecture.) If we start the LO at the IF ( LO minus IF = 0 Hz) and tune it upward from there to 3 GHz above the IF, then we can cover the
tuning range with the LO minus IF mixing product. Using this information, we can generate a tuning equation:

2. In the text, we shall round off some of the frequency values for simplicity, although the exact values are shown in the figures.Figure 2-4 illustrates analyzer tuning. In this figure, f LO is not quit high enough to cause the f LO f sig 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. 

Figure 2-4. The LO must be tuned to fIF + fsig to produce on the display

Since the ramp generator controls both the horizontal position of the trace on the display and the LO frequency, we can now calibrate the horizontal axis of the display in terms of the input signal frequency. 

We are not quit through with the tuning yet. What happens if the frequency of the input signal is 8.2 GHz? As the LO tunes through its 3.9 to 7.0 GHz range, it reaches a frequency (4.3 GHz) at which it is the IF away from the 8.2 GHz input signal. At this frequency we have a mixing product that is equal to the IF, creating a response on the display. In other words, the 

tuning equation could just as easily have been: 

f _Sig = f_LO + F_if

This equation says that the architecture of Figure 2-1 could also result in a tuning range from 7.8 to 10.9 GHz, but only if we allow signals in that range to reach the mixer. The job of the input low-pass filter in Figure 2-1 is to prevent these higher frequencies from getting to the mixer. We also want to keep signals at the intermediate frequency itself from reaching the mixer, as previously described, so the low-pass filter must do a good job of attenuating
signals at 3.9 GHz, as well as in the range from 7.8 to 10.9 GHz.

In summary, we can say that for a single-band RF spectrum analyzer, we would choose an IF above the highest frequency of the tuning range. We would make the LO tunable from the IF to the IF plus the upper limit of the tuning range and include a low-pass filter in front of the mixer that cuts off below the IF.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. The full tuning equation for this analyzer is:  

f_sig = f_LO1 – (f_LO2 + f_LO3 + ff_{inal IF})

However,

f_LO2 + f_LO3 + ff_{inal IF}

= 3.6 GHz + 300 MHz + 21.4 MHz

= 3.9214 GHz, the first IF

Figure 2-5. Most spectrum analyzers use two to four mixing steps to reach the final IF

So simplifying the tuning equation by using just the first IF leads us to the same answers. Although only passive filters are shown in the diagram, the actual implementation includes amplification in the narrower IF stages. The final IF section contains additional components, such as logarithmic amplifiers or analog to digital converters, depending on the design of the 

particular analyzer. 

Most RF spectrum analyzers allow an LO frequency as low as, and even below, the first IF. Because there is finite isolation between the LO and IF ports of the mixer, the LO appears at the mixer output. When the LO equals the IF, the LO signal itself is processed by the system and appears as a response on the display, as if it were an input signal at 0 Hz. This esponse, called LO feedthrough, can mask very low frequency signals

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   effecting 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. Generally, w do not want the reference level to change when we change the input attenuator, so the settings of the input attenuator and the IF gain are coupled together. 

A change in input attenuation will automatically change the IF gain to offset the effect of the change in input attenuation, thereby keeping the signal at a constant position on the display. 

Resolving signals

After the IF gain amplifier, we find the IF section which consists of the analog and/ or digital resolution bandwidth ( RBW) filters. 

Analog filters

Frequency resolution is the ability of a spectrum analyzer to separate two input sinusoids into distinct responses. Fourier tells us that a sine wave signal only has energy at one frequency, so we shouldn't have any resolution problems. Two signals, no matter how close in frequency, should appear as two lines on the display. But a closer look at our uperheterodyne receiver shows why signal responses have a definite width on the display. The output of a mixer includes the sum and difference products plus the two original signals (input and LO). A bandpass filter determines the intermediate frequency, and this filter selects the desired mixing product and rejects all other signals. Because the input signal is fixed and the local oscillator is swept, the products from the mixer are also swept. If a mixing product happens to sweep past the IF, the characteristic shape of the bandpass filter is traced on the display. See Figure 2-6. The narrowest filter in the chain determines the overall displayed bandwidth, and in the architecture of Figure 2-5, this filter is in the 21.4 MHz IF. 

Figure 2-6. As a mixing product sweeps past the IF filter, the filter shape is traced on the display

So two signals must be far enough apart, or else the traces they make will fall on top of each other and look like only one response. Fortunately, spectrum analyzers have selectable resolution (IF) filters, so it is usually possible to select one narrow enough to resolve closely spaced 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. Two equal-amplitude sinusoids separated by the 3 dB BW 

of the selected IF filter can be resolved

More often than not we are dealing with sinusoids that are not equal in amplitude. The smaller sinusoid can actually be lost under the skirt of th response traced out by the larger. This effect is illustrated in Figure 2-8. The top trace looks like a single signal, but in fact represents two signals: one at 300 MHz ( 0 dBm) and another at 300.005 MHz ( 30 dBm) . The low r trace shows the display after the 300 MHz signal is removed

Figure 2-8. A low-level signal can be lost under skirt of the response 

to a larger signal

3. If you experiment with resolution on a spectrum analyzer using the normal ( rosenfell) detector mode ( See Detector types later in this chapter) use enough video filtering to create a smooth trace. Otherwise, there will be a smearing as the two signals interact. While the smeared trace certainly indicates the presence of more than one signal, it is difficult to determine the amplitudes of the individual signals. Spectrum analyzers with positive peak as 

their default detector mode may not show the smearing effect. You can observe the smearing by selecting the sample detector mode.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 shape 4 . This type of filter exhibits a bandwidth selectivity of about 12.7: 1. 

Figure 2-9. Bandwidth selectivity, ratio of 60 dB to 3 dB bandwidths

For example, what resolution bandwidth must we choose to resolve signals that differ by 4 kHz and 30 dB, assuming 12.7: 1 bandwidth selectivity? Since we are concerned with rejection of the larger signal when the analyzer is tuned to the smaller signal, we need to consider not the full bandwidth, but the frequency difference from the filter center frequency to the skirt. To determine how far down the filter skirt is at a given offset, we use the 

following equation: 

4. Some older spectrum analyzer models used five-pole filters for the narrowest resolution bandwidths to provide improved selectivity of about 10:1. Modern designs achieve even better bandwidth selectivity using digital IF filters.This allows us to calculate the filter rejection: 

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