# Technically speaking Gettingt more from your spectrum analyzer

These days, most land mobile radio shops have at least one spectrum analyzer available. This piece of test equipment has become practically indispensable,

These days, most land mobile radio shops have at least one spectrum analyzer available. This piece of test equipment has become practically indispensable, considering the level of electromagnetic interference present in the spectrum today. Let’s look at some of the methods for enhancing the use of the spectrum analyzer.

Preamplifiers Preamplifiers can certainly boost the small-signal performance of a spectrum analyzer. However, as with practically any other electronic device, all preamplifiers are not created equal. The preamplifier should be used with a knowledge of how it might affect the overall operation of the spectrum analyzer. Basically, three factors must be considered in choosing the proper preamplifier: gain, noise figure and dynamic range. Let’s take a closer look at how these characteristics can affect the overall spectrum analyzer operation.

Let’s assume that we have a spectrum anaylzer with a noise figure of 30dB. Don’t confuse this with noise factor. Noise figure is stated in decibels. Noise factor is stated as a multiplication factor. To convert noise factor to noise figure, use the following formula:

Noise factor = 10^(noise figure/10).

For example, to convert a noise figure of 6dB to a noise factor, the calculator keystrokes are

 [/]  [=] [INV] [LOG]

which yields 3.981071705.

Suppose we have a spectrum analyzer with a noise figure of 30dB (not unusual) and a third-order intercept point (Ip(sub 3) of +10dBm. Let’s look at how different preamplifiers might affect the overall operation. Figure 1 above shows the setup for the spectrum analyzer and preamplifier.

Assume that the preamplifier has a gain of 20dB, a noise figure of 6dB and an Ip(sub 3) of +15dBm. There are several things we would like to know about the new setup. What is the new noise factor? What is the new (small-signal) signal-to-noise ratio? How is the dynamic range affected in terms of the third-order intercept point (Ip(sub 3))?

Generally speaking, the maximum input to the preamplifier should be limited to the maximum input rating of the spectrum anaylzer, minus the gain of the preamplifier. So, what is the overall noise figure of the preamplifier/spectrum analyzer combination? To determine this, we use the formula for noise factor for cascaded devices and then convert the noise factor to noise figure in decibels. The formula for noise factor of cascaded devices is:

F=F(sub 1) + (((F(sub 2)-1)/G(sub 1))+((F(sub 3)-1)/(G(sub 1)*G(sub 2))))

where

F = noise factor

F(sub 1) = noise factor of first device in cascade

F(sub 2) = noise factor of second device

G(sub 1) = gain of first device

G(sub 2) = gain of second device.

The overall noise factor (F) for the spectrum analyzer and preamplifier shown in Figure 1 is:

F = 4 + ((1000-1)/100) = 4 + (999/100)

= 4 + 9.99 = 13.99

This translates into a noise figure of

10 log (13.99) = 11.5dB.

Since the noise figure of the spectrum analyzer alone was 30dB, this represents a noise figure improvement of 30dB – 11.5dB, or 18.5dB, with the preamplifier connected.

What happens to the third-order intercept point (Ip(sub 3))? Table 1 at the left shows the correlation between the preamplifier Ip(sub 3) and the reduction in overall Ip(sub 3). These figures represent the preamplifier Ip(sub 3) minus the spectrum analyzer Ip(sub 3). These figures represent a worst-case scenario, where the intermod signals combine in phase to produce maximum level intermod.

In our example, the preamplifier Ip(sub 3) is +15dBm and the spectrum analyzer Ip(sub 3) is +10dBm. The difference is 5dB, so we look in Table 1 for 5dB. The nearest comparable figure is 6dB, which correlates to a degradation of -3.5dB in the Ip(sub 3) figure. The 5dB difference between the preamplifier and the spectrum anaylzer Ip(sub 3) figure would cause more than a -3.5dB degradation but less than the -4.6dB figure that correlates to the 3dB figure in the left-hand column of the table. Simple linear interpolation yields an Ip(sub 3) degradation figure of -3.9dB. Thus, the overall third-order intercept point (Ip(sub 3)) is now

+10dBM + (-3.9dB) = +6.1dBm.

This means that at the preamplifier input, the third-order intercept point will be 20dB below +6.1dBm, or -13.9dBm. Thus, we have gained in the low-signal performance and lost ground in the high-signal performance of the spectrum analyzer by adding the preamplifier. You can see by looking at Table 1 that if we use a preamplifier that has a much higher third-order intercept figure (Ip(sub 3)) than the spectrum analyzer, then the amount of degradation of the Ip(sub 3) point is much less. For example, Table 1 shows that if the Ip(sub 3) of the preamplifier is 20dB more than the Ip(sub 3) of the spectrum analyzer, the overall degradation of the Ip(sub 3) is only 0.8dB.

What happens if we cascade two preamplifiers ahead of the spectrum analyzer input? Let’s analyze an example to see the results. Figure 2 above shows the same spectrum analyzer preceded by two preamplifiers connected in cascade ahead of the input. Both preamplifiers 1 and 2 have identical specifications for gain, noise figure and third-order intercept (Ip(sub 3)). These figures are listed on the block diagram in Figure 2. The total gain of the preamplifiers is 40dB or multiplication factor of 10,000. The overall noise factor is calculated follows:

F=4+((4-1)/100)+((1000-1)/10,000)

=4+(3/100)+(999/10,000)

=0.03+0.0999=4.13

This is converted to noise figure by 10 log (4.13) = 6.17dB. Thus, the overall noise figure has improved by 30dB – 6.17dB = 23.8dB.

Now, what about the third-order intercept, Ip(sub 3)? Referring again to Figure 2, we see that the two preamplifiers have the same Ip(sub 3) of +30dBm. Referring to Table 1 again, when the difference between the two preamplifiers is 0dB, the table indicates a degradation of -6dB at the output of preamplifier 2. Thus, the Ip(sub 3) at the output of preamplifier 2 is 30dBm + (-6dB) = +24dBm.

This is 14dB greater than the spectrum analyzer Ip(sub 3), so we refer back to Table 1. Since 14dB is not listed, we can use the figures for 10dB and 15dB and interpolate. For 10dB, the degradation would be -2.4dB and for 15dB the degradation would be -1.4dB. By interpolation, we derive a figure of 0.8dB to be added to -2.4dB to get +1.6dB degradation. We apply this conversion factor to the spectrum analyzer Ip(sub 3) of +10dBm to get +10dBm + (-6dB) + +8.4dBm for Ip(sub 3).

Again, this is a worst-case scenario where all the IM signals combine in phase.

Summary When a preamplifier is used ahead of a spectrum analyzer, the maximum input to the preamplifer should not exceed the maximum rated input to the spectrum analyzer minus the gain of the preamplifier. The small-signal performance of the spectrum analyzer will be enhanced by a good preamplifier, but the dynamic range and the third-order intercept point, Ip(sub 3), will be reduced. Preamplifiers can be used to detect low-level signals. Don’t use preamplifiers unless it is necessary to boost the signal level, and avoid their use in the presence of very strong signals. Front-end overload comes very quickly!

Next time we will look at more tips and techniques for the spectrum analyzer. ‘Til next time–stay tuned!

References Coombs, Clyde F. Jr., Electronic Instrument Handbook, 1995, New York. Tektronix Test & Measurement, Choosing a Preamplifier for Use with a Spectrum Analyzer, 1992, Beaverton, OR.

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